LHC signals for Singlet Neutrinos from a Natural Warped Seesaw (I)
UUMD-PP-017-017
LHC signals for Singlet Neutrinos from a Natural WarpedSeesaw (I)
Kaustubh Agashe a , Peizhi Du a , Sungwoo Hong aa Maryland Center for Fundamental Physics, Department of Physics, University ofMaryland, College Park, MD 20742, U. S. A.email addresses : [email protected]; [email protected]; [email protected]
Abstract
Recently, it was shown in arXiv:1512.06742 that a straightforward implementation of the typeI seesaw mechanism in a warped extra dimensional framework is in reality a natural realization of“inverse” seesaw, i.e., the Standard Model (SM) neutrino mass is dominantly generated by exchangeof pseudo-Dirac
TeV -mass SM singlet neutrinos. By the AdS/CFT correspondence, this scenario is dual to these singlet particles being composites of some new strong dynamics, along with the SMHiggs boson (and possibly the top quark), with the rest of the SM particles being mostly elementary.We study signals from production of these heavy neutrinos at the Large Hadron Collider (LHC). Wefocus on the scenario where the strong sector has a global SU (2) L × SU (2) R × U (1) X symmetry;such a left-right (LR) structure being motivated by consistency with the electroweak (EW) precisiontests. The singlet neutrinos are charged under SU (2) R × U (1) X symmetry, thus can be producedfrom W ± R exchange, as in four-dimensional (4D) LR symmetric models. However, the direct couplingof light quarks to W ± R is negligible, due to W ± R also being composite (cf. 4D LR models); nonetheless,a sizable coupling can be induced by mixings among the various types of W ± bosons. Furthermore, W ± R decays dominantly into the singlet and composite partner of charged lepton (cf. SM lepton itselfin 4D LR model). This heavy charged lepton, in turn, decays into SM lepton, plus Z /Higgs, thus thelatter can be used for extra identification of the signal. For a benchmark scenario with W ± R of mass2 TeV and singlet neutrino of mass 750 GeV, we find that, in both the di-lepton + di-jet + Higgsand tri-lepton + Higgs channels, significant evidence can be seen at the LHC14 for an integratedluminosity of 300/fb and that even discovery is possible with slightly more luminosity. a r X i v : . [ h e p - ph ] D ec Introduction
The seesaw mechanism [1] is a very attractive and hence perhaps the most popular onefor explaining the extreme smallness of the Standard Model (SM) neutrino masses relativeto those of the charged fermions. The basic idea is illustrated by the following schematicformula generic seesaw : m ν ∼ m D M N (1)where m D denotes the Dirac mass term between the SM doublet left-handed (LH) neutrino( ν L ) and a SM singlet right-handed (RH) neutrino ( N R or simply N ), induced by the vacuumexpectation value (VEV) of the SM Higgs boson and M N is the Majorana mass term for thesinglet.However, it is perhaps fair to say that in its actual realizations (including details of fittingto the observed neutrino masses), one typically ends up with a tuning of parameters (albeit not always fine -tuned, i.e., not involving large cancellations therein); here, we give someexamples of this point. Then, we discuss a natural version in a warped extra dimensionalmodel [dual to a four dimensional (4D) framework of composite Higgs and partially compositerest of the SM] [3, 4], which is the subject of further study in this paper.In the original seesaw, the typical choice is that the above Dirac mass term betweenthe two neutrinos is of order the Higgs VEV, v (or somewhat smaller), and similarly, theMajorana mass term for singlet is close to the UV cut-off scale (denoted by M UV ):high-scale seesaw : m D (cid:46) v ( no tuning ) M N ∼ M UV ( no tuning, but see below! ) (2)(Note that in the above and in what follows, v can be replaced by m τ , i.e., largest of charged lepton masses with out qualitative change in conclusions.) Plugging Eq. (2) in Eq. (1), thisresults in the SM neutrino mass being much smaller than the electroweak symmetry breaking(EWSB) scale.However, the observed SM neutrino mass (assuming this is set by the largest of neutrinomass differences that have been confirmed, i.e., the atmospheric neutrino oscillations scale)requires that M UV in Eq. (2) be actually several orders of magnitude smaller than the Planckscale: m ν ∼ . eV ⇒ M UV ∼ GeV (cid:28) M Pl ∼ GeV (3)Of course, the latter hierarchy can be technically natural (i.e., radiatively stable), but thepoint is that realizing all this might require additional dynamics. For example, if this scale2orresponds to spontaneous breaking of a gauge symmetry [as in SU (2) L × SU (2) R × U (1) B − L or left-right (LR) symmetric models, i.e., N R is part of a doublet of SU (2) R ] by a scalarVEV, then we have to explain why this scalar mass term is much smaller than the Planckscale.An alternative is to set the singlet mass scale to be close to the IR (low-scale seesaw),for example, weak scale:low/TeV-scale seesaw : M N ∼ M IR ( ∼ TeV ) ( no tuning ) (4)but then the tuning is transferred to the Dirac mass term instead: m ν (cid:28) v ⇒ m D (cid:28) v (5)Finally, the so-called “inverse” seesaw [2] seeks to have natural choices for both the Dirac massterm between doublet and singlet neutrinos (i.e., (cid:46) v ) and the mass term for the singlet byitself (that too at the IR/weak scale). However, in the inverse seesaw, the singlet neutrinois Dirac fermion, requiring introduction of another left-handed (LH) singlet denoted by S : M NS ∼ M IR ( ∼ TeV ) ( no tuning ) (6)In addition the second singlet has a small Majorana mass term denoted by µ so that the SMneutrino mass formula ends up looking like:inverse seesaw : m ν ∼ m D M NS µ (7)Of course, tuning is then shifted to the Majorana mass term for S : m ν (cid:28) v ⇒ µ (cid:28) M NS (8)So, it seems that four-dimensional (4D) models of seesaw might not be entirely satis-factory as far as explaining fully the small observed SM neutrino mass. Recently, it wasemphasized [4] that • a natural realization of seesaw mechanism occurs in the warped extra dimensionalframework. This framework is dual, following the AdS/CFT correspondence, to varying degree of com-positeness of the SM particles. In a sense, this implementation actually features both high-scale and inverse seesaw mentioned above. Namely, from a bottom-up viewpoint, the SMneutrino mass is generated by exchange of pseudo-Dirac singlet states as in inverse seesawcase. Remarkably, This model was originally proposed in references [3], but the basis used in this earlier work obscured the physical nature of the seesaw mechanism. the smallness of the required Majorana mass term ( µ ) for the inverse seesaw is itselfdue to a high-scale seesaw:schematically, we have (with M IR ∼ TeV as usual)warped/composite seesaw : m ν ∼ m D M µ, µ ∼ M M UV ( no tuning ) (9)Note that, even with the above nice feature, we still need (as allued to above) the otherhierarchy for getting the observed SM neutrino mass, i.e., M UV (cid:28) M Pl : this seems to be atuning at first sight, but we will see that this is also explained in warped/composite seesaw.In detail, the dual CFT picture affords the most transparent understanding of this physicsas follows (see more discussion in [4] and some using 5D model in Sec. 2 of this paper).The SM Higgs boson arises as a composite of some new strong dynamics which confinesat the ∼ TeV scale. Rest of the SM (i.e., all the gauge fields and fermions) start out aselementary degrees of freedom which are external to the strong dynamics, but they “mix”with appropriate composites of the latter. Thus, the actual SM particles are admixturesof the two sectors. Such “partial compositeness” of the SM fields allows them to couple tothe SM Higgs, thus acquiring mass from its VEV. In particular, for the case of charged SMfermions, the picture is that external SU (2) L doublet and singlet fermions mix separately with respective composite ones, starting at the UV cut-off . Then, only in the far IR, i.e, at ∼ TeV scale, these two types of composites (and hence the corresponding external fermionsas well) “connect” to each other via the Higgs VEV.For the neutrino sector, the story starts out similarly, i.e., we add to the SM lepton sector,an external (chiral) SM singlet, denoted by N R , which mixes with an entire composite SMsinglet tower from ∼ TeV upwards. However, from then on, there is a departure in thescript (vs. that of charged fermions), again, kind of similarly to the usual seesaw models, butwith some crucial difference as follows. Obviously, this concerns the “fate” of the external N R : namely, we assume that the strong dynamics in isolation preserves lepton number sothat the composite singlets are purely Dirac to begin with. On the other hand, the external sector mass terms and interactions need not preserve lepton-number, for example, N R has aMajorana mass term, M N , which is close to the UV-cut-off, say, M Pl .However, even though lepton-number is violated at the UV cut-off, we can not write downa SM neutrino mass operator at this stage, since the SM Higgs boson VEV is not “born”yet. Instead, the relevant effect of Majorana N R is that its coupling to strong dynamicswill inject lepton-number violation into the strong dynamics also; in particular, integratingout N R (again, close to the UV cut-off) generates Majorana mass terms for the compositesinglet states: note that these Majorana mass terms are for the left chirality of composite,since that is the one with mass mixing term with external N R .4o, we start seeing the “ingredients” for a inverse seesaw model, with the seeds beingsown in the UV; in particular, it is the two chiralities of the composite singlet who play therole of the N , S fields of the usual 4D model of this type!Thus, we naturally havewarped/composite seesaw : M NS ∼ TeV/compositeness scale (10)Moreover, as already advertised above, we have an explanation for smallness of the Majoranamass term for S [i.e., µ in Eq. (7)]. Namely, for the TeV mass composites, this mass termwill precisely be of the form of µ in Eq. (9) above, i.e., the “TeV” in the numerator therecomes from the above-mentioned mass mixing term (between N R and LH composite) and M UV in denominator is just the (Majorana) mass term for N R with itself. We will argue ina bit that this “effective” UV scale can actually be naturally smaller than Planck scale. Thefinal cog in this wheel is the Dirac mass term for the composite singlet with the SM SU (2) L doublet neutrino: similarly to the case of the charged fermions, this arises from coupling ofcomposite singlet to Higgs VEV and composite doublet, latter mixing with the external SMneutrino. Of course, one difference from charged fermion case is “absence” of external leg onthe singlet side (since N R decoupled); so schematically, we get m D ∼ √ m τ v ( no tuning) (11)i.e., with two external fermions, we would have gotten m τ vs. its “square root” here withonly external doublet present . In other words, • the composite singlets act as a “bridge” between EWSB in the IR and lepton-numberviolation in the UV, both of which are required in order to generate (Majorana) SMneutrino mass.Note that plugging Eqs. (10), (9) and (11) into Eq. (7), we see that final formula lookslike high -scale seesaw, i.e., using Eq. (2) in Eq. (1)! In fact, the procedure used in mostof the previous literature [3] for the computation of the SM neutrino mass in this warpedextra-dimensional framework reinforces as follows this impression of high-scale seesaw. Inthis 5D model, we have a SM singlet propagating in the bulk, with a Higgs VEV-inducedDirac mass term with the SM lepton doublet field near the IR brane. In addition, thissinglet field has a Majorana mass term on the UV brane, i.e., bulk and IR brane preservelepton-number. In the so-called Kaluza-Klein (KK) basis for the singlet 4D states, first theusual mode decomposition is performed by neglecting the above Majorana mass term forthe singlet, resulting in zero and massive KK modes. The effects of the UV brane localized For simplicity, we assume here similar degree of compositeness for doublet and singlet charged lepton. and mixing them all up. It turns out that the exchange of only thewould-be zero-mode with a super-large Majorana mass term gives rise to the SM neutrinomass, which thus mimics a high-scale seesaw. However, some of us showed in [4] that this isnot so in the mass basis, i.e., it is physically an inverse seesaw (as is clear from the aboveCFT viewpoint).In fact, we can further “exploit” this process of communication between the UV (i.e.,lepton-number violation) and IR (i.e., EWSB) as follows. Firstly, it is clear that the lepton-number violating perturbation to the strong dynamics (again, from integrating out the ex-ternal Majorana singlet, N R ) has to be suitably renormalization group (RG) evolved fromthe UV scale to IR, i.e., over a large hierarchy. Assuming that the strong dynamics is ap-proximately conformal over this hierarchy as would be needed in order to get the observedsizes of SM fermion masses, we see that this transmission can be significantly modulatedby the anomalous dimensions of the operators involved. So, assuming sizable anomalousdimensions, • the effective seesaw scale can be much smaller (or larger, depending on sign of theanomalous dimensions!) than the Planck scale:again, heuristically speaking, M UV ∼ M Pl × ( anomalous scaling ↔
5D profiles ) ∼ GeV ( no tuning ) (12)where the requirement of the “intermediate” scale in second line corresponds to the choice of m D in second line of Eq. (11), using this and Eq. (9) in Eq. (7) and finally setting m ν ∼ . eV. Just to be clear, there is no new dynamics at this scale, cf. usual, 4D high-scale seesaw. In short, we then have a fully natural seesaw model here, i.e., with no large hierarchies in any of the fundamental parameters!Secondly, because we need the message of lepton-number violation to be brought downto the
TeV scale by particles beyond the SM, i.e., the composite singlets, we are obviouslyable to • probe the mechanism of generation of SM neutrino mass, namely, by producing thelightest of these messengers at the Large Hadron Collider (LHC)/future colliders (unlikethe case of high-scale seesaw). This corresponds to profiles for various modes in the extra dimensional dual. where, for example, this is associated with the breaking of SU (2) R × U (1) X gauge symmetry down to U (1) Y .
6f course, this is a feature in general of inverse seesaw models so that such signals have beenstudied before [5, 6], but (as we will show here) the compositeness of the singlets make adifference!In a series of papers (this being the first), we initiate the study of LHC signals for the ∼ TeV mass singlets in the natural realization of (inverse) seesaw in this warped/compositeHiggs setting. We begin here by focussing on a specific , but well-motivated model within theabove framework. Namely, • we assume that the strong dynamics has a global symmetry (in the EW sector) whichcontains SU (2) L × SU (2) R × U (1) X of which the SM subgroup, i.e., SU (2) L × U (1) Y is gauged by external fields [with U (1) Y being a combination of U (1) X and the U (1) contained in SU (2) R ] . In the canonical case,we would identify X = (B − L) as in 4D LR models, but in general we could choose otherrepresentations under the extra U (1) . The motivation for such an extension of the EW( global ) symmetry in the present context is not the one for the 4D LR models, i.e., parityrestoration at higher energy scales, but rather that it provides a custodial symmetry forsuppressing the contributions of the strong dynamics to the EW precision tests, in particular,the T parameter. Thus, even with the choice of X = (B − L) , there is then no need for an elementary (i.e., external to the strong sector) W ± R , i.e., charged gauge boson of SU (2) R group, in this model. Similarly, the combination of U (1) B − L and U (1) in SU (2) R which isorthogonal to U (1) Y – often denoted by Z (cid:48) – is not gauged, un like in 4D LR models, i.e.,the external sector does not respect the extended EW symmetry. We will mostly use theelementary-composite sector picture (called two-site model [12], but augmented now by thecomposite singlet neutrinos) in our actual LHC signal analysis.Even though we do not have elementary W ± R / Z (cid:48) in this model, given the above globalsymmetry of strong dynamics, we do have • composite W ± R and Z (cid:48) , which do couple to singlet neutrinos (cf. composites of SMgauge bosons obviously do not);this simultaneous similarity (i.e., “existence” of W ± R and Z (cid:48) ) and difference (their composite-ness vs. elementary nature) from 4D LR models will be crucial to the analysis of signals forthe present model. The warped 5D dual of this scenario is that the bulk EW gauge symmetry is extended as above andbroken down to the SM subgroup on the UV brane. As a bonus, with such a symmetry structure, we automatically realize the pure Diracness of compositesinglets vs. large, possibly close to UV cut-off, Majorana mass term for the external singlet. We will denote them simply by the same symbols, since there is no chance of confusion with elementaryones in this model. Also, strictly speaking, we have to assume degeneracy of spin-1 composites here in orderto classify mass eigenstates in this way: we will consider the case of non-degeneracy in a follow-up paper,where we will give more details of this issue. composites , since it is that sector which has the SU (2) R symmetry, i.e., • the composite (denoted by ψ e ) with which the external RH charged lepton mixes ispart of a doublet of the (global) SU (2) R of strong dynamics, whose other componentis the composite RH neutrino (denoted by ψ N ), i.e., with which external N R mixes asmentioned above. Both ψ ’s have Dirac mass ∼ TeV and are vector-like under the SM gauge and strong dynamicsglobal symmetries.We begin by considering the production of ψ N via decays of on -shell W ± R ; again such asignal has been studied extensively in the case of usual, 4D LR models [5], but the differencehere is that W ± R is composite vs. quarks inside proton being mostly elementary. So, naively,this coupling seems to be negligible (i.e., ∝ tiny admixture of composite in SM light quarksor the corresponding Yukawa couplings). Nonetheless, we discuss how • a significant, albeit still mildly suppressed relative to SM, light quark- W ± R coupling isinduced.This arises by a combination of elementary-composite mixing for W ± ’s corresponding to SU (2) L (denoted by W ± L ) and composite W ± L − W ± R mixing induced by Higgs VEV, withthe near degeneracy of these composites in a “minimal” model amplifying the Higgs VEVeffect (see reference [7, 8] for the 5D version of this effect). (We will consider the case of non -degenerate spin-1 composites in a follow-up paper.) In fact, such a mild suppression ofproduction of W ± R (as compared to usual 4D LR models) is perhaps “welcome” in the sensethat the LHC early run 2 searches are already constraining TeV W ± R in the usual case, butwith compositeness, such low scale for W R would then (i.e., given smaller cross-section forthe same mass) still be allowed. At the same time, as we will show, the coupling is sizableenough that discovery (for 2 TeV W ± R and ∼ GeV ψ e,N such that the above decay isallowed) by the end of run 2 ( ∼
300 fb − ) would be possible. called “electron” here for simplicity, even though we extend this to the second and third generations also In detail, one might need two such SU (2) R doublet composites per generation – corresponding to twodifferent 5D fields – in order to obtain the correct SM charged lepton vs. SM neutrino Dirac mass term,i.e., external charged lepton might actually mix with a different composite tower than the SU (2) R part-ners of composite SM singlets associated with the SM neutrino mass. However, this modification does not(qualitatively) affect the present discussion. Recall that there is no elementary gauge boson mixing directly with composite W ± R . This is dual to the 5D model with no IR brane-localized kinetic terms for bulk gauge fields. We could contemplate even lighter singlet neutrino, but accomplishing such a hierarchy might requiretuning, for example, too large brane-localized kinetic terms, given that gauge KK cannot be below ∼ TeVdue to constraints from EWPT. W ± R , first of all, the largest coupling of W ± R involves composite partner of SM e R and the composite singlet neutrino, i.e., ψ e and ψ N , cf. SM e R and singlet neutrino in the usual, 4D LR case. The singlet neutrino decays predominantly(as in 4D LR models) into SM doublet lepton and Higgs doublet (including physical Higgsand longitudinal W/Z ) via the associated Yukawa coupling : the channel we will focus onhere (based on smaller background, thus more visibility) is e L + W . On the other side, ψ e will similarly decay: we will consider e L + Z long /h final state here. Thus, we see that thereis • an “extra” Higgs/ Z (vs. usual, 4D LR models) among the decay products of the W ± R ,which, assuming it is tagged, can be used to reduce the SM background.Moreover, it then allows us to possibly reconstruct the full decay of ψ e , thus determining itsmass, which is same as that of ψ N [given the SU (2) R symmetry]. Including decays of W from ψ N , we then have • two search channels, i.e., dilepton + dijet (hadronic decay of W ) and tri-lepton (leptonicdecay of W), along with Higgs/ Z boson. We will study both of these and find them to be complementary, for example, rate is largerfor the former (based simply on corresponding branching ratios of W ), but so is possibly SMbackground, given that leptons are typically “cleaner”. (Of course, for the case of hadronicdecay of the W from ψ N , that side is also fully visible and hence can furnish information on ψ e,N masses.)Finally, in addition to W ± R , we consider production of ψ e,N pairs from decays of on -shell Z (cid:48) . Once again, the “direct” coupling of quarks inside proton to Z (cid:48) is negligible; however,mixing does create a larger coupling (just like for the case of W ± R above). Note that inusual, 4D LR models, Z (cid:48) is typically heavier than W ± R , for example, assuming both (beingelementary) get their mass from some scalar VEV, just like the case of SM W/Z . Hence,production cross-section of Z (cid:48) tends to be smaller than that of W ± R . However, in the seesawmodel being studied here, • the W ± R and Z (cid:48) can be almost degenerate, since their masses arise from the compos-iteness scale so that Z (cid:48) signal can be comparable to W ± R . Other decay channels for W ± R include various components of the Higgs doublet: these were studied in[8], but singlet neutrino was not included there. Note that this coupling is indeed small, given that it involves degree of compositeness of SM (doublet)lepton, but there is not much of an “option” here in terms of decay channel, given that lepton-number is(approximately) preserved. Note that even in the usual, 4D LR models, one can also get Higgs/ Z boson from singlet neutrino decay,but then we lose lepton(s), i.e., final state with be lh + MET, thereby increasing SM background (for example,SM
W h production will then be relevant), as opposed to our case of Higgs along with di-or-tri-leptons. SU (2) R extension of the SM EW symmetrymentioned above. In Sec. 3, we outline the “simplified”, i.e., two-site approach [12] to studyingthe 5D model that we will employ in our actual analysis of LHC signals. We then discuss ourmain results, starting with production cross-sections and decay branching ratios of variousheavy particles in Sec. 4, followed by computations of SM background and thus the discoverypotential for the new particles in Sec. 5. Here, we also mention/briefly discuss strategies(post-discovery) for distinguishing the composite/warped seesaw model from the usual, 4DLR one. We conclude and present some directions for future work in Sec. 6. In this section, we provide a brief review of seesaw model in 5D warped extra-dimensions.After discussing general features of warped seesaw, we will focus on a model with the ex-tended bulk gauge symmetry: SU (2) L × SU (2) R × U (1) X . Our studies of LHC signals areperformed using the simplified two-site model of the full 5D warped model. Hence, ourdiscussion about the full 5D model in this section will be brief, leaving details necessary forthe phenomenology to Sec. 3 of the two-site model. More details about the 5D results, alongwith their 4D CFT dual description, can be found in [4].We begin our discussion by taking usual Randall-Sundrum framework with all SM fermionsand gauge bosons propagating the bulk of a slice of AdS . For concreteness, we considerSM Higgs to be localized on the IR brane. The 5D SM gauge singlet field, N , which is theanalog of the the right-handed neutrinos of the usual, 4D seesaw models, propagates the bulk.Like all 5D fermion fields, N can be decomposed into both left ( L ( and right ( R ) chiralities(denoted by N L,R , respectively) from the 4D viewpoint. N R couples to SM SU (2) L leptondoublet, in particular left-handed neutrinos, and the Higgs on the IR brane with 5D Yukawacoupling y . In addition, N R acquires large Majorana mass, which is taken to be localizedon the UV brane. These can be summarized in the following 5D Lagrangian L (cid:51) y LHN + c N k ¯ N N + δ ( z − z h ) 12 m N k N R N R , (13)where since N is 5D fermion field, it is four component spinor, containing N L and N R c N k is 5D mass parameter for N (in units of the AdS curvature scale, k ) and m N is Majorana mass of N R . UV(IR) brane is at z = z h ( z v ) .The above model was studied in [3] using so-called KK-basis where KK decomposition wasdone without taking into account the large Majorana mass term from the beginning. Theeffects of the Majorana mass was added as a posteriori process and this leads to large Ma-10orana masses for zero- and KK-modes and large mixing among all modes. Hence, althoughanalysis using KK-basis produces correct neutrino mass formula, using a basis that is vastlydifferent from the mass basis obscures the physical picture. In particular, the results fromKK-basis naively suggest (or give the misleading impression) that the above 5D warped see-saw model is indeed of Type I in the sense that the SM neutrino mass is generated by the dynamical exchange of a super-heavy singlet mode, i.e., at the (effective) seesaw scale (formore discussion of this point, see [4]).However, as shown in [4], analysis based on the mass basis, including the Majorana massterm from the beginning, reveals very different dynamical picture. The mass eigenstates of4D effective theory (after KK-decomposition) of Eq. (13) is a tower of pseudo-Dirac singletfermions with tiny Majorana splitting. For the choice of c N ∼ − . that renders correct SMneutrino mass, dominant contributions to the SM neutrino masses come from the exchangeof a few low lying mass eigenstates (cf. super-heavy modes in the KK basis). Namely, theSM neutrino mass is generated not by an exchange of super-heavy Majorana singlet mode,but by exchanges of O (TeV) pseudo-Dirac singlet modes. Therefore, the dynamical natureof the warped seesaw is inverse seesaw [2], not Type I. Moreover, it is indeed very natural realization of it, because the SM neutrino mass is obtained with all dimensionful parameterstaken to be near the cut-off scale and all dimensionless parameters to be O (1) . This newfinding, then, re -focuses attention on LHC signals from the O (TeV) scale singlet pseudo-Dirac fermions that arise in this model. Since the production and decay channels depend ondetails of the model, now we describe a concrete model based on the extended bulk gaugesymmetry, whose simplified two-site version (presented in next section) will be used for ourcollider studies in Sec. 5. Natural realization with custodial symmetry
In order to have sizable signal production of the new particles in the 5D model (i.e., theKK excitations of SM) at the LHC, a KK scale of the order O (1) TeV is desirable; ofcourse naturalness of the EW scale also prefers such a low scale. However, minimal RSmodel with only the SM gauge symmetry in the bulk is in tension with EW precision tests,both oblique and non-oblique (from Z → b ¯ b coupling) corrections, and consistency requiresKK scale of (cid:38) O (10) TeV. This bound can be relaxed by extending the bulk EW gaugegroup to SU (2) L × SU (2) R × U (1) X . In particular, the extended gauge group providescustodial symmetry for both T-parameter and Z → b ¯ b coupling, and KK scale as low as O (1) TeV is allowed [9, 10]. There are also constraints from flavor/CP tests which generically Since QCD gauge group int he bulk will not play any role in our study, we will simply drop it fromhereon. In fact, even with the extended bulk gauge group, KK scale is constrained generically to be (cid:38) O (3) TeV. (cid:38) O (10) KK scale, but here we assume addition flavor structure (for example, flavorsymmetries) in order to ameliorate those bounds [11] .On the UV brane, the gauge symmetry is broken down from SU (2) R × U (1) X to U (1) Y by choice of boundary conditions (BC). Specifically, the gauge fields associated with thebroken generators ( SU (2) R × U (1) X ) /U (1) Y will have Dirichlet BC, denoted henceforth as“ − ”, whereas U (1) Y and SU (2) L has Neumann ( + ). All gauge fields are taken to be + on IRbrane. In particular, only fields with (++) BC have zero-modes up on KK-decomposition,i.e., only gauge fields for SM gauge group in this case. We use W R and Z (cid:48) to denote theextra gauge fields, i.e., for charged SU (2) R and ( U (1) R × U (1) X ) /U (1) Y , respectively: thesehave ( − +) BC and hence only have massive/KK modes.Higgs field, which we choose to be localized on the IR brane, is a bi-doublet of SU (2) L × SU (2) R , with zero charge under U (1) X : H ∈ (2 , . (14)This representation results in a custodial symmetry, i.e., the Higgs VEV breaks S (2) L × SU (2) R down to SU (2) V , which suppresses contributions from the gauge sector to the T -parameter: note that U (1) X remains unbroken in this process. The Higgs VEV will alsogenerate mixing between various modes of W R and W L , an effect which can be treatedperturbatively and which will be very important for LHC signals for the singlet neutrinos.We will make this point clearer in Sec. 3.Moving onto representation of fermions under the extended gauge group, first note that (justlike for gauge fields) SM fermions will arise as zero-modes of 5D fields with (++) BC. Webegin with the leptons, where we choose the simplest possibility, i.e., X is same as ( B − L ) inthis sector. Thus, we take L , i.e., the SM SU (2) L lepton doublet, to be a singlet of SU (2) R ,while the right-handed charged lepton (denoted by l ) is promoted to be a doublet of SU (2) R ,denoted by L R [as in the canonical, 4D (gauged) left-right (LR) symmetric models]: L ∈ (2 , − L R , ˜ L R ∈ (1 , − . (15)where numbers in the parenthesis denote representation under SU (2) L and SU (2) R , whilerepresentation of U (1) X is shown as a subscript [we will explain momentarily why there are two SU (2) R doublets]. Remarkably, akin to usual, 4D LR symmetric models, we see thatthe SU (2) R partner of (cid:96) has the precisely the characteristics to play the role of the N fieldmentioned above, i.e., it is a (i) singlet under SM gauge group; (ii) it has a Yukawa coupling Thus, special regions of parameter space and/or additional contributions to these observables (perhaps fromfurther model building) will be needed in order to have KK scale as low as O (1) TeV. Given that resonanceswith mass O (3) TeV or heavier is slightly beyond the LHC reach, having new colliders with higher energyreach are required and hence motivated for a better test. SU (2) R × U (1) X (under whichit is charged) is broken. As a by-product, such a choice gives rise to a way to produce N viadecay of W R . In fact, this will be the production channel for our signal process.In more detail, note that we will actually need two SU (2) R lepton doublets, namely: ˜ L R = N (++) → ( − +)˜ (cid:96) ( − +) R L R = ˜ N ( − +) (cid:96) (++) R (16)Here the SM lepton ( (cid:96) ) is obtained as the zero-mode from the 2nd multiplet above, i.e.,with (++) BC; its SU (2) R partner (denoted by ˜ N ) is chosen to be − on the UV brane(thus having no zero-mode at all): this is consistent with the bulk gauge symmetry since SU (2) R × U (1) X is broken on UV brane to U (1) Y (i.e. different BC’s for two components ofdoublet are allowed), while this symmetry is unbroken on IR brane (i.e. it should be sameBC for both fields, which is + in this case). Note that ˜ N then plays no role in the seesaw forthe SM neutrino mass (hence will be dropped from now on). On the other hand, the BC’sare “switched” in the 1st doublet, i.e., ˜ (cid:96) has no zero-mode, whereas the N here will be drivingthe SM neutrino mass seesaw (thus will be denoted as the singlet neutrino henceforth). Notethat N has (++) BC to “begin with”, but adding a UV brane localized Majorana mass term“repels” N profile away from UV brane, resulting in effective boundary condition of the form ( − +) and hence removing the corresponding zero-mode.The simple reason for having two SU (2) R doublets, instead of housing N and SM right-handed lepton in a single SU (2) R doublet, is the following. The N and SM right-handedlepton, i.e., (cid:96) , fields should have different 5D bulk mass parameters in order to producecorrect masses for charged lepton and neutrino [3], i.e., we require c < − . for the fieldgiving charged lepton zero-mode so that this mode is localized near the UV brane , thusgiving the observed charged lepton mass, whereas we need c ∼ − . for N (as mentionedabove), i.e., that would-be zero-mode should be peaked near the IR brane instead. However,by SU (2) R -invariance, fields in a doublet should have a common 5D mass parameter. Thus,we need to “split” the SM charged lepton and singlet neutrino multiplets as shown above.Following [10], i.e., in order to suppress corrections to the Zb ¯ b coupling, we choose therepresentations of the quarks to be somewhat non-minimal as follows. Q L ∈ (2 , u R ∈ (1 , d R ∈ (1 , (17)Here, Q L denotes the SM left-handed quarks doublet and u R , d R are the SU (2) L singlets.For the “extra"’ fields in SU (2) R doublet or triplet representations above, we take Dirichlet-Neumann ( − +) boundary condition in order to remove zero-mode (just like was done for Such a profile also needs to be chosen for the L zero-mode. U (2) L × SU (2) R × U (1) X SU (2) L × SU (2) R × U (1) X SU (2) L × SU (2) R × U (1) X ⇓ SU (2) L × U (1) Y ˜ L R L/L R Q L Q , L /u , R /d R H/t R Figure 1: RS model with extended bulk gauge symmetry SU (2) L × SU (2) R × U (1) X and singletneutrino. Gauge symmetries together with its breaking pattern are shown on the relevant positionalong the extra-dimension. The position of the fields shows where the zero-mode profile of thecorresponding 5D fields is localized. For fields with (close to) flat zero-mode profile, they are locatedin the middle of the bulk. leptons above). As usual, t R zero-mode is taken to be localized near the IR brane, while ( t, b ) L , i.e., Q L , has a (roughly) flat profile and rest of the quarks are peaked near the UVbrane (just like the SM leptons).We mentioned that the spectrum of N in 4D effective theory is a tower of pseudo-Diracfermions. Since the Majorana splitting ( O (MeV) ) for these pseudo-Dirac pairs is very tinycomparing to its Dirac mass ( O (TeV) ), we are unlikely to be able to probe any effects fromsuch Majorana splitting. Moreover, as far as investigating the discovery potential of thelightest pseudo-Dirac singlet mode is concerned, the existence of tiny Majorana splitting willnot make any difference. For this reason and for simplicity, in our collider study, we ignoreMajorana splitting and treat N as pure Dirac with ( − +) boundary condition, which willhave the same mass as its SU (2) R partner ˜ (cid:96) .The 5D fields discussed thus far are summarized in Fig. 1. The position of the fieldsshows where the zero-mode profile of the corresponding 5D fields is localized. Fields that arecloser to the UV (IR) brane signifies that their zero-mode profiles are peaked near the UV(IR) brane. For fields with (close to) flat zero-mode profile, they are located in the middleof the bulk. Couplings of KK modes
The couplings among various 4D particles are proportional tothe overlap of their respective profiles in the extra dimension. Now the light quarks arelocalized near the UV brane, while the KK modes are near the IR brane. However, thenon-zero (Neumann BC) profile of KK of SM gauge bosons at the UV brane does induce asignificant coupling to the light quarks. On the other hand, KK W ± R and Z (cid:48) vanish at the UV14rane (Dirichlet BC), rendering such a coupling to be negligible. Nonetheless, as we discussin Sec. 3, EWSB mixing among KK W L and W R does induces a sizable coupling of KK W ± R to light quarks provided there is degeneracy between KK W ± R and KK W ± L ,similarly KK Z and KK Z (cid:48) . This coupling can then be used in production of KK W ± R and Z (cid:48) . Onceproduced, their decay is dominantly to modes localized near IR brane such as (light) KKfermions and/or top quark/Higgs boson, since those couplings are the largest. Spectrum of KK modes
Mass of KK gauge boson is dictated by boundary condition of corresponding 5D gauge field.The mass of first KK mode of gauge fields with (+ +) boundary condition is typically O (1) × warped-down k and we denote it as m gauge . On the other hand, first KK mode of gaugefields with ( − +) boundary condition has slighter smaller mass than m gauge .KK fermion masses are determined by boundary condition and 5D mass m , or c = m k . Forfermion fields with c chosen such that the corresponding (would-be) zero-mode is localizednear the UV brane, we find that the KK mass is larger than KK gauge mass m gauge , regardlessof its boundary condition [assuming brane localized kinetic terms (BKT) are negligible]. Thisis the case for all leptonic fields, except for ˜ L R . In order to produce SM neutrino mass, ˜ L R has c ∼ − . and resulting KK mass is naturally smaller than m gauge . However, in theminimal setup, its mass is still bigger than m gauge , preventing the decay of W (1) R into N (1) and ˜ (cid:96) (1) . As is well-known, turning on BKT’s could lower the mass of corresponding KKmodes. We can show O (1) BKT on the IR brane for ˜ L R can result in mass of N (1) and ˜ (cid:96) (1) smaller than m gauge . Another interesting fact about BKT is that, both N (1) R and N (1) L can have similar coupling to gauge field W (1) R . In the absence of BKT, the coupling of N (1) L to W (1) R is mildly suppressed, i.e., by O (1) , as compared to N (1) R , since W R is peaked nearIR brane where N (1) L has vanishing boundary condition. Combination of these two featuresopens new decay channels for KK W (1) R . Namely, the decay of W (1) R into pair of N (1) R and ˜ (cid:96) (1) R together with N (1) L and ˜ (cid:96) (1) L , which are our signal channels.A similar analysis can be applied to the quark sector: we find that, in the absence ofBKT’s, the only KK fermions which are a bit lighter than the W (1) R (but still heavier than / m gauge ) are the SU (2) R partners of Q L (like the case of ˜ L R above). We assume thatBKT’s for these states are not turned on ( un like for ˜ L R ) so that KK W R can not decay intopairs of these extra fermions. The decay channel for W (1) R into SM Q L and the above extrafermions is kinematically open; however, given the (roughly) flat profile of Q L , this couplingis nonetheless suppressed compared to the coupling to N (1) and ˜ (cid:96) (1) so that this decay modecan be neglected.In this paper, we study the on-shell production of KK gauge bosons W (1) R and its decays to N (1) - ˜ (cid:96) (1) pair. Particles heavier than W (1) R are dropped for simplicity of study. Below, we15ummarize the spectrum of particles of interest: m gauge > m ˜ L R (cid:29) mass of SM particles (18)where KK gauge bosons included in our phenomenological study are W (1) L , W (1) R , and Z (1) , Z (cid:48) (1) . Full 5D warped model contains all the degrees of freedom with perturbative couplings. In thissense, it is fully calculable 5D effective theory and any relevant questions can be answered byexplicit computation. However, for a specific phenomenological search, only a finite subset ofdegrees of freedom and related couplings are involved and a simplified model consisted of onlyrelevant particles and couplings will be much more efficient in practice. Two site model of [12]provides one way to obtain a simplified 4D effective theory by a consistent truncation of a full5D warped model to the first KK modes. This approach not only simplifies phenomenologicalstudies, but also can encompass phenomenology of broader class of 5D warped models, orits 4D composite models, thereby allowing more inclusive/systematic searches.Two site model, as the name suggests, consists of two sectors/sites: the elementary sectorand the composite sector. The composite sector represents strong dynamics which confinesat O (TeV) scale, the scale where the scale invariance is spontaneously broken and compositeresonances are “born”. In principle, there will be towers of infinite resonances. However,as a phenomenological simplified model, only the lightest resonances, the relevant particlesfor the collider searches, are kept. Elementary sector, on the other hand, exhibits physicsexternal to strong dynamics, but with couplings to the composite sector. These couplingsinduce mixing between elementary and composite states and upon diagonalization, this leadsto massive mass eigen-modes, dual to first KK modes in 5D, and massless modes, dual tozero mode, i.e. SM fields. In this way, it is easily seen that both SM fields and the firstKK modes of 5D model are generically the admixture of elementary and composite states,the amount of compositeness being determined by the size of the mixing at the O (TeV) scale. Such a feature is known as Partial Compositeness in 4D strong dynamics, a robustmechanism that solves flavour hierarchy problem of the SM. 5D dual of partial compositenessis the localization of the zero-mode profile along the extra-dimension, localization near theIR (UV) brane being dual to more composite (elementary).Two site model of the natural warped seesaw that we reviewed in Sec. 2 can be describedas follows. We begin by discussing the singlet neutrino N R . In the elementary sector, thereis elementary field N R that has large Majorana mass term m N . In the composite sector, asalready mentioned in the introduction, there is a composite singlet Dirac fermion ( χ L , χ R ) O (TeV) Dirac mass. Finally, there is mass mixing between N R and χ L , i.e. they havethe same quantum number, with the size of the mixing being characterized by the relevantscale, i.e. of the order of O (TeV) . These can be summarized by the following Lagrangian(dropping kinetic terms for simplicity): L seesaw = L elementary + L composite + L mixing = m N N R N R + ( m D ¯ χ L χ R + ∆ ¯ χ L N R + h . c . ) (19)where m N ( m D ) is Majorana (Dirac) mass for elementary (composite) states and ∆ is themass mixing between the two. Both m D and ∆ are O (TeV), while m N (cid:29) TeV . Largeness ofthe Majorana mass m N allows us to integrate out N R , i.e. use equation of motion for N R ,to get L seesaw = ( m D ¯ χ L χ R + h . c . ) + m D ∆ m N χ L χ L . (20)Notice that integrating out N R generates the Majorana mass for left-handed χ L of the com-posite singlet fermion, that is, it transmits lepton-number violation into the composite sector.Since m D ∆ m N (cid:28) m D , it is clear that the composite fermion ( χ L , χ R ) becomes pseudo-Dirac andthe exchange of this pseudo-Dirac singlet fermion between the two left-handed SM neutrinosthen is the dynamical origin of the SM neutrino mass. Namely, it is the inverse seesaw forSM neutrino mass generation. Notice, however, that the way the small Majorana splittingis generated is by the “exchange” of super-heavy N R , which can be viewed as Type I seesaw.As mentioned in Sec. 2, since the Majorana splitting is much smaller than Dirac mass, wesimply drop it and treat ( χ L , χ R ) as a pure Dirac fermion for our collider analysis presentedin Sec. 5. For the rest of the study, we simply use ( N (1) L , N (1) R ) to denote ( χ L , χ R ) and putthem and their SU (2) R partner, denoted as ( ˜ (cid:96) (1) L , ˜ (cid:96) (1) R ), in the doublet ˜ L R .For the rest of the model, following [12], we consider an elementary sector with elementarygauge group [ SU (2) L × U (1) Y ] elem and a composite sector with global symmetry [ SU (2) L × SU (2) R × U (1) X ] comp . Focusing on the gauge sector first, there will be mixing terms betweenelementary gauge bosons and corresponding composite vector mesons, i.e. composite vectorbosons associate with [ SU (2) L × U (1) Y ] comp subgroup of the full global symmetry of thecomposite sector. These mixing terms between elementary and composite vector bosonsbreak both elementary and composite symmetries. However, it does so in a way that only onelinear combination of the elementary gauge boson and composite vector meson gets a mass,leaving the other orthogonal combination being still massless. Namely, there is unbrokengauge symmetry which we identify as the SM gauge group [ SU (2) L × U (1) Y ] SM . Thesemassless (massive) mass eigenstates are dual to zero-(KK-)mode SM gauge boson arisingin the 5D model. In this way, we understand that there is mixing between elementary and17omposite vector bosons, allowing the coupling between elementary fermions and compositevector mesons.On the other hand, since there exist no associated elementary gauge bosons, the chargedvector mesons for SU (2) R ( W (1) R ) and the one for ( U (1) R × U (1) X ) /U (1) Y ( Z (cid:48) (1) ), i.e. or-thogonal to U (1) Y , do not have mixing with elementary gauge bosons, i.e. purely composite.This feature is dual to the fact that the corresponding 5D gauge bosons have odd boundarycondition on the UV brane and have no zero-mode. SM fermion fields are admixture ofelementary and composite states (resulting from presence of mass terms along the lines ofwhat was discussed for singlet neutrino above). In this study, just for simplicity, we treat allSM fermions to be purely elementary, except ( b L , t L ) and t R . As we discussed in Sec. 2, themass for KK modes of all SM fermions are higher than gauge KK; however, the KK modesfrom the ˜ L R multiplet in Eq. (16) are taken to be lighter. This is mapped into the two sitemodel by the fact that all “excited” composite modes of the SM fermions are heavier thancomposite vector mesons, thus for simplicity, we neglect them in what follows. However, thecomposite SU (2) R doublet containing the singlet neutrino (discussed above) is light. Higgs ischosen to be pure composite state as a standard choice. The diagonalized Lagrangian beforeEWSB (see next section for this effect) containing all these degrees of freedom is given by L = L gauge + L fermion + L Higgs . (21)where we provide each part below one by one. First of all, L gauge is given by L gauge = − F µν + 12 ( D µ ρ ν D ν ρ µ − D µ ρ ν D µ ρ ν ) + m (cid:63) ρ µ + m (cid:63) φ ρ µ + ig F µν [ ρ µ , ρ ν ] , (22)where ρ µ = ( W (1) Lµ , B (1) µ ) (using the 5D notation, i.e., KK of SM gauge fields), ˜ ρ µ =( W (1) Rµ , Z (cid:48) (1) µ ) ( non -SM gauge bosons) and A µ = ( W (0) Lµ , B (0) µ ) (the SM gauge bosons), andwe have dropped gauge indices to avoid notational clutter. F µν is the field strength of A µ .All covariant derivatives in the Lagrangians are with respect to the unbroken SM gaugegroup, namely Dµ = ∂ µ − igA µ . Gauge couplings are SM gauge couplings g = ( g W , g Y ) andcomposite gauge couplings g (cid:63) = ( g (cid:63)W , g (cid:63)Y ) , and ˜ g (cid:63) = ( g (cid:63)R , g (cid:63)Z (cid:48) ) , where g (cid:63)Y = g (cid:63)R g (cid:63)X √ g (cid:63)R + g (cid:63)X .The elementary-composite mixing angle φ = ( φ W , φ Y ) is defined as sin φ = gg (cid:63) . Finally, m (cid:63) denotes the composite spin-1 mass before mixing with elementary states, hence this is alsothe mass for ˜ ρ ’s (i.e., W ± R and Z (cid:48) ) who do not have such mixing. Whereas, for compositepartners of SM gauge bosons, i.e., ρ ’s, the mass is modified by this mixing as indicated above.Note that we are providing phenomenologically most relevant terms only, dropping termswith 3 or more ρ ’s or ˜ ρ ’s. This is valid approximation since we are working to leading order Note that this also applies to the composites with which the external RH charged lepton mixes, i.e.,corresponding to the field (cid:96) from the L R multiplet in Eq. (16). ρ ’s or ˜ ρ ’s, arerelevant.Moving onto the fermion sector, L fermion (for the fields relevant for our collider study) isgiven by L fermion = ¯ ψ SM i /Dψ SM + ¯˜ L R ( i /D − m D ) ˜ L R − g tan φ ¯ ψ light ρ µ γ µ ψ light + g (cos φ Q L cot φ − sin φ Q L tan φ ) ¯ Q L ρ µ γ µ Q L + g (cid:63)Y ¯ t R B (1) µ γ µ t R (23) +˜ g (cid:63) cos φ Q L (¯ b L Z (cid:48) µ γ µ b L + ¯ t L Z (cid:48) µ γ µ t L ) + g (cid:63)Z (cid:48) ¯ t R Z (cid:48) µ γ µ t R +˜ g (cid:63) ¯˜ L R ˜ ρ µ γ µ ˜ L R + g (cid:63)Y ¯˜ (cid:96)B (1) µ γ µ ˜ (cid:96) where ψ SM denotes all SM fermions and ψ light = ψ SM − { Q L , t R } , i.e. light SM fermions.It is understood that all couplings should be multiplied by appropriate charges to getfinal coupling, which we do not show explicitly. The mixing angle between elementary andcomposite states of the associated fermion ψ is denoted by φ ψ , with sin φ ψ = 1(0) correspondsto pure elementary (composite). The specific representations of fermions are discussed inSec. 2. As mentioned earlier, here we assume that light SM fermions are purely elementary,i.e. sin φ ψ light = 1 (corresponding to the zero-modes being localized near the UV brane inthe 5D model), and Q L is slightly composite (roughly flat profile) and t R is fully composite(localized near the IR brane), i.e. sin φ t R = 0 . Finally, L Higgs has the form L Higgs = | D µ H + ig cot φ ρ µ H − i ˜ g (cid:63) H ˜ ρ µ | + V ( H ) − y ¯ L H ˜ L R , (24)where H denotes Higgs bi-doublet H = ( iσ H, H ) and H denotes SM Higgs doublet. L is SM lepton doublet and y is the Yukawa coupling constant. All the vector fields in theLagrangians shown above are in matrix forms. Final results can be obtained by taking tracesof the above Lagrangians with appropriate normalization.Note the sizable couplings of light quarks to ρ ’s, i.e., excited SM gauge bosons, in 2ndline of Eq. (23); these are nonetheless suppressed compared to the SM gauge couplings bythe smallness of the elementary-composite mixing factor and correspond to the profile of thegauge KK modes at the UV brane in the 5D picture. In any case, it is these couplings thatwill will be relevant for production of the spin-1 states at the LHC. On the other hand, thecoupling of light quarks to non -SM gauge bosons, i.e., W ± (1) R and Z (cid:48) (1) (denoted collectivelyby ˜ ρ ) is negligible, due to the absence of the elementary counterparts (and dual to profileof those gauge KK vanishing on the UV brane). However, as we will see below, even ere asizable coupling will be generated due to EWSB effects. As far as decay of spin-1 states isconcerned, it is the couplings in last line of Eq. (23), i.e., to composite leptons, to top quarkin line above it and to Higgs particles from Eq. (24) which dominate.19 .1 Higgs induced gauge mixing When Higgs gets a VEV and the electroweak symmetry is spontaneously broken, it generatesmixing among gauge bosons and fermions. In order to obtain mass spectrum, then, massmatrices should be diagonalized. In this section, we shall discuss the diagonalization of massmatrices and show, in particular, that the mass eigenstates of massive vector bosons consistof O (1) components of both W (1) L and W (1) R . That is, EWSB induces a significant mixingbetween W (1) L and W (1) R , and this will be the main production channel for W (1) R (as mentionedearlier). We choose g (cid:63)W and g (cid:63)R to be the same for our benchmark points.The mass matrix for charged vector bosons is given by (cid:16) W +(0) L W +(1) L W +(1) R (cid:17) M (cid:16) W − (0) L W − (1) L W − (1) R (cid:17) T (25)where M = 14 g W v g W v cot φ W − g W g (cid:63)W v g W v cot φ W m (cid:63) cos φ W + ( g W cot φ W v ) − g W cot φ W g (cid:63)W v − g W g (cid:63)W v − g W cot φ W g (cid:63)W v m (cid:63) + ( g (cid:63)W v ) (26)Note that we assume the same purely composite mass m (cid:63) for all composite gauge fields,i.e., before mixing with elementary states; this mixing does perturb the mass for excited SM gauge bosons as seen above. We will return to the more general case of non -degeneratecomposites in a follow-up paper.Performing explicit diagonalization of the above matrix analytically can be quite challenging.However, we can use the following method to get an approximate result. Our procedure willbe valid as the following relations hold: g (cid:63) v (cid:28) m (cid:63) and g (cid:28) g (cid:63) , ˜ g (cid:63) (27)We demand that the mass matrix can be fully diagonalized by the following transformationby U . U † M U = M (28)where U = U U U (29)20ith U = c − s s c
00 0 1 U = C − S S C (30) U = c (cid:63) − s (cid:63) s (cid:63) c (cid:63) . Here s, S, s (cid:63) represent the sines of θ , θ , and θ , whereas c, C, c (cid:63) represent cosines ofassociated angles. Making use of the approximations of Eq. (27), one readily finds that tan 2 θ ≈ g (cid:63)W v m (cid:63) + g (cid:63)W v tan 2 θ ≈ − g (cid:63)W v m (cid:63) + g (cid:63)W v (31) tan 2 θ ≈ − g (cid:63)W v φ W m (cid:63) The last formula corresponds to the mixing between two composite vector bosons, W (1) L and W (1) R . Since g (cid:63) v (cid:28) m (cid:63) , we would naively think that this mixing is small. However, using sin φ W = g W g (cid:63)W , we get tan 2 θ ≈ − g (cid:63)W v g W g (cid:63)W m (cid:63) ) (32)and, as far as g (cid:28) g (cid:63) , this mixing angle is O (1) ! That is, in most of the parameter spaceof interest, we get a significant mixing between W (1) L and W (1) R . (see Fig. 2) The samefeature was pointed out in [ ? ] using full 5D model, instead of two site model presented here.The origin of the above large mixing can be understood as follows. From the mass matrixEq. (26), one can find m W (1) L − m W (1) R = tan φ W m (cid:63) (33)and using sin φ W ≈ tan φ W ≈ g W g (cid:63)W (cid:28) , Eq. (32) can be rewritten as follows. tan 2 θ ≈ − g (cid:63)W v (cid:18) M W (1) L − M W (1) R (cid:19) (34)21 .0 2.5 3.0 3.5 4.0 4.5 5.00.10.20.51 m * s * c * Figure 2: The figure denotes sine and cosine of mixing angle( s (cid:63) , c (cid:63) ) between W (1) L and W (1) R as afunction of m (cid:63) , with g (cid:63)W = g (cid:63)R = 3 . SM parameters are chosen to be standard values g W = 0 . and v = 246 GeV.
This expression manifests the fact that the large mixing arises when W (1) L and W (1) R havealmost degenerate masses, i.e. the mass gap m W (1) L − m W (1) R is suppressed or comparable to g (cid:63)W v .The relation with the mass basis denoted by W , W L and W R is given by WW L W R = U † U † U † W (0) L W (1) L W (1) R . (35)Since g (cid:63) v (cid:28) m (cid:63) , θ ≈ θ (cid:28) , we can approximate s = S . After dropping all termswith two or more s or S, we can get W = C ( c W (0) L + s W (1) L ) + S W (1) R W L ≈ − sW (0) L + c ( c (cid:63) W (1) L + s (cid:63) W (1) R ) (36) W R ≈ − SW (0) L + C ( − s (cid:63) W (1) L + c (cid:63) W (1) R ) . The typical size of these mixing angles are s ≈ | S | ∼ g (cid:63)W v m (cid:63) (cid:28) s (cid:63) ∼ − g (cid:63)W v g W g (cid:63)W m (cid:63) ) ∼ . (37)Given the above large mixing between W (1) L, R induced by the Higgs VEV, it is clear that lightquarks will now couple similarly (and significantly) to both the mass eigenstates, cf. in thebasis prior to EWSB, the coupling to one of the states, i.e., W (1) R , was negligible.22he masses of the physical states will also be perturbed due to the EWSB effects. Here,for simplicity, we kept only two massive states W (1) L and W (1) R to obtain the mass splitting,assuming that the small fraction of W (0) in the mass eigenstate does not make any difference.With such mass splitting, the physical mass for W L and W R are given by m W L/R ≈ m (cid:63) + 14 g (cid:63)W v ± (cid:115) g W g (cid:63)W m (cid:63) + 116 g (cid:63)W v (38)where the +( − ) sign is for m W L ( m W R ) .Similar analysis can be done for neutral gauge bosons. The mass matrix is given by (cid:16) Z (0) Z (1) Z (cid:48) (1) (cid:17) M (cid:16) Z (0) Z (1) Z (cid:48) (1) (cid:17) T (39)where M = 14 g Z v g Z v cot φ Z − g Z g (cid:63)Z (cid:48) c (cid:48) v g Z v cot φ Z m (cid:63) cos φ Z + ( g Z cot φ Z v ) − g Z cot φ Z g (cid:63)Z (cid:48) c (cid:48) v − g Z g (cid:63)Z (cid:48) c (cid:48) v − g Z cot φ Z g (cid:63)Z (cid:48) c (cid:48) v m (cid:63) + ( g (cid:63)Z (cid:48) c (cid:48) v ) . (40)Here c (cid:48) = (cid:112) − tan θ W and θ W is Weinberg angle in the composite sector. We assume thatthe composite sector has the same Weinberg angle as the SM. Mass eigenstates are denotedby Z , Z and Z (cid:48) , and are related to gauge basis fields by Z = C ( c Z (0) + s Z (1) ) + S Z (cid:48) (1) Z ≈ − sZ (0) + c ( c (cid:63) Z (1) + s (cid:63) Z (cid:48) (1) ) (41) Z (cid:48) ≈ − SZ (0) + C ( − s (cid:63) Z (1) + c (cid:63) Z (cid:48) (1) ) The typical size of mixing angles are s ≈ | S | ∼ g (cid:63)Z v m (cid:63) (cid:28) s (cid:63) ∼ − g (cid:63)Z v g Z g (cid:63)Z m (cid:63) ) ∼ (42)And the spectrum of the mass eigenstate is m Z /Z (cid:48) ≈ m (cid:63) + 14 g (cid:63)Z g (cid:63)Z (cid:48) c (cid:48) v ± (cid:115) g Z g (cid:63)Z m (cid:63) + 116 g (cid:63)Z g (cid:63)Z (cid:48) c (cid:48) v . (43) Apart from mixing in the gauge sector, EWSB also induces mixing in the fermion sector.As discussed earlier, composite “excited” modes for SM particles are neglected because they23re heavier than composite vector bosons and composite states of singlet neutrino. For thisreason, we focus on the mixing among SM lepton doublet L and the composite SU (2) R doublet ˜ L R . The relevant parts of the Lagrangian containing Yukawa coupling of L and ˜ L R are as follows: L (cid:51) yL i H ˜ L Ri + m D ¯˜ L Ri ˜ L Ri (44)where y is the Yukawa coupling and i denotes the generation index of leptons, i = { e, µ, τ } . m D is the Dirac mass for composite ˜ L i . The elementary (composite) SU (2) L ( SU (2) R )doublet L ( ˜ L R ) is defined as L e = ( ν (0) e L , e (0) L )˜ L Re = ( N (1) e , ˜ e (1) ) . (45)When the Higgs field gets a VEV, the Lagrangian Eq. (44) generates neutrino Mixing as canbe seen from yv √ ν (0) L N (1) R + m D ¯ N (1) L N (1) R = m D ( ¯ N (1) L + y D v √ m D ¯ ν (0) L ) N (1) R (46)From this, we can obtain physical mass eigenstates denoted as N L , N R , and ν L : N L ≈ N (1) L + V (cid:96)N ν (0) L N R = N (1) R (47) ν L ≈ ν (0) L − V (cid:96)N N (1) L where the mixing is given by V (cid:96)N = yv √ m D . The same Lagrangian also introduces electronmixing after EWSB (we can safely neglect the SM electron Yukawa coupling or mass termhere as compared to the others): y L v √ e (0) L ˜ e R + m D ¯˜ e (1) L ˜ e (1) R = m D (¯˜ e (1) L + y D v √ m D ¯ e (0) L )˜ e (1) R . (48)Again, from this, we can obtain physical mass eigenstates denoted as ˜ e L , ˜ e R , and e L : ˜ e L ≈ ˜ e (1) L + V (cid:96)N e (0) L ˜ e R = ˜ e (1) R (49) e L ≈ e (0) L − V (cid:96)N ˜ e (1) L .
24n principle, there is a similar effect from mixing of SM SU (2) L singlet charged lepton (afterEWSB) with composite SU (2) L doublets; however, since we assumed that such compositesare heavy, we can neglect it. Moreover, electrons and neutrinos have the same mixing V (cid:96)N .This is because (1) N and ˜ (cid:96) are in the same SU (2) R doublet with the same mass m D ,together ν L and l L being in the same SU (2) L doublet and (2) these two mixings originatefrom the same Yukawa coupling. In this section, based on our discussion in previous section, we first summarize couplingsrelevant to our collider study in Sec. 5. Then, we specify the choice of parameters used foractual analysis, together with related bounds. We then discuss production and dominantdecay channels of heavy gauge bosons, i.e. W L and W R . In particular, we show that W R → N ˜ (cid:96) is indeed the dominant decay channel for most of the parameter space of interest,providing abundance production of N and ˜ (cid:96) . We end our discuss by providing formulae fordecay widths of N and ˜ (cid:96) . There are three types of couplings that we need to consider: (1) couplings between W L / W R and SM fermions (2) couplings of W L / W R to N - ˜ (cid:96) pair, and (3) couplings among N ( ˜ (cid:96) ) – SM H , longitudinal W/Z – SM lepton (cid:96) ( ν ) via Yukawa coupling.(1) The first type of coupling can be obtained by using Eq. (23) and EWSB inducedmixing Eq. (36): δ L (1) = g W g (cid:63)W c (cid:63) W + Lµ ¯ ψ L γ µ ψ (cid:48) L + g W g (cid:63)W s (cid:63) W + Rµ ¯ ψ L γ µ ψ (cid:48) L + h.c (50)These couplings are responsible for the production of W L and W R via light quarks fusioninside proton. Notice that they suppressed by the factor g W g (cid:63)W and mixing angle comparedto 4D LR models. However, as we will show in Sec. 5, these couplings, even with suchsuppressions, still render large enough signal production to be discoverable in near future.(2) The second type of coupling can be understood from Eq. (23) and mixing induced byEWSB Eq. (36): δ L (2) = g (cid:63)W s (cid:63) W + Lµ ¯ N γ µ ˜ (cid:96) + g (cid:63)W c (cid:63) W + Rµ ¯ N γ µ ˜ (cid:96) + h.c. (51)These couplings lead to the decays of W L and W R to N and ˜ (cid:96) .(3) The third type of couplings are similarly obtained from Eq. (23), Eq. (24) and mixing25nduced by EWSB Eq. (47)(49): δ L (3) = g W V (cid:96)N W + µ ¯ N L γ µ (cid:96) L + { N ↔ ν ; (cid:96) ↔ ˜ (cid:96) } + g Z V (cid:96)N Z µ ¯ N L γ µ ν L + yH ¯ N R ν L + { N ↔ ˜ (cid:96) ; ν ↔ (cid:96) } + h.c. (52)These couplings lead to the decays of N and ˜ (cid:96) to H/W/Z and (cid:96)/ν . The composite sector generally contains many parameters, such as g (cid:63) ’s and ˜ g (cid:63) ’s. In ourstudy, as our benchmark points, we assume all φ ’s are the same, i.e. the ratio g/g (cid:63) are thesame for all SM gauge groups. This choice is mainly for the sake of simplicity, and otherchoices with small variations will not lead to much difference in the final results. Besides, wefix g (cid:63)W = g (cid:63)R , or equivalently we assume there exists Z symmetry connecting SU (2) L and SU (2) R . This is well motivated by the consistency with EW precision tests, e.g. to suppressthe corrections to the coupling Z → b ¯ b . With these choices, we are left with basically onlyone free gauge coupling in composite sector g (cid:63)W . The composite gauge coupling g (cid:63)W has alower bound ∼ , which comes from the requirement that the Landau pole does not appearbelow the GUT scale. We choose g (cid:63)W = 3 as a benchmark points.The mass parameter m (cid:63) for heavy gauge bosons is constrained by EW precision tests.With extended symmetry group SU (2) L × SU (2) R × U (1) X , the bound is given by (cid:38) TeVin most parts of parameter space. Partly motivated by the discoverability at the LHC, wechoose m (cid:63) = 2 TeV for our study. Such a low mass might be achieved in some corners ofthe parameter space or by invoking additional effects in EW precision tests (see for example[14]). Also, we choose cos φ Q L = 0 . , which may be on the edge of constraints from the EWprecision test. This, again, can potentially be allowed by introducing additional structure inthe model.Next, | V (cid:96)N | is constrained by various experiments and the results are summarized in [15]. Considering consistency with these experimental bounds, we choose the | V (cid:96)N | = 0 . forall three generations.In order for W L and W R to be able to decay to the pair N - ˜ (cid:96) , m ˜ L R needs to be smallerthan half of m (cid:63) . In principle, this mass is also constrained correlated with constraints of | V (cid:96)N | . With the choice we make | V (cid:96)N | = 0 . , however, there is no effective bound on m ˜ L R . Nevertheless, given that heavy gauge bosons, N , and ˜ (cid:96) all “live” in the same compositesector, too big hierarchy between m ˜ L R and m (cid:63) will lead to unwanted tuning. Taking intoaccount all these considerations, we choose m ˜ L R = 750 GeV in our study.26 .3 W L /W R production and decay As mentioned already, W L and W R are produced via couplings in Eq. (50). Decay width fordominant decay channels are shown below, which are computed using couplings Eq. (51).Since the analytic expression for decay widths of mass eigenstates W L and W R are quitecomplicated, we instead provide expressions for gauge fields in gauge basis, namely W (1) L and W (1) R . This will be sufficient for the purpose of our discussion. All the decay widthspresent in this paper are given with the assumption m (cid:63) > m ˜ L R (cid:29) mass of SM particles,thus masses of SM particles are reasonably neglected. Decay widths for W (1) L are given by Γ( W (1) L → W H/W Z ) = g (cid:63)W m (cid:63) π cos φ W Γ( W (1) L → tb ) = g (cid:63)W cos φ Q L m (cid:63) π cos φ W (53) Γ( W (1) L → ψψ (cid:48) ) = N c g W g (cid:63)W m (cid:63) π cos φ W where ψ and ψ (cid:48) denote SM fermions, and N c shows the degree of freedom of correspondingfermion ψ : 3 for quarks and 1 for leptons. Next, decay widths for W (1) R are given by Γ( W (1) R → N i ˜ (cid:96) i ) = g (cid:63)W (cid:32) m L R m (cid:63) (cid:33) (cid:115) − m L R m (cid:63) m (cid:63) π Γ( W (1) R → W Z/W H ) = g (cid:63)W m (cid:63) π (54)where subscript i is generation index.From Eq. (53) and Eq. (54), we see that W (1) R does not decay to quarks and W (1) L doesnot decay to N - ˜ (cid:96) pair. All this is what we anticipated already. For the illustrative purpose,in Fig. 3, we show the results ignoring W (0) component in the mixing, which would lead toan error of the size g (cid:63)W v m (cid:63) < . . From there, we see that W R indeed decays dominantlyto N - ˜ (cid:96) pair, providing production mechanism for them. This can be contrasted to the caseof 4D LR models, where the dominant decay is into jets. For our collider study in Sec. 5,however, we used full model including Higgs induced mixing and mass splitting. N and ˜ (cid:96) production and decay As mentioned in the last section, N and ˜ (cid:96) are produced from on-shell decay of W L and W R via couplings in Eq. (51). Decays of them are proceeded via the couplings Eq. (52), resulting27 .0 2.5 3.0 3.5 4.0 4.5 5.00.00.10.20.30.4 m W L B r an c h i ng R a t i o m W R B r an c h i ng R a t i o WZWHN l ˜ tb Figure 3: The plot on the left (right) panel shows branching ratios of W L ( W R ) as a function of itsmass. in decay widths: Γ( N → W (cid:96) ) = g W | V (cid:96)N | m ˜ L R π Γ( N → H/Zν ) = g W | V (cid:96)N | m ˜ L R π Γ(˜ (cid:96) → W ν ) = g W | V (cid:96)N | m ˜ L R π (55) Γ(˜ (cid:96) → H/Z(cid:96) ) = g W | V (cid:96)N | m ˜ L R π . In principle, there will be three body decays via virtual W R . However, we have checked that,for the choice of parameters we made, such three body decays are suppressed compared to2 body decays.So far, we have focused on production and decay of charged gauge bosons, W L and W R ,and resulting production of singlet neutrino N . In addition to these, however, the model alsocontains neutral gauge bosons Z and Z (cid:48) (see Sec. 3). The relevant couplings for these neutralgauge bosons can be obtained in a similar way as those for charged ones. In particular, justlike Eq. (50) for charged gauge bosons, Z ( Z (cid:48) ) couplings to light quarks is basically g Z g (cid:63)Z timesa factor for EWSB induced mixing, and it is via this couplings that neutral gauge bosonsare produced at the LHC. In our framework (i.e. 5D/composite LR model), since Z and Z (cid:48) arise as composite vector mesons of the strong dynamics in the same way as the chargedones do, they have the same/comparable mass as W L ( W R ). This, then, naturally leads tothe comparable production rates for Z and Z (cid:48) , i.e. they are not suppressed compared to W L and W R . This feature can be contrasted to the case of 4D LR models, where production of Z (cid:48) is suppressed compared to W R due to the fact that Z (cid:48) , as an elementary particle, is heavierthan W R . Moving onto the decays of the neutral gauge bosons, for the same reason for thecharged gauge bosons, Z and Z (cid:48) also have significant branching ratio to a pair of N . In thisway, we see that, production and decay of these neutral gauge bosons provide another way toabundantly produce a pair of singlet neutrinos N . This signal channel, however, has almost28he same process topology as 4D LR. Instead, we are planning to study the production ofthe singlet neutrino via on-shell decay of neutral gauge boson in our follow-up paper, but ina slightly different set up with interesting features/differences that only 5D framework canfurnish. In this section, we present our results for phenomenological studies of the LHC signals forthe model described in Sec. 3. In particular, we study the pair production of the singletneutrino ( N ) and its SU (2) R partner ( ˜ (cid:96) ) via the one-shell decay of W R and W L , and theirsubsequent decays to SM particles. We consider two benchmark points depending on how N and ˜ (cid:96) cascade decay to SM particles: Di-lepton - and
Tri-lepton -channels.For Di-lepton channel, the production and the cascade decays of N and ˜ (cid:96) are as follows: pp > W L /W R > N ˜ (cid:96) ± , N > (cid:96) ± (cid:0) W ∓ > jj (cid:1) , ˜ (cid:96) ± > (cid:96) ± (cid:0) H/Z > b ¯ b (cid:1) . (56)Hence, the final states of the Di-lepton channel consist of (cid:96)(cid:96)jjb ¯ b , where, for the lepton pair,only opposite sign combination can arise since we are ignoring small Majorana splitting for N . That is, this process is lepton-number conserving. In particular, this channel contains two leptons, and hence the name for the channel.For Tri-lepton channel, on the other hand, we take the leptonic decay for SM W boson from N . In detail, we get: pp > W L /W R > N ˜ (cid:96) ± , N > (cid:96) ± (cid:0) W ∓ > (cid:96) ∓ ν (cid:1) , ˜ (cid:96) ± > (cid:96) ± (cid:0) H/Z > b ¯ b (cid:1) . (57)Hence, the final states of the Tri-lepton channel consist of (cid:96)(cid:96)(cid:96)νb ¯ b . This time, it contains three leptons, explaining the name of the channel.Notice that in both channels, we add contributions from both H and Z decaying into b ¯ b .This is because resolutions of LHC detectors may not be good enough to distinguish thosetwo cases, and at the same time, we will achieve a slight increase in the signal rate.The Feynman diagrams for both signal processes are shown in Fig. 4. The topology ofour signal processes are characterized by several resonance peaks in various invariant massvariables. In particular, invariant masses of W R and N/ ˜ (cid:96) , which we take to be M W R = 2 TeV and M N = 750 GeV in our study, will draw sharp distinctions between signal andSM backgrounds. For Tri-lepton channel, however, due to the presence of neutrino and themultiplicity of leptons (i.e. combinatorics issue), naively, one would think that resonancepeaks are less pronounced. However, as we show below, by reconstructing the longitudinalcomponent of the neutrino’s momentum and by figuring out the identification of each lepton,29 ¯ d W (1)+ L W (1)+ R N W + H b ¯ bjjℓ − ℓ + ˜ ℓ + v v u ¯ d W (1)+ L W (1)+ R N W + H b ¯ bℓ + νℓ − ℓ + ˜ ℓ + v v Figure 4: The left panel shows Feynman diagram for the signal process of Di-lepton channel. Theright panel shows Feynman diagram for the signal process of Tri-lepton channel. Double (single)lines denote composite (elementary) particles. Here composite gauge bosons are in gauge basis W (1) L and W (1) R in order to show the mixing induced by Higgs VEV explicitly. i.e. which lepton is to be paired with b ¯ b , neutrino, and (cid:96)ν , respectively, we are able toconstruct all invariant mass peaks.Event simulations are performed by employing a sequence of simulation tools. We firstcreated our two-site simplified model files using FeynRules [16] based on Heavy VectorTriplets models [17]. Then we used them as inputs model in a Monte Carlo event generator
MG5@aMC [18] to generate parton level events. In this procedure, parton distributionfunctions parameterized by
NN23LO1 [19] is used. All the simulations are done at theleading order with a √ s = 14 TeV pp collider. The generated parton level events are thenstreamlined to Pythia 6.4 [20] to take care of showering and hadronization/fragmentation.Since all our channels contain only regular jets, i.e. no boosted gauge bosons leading tofat jets, we directly pass on the output from
Pythia 6.4 to Delphes 3 [21].
Delphes 3 ,interfaced with
FastJet [22, 23], provides a way to incorporate the detector effects and jetformation. The jets are constructed with the anti- k t algorithm [23] with a radius parameter R = 0 . .In Sec. 5.1, we present our results for Di-lepton channel. Results for Tri-lepton channel followin Sec. 5.2. We also briefly discuss phenomenological distinctions between our 5D left-rightsymmetry model and that of 4D. In particular, we will point out several salient features ofour case by which two frameworks can be distinguished once discovery is made. + dijet + H/Z channel
We begin by considering the production of N − ˜ (cid:96) pair and their decays at the LHC. In ourcurrent study, we consider ( N, ˜ (cid:96) ) as a SU (2) R doublet and as a consequence the productionof this doublet pair should be proceeded via decay of W (1) R gauge boson. However, sinceSM quarks are not charged under SU (2) R gauge group, W (1) R can only be produced via30ts mixing with W (1) L . Namely, once W (1) L is produced via quark fusion inside the protonthrough its SU (2) L -coupling, EWSB-induced mixing between W (1) L and W (1) R leads to theproduction of W (1) R . W (1) R then subsequently decays into N − ˜ (cid:96) pair. As shown in Sec. 3,the size of W (1) R − W (1) L mixing angle is tan 2 θ ≈ − g W(cid:63) g R(cid:63) v (cid:32) M W (1) L − M W (1) R (cid:33) (see Eq. (34)), and whenthe mass splitting, M W (1) L − M W (1) R , is small enough we acquire significant mixing, leadingto enhanced production for signal. This can be realized when the masses of W (1) L and W (1) R are approximately degenerate and the mass scale itself is low enough. Motivated by theconsistency with the electroweak precision measurements (EWPM), our 5D warped extra-dimensional seesaw model or its two-site simplified model has built-in left-right symmetries,allowing desired mass degeneracy. In addition, the consistency with EWPM permits themass of M W (1) L /M W (1) R as low as O (2) TeV. Such a low mass for W (1) L /W (1) R further allows, inaddition to large mixing, resonance enhancement for the signal production cross section atthe LHC. Moving onto the decay of W (1) R , as elaborated in Sec. 4.3, it will dominantly decayinto ( N, ˜ (cid:96) ) pair. Therefore, making use of all these features, we can secure enough statisticsfor signal production at 14 TeV LHC. In Di-lepton channel, N decays to W ± (cid:96) ∓ and SM W boson, in turn, decays hadronically producing two jets. On the other hand, ˜ (cid:96) ± decays to (cid:96) ± H/Z , which is then followed by decay of
H/Z to b ¯ b . As is evident from these cascadedecays of N and ˜ (cid:96) ± , (i) signal process does not contain any neutrinos and hence no missingenergy and (ii) there are several invariant mass variables which are all fully reconstructible.Those invariant mass variables include, M jj , M b ¯ b , M jj(cid:96) , M b ¯ b(cid:96) , and M All , where M All is theinvariant mass of all reconstructed/visible particles. If successfully reconstructed, for signal,the distributions of these variables will be peaked at M W , M H/Z , M N , M N , and M W R ,respectively.There are several SM backgrounds we need to consider and we describe them one by one now. (1) t¯tjj : The relevant process is pp > t ¯ tjj > (cid:96) − (cid:96) + ν ¯ νb ¯ bjj , where t > b ( W + > (cid:96) + ν ) , andsimilarly for ¯ t , is considered. Being a purely QCD process, this is the background with largestcross section. Background reduction will be achieved by means of a combination of variousinvariant mass cuts. Particularly useful ones will be M All and M b ¯ b(cid:96) /M jj(cid:96) cuts. In principle,missing transverse momentum /E T , the opposite of the vectorial p T sum of reconstructedobjects in the event, can provide useful reduction, although we found other cuts are moreefficient. (2) t¯tH / Z : The relevant process is pp > t ¯ tH/Z > (cid:96) − (cid:96) + ν ¯ νbb ¯ b ¯ b , where t > b ( W + > (cid:96) + ν ) ,and similarly for ¯ t , and H/Z > b ¯ b are considered. If two b ’s in the signal process are b-tagged31s a part of selection criteria, then in order for this background to pass the selection criteria,two of four b ’s must be un-tagged as regular two jets, leading to a large reduction of thebackground. Moreover, M All , M b ¯ b(cid:96) /M jj(cid:96) and M jj cuts will be useful. (3) jj (cid:96)(cid:96) H / Z : The relevant process is pp > jj(cid:96) − (cid:96) + H/Z, H/Z > b ¯ b , where the lepton paircomes mostly from decay of on-shell Z (and off-shell photon). Therefore, in this process,the distribution of the di-lepton invariant mass, M (cid:96)(cid:96) , will be sharply peaked at the mass ofthe Z boson, M Z . However, since two leptons in the signal process do not reconstruct M Z ,the condition M (cid:96)(cid:96) (cid:54) = M Z will remove most of this background. In addition, M All , M b ¯ b(cid:96) /M jj(cid:96) and M jj cuts will be useful. (4) irred (irreducible background): The relevant process is pp > (cid:96) − (cid:96) + W ± H/Z, W ± >jj, H/Z > b ¯ b . Similarly to jj (cid:96)(cid:96) H / Z background, the lepton pair will mostly arise from theon-shell decay of Z and the cut M (cid:96)(cid:96) (cid:54) = M Z will significantly reduce this events. Even though jj ( b ¯ b ) will successfully reconstruct M W ( M H/Z ) , M All and M b ¯ b(cid:96) /M jj(cid:96) cuts will still provideadditional significant reduction of this background events.Defining N (cid:96) , N b and N j as the number of isolated leptons, b-tagged jets and non-b-taggedjets, respectively, we select events using the following selection criteria: N (cid:96) > with | η (cid:96) | < . N b > with | η b | < (58) N j > with | η j | < . In addition, we impose a set of basic cuts p T j /p T b > GeV and p T (cid:96) > GeV at parton levelevent simulation, partly to avoid possible IR-divergence issues for background simulations.We reimpose such cuts on objects (hardest two jets, two b -jets, and two leptons) that passselection criteria of Eq. (58). We use p T to evaluate hardness of the reconstructed objectsand take the hardest two. In Fig. 5, we show distributions of various variables for signal andbackground events that pass selection criteria and basic cuts. In particular, we see that M All (top row, left), the invariant mass of all reconstructed objects, i.e. hardest two j ’s + two b ’s + two (cid:96) ’s, for signal is peaked at 2 TeV, the mass of W R we take, and is well-separated fromall backgrounds, providing a strong cut to reduce backgrounds. Similar sharp distinctionsare drawn for M jj(cid:96) (mid row, right) and M b ¯ b(cid:96) (mid row, left), but with slightly larger overlapwith backgrounds. These two variables reconstruct the mass of N and ˜ (cid:96) , respectively. It maybe worth describing the way we reconstruct these variables. The subtlety might be that sincethere are two leptons in the final states, it would be crucial to figure out which lepton is to32 GttjjttH / Z jjllH / Z irred M All U n i t - no r m a li z e d eve n t s SGttjjttH / Z jjllH / Z irred M ll U n i t - no r m a li z e d eve n t s SGttjjttH / Z jjllH / Z irred M bbl U n i t - no r m a li z e d eve n t s SGttjjttH / Z jjllH / Z irred M jjl U n i t - no r m a li z e d eve n t s SGttjjttH / Z jjllH / Z irred M jj U n i t - no r m a li z e d eve n t s SGttjjttH / Z jjllH / Z irred M bb U n i t - no r m a li z e d eve n t s SGttjjttH / Z jjllH / Z irred U n i t - no r m a li z e d eve n t s Figure 5: Di-lepton Channel: Distributions of variables: M All (top row, left), M (cid:96)(cid:96) (top row, right), M b ¯ b(cid:96) (mid row, left), M jj(cid:96) (mid row, left), M jj (bottom row, left), M b ¯ b (bottom row, mid) and MET ( /E T ) (bottom row, right) for signal (solid blue) and backgrounds (dotted, t ¯ tjj -purple, t ¯ tH/Z -red, jj(cid:96)(cid:96)H/Z -orange, irred-green)
33e paired with b -pair, and similarly for j -pair. We found, for example, that naively plottingthe invariant mass of b -pair with both leptons (similarly j -pair with both leptons) does notreveal sharp peak at M N and resulting distribution is broadly extended with large overlapwith background distributions. In order to achieve sharper distinction, we make use of thefact that the masses of N R and ˜ (cid:96) R are equal due to SU (2) R invariance. Namely, we identifythe lepton that goes with b -pair ( (cid:96) b ) and the one that goes with j -pair ( (cid:96) j ) by minimizing | M b ¯ b(cid:96) b − M jj(cid:96) j | . (59)As can be seen from Fig. 5, this criterion successfully reconstructs M N for majority of events,albeit imperfect. In this way, both M b ¯ b(cid:96) and M jj(cid:96) provide another set of very useful cuts.Next very useful variable is M (cid:96)(cid:96) (top row, right). As anticipated above while we discuss eachbackgrounds, M (cid:96)(cid:96) distributions for jj (cid:96)(cid:96) H / Z and irred backgrounds are sharply localized at M Z . In addition, other backgrounds also tend to be distributed over smaller M (cid:96)(cid:96) valuescompared to signal (see the inset plot of M (cid:96)(cid:96) distribution of Fig. 5). The bottom row ofFig. 5 shows M jj , M b ¯ b and /E T distributions. We see that M jj ( M b ¯ b ) distribution for signalevents develops a peak at M W ( M H/Z ) as expected. This is not true, on the other hand,for two major backgrounds: t¯tjj and t¯tH / Z . Therefore, these variables will supplementabove described variables to attain additional suppression of background events. Finally,the missing transverse momentum variable also helps a bit. This is expected based on theinsight that the backgrounds t¯tjj and t¯tH / Z have larger /E T than signal. We provide the cutflows for signal and the major SM backgrounds in Table 1. We find that the Di-lepton channelmay provide a sensitivity to uncover warped seesaw nature by ∼ . σ with an integratedluminosity of L = 300 fb − and even by ∼ σ with L = 3000 fb − . + H/Z channel
In this section, we present the results for Tri-lepton channel. Similarly to the Di-leptonchannel discussed in previous section, N − ˜ (cid:96) pair is produced via the decay of W (1) R usinglarge mixing between W (1) R and W (1) L . In Tri-lepton channel, N decays to W ± (cid:96) ∓ and SM W boson, in turn, decays leptonically producing (cid:96)ν . Like in Di-lepton channel, ˜ (cid:96) ± decaysto (cid:96) ± H/Z , with subsequent decay of
H/Z to b ¯ b . As is evident from these cascade decaysof N and ˜ (cid:96) ± , (i) signal process now does contain neutrino, leading to missing energy and(ii) there are three leptons in final states. The existence of neutrino (or missing particle ingeneral) and the large multiplicity of leptons can be a potential obstacle in reconstructionof resonance peaks. However, we will show below that such difficulty can be, at least partly,overcome by reconstruction of longitudinal momentum of neutrino and by cleverly figuringout lepton identifications. Once these are done, various invariant mass variables can besuccessfully reconstructed and used to reduce backgrounds. Those invariant mass variables34uts Signal t¯tjj t¯tH / Z jj (cid:96)(cid:96) H / Z irred No cuts 0.76 . × N (cid:96) > , N j > , N b > with basic cuts 0.12 . × M (cid:96)(cid:96) ∈ [400 , ∞ ] GeV 0.11 25.63 0.045 0.0094 0 M All ∈ [1600 , ∞ ] GeV 0.11 6.50 0.01 0.0028 0 M b ¯ b ∈ [0 , GeV 0.09 2.04 0.0034 0.0014 0 M b ¯ b(cid:96) ∈ [550 , ∞ ] GeV 0.07 0.055 0.00091 0.00047 0 /E T ∈ [0 , GeV 0.058 0.018 0.00072 0.00047 0
S/B S/ √ S + B ( L = 300 fb − ) 3.62 – – – – S/ √ S + B ( L = 3000 fb − ) 11.4 – – – – Table 1: Cut flows for signal and major background events in terms their cross sections. The crosssections are in fb. The numbers in the first row (“No cuts”) are cross sections obtained with basiccuts at the generation level to avoid divergence (for both signal and backgrounds). In the secondrow, the same basic cuts are reimposed to both signal and background events along with multiplicityrequirements for b-jet, non-b-jet and leptons. Once the cross section decreases such that the netnumber of events at L = 3000 fb − is less than 1, we report it as “0”. include M (cid:96)ν , M b ¯ b , M (cid:96)(cid:96)ν , M b ¯ b(cid:96) , and M recon W R , where M recon W R is the invariant mass constructedfrom all reconstructed visible particles and reconstructed neutrino four momentum. Whenproperly reconstructed, signal distribution of these variables will be peaked at M W , M H/Z , M N , M N , and M W R , respectively. Additional invariant mass variables exist: M (cid:96)(cid:96) , M (cid:96)(cid:96)(cid:96) , and M All , where M All is the invariant mass of all reconstructed/visible particles without neutrino.These variables do not correspond to any of resonance peaks appeared in the signal process.However, they will still provide very strong distinctions between the signal and backgrounds.There are several SM backgrounds we need to consider and we describe them one by one now. (1) t¯tW : The relevant process is pp > t ¯ tW ± > (cid:96) − (cid:96) + (cid:96) ± ν ¯ νν (¯ ν ) b ¯ b , where t > b ( W + > (cid:96) + ν ) ,and similarly for ¯ t , is considered. All SM W ’s decay leptonically: W ± > (cid:96) ± ν (¯ ν ) . (2) irred (irreducible background): The relevant process is pp > (cid:96) − (cid:96) + W ± H/Z, W ± >l ± ν (¯ ν ) , H/Z > b ¯ b . (3) (cid:96) − (cid:96) + Wjj : The relevant process is pp > (cid:96) − (cid:96) + W ± jj, W ± > l ± ν (¯ ν ) . Since we will selectevents with two b ’s are tagged, only very small fraction of events with two regular jets mis-tagged as b-tagged jets will contribute to the backgrounds. Mistage rate is typically (cid:46) [24] and uds -jet mistag rate can even be as small as . [25]. The cross section of theprocess is σ ∼ fb and the surviving events with two mistagging is ∼ O (0 . fb. Thiscorresponds to roughly ∼ O (3) events at an integrated luminosity of L = 300 fb − . It will bevery unlikely that any of these events will in the signal region given the number of invariant35ass cuts that it should pass. Hence we will not explicitly consider this background for ouranalysis.Defining N (cid:96) and N b as the number of isolated leptons and b-tagged jets, respectively, weselect events using the following selection criteria: N (cid:96) > with | η (cid:96) | < . N b > with | η b | < (60)In addition, we impose a set of basic cuts p T b > GeV and p T (cid:96) > GeV at parton levelevent simulation, partly to avoid possible IR-divergence issues for background simulations.We reimpose such cuts on objects (hardest two b -jets, and three leptons) that pass selectioncriteria of Eq. (60). We use p T to evaluate hardness of the reconstructed objects.Next, we discuss the way we reconstruct longitudinal component of neutrino’s four momen-tum. Together, we also discuss how we figure out lepton identifications. Namely, we wantto know, out of three leptons selected as described above, which one is produced togetherwith b ¯ b from the decay of ˜ (cid:96) ± (we call it (cid:96) b ) and which one is produced directly from thedecay of N (we call it (cid:96) W ), and finally which one is the decay product of SM W (we call it (cid:96) ν ). First of all, for a given choice of lepton (a candidate for (cid:96) ν ), the z-component of theneutrino’s momentum can be obtained by requiring M W = ( p νµ + p (cid:96)µ ) (61)where M W is the mass of the SM W boson. For p νµ , we use the fact that neutrino is massless, ( p νµ ) = 0 . Then, the above equation is a quadratic equation for the z-component of p νµ , and ifsolutions exist, there are two solutions, unless determinant vanishes by numerical coincidence.In this case, we pick up p νz that minimizes the sum of z-component of all particles’ momenta,i.e. sum of p z of two b ’s, three (cid:96) ’s and ν . This is based on the insight that W R is mostlyproduced at rest. In case when the determinant of the quadratic equation is less than 0, sothat no solution exists, we set p νz = − (cid:88) all visible p z . (62)This choice again is motivated by the intuition that W R is mostly produced at rest. Oncez-component of neutrino’s momentum (or equivalently full p νµ ) is reconstructed this way fora given choice of (cid:96) (again a candidate for (cid:96) ν ), we then determine (cid:96) b and (cid:96) W by minimizing | M b ¯ b(cid:96) b − M (cid:96) ν (cid:96) W ν | . (63) The subscript is designed to indicate a set of particles that the lepton accompanies. Gttwirred M W R recon U n i t - no r m a li z e d eve n t s SGttwirred M All U n i t - no r m a li z e d eve n t s SGttwirred M bbl U n i t - no r m a li z e d eve n t s SGttwirred M ll ν U n i t - no r m a li z e d eve n t s SGttwirred M lll U n i t - no r m a li z e d eve n t s SGttwirred M ll U n i t - no r m a li z e d eve n t s Figure 6: Tri-lepton Channel: Distributions of variables: M recon W R (top row, left), M All (top row,right), M b ¯ b(cid:96) (mid row, left), M (cid:96)(cid:96)ν (mid row, right), M (cid:96)(cid:96)(cid:96) (bottom row, left), and M (cid:96)(cid:96) (bottom row,right) for signal (solid blue) and backgrounds (dotted, t ¯ tW -red and irred-green) SU (2) R invariance and resulting mass degeneracy.In this way, for each choice of (cid:96) ν , we determine full p νµ and identify, for the remainingtwo leptons, which lepton is (cid:96) b and which lepton is (cid:96) W . We repeat this procedure for allthree possible choices of (cid:96) ν . Final decision is made for the combination { (cid:96) ν , (cid:96) W , (cid:96) b } thatrenders minimum value for Eq. (63). In Fig. 6, we show distributions of various invariantmass variables for signal and background events that pass selection criteria and basic cuts.These invariant mass variables are constructed using { (cid:96) ν , (cid:96) W , (cid:96) b } -identification and full p νµ reconstructed as described above. In particular, in addition to M All , M (cid:96)(cid:96) , M b ¯ b and M (cid:96)(cid:96)(cid:96) ,which are all possible without knowing detailed information about lepton identification andfull momentum for neutrino, now we can also explicitly compute M W recon R , M b ¯ b(cid:96) b , and M (cid:96) ν (cid:96) W ν .These latter variables would not be possible without figuring out lepton identification, i.e. { (cid:96) ν , (cid:96) W , (cid:96) b } , and full momentum for neutrino. To be more precise, we can actually calculate M b ¯ b(cid:96) b and M (cid:96) ν (cid:96) W ν by simply considering all possible combination of two leptons, and wefound that such computed distributions do not reveal any sharp peak and rather show verybroad distributions, failing to provide strong cuts to reduce background. In Fig. 6, we showdistributions of M b ¯ b(cid:96) b (mid row, left) and M (cid:96) ν (cid:96) W ν (mid row, right). Both distributions aresharply peaked at 750 GeV, a input value for M N . In the case of M W recon R , we really needto know full p νµ to be able to compute it. The left panel of the top row in Fig. 6 shows M W recon R distribution and it is indeed peaked at/near 2 TeV, a input value for W (1) R . This isto be compared to the M All distribution shown in the right panel of the top row in Fig. 6.Again, M All is the invariant mass for all reconstructed visible particles, i.e. two b ’s andthree (cid:96) ’s, but without neutrino. Although M All distribution also develops a peak with goodseparation from background distributions (dotted red ( ttw ) and dotted green ( irred )), theposition of the peak is shifted toward the smaller value, reflecting the existence of neutrino.We found that both M W recon R and M All , separately, provide very efficient cuts. Overall, wesee that above described prescription for reconstructing { (cid:96) ν , (cid:96) W , (cid:96) b } -identification and full p νµ is very effective and successful. We also note that M (cid:96)(cid:96) distribution for irred is sharplypeaked at M Z showing that two leptons come from on-shell decay of Z boson. Finally, M (cid:96)(cid:96)(cid:96) -distribution for backgrounds are clustered for smaller values and well-separated from that ofsignal. We provide the cut flows for signal and the major SM backgrounds in Table 2. Wefind that the Tri-lepton channel may provide a sensitivity to discover N , ˜ (cid:96) and W R by ∼ σ with an integrated luminosity of L = 300 fb − and even by ∼ σ with L = 3000 fb − .We close our discussion by pointing out several phenomenological features that can drawdistinction between 4D LR and 5D/composite LR models. (cid:73) First of all, the production of W ± R in 4D LR models is via the unsuppressed coupling to For distinguishing between various 4D seesaw models, see, for example, [26]
Signal t¯tW irred
No cuts 0.42 . N (cid:96) > , N b > with basic cuts 0.060 0.30 0.011 M W recon R ∈ [1400 , ∞ ] GeV 0.60 0.022 0.00074 M All ∈ [1000 , ∞ ] GeV 0.059 0.0040 0 M (cid:96)(cid:96)(cid:96) ∈ [500 , ∞ ] GeV 0.059 0.0030 0
S/B S/ √ S + B ( L = 300 fb − ) 4.10 – – S/ √ S + B ( L = 3000 fb − ) 13.00 – – Table 2: Cut flows for signal and major background events in terms their cross sections. The crosssections are in fb. The numbers in the first row (“No cuts”) are cross sections obtained with basiccuts at the generation level to avoid divergence (for both signal and backgrounds). In the secondrow, the same basic cuts are reimposed to both signal and background events along with multiplicityrequirements for b-jet and leptons. Once the cross section decreases such that the net number ofevents at L = 3000 fb − is less than 1, we report it as “0”. quarks, whereas in the case of 5D LR, it is via suppressed/smaller couplings, leadingto smaller production rate. (cid:73) For 5D/composite LR, the production of N via the decay of W ± R accompanies its SU (2) R partner ˜ (cid:96) . This, in turn, renders additional Higgs/ Z . Therefore, in 5D/compositeLR models, there are two extra resonance bumps, those of ˜ (cid:96) and Higgs/ Z . Both struc-tures were crucial in reducing background. Perhaps more importantly, once discoveryis made, these extra resonance peaks will be critical in discriminating 4D vs. 5D LRnature. (cid:73) The distribution of the di-lepton invariant mass will have (i) different shape and (ii)different dependence of endpoints on M W ± R and M N . To be more specific, for usual4D LR, the signal process is two-step cascade decay, leading to smooth distribution,except perhaps at endpoint , where, depending on spin correlations, there could be asharp/“vertical” drop [27]. For 5D/composite LR, on the other hand, having heavy ˜ (cid:96) , in addition to N , in the decay of M W ± R , the shape of the distribution will be thatof antler with a cusp, i.e., a derivative discontinuity, in roughly middle of distribution[28]. The end point for 4D LR is located at ∼ (cid:113) M W R − M N , that of 5D LR beingdifferent from this. Searches have been done (and are ongoing) at the LHC for
TeV -mass SM singlet neutrinosinvolved in the generation of super-small SM neutrino mass via various 4D models of seesaw .However, we have tried to present a case here that many these require a small parameter in39rder to obtain the right size of the SM neutrino mass, thus in some cases reducing the originalattraction of the seesaw. In fact, we feel that there might not be any strong motivation forsinglets in these models to be at ∼ TeV other than getting a signal at the LHC from them. Inearlier work, some of us had demonstrated that a completely natural realization of TeV-scaleseesaw occurs instead in a warped extra -dimensional framework, which is dual (as per theAdS/CFT correspondence) to the SM Higgs being a composite particle arising from somenew strong dynamics.In this paper (and a follow-up), we initiated the study of the LHC phenomenology of thisframework of a natural TeV-scale seesaw. In particular, here, we showed that signals similarto the 4D models arise in this warped/composite framework as well. At the same time, thedetails of the phenomenology are different in an interesting manner. Hence, one can suitablyadapt existing searches for singlet neutrinos in 4D models to the natural 5D one.The easiest way to see how these features arise is using a (effective) two-site picture ofthis framework. Namely, we have two sectors of the theory: elementary and composite. TheSM Higgs is contained in the composite sector, whose characteristic mass scale is ∼ TeVso as to address the Planck-weak hierarchy problem; whereas, the rest of SM particles areadmixtures of those in the two sectors, i.e., partially composite/elementary. Specifically, thedegree of compositeness of the non-Higgs SM particles reflects the size of their mass, i.e.,the top quark is significantly composite, while the light quarks are negligibly so. Moreover,lepton-number is preserved by the composite sector, but broken at the UV cut-off in theelementary sector. So, if we include an elementary SM singlet RH neutrino ( N R ), then itwill naturally have a super-large, even Planck-scale, Majorana mass. However, by itself, thislepton-number violation is not quite sufficient to induce Majorana mass for SM neutrino,since we also require EWSB/Higgs VEV for this purpose. Thus, this information aboutlepton-number violation has to be transmitted from the elementary to the composite sector,where the SM Higgs resides. In this way, one can “sew” together the two necessary ingredientsin order to generate the SM neutrino mass.A simple and natural way for sharing lepton-number violation between the two sectorsis for the above elementary N R to also mix with composite sector TeV-mass singlets. Thesesinglet states are purely Dirac to begin with, but as a result of the above coupling to ele-mentary N R , they acquire a tiny Majorana mass component. It can be shown that it is theexchange of these (now pseudo -Dirac) singlet states generates – without any tuning – theright size of the SM neutrino mass. Thus, the TeV-mass singlets play a crucial role in thisentire process: their observation at the LHC would provide a vital test of this mechanismof the SM neutrino mass generation. Just to emphasize, the TeV -mass for these compos-ite singlets is natural, being directly related to the electroweak scale (cf. usual 4D models,where some extra assumptions are typically needed in order to get such a mass for the singlet40eutrinos).The obvious next question is how to produce these TeV-mass composite neutrinos N R at the LHC, given that they are SM singlets . The analogous 4D models provide a recipe:typically this is achieved in these models in the context of extending the SM EW symmetryto the left-right (LR) structure, i.e., SU (2) L × SU (2) R × U (1) B − L , with SU (2) R × U (1) B − L broken down to SM hypercharge at the TeV scale. The point is that N R – while being SMsinglet – is a doublet of SU (2) R , thus can be produced via decay of charged W R . W R is, inturn, produced via q ¯ q annihilation with the associated W R couplings of SM EW strength.Indeed, a similar LR symmetric pattern is motivated in the warped/composite Higgsframework, albeit for a different reason (i.e., than parity restoration in usual 4D models).The purpose of the extra symmetry is to protect ρ parameter from receiving large corrections.So, we assume this extension only in the composite sector as simply a global symmetry.There is then no elementary charged W R gauge boson (unlike for the SM W L ), but we dohave composite charged W R ’s. However, in this way, it seems naively that we do not have away to produce W R , since the SM quarks inside proton are mostly elementary, leading to anegligible direct coupling to composite-sector W R .Remarkably, we found that elementary-composite W L mixing, followed by composite W L - W R mixing via Higgs VEV, induces the required coupling of composite charged W R ’s toquarks. It is the degeneracy among spin-1 composites which ensures that the second mixingeffect is rather large for a few TeV composite W ’s. The end result is that coupling of lightquarks to W R in these models is suppressed compared to the typical SM EW coupling, butit still sizable. Consequently, although production rates for W R are smaller than in 4D LRcase, as we showed here, it is still enough for discovery. We would like to emphasize here thatthis subtle effect has been discussed earlier in the context of LHC signals for these spin-1states in general, i.e., independent of neutrino mass considerations. However, this featurewas not really exploited before, in the sense that decay modes of W R studied in that context(for example, W/Z/
Higgs) were also accessible via W L , i.e., production of W R was not really“needed” (cf. here N R only couples to W R ).Note that, in the W R decay, the composite N R is accompanied by composite chargedlepton, since the associated coupling is, for example, larger than coupling to one compositeand one elementary states (cf. in 4D models, it would be simply the SM charged lepton).Composite charged lepton decays into SM charged lepton, plus Higgs/longitudinal Z , while N R decays (just like in 4D models) into SM charged lepton and W , latter decaying eitherleptonically or hadronically. Thus, the final state is either (di-lepton + W -jet + Higgs/ Z )or (tri-lepton + MET + Higgs/ Z ). Note that the dileptons in first channel are of opposite sign, given the pseudo-Dirac nature of these singlets (cf. same-sign dileptons from Majorana singlets in some 4D LR models). 41e performed a detailed analyses of both these channels for singlet neutrino productionvia decay of composite W R , finding that, for both channels, significant evidence can beobserved for ∼ TeV W R and composite N R /composite charged lepton of mass 750 GeV,with an integrated luminosity of
300 fb − , and even discovery with slightly more integratedluminosity. It is clear that the extra boson in final state permits distinguishing this frameworkfrom 4D LR models. In addition, this feature is crucial for reducing the SM background,especially given smaller rate than in 4D LR models and the absence of the “smoking-gun”,i.e., same-sign dileptons; indeed, it is noteworthy that in spite of these seeming challenges,we are able to extract a reasonable signal.Finally, we would like to provide a “preview” of part II, where we will consider signalsof singlet neutrinos from production and decay of particles absent in 4D LR models. Inparticular, one idea is to relax the degeneracy of spin-1 composites that was assumed here.In the light of the above discussion, this direction actually results in suppressing the charged W R signal, but we will show that a “new” type of signal appears from a neutral heavy boson,i.e., which is not accompanied by a charged channel (unlike in the 4D LR case, where chargedspin-1 channel is actually dominant, W R being lighter than the corresponding extra neutralgauge boson). We will also study production of composite SU (2) L doublet leptons inherentto this framework (cf. absent in the 4D LR models); singlet neutrinos can be produced intheir decays via a Yukawa coupling, i.e., in dependent of the couplings of N R to W R , thus ofthe representation of N R under the extended EW symmetry [cf. signals studied earlier doreply on singlet being charged under SU (2) R × U (1) B − L ]. Overall, our work leads to a newperspective on the nature and relevance of LHC signals of TeV-scale singlet neutrinos. Acknowledgements
We would like to thank Chien-Yi Chen, Roberto Contino, Bhupal Dev, Shrihari Gopalakr-ishna, Doojin Kim and...for discussions and David Curtin for help with simulations. Thiswork was supported in part by NSF Grant No. PHY-1315155 and the Maryland Center forFundamental Physics. SH was also supported in part by a fellowship from The KwanjeongEducational Foundation.
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