Production of exotic composite quarks at the LHC
O. Panella, R. Leonardi, G. Pancheri, Y. N. Srivastava, M. Narain, U. Heintz
PProduction of exotic composite quarks at the LHC
O. Panella , R. Leonardi ,
2, 1
G. Pancheri , Y. N. Srivastava , M. Narain , and U. Heintz Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy ∗ Dipartimento di Fisica e Geologia, Universit`a degli Studi di Perugia, Via A. Pascoli, I-06123, Perugia, Italy Laboratori Nazionali di Frascati, INFN, Frascati Italy Physics Department, Brown University, Providence, USA (Dated: July 2, 2018)We consider the production at the LHC of exotic composite quarks of charge Q = +(5 / e and Q = − (4 / e . Such states are predicted in composite models of higher isospin multiplets ( I W = 1 or I W = 3 / / ep T / jj final state signature we focus on pp → U + j → W + + j j → (cid:96) + p T / jj and then perform a fastsimulation of the detector reconstruction based on Delphes . We then scan the parameter space ofthe model ( m ∗ = Λ) and study the statistical significance of the signal against the relevant standardmodel background ( W jj followed by leptonic decay of the W gauge boson) providing the luminositycurves as function of m ∗ for discovery at 3- and 5- σ level. PACS numbers: 12.60.Rc; 14.65.Jk; 14.80.-j
I. INTRODUCTION
The idea of a further level of compositeness, i.e. thatquarks and leptons might not be truly elementary par-ticles [1] but are instead bound states of some as yetunknown entities has been investigated phenomenologi-cally since quite some time back [2–7]. One immediateconsequence of this composite scenario is of course thatat some high energy scale, the compositeness scale Λ, ex-cited fermions, quarks and leptons, of mass m ∗ ≈ Λ areexpected. The interactions of such states with the ordi-nary quarks and leptons have been modeled on the baseof the symmetries of the standard model and are of themagnetic moment type [7].To the best of our knowledge theoretical and phe-nomenological studies about the production at collidersof such excited states have concentrated on the multipletsof isospin I W = 0 , / I W = 0 , / I W = 1 , /
2. As a consequence one finds for instancethat the multiplet with I W = 3 / U + of charge +5 / e and quarks D − of charge − / e .We remind that alternative scenarios beyond the stan-dard model (BSM) like Little Higgs and Composite ∗ ( Corresponding Author )Email: [email protected]
Higgs [13] models predict the existence of vector-likequarks [14–17] which are color-triplet spin 1/2 fermionswhose left- and right-handed components have the sametransformation properties under the SU(2) gauge group.Such models also predict the existence of vector-likequarks with exotic charges usually denoted as T / and B − / or X and Y [18–20].Alternative possibilities of high charge high massquarks, partners of the top quark have also been pro-posed [21] to be tested at the LHC and events of thetype t ¯ tW + W − have been discussed.In [22] a detailed study of the production at LHC ofvector-like quarks with electric charges q = +(5 / e , q = − (4 / e has been reported showing that at a centerof mass energy of √ s = 14 TeV and with 100 fb − of in-tegrated luminosity a heavy quark mass of 3.7 TeV couldbe reached.We may recall recent experimental searches for pairproduction of vector-like top quark partners of chargeq=5/3 e ( T / ) at LHC both at Run I [23], where top-quark partners with masses below 800 GeV are excludedat 95% C.L. assuming that they decay to tW , and atRun II [24] where a data set of 2 . − has been used toobtain exclusion limits, at √
13 TeV, of 960 (940) GeVrespectively on the mass of a right-handed (left-handed) T / .Experimental searches of compositeness, already withearlier data of Run I of the LHC ATLAS [10] as well asCMS [25] have put lower limits on the mass of excitedquarks, respectively m ∗ > . m ∗ > .
58 TeV,from searches in the 2-jet final state. In [26] an experi-mental search for narrow resonances decaying to di-jetsis presented which uses 12.9 fb − data from Run II of theLHC and excludes excited quarks (with standard isospinand electric charges) with masses below m ∗ ≈ . m ∗ ≈ . − data samples [27]. Similar searches performed a r X i v : . [ h e p - ph ] M a r by the ATLAS Collaboration with 3.6 fb − of proton-proton collisions at √ s = 13 TeV report a heavy quarkmass limit of 5.2 TeV [28]. We also quote phenomenolog-ical studies of searches at the LHC in the diphoton [29]and γ -jet [30] final state signatures, showing that in thesimplified scenario (Λ = m ∗ ) with an integrated luminos-ity of O (200) fb − excited quark masses up to ≈ σ level.Further details about mass limits and searches throughother signatures of the excited quarks (and leptons) canbe found in the excellent review [31] about Run I, andearlier Run II, searches at LHC for exotic particles.It is important to realize however that the above stronglimits on the masses of the excited quarks do applywithin the hypothesis of standard weak isospin assign-ments ( I W = 0 , / I W = 1 , /
2) be their electric charge exotic ornot, do not couple to the gluon field (which has I W = 0),and thus it is not possible to produce them resonantly viaquark-gluon scattering [12] (see also discussion below).The possibility of excited quarks was suggested in thecontext of the SSC [5] but only within the hypothesis ofisospin singlets and doublets ( I W = 0 , / S ¯ ppS collider [12] the possibilityof possible exotic final states within higher isospin mul-tiplets ( I W = 1 , /
2) were explored in p ¯ p collisions. Thephenomenology at high energy colliders of the exoticallycharged excited fermions from a composite scenario withextended isospin multiplets has however been neglectedfor a long time after they had been pointed out in [12].Only recently these exotic fermions have received someattention with respect to the lepton sector. Indeed someof the present authors have studied the production atLHC of the doubly charged leptons of the I W = 1 , / ν ∗ ) is of the Majorana typeand study the corresponding like sign dilepton signatureat the LHC. Incidentally the theoretical possibility dis-cussed in [35] has been experimentally searched for bythe CMS Collaboration and through an analysis of the2015 data [36] of Run II a heavy composite Majorananeutrino is excluded up to m ∗ ≈ .
35 TeV for a value ofthe compositeness scale fixed at Λ = 5 TeV.Taking up the model in [12], here we focus on the phe-nomenology of quarks with higher charges, belonging toweak isospin quartets, I W = 3 / I W = 1, which con-tain quarks with charges 5 / − / / − / u -quarks of the standard model(SM). A peculiar property of the exotic states U + ofcharge q = 5 / e is that they couple only to the W gaugeboson [12]. This can be understood by applying the W U +(5 / ¯ uu ¯ db ) U +(5 / u ¯ d ¯ uWa ) U +(5 / uu dW U +(5 / uu dW FIG. 1. Example processes of U + resonant productionin pp collisions: a ) the Feynman diagrams for the process uu → U + d showing explicitly W exchange in the t -channel(left) and u -channel (right); b ) the Feynman diagrams con-tributing to the process u ¯ d → U + ¯ u . On the left the s -channelannihilation. On the right t -channel W exchange. The heavyline is the exotic quark U + , the heavy dot is the magnetictype coupling characteristic of excited quarks (of electroweakstrenght in this case). standard rules of addition of quantum angular momen-tum and by keeping in mind that that the electroweakgauge bosons ( B µ , (cid:126)W ) have respectively I W = 0 ,
1. Thenby recalling that the standard model quarks and lep-tons appear in isospin singlets ( I W = 0) and doublets( I W = 1 /
2) it is clear that the excited triplet ( I W = 1)can only couple to the SM singlet via the gauge field (cid:126)W .Similarly the ( I W = 3 /
2) multiplet can only couple tothe SM doublet again via the W gauge field. By thesame token the gluon field which has ( I W = 0) cannotcouple to a transition current between the higher isospinmultiplets ( I W = 1 , /
2) and the standard model parti-cles. We conclude these considerations by noting that inour composite scenario the direct coupling of the excitedquarks (and leptons) to the SM gauge bosons γ, Z, g , (e.g. γ, Z, g → q ∗ ¯ q ∗ ) are expected to be highly suppressed bythe presence of form factors. This would be very muchsimilar to what happens in nuclear physics with nucleus-antinucleus pair production which is strongly suppressedat Q ≈ m A even if the nucleus has a huge electric charge( Ze , with Z (cid:29) T / U + quark of the present modelthat are singly produced.The exotic quarks U + have only one decay channel U + → W + u with B ( U + → W + u ) = 1. This implies thatthey could be resonantly produced via the 2 → uu → U + d and hence decay with unit probability to W u .We will discuss therefore the production of the exotic excited quarks U + , D − at the LHC: pp → U + j , (1a) pp → D − j , (1b)and finally assuming the leptonic decay of the W -gaugeboson W → (cid:96)ν (cid:96) we concentrate on the (cid:96) /p T j j signa-ture(s): pp → U + j → W + j j → (cid:96) + /p T j j , (2a) pp → D − j → (cid:96) − /p T j j . (2b)The production of the state of charge Q = 5 / e has thelargest production cross-section for a pp machine such asthe LHC due to the availability of two valence u quarksfrom the colliding particles. The production of 4 / d from the sea and hence its rate is somewhatlower.We show in Fig. 1 the Feynman diagrams describingsome of the parton sub-process contributing Eq. 2a whichcan produce such exotic final state, U + (5 / d − quarks in the initial stateand thereby the corresponding production cross sectionare expected to be somewhat smaller than those of theprocesses in Eq. 2a. Here it will be the dd initiated pro-cess that dominates ( t and u -channel exchange of a W ).Our phenomenological study of the production of ex-otic excited quarks in the (cid:96) /p T j j channel is particularlyinteresting in view of the recent claim of the CMS collab-oration of having observed excesses, relative to the stan-dard model (SM) background, in the data of the Run I atthe LHC at √ s = 8 TeV in the eejj and e /p T j j channels.Indeed the analysis in [37] for a search of right-handedgauge boson, W R , based on 19.7 fb − of integrated lu-minosity collected at a center of mass energy of 8 TeVreports a 2.8 σ excess in the eejj invariant mass distribu-tion in the interval 1 . < M eejj < . − of integrated lu-minosity reported an excess of 2.4 σ and 2.6 σ in the eejj and ep T / jj channels respectively.The absence of a corresponding excess in the µ/p T jj channel, as reported in [38], will be difficult to explainsolely in terms of heavy exotic quark U + or D − resonantproduction, via the processes in Eqs (2a,2b) , because thelepton comes from the W gauge boson and thus electronsand muons will have the same yield. However within ourcomposite fermions scenario the signature (cid:96)/p T jj couldget a contribution also from an excited neutrino ν ∗ (cid:96) beingproduced in association with a lepton pp → (cid:96)ν ∗ (cid:96) and thendecaying as ν ∗ (cid:96) → ν (cid:96) Z → ν (cid:96) jj . One could therefore qual-itatively explain the fact that the excess is observed onlyin the e/p T jj via the combined production and decay ofa heavy composite exotic quark U + and an excited neu-trino by simply assuming that the ν ∗ µ has a higher massthan ν ∗ e . We perform a detailed fast simulation of signal andSM background via the Delphes package [39] and ob-tain luminosity curves, with the statistical error, as func-tion of the parameter ( m ∗ ) at the 3- and 5- σ level. Wefind that for different values of the integrated luminosity:(30,300,3000) fb − , commonly used in the study of theLHC Run II ( √ s = 13 TeV) searches, the correspond-ing mass discovery reach at the 3- σ level is respectively m ∗ ≈ (2800 , , I W = 3 / √ s = 13TeV has the potential of observing the signature or alter-natively excluding larger values of the exotic heavy quarkmasses ( m ∗ ) compared to those values already excludedfrom analyses of Run I [40, 41] but applicable only to thestandard excited quarks (with non-exotic charges).The rest of the paper is organized as follows: In Sec. IIwe review the theoretical composite model; in Sec. III wediscuss the heavy exotic quark production cross sectionsand decay rates; in Sec. IV we discuss the (cid:96)/p T jj signatureand the main associated standard model background anddiscuss the kinematic cuts needed to optimize the statis-tical significance; in Sec. V we present the results of thefast simulation obtained through the Delphes [39] soft-ware and present the 3- and 5-sigma luminosity curves inthe parameter space; finally Sec. VI gives the conclusionswith outlooks.
II. THE EXTENDED WEAK-ISOSPIN MODEL
It is well known that in hadronic physics the strongisospin symmetry allowed to discover baryon and mesonresonances well before the observation of quarks and glu-ons. The properties of the hadronic states could be delin-eated using the SU(2) and SU(3) symmetries. In analogywith this it may be expected that, for the electroweaksector, the weak isospin spectroscopy could reveal someproperties of excited fermions without reference to a par-ticular internal structure.The standard model fermions have I W = 0 and I W =1 / I W = 0 and I W = 1,so, combining them, we can consider fermionic excitedstates with I W ≤ /
2. The multiplets with I W = 1(triplets) and I W = 3 / U + UD , D = UDD − , Ψ = U + UDD − , with similar multiplets for the antiparticles. While refer-ring to the original work in [12] for a detailed discussionof all couplings and interactions, we discuss here onlythe main features of these higher multiplets. We referto [32] for further details and here we mention only that FIG. 2. (Color online) The width of the exotic quark U + asa function of its mass. The solid (blue) line is the analyticalresult in Eq. 6 which is compared with the CalcHEP output,dots (orange) as obtained form the implementation of ourmodel. The agreement is excellent. the higher isospin multiplets ( I W = 1 , /
2) contributesolely to the iso-vector current and do not contributeto the hyper-charge current. In order to calculate indetail production and decays of these excited fermions,we need to discuss the nature of their couplings to lightfermions and the gauge fields. Because all the gauge fieldscarry no hyper-charge Y , a given excited multiplet cou-ples (through the gauge field) only to a light multipletwith the same Y . Also the coupling has to be of theanomalous magnetic moment type, for current conserva-tion. The decay modes and reaction cross sections canbe calculated using the following effective lagrangian interms of the transition currents: L ( I W =3 / = gf / Λ (cid:88) M,m,m (cid:48) C ( 32 , M | , m ; 12 , m (cid:48) ) × (cid:0) ¯Ψ M σ µν q Lm (cid:48) (cid:1) ∂ ν ( W m ) µ + h.c. (3) L ( I W =1)int = gf Λ (cid:88) m =0 , ± (cid:2)(cid:0) ¯U m σ µν u R (cid:1) + (cid:0) ¯D m σ µν d R (cid:1)(cid:3) ∂ ν ( W m ) µ + h.c. (4)In the above equation g is the SU(2) coupling, f and f / are unknown dimensionless couplings expected tobe of order one. We will assume them exactly equal to 1throughout the paper. The mass of the excited fermions m ∗ will be assumed to coincide with the compositenessscale Λ ( m ∗ = Λ) and the C ’sare Clebsch-Gordon coeffi-cients.In particular we see that the particles of these highermultiplets with exotic charges interact with the standardmodel fermions only via the physical W gauge field. Forthe exotic quark U + of charge q = +(5 / e belonging tothe I W = 1 triplet and the one of the I W = 3 / L ( I W =3 / U + = g f / Λ (cid:0) ¯ U + σ µν P L u (cid:1) ∂ ν W µ + h.c. (5a) L ( I W =1)int U + = g f Λ (cid:0) ¯ U + σ µν P R u (cid:1) ∂ ν W µ + h.c. (5b)where: P L = (1 − γ ) / P R = (1 + γ ) / σ µν = i [ γ µ , γ ν ] /
2; as usual g isthe SU(2) coupling constant g = e/ sin θ W ; the field U + stands for the exotic quark field both for the case I W = 1and I W = 3 / u is the u-quark field. The effective La-grangian in (5) is a dimension five operator and henceone inverse power of the new physics scale (the compos-iteness scale) Λ appears. In the following phenomenologywe will consider the simplified model Λ = m ∗ .With the above interaction Lagrangian we can easilycompute the total decay width of the exotic state U + ofcharge q = (5 / e . Indeed as it only interacts via the W gauge boson its only decay channel is U + → W + u , and:Γ U + = Γ( U + → W + u )= α QED f / sin θ W m ∗ (cid:18) M W m ∗ (cid:19) (cid:18) − M W m ∗ (cid:19) (6)hence we see that for m ∗ (cid:29) M W , and assuming f / ∼ U + /m ∗ ≈ O ( α QED ). This behavior is shown explicitlyin Fig. 2 where the width Γ U + is plotted versus the mass m ∗ .We have implemented the interactions of the exoticquarks discussed in section II within the CalcHEP soft-ware [42]. This has been done with the help of Feyn-Rules [43], a Mathematica package that from a givenmodel lagrangian produces as output the Feynman rulesin a format that can be read by various software toolssuch as CalcHEP and Madgraph. we note that the stan-dard model background to the process described in Eq. 1has been discussed in [44–47].In Fig. 2 we give a first comparison of the CalcHEPoutput within our newly implemented model versus ananalytical computation of the width of the exotic massivequark U + . The agreement is excellent. III. PRODUCTION CROSS SECTIONS
The exotic quark U + interacts with the ordinaryquarks through a typical magnetic type interaction onlyvia the W gauge boson and in pp collisions it can be beproduced via the first generation sub-processes: (a) uu → U + d ( t and u -channel W exchange); (b) u ¯ d → U + ¯ u ( s and t -channel W exchange) as depicted in Fig. 1. Withinthe first generation we have the parton sub-processes: u u → U + d → W + u d (7a) u ¯ d → U + ¯ u → W + u ¯ u (7b)which may be observed in either a final state with 4 jetsor 2 jets and W + decaying electroweakly. Together withsuch a high charge member of the mutiplet, the lowercharge exotic quark member of the multiplet would alsobe produced. An exotic excited fermion of charge Q = − (4 / e may be produced through d d → D − u → W − d u (8a) d ¯ u → D − ¯ d → W − d ¯ d (8b)Similar diagrams to those depicted in Fig. 1 will de-scribe the production of the exotic state D − . We nowdiscuss the production cross sections of the 2 → A. Partonic cross section
Following notation and conventions of ref. [12, 34] we give here the basic cross-sections of the partonic sub-processes.The case of the weak isospin I W = 1 is characterized by the absence of interference between ˆ t − and ˆ u − channel (orˆ s − and ˆ t − channel). The partonic cross-section for the processes uu → U + d and u ¯ d → U + ¯ u are given by: (cid:18) d ˆ σd ˆ t (cid:19) uu → U + d = 14ˆ s m ∗ g f π (cid:40) ˆ t (cid:2) m ∗ (ˆ t − m ∗ ) + 2ˆ s ˆ u + m ∗ (ˆ s − ˆ u ) (cid:3) (ˆ t − M W ) + ˆ u (cid:2) m ∗ (ˆ u − m ∗ ) + 2ˆ s ˆ t + m ∗ (ˆ s − ˆ t ) (cid:3) (ˆ u − M W ) (cid:41) (9) (cid:18) d ˆ σd ˆ t (cid:19) u ¯ d → U + ¯ u = 14ˆ s m ∗ g f π (cid:40) ˆ s (cid:2) m ∗ (ˆ s − m ∗ ) + 2ˆ t ˆ u + m ∗ (ˆ t − ˆ u ) (cid:3) (ˆ s − M W ) + ˆ t (cid:2) m ∗ (ˆ t − m ∗ ) + 2ˆ s ˆ u + m ∗ (ˆ s − ˆ u ) (cid:3) (ˆ t − M W ) (cid:41) (10)The case of the weak isospin I W = 3 / t − and ˆ u − channel(or ˆ s − and ˆ t − channel) which had been neglected in ref. [12]. The partonic cross-sections for the processes uu → U + d and u ¯ d → U + ¯ u are given by: (cid:18) d ˆ σd ˆ t (cid:19) uu → U + d = 14ˆ s m ∗ g f / π (cid:40) ˆ t (cid:2) m ∗ (ˆ t − m ∗ ) + 2ˆ s ˆ u − m ∗ (ˆ s − ˆ u ) (cid:3) (ˆ t − M W ) + ˆ u (cid:2) m ∗ (ˆ u − m ∗ ) + 2ˆ s ˆ t − m ∗ (ˆ s − ˆ t ) (cid:3) (ˆ u − M W ) + 1(ˆ u − M W ) 1(ˆ t − M W ) (cid:18) ˆ s ˆ t ˆ u + 38 ˆ u ˆ tm ∗ (cid:19)(cid:27) (11) (cid:18) d ˆ σd ˆ t (cid:19) u ¯ d → U + ¯ u = 14ˆ s m ∗ g f / π (cid:40) ˆ s (cid:2) m ∗ (ˆ s − m ∗ ) + 2ˆ t ˆ u − m ∗ (ˆ t − ˆ u ) (cid:3) (ˆ s − M W ) + ˆ t (cid:2) m ∗ (ˆ t − m ∗ ) + 2ˆ s ˆ u − m ∗ (ˆ s − ˆ u ) (cid:3) (ˆ t − M W ) + 1(ˆ s − M W ) 1(ˆ t − M W ) (cid:18) ˆ s ˆ t ˆ u + 38 ˆ s ˆ tm ∗ (cid:19)(cid:27) (12)The above formulas have also been checked against theresults reported in [34] by means of using the crossingsymmetry. The total integrated cross-section correspond-ing to the above differential cross section is given for theprocess u ¯ d → U + ¯ u (which receives contributions bothfrom the s and t -channels in FIG. 3. One can see that athigh energies the integrated cross section rises logarith-mically due to the effect of the t -channel W propagator.Also the standard (1 / ˆ s ) behavior of the cross section isnot found because of the magnetic type coupling. Theasymptotic form of the integrated partonic cross sections ( t -channel) is :ˆ σ = (cid:90) − ˆ s + m ∗ d ˆ t d ˆ σd ˆ t (13)= ⇒ ˆ s (cid:29) M W , m ∗ ∼ πα QED f sin θ W m ∗ log( sM W )as can also be seen from FIG. 3. B. Production rates at the LHC
We now present here the production cross sectionsfor the exotic quark U + in pp collisions expected atthe CERN LHC collider according to Feynman’s partonmodel. The QCD factorization theorem, allows to ob-tain the hadronic cross section in terms of convolution FIG. 3. (Color online) For illustrative purposes we givean example of the parton-parton cross-section as indicated inEq. 13 (no parton ditribution functions). We show ˆ σ ( u ¯ d → U + ¯ u ) for m ∗ = 300 GeV for the case of the weak isospin I W = 1 (in this case there is no interference between the t − and s − channel) and with a choice of the coupling f q = 1.The solid line (blue) is the dominant t -channel and the dashedline (orange) is the s -channel. The dots are the correspond-ing values obtained by running the same process in CalcHEPwithin the model implemented with the help of the FeynRulespackage. The agreement is excellent, within a few percent. of the partonic cross sections ˆ σ ( τ s, m ∗ ), evaluated at thepartons center of mass energy √ ˆ s = √ τ s , and the uni-versal parton distribution functions f a which depend onthe parton longitudinal momentum fractions, x , and onthe factorization scale ˆ Q : σ = (cid:88) a,b (cid:90) m ∗ s (cid:90) τ dτ dxx f a ( x, ˆ Q ) f b ( τx , ˆ Q ) ˆ σ ( τ s, m ∗ ) . (14)In Fig. 4 we show a comparison of the production crosssections of pp → U + j at √ s = 8 ,
13 TeV betweenthose obtained with an analytical/numerical computa-tion based on Eq. 14 (solid line) and those obtained froma CalcHEP numerical simulation based on the imple-mented model (full dots). The left panel of Fig. 4 isfor the I W = 1 case while the right panel is for I W = 1.The integrated hadronic cross sections are furthershown in Fig. 5 where we present the results for twodifferent values of the LHC energy, namely √ s = 8 , √ s = 8 TeV the totalintegrated cross section for the production of U + (5/3)and D − (4 /
3) for I W = 1 (left) and I W = 3 / U + (5 /
3) islarger. This is almost entirely due to the fact that pro-ducing U + involves the subprocess uu → U + d i.e. withtwo valence u -quarks in the initial state. Similar con-siderations apply to the results at higher energies (bot-tom panels). For the production of U + we have, withinthe first two generations, the following contributing sub-processes: (a) uu → U + d ; (b) u ¯ d → U + ¯ u ; (c) uc → U + s ; (d) u ¯ s → U + ¯ c ; IV. SIGNAL AND SM BACKGROUND
The relevant standard model background to our signa-ture is given by electroweak
W jj production followed bythe leptonic decay of the W gauge boson, W → (cid:96)ν (cid:96) : pp → W jj → (cid:96)/p T jj (15)This SM background is known to be important and hasbeen discussed throughly in the literature. We have sim-ulated it by using the CalcHEP generator.We would like to address here the main kinematic dif-ferences between the signal and the relevant SM back-ground in order to choose suitable cuts for optimizingthe statistical significance.One first thing to consider is that one of the two jetsis from the heavy quark decay that makes it very ener-getic with a Jacobian peak in the transverse momentumspectrum near p T ≈ ( m ∗ / − M W /m ∗ ) (16)Using the p T of the jets as a discriminant gives verygood accuracy in identifying the jet coming from thedecay of the heavy quark correctly, especially for highmasses. Hence we identify the hardest jet (j1) in theevent as the one from heavy quark decay.We first define the transverse momentum of the highest p T -jet as p T j . The main kinematic feature of our signalprocess is the production of a very heavy excited quark U + with mass m ∗ ≈ O (TeV). At very high masses it willthen be a reasonable approximation to assume the exoticheavy particle to be produced nearly at rest. It will decayin a pair of almost back to back high p T jet and a high p T W gauge boson. We expect both the p T j and p T W distributions to be peaked at p T ≈ ( m ∗ / − M W /m ∗ )and to be relatively similar in shape. These qualitativefeatures are indeed confirmed by our numerical simula-tion of the signal distributions. Fig. 6 (bottom left andbottom right panels) show the p T j and p T W distribu-tions for m ∗ = 1000 GeV which are clearly both peakedaround p T ≈
400 GeV in this case.Fig. 6, Fig. 7, Fig. 8 and Fig. 9 show several normalizeddistributions with respect to both transverse momentumand angular variables. Fig 6 shows different transversemomentum distributions: the transverse momentum ofthe lepton p T (cid:96) , the second-leading p T ( j
2) and that of theleading p T j are shown in Fig. 6(a,b,c) while the W gaugeboson transverse p T distribution is given in Fig. 6(d).From the point of view of the transverse momentumdistributions of the jets (leading and second-leading) inFig. 6, signal and background are very well separated, forthe given values of the parameters ( m ∗ = 1000 GeV andΛ = 10 TeV). This suggests that a very efficient way weto reduce drastically the background while keeping mostof the signal is a cut on the transverse momentum of -3 -2 -1
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 σ ( f b ) m * (GeV) √ s = T e V √ s = T e V pp → j U + I W =1 -3 -2 -1
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 σ ( f b ) m * (GeV) √ s = T e V √ s = T e V pp → j U + I W =3/2 FIG. 4. (Color online) The total production rates of pp → jU + at the LHC for two different values of the energy of the center ofmass √ s = 8 ,
13 TeV and for the two choices of the weak isospin of the exotic states, I W = 1 on the left panel and I W = 3 / Q = m ∗ . The parametrization of the parton distribution function is NNPDF3.0 [48]. the leading jet at ≈
200 GeV and, possibly, a cut in thetransverse momentum of the second-leading jet at ≈ η, φ ) plane, ∆ R = (cid:112) (∆ η ) + (∆ φ ) , ( η is the pseudorapidity and φ the azimuthal angle in thetransverse plane). The corresponding ∆ R distributionsare peaked at (∆ R ) min ≈
3. Therefore, in the reconstruc-tion process, the two jets can be easily separated as wellas the lepton is cleary separated from the jets.Differently than with the p T distributions we can seefrom Fig. 8(a,b,c) that the pseudorapidity distributionsof the leading jet in p T , η ( j ), and the second-leadingjet in p T , η ( j ), and those of the lepton, η ( (cid:96) ), are quitesimilar for signal and background. The missing trans-verse energy distribution is shown Fig 8(d). Here signaland background are quite separated but we have checkedthat a cut on the missing transverse energy is less effec-tive than one on the transverse momentum of the leadingjet, p T ( j ).Let us also comment on the fact that the (cid:96)ν (cid:96) jj sig-nature from a heavy composite quark state of charge(+4/3) e has the potential to explain the excess observedin a search for 1 st generation lepto-quarks (LQ) by theCMS collaboration [37] in the e/p T jj invariant mass dis-tribution in the interval M ej ≈
600 GeV. Fig. 9 (a,b)shows, at the reconstructed level and for a particularpoint of the parameter space (Λ = m ∗ = 1000 GeV), thatthe ej (electron and leading-jet) and ej (electron andsecond-leading jet) invariant mass distribution can easilyaccomodate an excess in the interval where it has beenclaimed by the CMS collaboration. Our model wouldpredict the same excess in the muon channel because the leptons arise from the decay of the W gauge boson. Somemechanism would have to be conceived in our model tosuppress this excess in the muon channel. As alreadymentioned in the introduction we observe that this sig-nature could also be affected by the production of anexcited neutrino ( N = ν ∗ ) in association with the cor-responding lepton followed by the decay of the heavyneutrino to a lepton and a gauge boson decaying to twojets, thus obtaining (cid:96)/p T jj . The differences in the elec-tron and muon channels could then be ascribed to a masshierarchy between the excited electron and muon heavyneutrinos.We point out that within our final state signature( (cid:96)ν (cid:96) jj ) it is always possible to define a cluster trans-verse mass variable ( M T ) in terms of the reconstructedtransverse momentum of the W gauge boson ( p T W = p T (cid:96) + p T ν ) and the transverse momentum of the leadingjet (or highest p T jet) p T j : M T = (cid:18)(cid:113) p T W + M W + p T j (cid:19) − ( p T W + p T j ) (17)The transverse mass distribution is strongly correlatedwith the heavy exotic quark mass m ∗ . Relevant informa-tion about the mass of the heavy exotic quark U + canbe obtained from the transverse mass distribution M T .This is indeed the case as can be seen from Fig. 9(lower-left) where the transverse mass distribution obtained forthe parameter value ( m ∗ = Λ = 1000 GeV) shows aclear peak characterized by a relatively sharp end-pointat M T ≈ m ∗ . This is expected since in the resonant pro-duction the heavy exotic quark, U + is decaying to (cid:96)ν (cid:96) j and the jet from U + is expected to be the leading, whilethe second-leading jet is the one produced in associationwith U + , in pp → U + j .Finally we have also reconstructed the invariant mass -2 -1 pp → U + j pp → D - j LHC-8 TeVI W =1 σ ( f b ) -2 -1 pp → U + j pp → D - j LHC-8 TeVI W =3/210 -2 -1 pp → U + j pp → D - j LHC-13 TeVI W =1 m * (GeV) σ ( f b ) -2 -1 pp → U + j pp → D - j LHC-13 TeVI W =3/2 m * (GeV) FIG. 5. (Color online) The total integrated cross-sections at the LHC energies of √ s = 8 ,
14 TeV for the production of theexotic quarks U + , of charge Q = +(5 / e and D − of charge Q = − (4 / e . We have used the NNPDF3.0 [48] parton distributionfunctions. The uncertainty bands (magenta and orange) correspond to running the factorization and renormalization scale from Q = M W (solid line) up to Q = m ∗ (dashed line). All contributing sub-processes within the first two generations (18) havebeen summed up. distribution of the decay products of the heavy excitedquark U + : (cid:96)ν (cid:96) j . Indeed it is possible to reconstructthe longitudinal neutrino momentum p z ( ν ) up to a two-fold ambiguity [49]. The resulting reconstructed invari-ant mass M (cid:96)νj is shown in Fig. 9(lower-right).In order to still reconstruct the invariant mass of theexotic quark to some degree of accuracy, we can followthe method described in [49] modified to adatpt it toour case. We use the conservation of four-momentumto solve for the longitudinal momentum of the neutrino( p νL ). Conservation of four-momentum, p W = p (cid:96) + p ν ,gives the following equation: M W = ( p (cid:96) + p ν ) . (18)The only unknown quantity in Eq. 18 is the longitudinal momentum of the neutrino. Expanding the right-handside of Eq. 18 we obtain a second-order equation for p νL :(1 − B )( p νL ) − A B p νT p νL + ( p νT ) (1 − A ) = 0 (19)where p νT = | p νT | while p νL and p (cid:96)L are the true components(with sign) of the neutrino and lepton momentum alongthe (longitudinal) z -axis and: A = M W + 2 p (cid:96)T · p νT E (cid:96) p νT , B = p (cid:96)L E (cid:96) . (20)It has the solutions: p νL = 11 − B (cid:104) AB ± (cid:112) A + B − (cid:105) p Tν (21) / N ( d N / d P t l )( b i n w i d t h G e V ) PT(l) (GeV) / N ( d N / d P t j )( b i n w i d t h G e V ) PT(j2) (GeV) / N ( d N / d P t j )( b i n w i d t h G e V ) PT(j1) (GeV) / N ( d N / d P t W )( b i n w i d t h G e V ) PT(W) (GeV)
FIG. 6. (Color online) Transverse momentum distributions of the signal, dark line (blue), and of the SM background, lightline (red): upper left panel, lepton distribution; upper right panel the second-leading jet distribution; lower left panel, leadingjet and finally the W gauge boson transverse momentum distribution. These distributions clearly show that the most effectivekinematic cut in order to optimize the statistical significance S is one on the p T of the leading jet ( p Tj ≈ O (200) GeV that willhighly suppress the background while almost will not affect the signal. (d) Transverse p T of the W gauge boson distributionof our signal pp → U + j → W + j j superimposed with the standard model W jj background. / N ( d N / d ∆ R jj )( b i n w i d t h . ) ∆ R(j,j) ( / N )( d N / d ∆ R )( b i n w i d t h . ) ∆ R(l,j)
FIG. 7. (Color Online) Normalized ∆ R distributions of signal, dark line (blue), and SM background, light line (red), clearlyshow that the two jets are well separated (plot on the left -∆ R jj -) as well as the lepton and the jets (plot on the right -∆ R (cid:96)j -). Note that the discriminant ( D ) of the second order equa-tion is the quantity in the square root, D = A + B − D >
0, two realsolutions; (ii) D = 0, one real solution; (iii) D <
0, twocomplex solutions. If the discriminant is zero there is only one solution for p νL which can be used to fully reconstruct the neutrino.If the discriminant is negative, the event is rejected. Ifthe discriminant is positive, there are two possible p νL solutions. Using both of them, the two possible neu-0 / N ( d N / d η j )( b i n w i d t h . ) η (j1) (GeV) 0 0.005 0.01 0.015 0.02 0.025 0.03 -8 -6 -4 -2 0 2 4 6 8 / N ( d N / d η j )( b i n w i d t h . ) η (j2) (GeV) / N ( d N / d η l )( b i n w i d t h . ) η (l) (GeV) / N ( d N / d M E T )( b i n w i d t h G e V ) MET (GeV)
FIG. 8. (Color Online) Various (normalized) distributions of the signal pp → e/p T jj , dark line (blue), in the case of anexotic quark state U + (5 /
3) mass m ∗ = 1000 GeV and for a compositeness scale Λ = 10 TeV as well as of the SM background pp → W jj → (cid:96)/p T jj , light line (red), at √ s = 13 TeV. We have used the NNPDF3.0 [48] parton distribution functions evaluatedat the scale Q = m ∗ . N.B. we have considered here all 14 subprocesses for a total of 29 Feynman diagrams within the firstgeneration of quarks. In the top (left and right) panels and in the lower left panel we show respectively the pseudo-rapiditydistributions of: (a) the highest p T jet (j1); (b) the second-leading jet (j2); (c) the lepton. In the bottom right panel we showthe missing transverse energy (MET) distribution. trino momentum vectors are constructed and, combin-ing them with the lepton momentum, the two W candi-date are re-constructed. We select the p νL solution thatgives the more central W , i.e. with the smaller pseudo-rapidity. Then we can reconstruct the corresponding in-variant mass M (cid:96)ν (cid:96) j . Fig. 9 shows the distribution in theinvariant mass of the lepton, jet and neutrino. There isa clear peak in correspondence of the exotic quark mass. V. FAST DETECTOR SIMULATION ANDRECONSTRUCTED OBJECTS
In order to take into account the detector effects, suchas efficiency and resolution in reconstructing kinematicvariables, we interface the LHE output of CalcHEP withthe software
Delphes that simulates the response of ageneric detector according to predefined configurations.We use a CMS-like parametrization. For the signal weconsider a scan of the parameter space (Λ = m ∗ ) withinthe range m ∗ ∈ [500 , cut p T ( j p T ( j M T t >
180 GeV – –t >
200 GeV – –t >
180 GeV >
100 GeV –t >
180 GeV – >
400 GeVTABLE I. Various cuts which have been studied in order tomaximise the statistical significance. It turns out that cut t is the most efficient cut. We have studied four different choices of kinematical cuts t . . . t as described in Table I. Although the variouschoices perform quite similarly, it turns out that the mostefficient choice is found to be cut t : p T ( j leading ) ≥
180 GeV , (22a) p T ( j second-leading ) ≥
100 GeV . (22b)For each signal point and for the standard model back-ground we generate 10 events in order to have enoughstatistics to evaluate the reconstruction efficiencies ( (cid:15) s ,1 / N ( d N / d M j l )( b i n w i d t h G e V ) M(j1,l) (GeV) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 200 400 600 800 1000 1200 1400 / N ( d N / d M j l )( b i n w i d t h G e V ) M(j2,l) (GeV) / N ( d N / d M t )( b i n w i d t h G e V ) MT (GeV) / N ( d N / d M l ν j )( b i n w i d t h G e V ) M(l, ν ,j) (GeV) FIG. 9. (Color online) Various invariant and transverse mass distributions for a choice of m ∗ = Λ = 1000 GeV at √ s = 13TeV for the signal, dark line (blue), and the SM background, light line (red). In the top left and top right panels we showthe invariant mass distribution of the lepton with j the highest p T jet (leading) and with j the second leading jet. In thebottom panels we show the transverse mass M T distribution (left) and the reconstructed invariant mass, M ( (cid:96)ν (cid:96) j ), of the decayproducts of the exotic quark U + (right). (cid:15) b ) of the detector and of the cuts previously fixed (seeEq. 22a, 22b). We select the events with two jets, onelepton and /p T in the final state. This is justified becausethe two jets are well separated, as opposed for instance towhat happens the signal pp → (cid:96)(cid:96)jj studied in ref. [35],due to a heavy composite Majorana neutrino, where itwas found that depending on the heavy neutrino mass( m ∗ ) it is possible to have merging of the two jets in asizeable fraction of the events. Once we have the numberof the selected events we evaluate the reconstruction effi-ciencies. The efficiencies are shown for the choice of cuts t (see Table I) in Table II. Then for a given luminosity L it is possible to estimate the expected number of eventsfor the signal ( N s ) and for the background ( N b ): N s = Lσ s (cid:15) s , N b = Lσ b (cid:15) b , (23)and finally the statistical significance ( S ) is evaluated as: S = N s √ N s + N b . (24) It is then possible to obtain the luminosities needed toobtain an effect of a given statistical significance as : L = S σ s (cid:15) s (cid:20) σ b (cid:15) b σ s (cid:15) s (cid:21) (25)Therefore luminosity curves at 5- and 3- σ level (i.e. fix-ing S = 3 or S = 5) can be straightforwardly given asa function of the mass m ∗ of the exotic quark. Fig. 10shows such 3- and 5 sigma luminosity curves which canalso be used to get indications on the potential for dis-covery (or exclusion) at a given luminosity reached bythe experiments at Run II of the LHC. VI. CONCLUSIONS
We have presented the first study of the productionat the CERN LHC of new exotic quark states of charge q = (5 / e and q = − (4 / e which appear in compositemodels of quarks and leptons when considering higher2 * (GeV)10 -1 L (f b - ) I W =1LHC - 13 TeV 3- σ σ * (GeV)10 -1 I W =3/2LHC - 13 TeV 3- σ σ FIG. 10. (Color online) Luminosity curves at 5- σ and 3- σ level for √ s = 13 TeV as a function of the excited quark mass m ∗ after including the fast simulation efficiencies of the detector reconstruction. For I W = 1, and for values of the integratedluminosity equal to L = (30 , , − we find a 3-sigma level mass reach respectively up to m ∗ ≈ (2230 , , I W = 3 / m ∗ ≈ (2930 , , σ and 5- σ curves define the band of the luminositycurves within the statistical error. Background σ b before cut (fb) σ b after cut (fb) ( (cid:15) b )8200000 14678 0.00179 Signal ( I W = 1) m ∗ (GeV) σ s before cut (fb) σ s after cut (fb) ( (cid:15) s )500 7782 5416.74 0.696061000 1277 1064.33 0.833461500 344.6 298.489 0.866192000 107.7 95.1185 0.883182500 39.05 34.7037 0.88873000 13.5 12.0555 0.8933500 4.281 3.84352 0.897814000 1.424 1.28213 0.900374500 0.4957 0.446665 0.901085000 0.1799 0.162518 0.90338 Signal ( I W = 3 / m ∗ (GeV) σ s before cut (fb) σ s after cut (fb) ( (cid:15) s )500 11080 5819.11 0.525191000 2240 1649.89 0.736561500 806.3 646.065 0.801262000 343.2 283.964 0.82742500 159.9 134.147 0.838943000 60.25 51.8626 0.860793500 23.55 20.0983 0.853434000 9.347 7.57986 0.810944500 3.191 2.60797 0.817295000 1.043 0.845737 0.81087TABLE II. Efficiencies of the standard model W jj back-ground and of our signature for the I W = 3 / I W = 1cases. The estimated efficiencies refer to the choice of kine-matic cut t described in Tab. I or Eqs. 22a, 22b. isospin multiplets I W = 1 and I W = 3 /
2. Such stateshave been discussed quite sometime back [12] but theirphenomenology has been, somewhat surprisingly, not ad- dressed in detail. Only very recently [32–34] some atten-tion has been devoted to the phenomenology of exoticdoubly charged states appearing in the lepton sector ofthe extended weak isospin model of ref. [12]. Here we ex-plore, to the best of our knowledge for the first time, thephenomenology of the hadron sector of the same modelwith respect to the CERN LHC experiments, with a focuson the Run II at a center of mass energy of √ s = 13 TeV.This is the main motivation which started the presentwork which however acquires a relevant importance inview of the fact that the model considered here has thepotential of explaining, at least qualitatively, the excessabove the SM background reported very recently by theCMS collaboration in the analysis of the data of Run Iat √ s = 8 TeV in the e /p T j j channel [38].This is particularly interesting in view of the fact thatthe recent studies [35] of the lepton sector of extendedweak-isospin composite multiplets suggest a possible ex-planation of the concomitant CMS excess observed in the eejj channel [37] in terms of an hypothetical compositeMajorana neutrino. In [35] it has been also suggestedthat the composite scenario could also be connected tothe recent anomaly reported by the ATLAS collaboration σ σ L (fb − ) m ∗ (GeV) m ∗ (GeV)30 2930 + 70 −
50 2660 + 60 − −
30 3280 + 60 − ±
60 3880 + 60 − I W = 3 /
2, for m ∗ at3- and 5- σ level within the statistical error at different valuesof the integrated luminosity L = (30 , , − . W jj ) based on the
Delphes software [39].Finally we compute the luminosity curves as func-tions of m ∗ for 3- and 5- σ level statistical significanceincluding the statistical error. For different values ofthe integrated luminosity L = (30 , , − wefind for instance that, for I W = 3 / σ level) respectively masses upto m ∗ ≈ (2930 , , , m ∗ ) could be fully ex-plored. Also the effect of expected contact interactionsshould be taken into account. This could improve thesensitivity of the signature to larger portions of the pa- rameter space. ACKNOWLEDGMENTS
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60 1980 + 40 − ±
30 2540 + 40 − ±
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