aa r X i v : . [ h e p - ph ] F e b Signatures of new physics at 14 TeV
Riccardo Barbieri
Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
Abstract
I give an overview of the ideas and of the problems that orient the expectations for newphysics at the Large Hadron Collider and, whenever I can, I describe the correspondingsignals. A road map The Large Hadron Collider will make the first thorough exploration of the energy range at or wellabove the Fermi scale, G − / F , one of the two established fundamental scales in particle physics,the other being Λ QCD . This is enough to make the emergence of new phenomena highly plausible,whose description would require a revision of the Standard Model (SM) of elementary particles.Which new phenomena or, in the standard jargon, which new physics ? The theoretical proposalsare so many and so diverse that an impression of great confusion may easily be generated especiallyin a young person just approaching the field, as there are many present here. The aim of this talkis to help correcting this impression. I try to do this by describing a sort of road map that I will usemyself to follow the flow of the experimental data with the focus on possible new phenomena. Tothe extent that this is possible, and to the best of my knowledge, in each case I will correspondinglyindicate the relevant experimental signatures.In my view the main problems and the main ideas that orient the expectations for new physicsat the LHC are the following (not in order of preference, see below): • Higgsless models
That there be no Higgs boson is implausible. Yet, since no Higgs boson has been directly seen sofar, one may want to take the conservative view that no Higgs boson indeed exists. I would notgive much weight to this possibility, were it not for the relatively recent suggestion[1, 2, 3] thatpart of the role of the Higgs boson could be played, in a potentially calculable way, by appropriatevectors, as we shall see. • The naturalness problem of the Fermi scale
In a nutshell the famous naturalness problem[4, 5] of the Fermi scale amounts to make the followinghypothesis. There is a neat, not accidental reason that explains why short distance physics,whatever it may be, does not disturb the beautiful agreement of the Standard Model with thedata. This is guaranteed if the short distance physics has in its infrared spectrum a naturally lightHiggs boson. This highly motivated hypothesis remains the best theoretical reason for expectingnew physics to show up at the LHC. We know of two possible explanations, although at differentlevel of consistency, for a naturally light Higgs boson. One rests on supersymmetry [6, 7, 8]. Theother sees the Higgs doublet as a pseudo-Goldstone boson of a suitably broken global symmetry[9].I generically refer in the following to this second possibility as the composite
Higgs boson picture.Other names used in the literature in related contexts are
Little Higgs [10] or holographic models[11,12]. This interpretation may be related with the existence of a compactified extra dimension, eitherin a true or in a metaphorical sense (via the so called AdS/CFT correspondence[13]). • Dark matter: a numerical coincidence
To discover at the LHC an elementary constituent for Dark Matter (DM), seen in astrophysicaland cosmological observations, would be a triumph for physics. The reasons we have to think thatthis might be the case rest on a numerical coincidence which will be worth recalling[14, 15]. In turnthis suggests the usefulness of taking a broad view when considering possible related signatures. • The G − / F /M P l hierarchy as a manifestation of extra dimensions
1t is appealing to think that the huge difference between the Fermi and the Planck scales maybe a manifestation of a suitably compactified extra dimension, one or more[16, 17, 18]. If this istrue, significant gravitational phenomena could actually take place in particle physics experimentsalready at energies not too far from the Fermi scale itself and therefore potentially visible at theLHC. I find this possibility less likely than for any of the previous cases, which is why I shall notdiscuss it further. Nevertheless, this same scenario might be in the background of some of themore concrete possibilities mentioned above.For reasons of time I shall not discuss the discovery potential at the LHC of new physics bymeasurements of flavour physics. Such potential exists, though, as exemplified by the case of the B s → l + l − decay. In a new indefinite sector that replaces the Higgs doublet of the SM some dynamics breaks aglobal SU (2) L × SU (2) R × U (1) B − L symmetry down to SU (2) L + R × U (1) B − L . At the same timethe gauge group SU (2) L × U (1) Y gets broken down to U (1) em as desired. There are ways todescribe this in a manifestly gauge invariant way or even to make the dynamics explicit. Thegeneric situation that results, however, either leaves many unknown parameters, like in the so-called Electroweak Chiral Lagrangian[19, 20], or, when calculable, it is hardly compatible with theElectroWeak Precision Tests (EWPT)[21, 22, 23], like in standard Technicolour[24, 25]. It looksto me that more recent studies (models) have not substantially changed this situation. A featurethat has emerged, though, which may deserve attention has to do with the unitarity problem ofHiggsless models.It is known since the seventies that in the SM with massive W and Z - call them collectively V- but without a Higgs boson, the V V scattering amplitudes saturate unitarity already at a centerof mass energy of 1 ÷ . deconstructed version of them[27, 28], where theexchange in the V V amplitude of heavy vectors - denoted by ˆ V - can prevent it from growing toofast . In this way the saturation of unitarity of V V scattering can be postponed in a calculableway to energies higher than 1 ÷ . V s can be the beginning of a tower of states,all with the same quantum numbers, hence the possible name for them of Kaluza Klein (KK)vectors. Although real calculability is achieved where the consistency with the EWPT gets moreproblematic[3, 32], this physical mechanism of keeping unitarity under partial control deservesattention. For this reason I summarize in Table 1 the main properties of the KK ˆ V s, with thecaveat that some of these properties are model dependent. In this Table g S is a strongish coupling,say g S ≈ ÷ g is the standard weak coupling. The scale v , which is notthe vacuum expectation value of a Higgs field, is nevertheless still related to the W-mass in theusual way, v = √ m W /g = 175 GeV.The KK vectors can be searched at the LHC via vector boson fusion, qq → qq ˆ V , or bydirect production, q ¯ q → ˆ V , although through a suppressed coupling[33, 34, 35]. In turn ˆ V willdecay into a pair of V bosons or into a pair or third generation quarks. A preliminary study of For an early model with a single heavy vector see ([29, 30, 31]). A ( V V ) ≈ s/v ≈ s/f m ˆ V ≈ g S v ≈ g S f ˆ V V V g S g S f ¯ f ˆ V ≈ g ( g/g S ) ≈ g ( g/g S ) Q ¯ Q ˆ V ? strongish KK − quarks − Yes, with ≈ TeV massTable 1:
Main phenomenological properties of Higgsless and Composite Higgs models. A ( V V ) is the
V V -amplitude without the exchange of any KK vector, ˆ V . m ˆ V is the mass of the (first) KK vector. ˆ V V V is the strength of the triple coupling. f ¯ f ˆ V is the typical strength of the KK vector coupling to the lightfermions. Q ¯ Q ˆ V is the coupling of the KK vector(s) to the third quark generation. v = √ m W /g = 175GeV. qq → qq ˆ V → qqW Z → qq jj ll can be found in Ref. [36]. The decay of the KK vector into apair of light fermions, like µ + µ − , is probably useless because of the small branching ratio. A highluminosity looks in any event mandatory for these searches (see below). Composite
Higgs boson models
For many reasons it is in any case far more likely that a Higgs boson exists. A way to protect itsmass from large corrections is to make it an approximate Goldstone boson of a suitably brokenglobal symmetry[9]. The set up is not very different from the one described at the beginning ofthe previous Section, except for the fact that: i) The SM gauge group is fully inside the residualunbroken global group, H , and therefore remains also unbroken at a first stage; ii) (Some of)the Goldstone bosons associated with the breaking of the full global group G down to H musttransform under the SM gauge group as the standard Higgs doublet and are called ”CompositeHiggs boson”. This framework involves therefore two scales: the scale f at which G → H and theusual vacuum expectation value v of the Higgs field, with f > v . There exists a 5-dimensionalvariation of this scheme, where the Composite Higgs boson is interpreted as the fifth componentof a vector in 5D. A simple example of a symmetry structure that works, with some advantageousphenomenological properties, is when G = SO (5) × U (1) B − L and H = SO (4) × U (1) B − L [12].The main features of this picture are the following (See Table 1). The scale f cannot be tooseparated from v unless one is ready to pay a fine tuning of order ( v/f ) . The hV V couplingsof the Higgs field h with the W and the Z are suppressed, relative to the ones of the SM Higgsboson, by a factor (1 − v /f ) / [37, 38]. Therefore, as indicated in Table 1, the amplitude A ( V V ),even with the inclusion of the Higgs boson exchange, grows with s as ≈ s/f and this growthmust be partially compensated by KK vector exchanges. As usual the Higgs boson mass mustbe protected from large radiative corrections, especially the one due to the top exchange. In theComposite Higgs boson picture this happens because of the exchange of heavier vector-like quarks,which I shall call in the following KK quarks because they can occur in towers. Depending on3he scheme, they can have charge 2/3 ( T ), 1/3 (B) or even exotic charges, like 5/3 ( X ). Finally,even Composite Higgs models, in their simplest versions and for not too large f (i.e. a limitedfine tuning), are not easily accommodated with the constraints of the EWPT[39, 38, 40]. Perhapsthe most plausible explanation of this problem is that we are ultimately dealing with a strongcoupling theory and therefore we have a limited ability to do precise calculations.The searches for KK vectors is similar here to the Higgsless case discussed above, with thedifference that the KK vectors may be heavier (See Table 1). If one takes a 5-dimensional view, asI have indicated, there is also a pretty strong case for the existence of KK gluons decaying predom-inantly into t ¯ t pairs. The search for pp → ˆ g → t ¯ t with sufficient luminosity looks promising[41].Relative to the KK vectors, the search for the KK quarks might actually be more fruitful,since their masses, always pending the issue of the EWPT, might be significantly lower than theones of the KK vectors. Denoting them collectively by Q KK , their production by q ¯ q → Q KK ¯ Q KK and their subsequent decays, Q KK → Q V, Q h , may give rise to significant signals even withrelatively moderate luminosities[42, 43]. Supersymmetry is the other possible explanation for a natural Fermi scale. Relative to the Com-posite Higgs picture it has at least the advantage of being straightforwardly compatible with theEWPT. There is a basic reason for this. Unlike the case of the Composite Higgs boson, the can-cellation of the divergent contributions to the Higgs mass takes place between loops of particlesthat have different spin (top/stop, gauge-vectors/gauginos, etc.). Hence they cannot mix witheach other and cannot produce tree level corrections to the EWPT. Needless to say it would beunreasonable not to mention the many other important and independent motivations that su-persymmetry has in its own (gauge coupling unification[44, 45, 8] for one). Nevertheless it issupersymmetry as a solution of the naturalness problem of the Fermi scale that motivates itsvisibility at the LHC and this is what matters here.The phenomenology of the Minimal Supersymmetric Standard Model (MSSM) with super-symmetry breaking parameters as in minimal Supergravity, or mSUGRA[46, 47, 48], and a stableneutralino as the Lightest Supersymmetric Particle (LSP) is probably the most studied case ofphysics beyond the SM. Gluino and squark pair production, with their subsequent chain decaysending into a neutralino LSP, gives rise to the characteristic missing energy signal generally ac-companied by jets and most often high p T leptons. The conclusion that a very significant portionof the parameter space of mSUGRA can be successfully explored in this way at the LHC evenwith a relatively modest integrated luminosity is important and reassuring[49]. A limit of thisanalysis, on the other hand, is that it rests on the special s-particle spectra produced by thebenchmark points of the mSUGRA parameter space. A complementary analysis based on fews-particle masses and motivated by naturalness could take the gluino and, for simplicity, a single The stop is the s-particle with the strongest coupling to the Higgs boson (so that m Z ≈ m H u ≈ m t ) and thegluino influences the stop mass via the strong gauge coupling (so that m t ≈ m g ). I am allowing for non-unifiedgaugino masses. ˜ t L , ˜ b L , ˜ t R and ˜ g with masses in the 500 GeV range and all other s-particles heavier, except for oneneutralino, are consistent with flavour-physics constraints if the mixing angles in the coupling ˜ g ¯ d L ˜ d L are comparable χ . In such a case the relevantsearches would again be gluino and stop pair production with dominant decays of the gluino into t ˜ t or q ¯ q + χ and of the stop into t + ˜ g or t + χ , depending on which is the lighter of the two, thestop or the gluino .It is also true that mSUGRA need not be the end of the story. Letting aside for the timebeing the issue of the Higgs boson system, there is at least the possibility that the supersymmetrybreaking scale is low enough that the gravitino, rather than the neutralino, be the LSP. In thiscase χ , if it is the next-to-lightest supersymmetric particle, would decay as χ → γ + g / or, ifallowed by phase space, as χ → Z + g / or even χ → h + g / → b ¯ b + g / [50, 51, 52, 53]. Inprinciple, for a special choice of the parameters, it is also possible that these decays take place witha displaced vertex in the detector. I do not see this as a priority in the supersymmetry searches,though. More likely, in my mind, is the possibility that the gluino[54, 55] or the stop[56] have,for a reason or another, a long lifetime and behave in the detector as stable particles. It is againreassuring to see that dE/dx and time-of-flight measurements can recognize the corresponding”R-hadrons” in an efficient way[57]. The unsuccessful searches of the Higgs boson, standard or non standard, at LEP2 are a matterof concern for the supersymmetric picture, since we have always thought that supersymmetryrequires at least one relatively light Higgs boson. There are two possible attitudes that one cantake with respect to this problem, both defendable in my mind, which I describe in turn.The first attitude takes the MSSM as a strict guideline. As very well known, an upper boundholds in this case for the mass of one of the CP even scalars forming the supersymmetric Higgsboson system m h ≤ M Z cos β + 3 m t π v log m t m t , (5.1)where tan β = v /v is the usual ratio of the two doublet vacuum expectation values, m t is anaverage stop mass squared and I have neglected for simplicity an effect proportional to the squareof the so called A t term. To comply with the LEP2 bound one considers a relatively large valueof tan β , so as to maximize the tree level contribution to (5.1), and a stop mass close to about 1TeV, since the radiative term grows logarithmically with it. A large tan β could be suggested byinterpreting the (theoretically uncertain) anomaly in the muon g − M Z ≈ (2 ÷ m t , that has to be cancelled by an unpleasant fine tuning.If this is true, the lightest supersymmetric Higgs boson is just around the corner of the LEP2bound, m h = 115 ÷
120 GeV, and it has very SM-like properties.An alternative view, which I find motivated, gives weight to the following considerations.Even assuming, for good reasons indeed, that supersymmetry is relevant in nature, no theorem to the ones of the CKM matrix. The angular distributions in these decays depend on other parameters than the masses, but this, at least in afirst stage of the analysis, is probably a negligible effect. maximally natural
Fermiscale with little fine tuning. Therefore, since the top, and so the stop, are the particles withthe strongest coupling to the Higgs boson, it makes especially sense to insist on a moderate stopmass. Maybe (5.1) is not the key equation and the supersymmetric Higgs boson system is notthe one of the MSSM. This view has been taken by many with different proposals. One that hasreceived attention is based on the Next-to-Minimal-Supersymmetric-Standard-Model (NMSSM)and wants a Higgs boson of mass around 100 GeV, in any case lower than the LEP2 bound of 115GeV, which decays into two τ ¯ τ pairs[58, 59]. A reanalysis of the LEP data on this would in factbe welcome.There are different ways, however, of evading the LEP2 bound, also based on the NMSSM,which can be in some cases less fine tuned and may lead to very peculiar properties of the Higgsboson system. Here the crucial formula is the one that replaces (5.1) in the NMSSM m hNMSSM ≤ M Z cos β + λ v sin β + 3 m t π v log m t m t , (5.2)with an extra tree-level contribution proportional to the square of the Yukawa coupling λSH H between the two Higgs doublets and the singlet S . What counts therefore is the value of λ , withtwo different cases that are interesting to consider. • λ (10 T eV ) ≤ λ / (4 π ) and that the presence of higher dimensional operators at a scale of 10 TeVor more does not disturb the perturbative calculation of the effects on the EWPT. By evolving λ to the Fermi scale, which is where it counts for (5.2), one has λ ( G − / F ) ≤
2. Since λ getsnon perturbative at relatively low energies, all this is a priori not consistent with perturbativeunification of the gauge coupling, unless one specifies in an appropriate way the change of regimethat has to intervene above about 10 TeV. λ ( G − / F ) ≤ λ as, e.g., h → h h → V → l + l − j or A → h Z → V V Z → l + l − j .(As customary, h is a scalar and A a pseudoscalar.) The corresponding searches appear to bepossible with a significant integrated luminosity[62]. Since the lightest Higgs boson can be heavierthan in the MSSM, this picture has no fine tuning problem at all, even allowing for relatively heavystop and gluino (up to about 1 TeV and 2 TeV respectively) although probably still detectable atthe LHC. • λ ( M GUT ) ≤ λ at the low scale depends on the spectrum of matter between M GUT and G − / F . Since onedoes not want to disturb the success of supersymmetric gauge-coupling unification, this matterat intermediate energies has to occur in full SU (5) supermultiplets, like it happens in severalmotivated models. In this case λ ( G − / F ) ≈ . ÷ . ( G − / F ) ≈ . ÷ . m h ≈ ÷
125 GeV is possible with amoderate stop mass , say up to 300 GeV[64]. It is also possible that this quasi-standard scalaris not the lightest member of the full Higgs boson system, which in the NMSSM is made of onecharged state, 3 neutral scalars and two pseudoscalars. Among the pseudoscalars there can in factbe a quasi-Goldstone boson of an approximate Peccei Quinn symmetry, A [65, 66, 64]. In thisquasi-symmetric limit, h can decay into a pair of stable neutralinos or as h → A A → b ¯ b b ¯ b , notthe easiest mode to study at the LHC[67]. Suppose that there exists a neutral stable particle, χ , of mass m χ = O ( G − / F ) that has been inequilibrium in the primordial hot plasma and, when the temperature of the plasma gets below itsmass, its number density is reduced by χχ ↔ f ¯ f , with f a lighter standard particle. This is easilyarranged by a discrete parity under which χ → − χ . Up to corrections vanishing as M W /m χ , thepresent relic energy density of the χ particle, in units of the critical density, is given byΩ χ h = 688 π / T γ x f √ g ∗ ( H /h ) M P l σ ≈ . pbσ (6.1)where H is the present Hubble constant, T γ is the CMB temperature, g ∗ is the number of effectivedegrees of freedom in the plasma at T f when the χ number density gets frozen, x f = m χ /T f ≈ ÷
25, and σ is the thermal-averaged non-relativistic cross section for χχ → f ¯ f . I have explicitlywritten down this formula to make evident that the final numerical result comes from a combi-nation of many different physical constants. Now the remarkable and famous coincidence[14, 15]is that, on one side, σ ≈ pb is the typical weak interaction cross section for a particle of mass m χ = O ( G − / F ) and, on the other side, the observed energy density of cosmological Dark Matteris [68] Ω DM h = 0 . ± . . (6.2)This is enough to take seriously the possibility that a particle like χ , generally called WeeklyInteracting Massive Particle (WIMP), make the Dark Matter in the universe and can perhaps bediscovered at the LHC.As well know and evident from Section 4, a strongly motivated candidate for this WIMP isthe supersymmetric neutralino LSP, which has the potential advantage of being copiously pro-duced in the chain decays of strongly interacting particles with a large production cross section.Nevertheless, the above considerations suggest the usefulness of taking a broader point of view.I substantiate this statement by briefly describing two ”minimal” examples of consistent DarkMatter candidates.In the first one[69, 70] the SM is extended to include a second Higgs doublet H I , I for inert ,with the following property: i) it is not coupled to fermions because of an imposed H I → − H I parity to avoid any potential flavour problem; ii) it has a positive mass squared so that it getsno non-vanishing vacuum expectation value (hence the name of inert). This extra doublet leadsto one charged and two neutral scalars, H , A , whose masses depend on their interactions with7he standard Higgs doublet. The lightest of them is stable and, if neutral, makes a possibleDark Matter candidate. Its relic abundance has been studied and shown to be consistent withobservations in a mass range between about 40 and 80 GeV and a small splitting, ∆ m ≈
10 GeV,with the heavier scalar, also neutral[70, 71, 72]. The inert doublet can have a significant impacton the decay properties of the standard Higgs boson or, indirectly, on its mass range, as indicatedby the EWPT[70]. At the LHC the detection of pp → A H , with the heavier scalar decaying intothe lighter one plus a virtual Z, is very challanging[70, 73].The second example[74, 75, 76] makes use of fermions: a lepton-like vector doublet, L = ( ν, E )and L c = ( E c , ν c ) and a singlet N . Other than the covariant kinetic terms, the general Lagrangianthat involves them is L = − λLHN − λ ′ L c H + N + M L LL c + 12 M N + h.c. (6.3)where H is the standard Higgs doublet. After electroweak symmetry breaking the spectrumconsists of one charged state, E ± , and three neutral Majorana fermions, ν , , , the lightest ofwhich can be a Dark Matter candidate. For some fixed values of the two Yukawa couplings λ, λ ′ ,even in this case the relic density has been studied and shown to be consistent with observationsin a region of the ( M, M L ) plane. In such a region, one has also studied[76] the expectations fora signal in direct DM searches with bolometric detectors and at the LHC for pp → E ± ν , → W ± Zν ν → l + E T . In the LHC case, suitable cuts can lead to a discovery but the luminosityrequirements are severe, to say the least. In general, I believe that the lesson of these ”minimal”models has to be kept in mind. We expect that the LHC will unravel the physics of electroweak symmetry breaking by discoveringthe Higgs and/or new phenomena not included in the SM. This is based on the fact that the energyrange at or well above the Fermi scale will be explored for the first time. To me this makes thesituation at the LHC quite different from the one of the previous hadron colliders. The LHCcase is more open to surprises, suggesting that one should correspondingly take a broader pointof view when talking of possible signals of new physics. Nevertheless some possibilities stand up,which are, in my mind, the ones I have described. The related signals are summarized in Table 2,where I also grossly indicate in each case, and to the best of my knowledge, the needed integratedluminosity for discovery. The tentative and biased character of this Table is evident. It goeswithout saying that most of these entries are mutually exclusive.I want to conclude with a general remark. The physics of the Fermi scale is the physics ofelectroweak symmetry breaking, which can be considered in many respects the current centralquestion of particle physics and is the focus of the activity at the LHC. At a somewhat deeperlevel and from a broader perspective I think that an equally, if not more, important question isthe following: Which is the next relevant symmetry in particle physics, if any?The role of symmetries in describing the physics of the fundamental interactions does not haveto be illustrated. Symmetries have been crucial in keeping the greatest economy in the numberof principles and equations, which is the basic character of particle physics. Their enumeration,8
L dt ≤ f b − mSUGRA pp → ˜ g ˜ g, ˜ t ˜ tχ → g / + γ/Z/h R-hadrons R L dt = 1 ÷ f b − SM-like Higgs bosonKK quarks R L dt > f b − Susy Higgs boson systemMinimal Dark MatterKK weak bosonsKK gluonsTable 2:
Summary of signals as described in the text with a tentative estimate of the needed integratedluminosity for discovery. Most of these entries are mutually exclusive. The cases indicated under R L dt > f b − may in fact be very challenging. from Maxwell on, is unnecessary. The last one that has been experimentally established is thegauge symmetry of the SM. The assumption that symmetries will continue to play a central rolein particle physics is implicit in all the considerations developed in the previous pages. Such anassumption is being currently questioned in some circles. The LHC should shed light on this issue. Acknowledgments
This work is supported by the EU under RTN contract MRTN-CT-2004-503369 and by the MIURunder contract 2006022501. I thank Guido Altarelli, Alex Pomarol, Riccardo Rattazzi, Alessan-dro Strumia, Brando Bellazzini, Slava Rychkov, Alvise Varagnolo, Gian Giudice, MichelangeloMangano, Guido Marandella, Michele Papucci, Lawrence Hall, Yasunori Nomura, Sergio Ferrara,Carlos Savoy, Duccio Pappadopulo, Gino, Isidori, Francesco D’Eramo, Leone Cavicchia, RobertoFranceschini for many useful discussions and comments.
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