Extending the sensitivity to New Physics beyond the anticipated reach of the LHC is a prime aim of future colliders. This paper summarises the potential of an e+e- linear collider, at and beyond 1 TeV, using a realistic simulation of the detector response and the accelerator induced background. The possible LC energy-luminosity trade-offs offered in probing multi-TeV scales for new phenomena with electro-weak observables are also discussed

Battaglia, Marco

De Curtis, Stefania

Dominici, Daniele

Riemann, Sabine

CERN Document Server

arXiv:hep-ph/0112270v1  20 Dec 2001Probing New Scales at a e+e− Linear ColliderMarco Battaglia∗CERN, CH-1211 Geneva 23, SwitzerlandStefania De Curtis† and Daniele Dominici‡Dip. di Fisica, Universita’ degli Studi, Firenze, Italy andINFN, Sezione di Firenze, Firenze, ItalySabine Riemann§DESY Zeuthen, Germany(Dated: February 11, 2014)Extending the sensitivity to New Physics beyond the anticipated reach of the Lhc isa prime aim of future colliders. This paper summarises the potential of an e+e− linearcollider, at and beyond 1 TeV, using a realistic simulation of the detector response andthe accelerator induced background. The possible LC energy-luminosity trade-offs offeredin probing multi-TeV scales for new phenomena with electro-weak observables are alsodiscussed.I. INTRODUCTIONThe Lhc is expected to directly probe possible New Physics beyond the Standard Model (SM) up to a scaleof a few TeV. While its data should provide answers to several of the major open questions in the presentpicture of elementary particle physics, it is important to start examining how this sensitivity can be furtherextended at a next generation of colliders. Today we have a number of indications that New Physics couldbe of supersymmetric nature. If this is the case, the Lhc will have a variety of signals to discover these newparticles and the linear collider (LC) will be required to complement the probe of the SUSY spectrum withdetailed measurements. However, beyond Supersymmetry there is a wide range of other scenarios invoking newphenomena at, and beyond, the TeV scale. They are aimed at explaininig the origin of electro-weak symmetrybreaking, if there is no light elementary Higgs boson, at stabilising the SM, if SUSY is not realised in nature,or at embedding the SM in a theory of grand unification.Many of such scenarios predict the existence of new particles that would be manifested as rather spectacularresonances in e+e− collisions, if the achievable centre-of-mass energy is sufficient. A high energy LC representsan ideal laboratory for studying this New Physics [1, 2]. It also retains an indirect sensitivity, through a precisionstudy of the virtual corrections to electro-weak observables, when their mass exceeds the available centre-of-massenergy. This paper summarises the results of a series of studies aimed at quantifying the potential of a highenergy, high luminosity e+e− LC in extending to high scales the probe for New Physics. While a significantactivity has already addressed the issues related to a TeV-class collider, we now review the potential of amulti-TeV LC, such as Clic.II. ELECTRO-WEAK OBSERVABLES AT A MULTI-TEV LCThe analysis of the Lep and Slc data has provided a significant experience in the extraction of electro-weakobservables, optimising their statistical sensitivity and controlling their systematic uncertainties. At largercentre-of-mass energies, the relevant e+e− → f f¯ cross sections are significantly reduced and the experimentalconditions at the interaction region need to be taken into account in validating the anticipated accuracies onthe cross section σff¯ , forward-backward asymmetries Aff¯FB and left-right asymmetries Aff¯LR determination at√s = 1 TeV - 5 TeV. Since the two-fermion cross section is of the order of only 10 fb, it is imperative toachieve high luminosity by reducing the beam-spot sizes. In this regime the beam-beam effects are importantand the primary e+e− collision is accompained by several γγ → hadrons interactions. Being mostly confined∗Marco.Battaglia@cern.ch†decurtis@fi.infn.it‡dominici@fi.infn.it§riemann@ifh.de2in the forward regions, this γγ background reduces the polar angle acceptance for quark flavour tagging anddilutes the jet charge separation using jet charge techniques. These experimental conditions require efficientand robust algorithms to ensure sensitivity to flavour-specific f f¯ production. The statistical accuracy for thedetermination of σff¯ , Aff¯FB and Aff¯LR has been studied, for µ+µ− and bb¯, taking the Clic parameters at√s= 3 TeV. The Simdet parametrised detector simulation has been used and the γγ → hadrons background,corresponding to 10 overlayed bunch crossings, has been added to e+e− → µ+µ−, bb¯ events. bb¯ final stateshave been identified using an algorithm based on the sampling of the decay charged multiplicity of the highlyboosted b hadrons at Clic energies [3]. Similarly to Lep analyses, the forward-backward asymmetry has beenextracted from a fit to the flow of the jet charge Qjet defined as Qjet =∑iqi|piT |k∑i|piT |k, where qi is the particlecharge, pi its momentum, T the jet thrust axis and the sum is extended to all the particles in a given jet. Herethe presence of additional particles, from the γγ background, causes a broadening of the Qjet distribution andthus a dilution of the quark charge separation. The track selection and the value of the power parameter kneeded to be optimised as a function of the number of overlayed bunch crossings. The results are summarisedin terms of the relative statistical accuracies δO/O in Table I. Another important issue is the accuracy on theluminosity determination, that needs to be controlled to 0.5%, or better.III. SENSITIVITY TO A Z′ BOSONThere is a wide range of New Physics scenarios predicting the existence of new vector particles with massesin the TeV range. One of the simplest extensions of the SM consists in the introduction of an additional U(1)gauge symmetry, whose breaking scale is close to the Fermi scale. This extra symmetry is for instance predictedin some grand unified theories. The extra Z ′ associated to this symmetry naturally mixes with the SM Z0.The mixing angle is strongly constrained by precision electroweak data to be of the order of few mrad whiledirect searches at Tevatron for a new Z ′ boson set a lower mass limit around 600 GeV. Further improvementsare expected by precision electro-weak data obtained at a Giga-Z facility.The search for such an extended gauge sector offers an interesting framework for studying the sensitivity toscales beyond those directly accessible, even at a multi-TeV collider. It also raises the issue of the ability todiscriminate between different models. Main classes of models with additional Z ′ bosons include E6 inspiredmodels and the left-right models (LR) (for a recent review see [4]). Concerning the E6 models, the Z′ fermioncouplings depend on the angle θ6 which defines the embedding of the extra U(1) in the E6 group.In this study we have considered the so-called η model with θ6 = − arctan√5/3, the χ model with θ6 = 0and, as a reference model, the so called sequential SM (SSM) which has an additional Z ′ boson with SM-likecouplings.There has been a significant interest in the Lhc and LC potential in the search for a new Z ′ boson. At theLC, the indirect sensitivity to its mass,MZ′ , can be parametrised in terms of the available integrated luminosityL, and centre-of-mass energy, √s. In fact the scaling law for large MZ′ can be obtained by considering theeffect of the Z ′ − γ interference in the cross section σ. For s << M2Z′ and assuming that the uncertainties δσare statistically dominated, we get the range of mass values giving a significant difference:|σSM − σSM+Z′ |δσ∝ 1M2Z′√sL >√∆χ2 (1)and the sensitivity to the Z ′ mass scales as:MZ′ ∝ (sL)1/4 (2)This relationship shows that there is a direct trade-off possible between√s and L, which should be takeninto account when optimising the parameters of a high energy LC.The σff¯ and Aff¯FB (f = µ, b) values have been computed, for 1 TeV <√s < 5 TeV, both in SM and includingthe corrections due to the presence of a Z ′ boson with 10 TeV < MZ′ < 40 TeV, with the couplings predictedby the models mentioned above. This has been obtained by implementing them in the Comphep program.The relative statistical errors on the electroweak observables are obtained by rescaling the values of Table I fordifferent energies and luminosities. The sensitivity has been defined as the largest Z ′ mass giving a deviation ofthe actual values of the observables from their SM predictions corresponding to a SM probability of less than5%. This sensitivity has been determined, as a function of the√s energy for an integrated luminosity L of1 ab−1 and 5 ab−1, and rescaled to other values of L using the formula (2) and assuming the uncertainties tobe dominated by statistics. Results are summarised in Figure 1. For the η model the sensitivity is lower: forexample to reach a sensitivity of MZ′=20 TeV, 10 ab−1 of data at√s=5 TeV would be necessary.3TABLE I: Relative statistical accuracies on electro-weak observables, obtained for 1 ab−1 of Clic data at√s = 3 TeV,including the effect of γγ → hadrons background.Observable Relative Stat. AccuracyδO/O for 1 ab−1σµ+µ− ±0.010σbb¯ ±0.012AµµFB ±0.018AbbFB ±0.055√s  (TeV)L  (ab-1 )0123451 1.5 2 2.5 3 3.5 4 4.5 5√s  (TeV)L  (ab-1 )0123451 1.5 2 2.5 3 3.5 4 4.5 5√s  (TeV)L  (ab-1 )0123451 1.5 2 2.5 3 3.5 4 4.5 5FIG. 1: The 95% C.L. sensitivity contours in the L vs.√s plane for different values of MZ′ in the SSM model (left)and in the E6 χ model (center) and for different values of the compactification scale M in a five dimensional extensionof the SM with fermions on the boundary (right).IV. SENSITIVITY TO KALUZA-KLEIN EXCITATIONS IN THEORIES WITHEXTRA-DIMENSIONSTheories of quantum gravity have considered the existence of extra-dimensions for achieving the unificationof gravity at a scale close to that of electroweak symmetry breaking. String theories have recently suggestedthat the SM could live on a 3+δ brane with δ compactified large dimensions while gravity lives on the entire tendimensional bulk. The corresponding models lead to new signatures for future colliders ranging from Kaluza-Klein (KK) excitations of the gravitons [5] to KK excitations of the SM gauge fields with masses in the TeVrange [6].Among the models with extra dimensions we have considered the five dimensional extension of the SM withfermions on the boundary which predicts KK excitations of the SM gauge bosons with couplings√2 largerthan those of the SM. KK masses are given by Mn = nM , with M the compactification scale of the fifthdimension. Indirect limits on M ∼ 4 TeV from electroweak measurements already exist [7]. These modelspredict excitations of the Z0 and of the photon which are almost degenerate in mass.In this analysis we have included in the cross section calculations only the exchange of the first KK excitationsZ(1) and γ(1), neglecting the effect of the remaining towers which give a small correction. The scaling law forthe limit on M can be obtained by considering the interference of the two new nearly degenerate gauge bosonswith the photon in the cross section and taking the s << M2 limit. The result is the same as eq. (2). Theanalysis closely follows that for the Z ′ boson discussed above. In Figure 1 we give the sensitivity contours asa function of√s for different values of M . We conclude that the sensitivity achievable for the compactificationscale M for an integrated luminosity of 1 ab−1 in e+e− collisions at√s = 3 TeV - 5 TeV is of the order of40 TeV - 60 TeV. Results for a similar analysis, including all electro-weak observables are discussed in [8].4V. SENSITIVITY TO CONTACT INTERACTIONSThe scenarios investigated above address specific models of New Physics beyond the SM.Fermion compositeness or exchange of very heavy new particles can be described in all generality by four-fermion contact interactions [9]. These parametrise the interactions beyond the SM by means of an effectivescale, Λij ,LCI =∑i,j=L,Rηijg2Λ2ij(e¯iγµei)(f¯jγµfj). (3)The strength of the interaction is set by convention as g2/4pi = 1 and models can be considered by choosingeither |ηij | = 1 or |ηij | = 0 as detailed in Table II. The contact scale Λ can be interpreted as effect of newparticles at a mass MX , 1/Λ2 ∝ λ2/M2X .In order to estimate the sensitivity of electro-weak observables to the contact interaction scale Λ, the statisticalaccuracies discussed in Section II have been assumed for the µµ and bb¯ final states. The systematics of theassumed 0.5% include the contributions from model prediction uncertainties. Results are given in terms ofthe lower limits on Λ which can be excluded at 95% C.L., in Figure 2. It has been verified that, for thechannels considered in the present analysis, the bounds for the different Λij are consistent. High luminositye+e− collisions at 3 TeV can probe Λ at scales of 200 TeV, and beyond. For comparison, the correspondingresults expected for a LC operating at 1 TeV are also shown. Beam polarisation represents an important toolin these studies. First, it improves the sensitivity to new interactions, through the introduction of the left-rightasymmetries ALR and the polarised forward-backward asymmetries ApolFB in the electro-weak fits. If both beamscan be polarised to P− and P+ respectively, the relevant parameter is the effective polarisation defined asP = −P− + P+1− P− + P+ . In addition to the improved sensitivity, the uncertainty on the effective polarization, canbe made smaller than the error on the individual beam polarization measurements. Secondly, in the case of asignificant deviation from the SM prediction would be observed, e− and e+ polarization is greatly beneficial todetermine the nature of the new interactions. This has been studied in details for a LC at 0.5–1.0 TeV [10] andthose results also apply, qualitatively, to a multi-TeV collider.VI. CONCLUSIONSExtending the sensitivity to New Physics beyond the anticipated reach of the Lhc, is a prime aim of futurecolliders. By accurately measuring electro-weak observables, a LC able to achieve e+e− collisions at and beyond1 TeV, with high luminosity, can indirectly probe scales extending from tens to several hundreds TeV.REFERENCES[1] M. Battaglia et al., in Physics and Experiments with Future Linear e+e− Colliders, (A. Para and H.E. Fiskeditors), AIP Conference Proceedings, New York, 2001, 607 and hep-ph/0101114.[2] D. Dominici, in these proceedings, hep-ph/0110084[3] M. Battaglia, in Physics and Experiments with Future Linear e+e− Colliders, (A. Para and H.E. Fiskeditors), AIP Conference Proceedings, New York, 2001, 813 and hep-ex/0011099.[4] A. Leike, Phys. Report 317 (1999) 143[5] G.F. Giudice, R. Rattazzi and J.D. Wells, Nucl. Phys. B544 (1999) 3; E. A. Mirabelli, M. Perelstein andM. E. Peskin, Phys. Rev. Lett. 82 (1999) 2236; T. Han, J.D. Lykken, R.-J. Zhang, Phys. Rev. D59 (1999)105006.[6] See, for example, I. Antoniadis, K. Benakli and M. Quiros, Phys. Lett. B331 (1994) 313, ibidem B460(1999) 176; T. Rizzo, Phys. Rev. D64 (2001) 015003.[7] See, for example, T.G. Rizzo and J.D. Wells, Phys. Rev. D61 016007 (2000); P. Nath and M. Yamaguchi,Phys. Rev. D60 (1999) 116006; M. Masip and A. Pomarol, Phys. Rev. D60 (1999) 096005; R. Casalbuoni,S. De Curtis, D. Dominici and R. Gatto, Phys. Lett. B462 (1999) 48; A. Strumia, Phys. Lett. B466 (1999)107.[8] T. Rizzo, in these proceedings, hep-ph/0108235[9] E. Eichten, K. Lane and M. Peskin, Phys. Rev. Lett. 50 (1983) 811; H. Kroha, Phys. Rev. D46 (1992) 58.[10] S. Riemann, LC Note LC-TH-2001-007 (2001).5TABLE II: Definition of different models of contact interaction.Model LL RR LR RL VV AA V0 A0ηLL ±1 0 0 0 ±1 ±1 ±1 0ηRR 0 ±1 0 0 ±1 ±1 ±1 0ηLR 0 0 ±1 0 ±1 ∓1 0 ±1ηRL 0 0 0 ±1 ±1 ∓1 0 ±10 100 200 300   [TeV]LLRRRLLRVVAAV0A01 ab-1,  P-=0.8, e+e- →m +m -CLIC(3 TeV): P+=0.6, D sys=0.5%, D L=0.5%LC (1TeV):   P+=0.6, D sys=0.2%, D L=0.5%D P/P=0.5%0100200300400   [TeV]LLRRRLLRVVAAV0A01 ab-1,  P-=0.8, e+e- →b b-P+=0.0:P+=0.6:D P/P=0.5%D P/P=0%D sys=0 D sys=0.5%,LC, 1 TeVP+=0.4FIG. 2: Limits on the scale Λ of contact interactions in e+e− → µ+µ−, bb¯ for Clic operating at 3 TeV (dashedhistogram) compared to a 1 TeV LC (filled histogram) for different models and the µ+µ− (left) and bb¯ (right) channels.The electron polarisations P− is taken to be 0.8 and the positron P+ to be 0.6. For comparison the upper bars in theright plot show the sensitivity achieved without positron polarisation. The influence of systematic uncertainties is alsoshown.

Probing New Scales at a e+e- Linear Collider

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