Direct production of Kaluza-Klein states in the TeV range is studied for the
experimental environment at the multi-TeV $e^+e^-$ collider CLIC. The
sensitivity of such data to model parameters is discussed for the
Randall-Sundrum(RS) and TeV scale extra dimensional models.Comment: 5 pages, 5 figures, to appear on the Proceedings of the Snowmass 2001
  Summer Study, Snowmass CO (USA), July 200

Battaglia, M.

De Roeck, A.

Rizzo, T.

English

arXiv

Direct production of Kaluza-Klein states in the TeV range is studied for the experimental environment at the multi-TeV $e^+e^-$ collider CLIC. The sensitivity of such data to model parameters is discussed for the Randall-Sundrum(RS) and TeV scale extra dimensional models.Direct production of Kaluza-Klein states in the TeV range is studied for the experimental environment at the multi-TeV $e^+e^-$ collider CLIC. The sensitivity of such data to model parameters is discussed for the Randall-Sundrum(RS) and TeV scale extra dimensional models

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arXiv:hep-ph/0112169v1  12 Dec 2001SLAC-PUB-9082Graviton Production at CLICM. Battaglia∗ and A. De Roeck†CERN, Geneva, SwitzerlandT. Rizzo‡Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 USA(Dated: December 26, 2013)Direct production of Kaluza-Klein states in the TeV range is studied for the experimental envi-ronment at the multi-TeV e+e− collider CLIC. The sensitivity of such data to model parameters isdiscussed for the Randall-Sundrum(RS) and TeV scale extra dimensional models.I. INTRODUCTIONFor the past few years the phenomenology of large (extra) dimensions has been explored at the TeV scale.These theories aim to solve the hierarchy problem by bringing the Gravity scale closer to the Electroweak scale.Extra dimension signatures at future colliders, particularly at CLIC, have been discussed extensively in [1]. Herewe report on a study using two models which can produce measurable resonances in the two-fermion productioncross section, in the multi-TeV range which would be accessible at CLIC. CLIC is conceived to be an e+e−linear collider (LC) optimized for a centre of mass (CMS) energy of 3 TeV with L ∼= 1035cm−2s−1, using a novelacceleration concept called two-beam acceleration [2].For these studies the CLIC physics working group tools have been used, which include smearing of the CMSenergy of the collisions according to the CLIC luminosity spectrum [3]; overlaying the hadronic backgroundfrom γγ events [3]; and producing the detector response by SIMDET, a fast simulation package [4]. Events ofthe type e+e− → ff have been generated with the PYTHIA event generator[5].II. RANDALL-SUNDRUM MODELIn the extra-dimension scenario proposed by Randall-Sundrum(RS) [6] the hierarchy between the Planckand the Electroweak scale is generated by an exponential function called ’warp factor’. This model predictsKaluza-Klein graviton resonances with both weak scale masses and couplings to matter. Hence the productionof TeV scale graviton resonances is expected in two fermion channels[7]. In its simplest version, with two branesand one extra dimension, and where all of the SM fields remain on the brane, the model has two fundamentalparameters: the mass of the first Kaluza-Klein state, m1, and the parameter c = k/MPl, where k is related tothe curvature of the 5-dimensional space and MPlis the 4-d effective Planck scale. The parameter c controlsthe effective coupling strength of the graviton and thus the width of the resonances, and should be less thanone but yet not too far away from unity.The resulting spectrum for e+e− → µ+µ− is shown in Fig. 1. The cross sections are huge and the signalcannot be missed at a LC with sufficient CMS energy. If such resonances are observed – perhaps first by theLHC in the range of a few TeV– it will be important to establish the nature of these newly produced particles,i.e. to measure their properties (mass, width and branching ratios) and quantum numbers (spin). Note thatthe mass m1 of the first resonance determines the resonance pattern: the masses of all higher mass resonancesare then fixed.The signal for one KK resonance (G1) is implemented in PYTHIA 6.158 [5] via process 41. For this studyPYHTIA has been extended to include two more resonances (G2, G3, corresponding to processes 42 and 43) toallow to check the measurability of the graviton self-coupling. The decay branching ratios of these resonanceswere modified according to [7, 8]. In particular the gravitons can decay into two photons in about 4% of thecases, a signature which would distinguish them from e.g. new heavy Z ′ states[9].∗marco.battaglia@cern.ch†deroeck@mail.cern.ch‡rizzo@slac.stanford.edu2050010001500200025002160 2180 2200 2220 2240√s (GeV)s (fb)cc201002003004005006000.26 0.265 0.27 0.275 0.28x 10 -1FIG. 1: (Left) KK graviton excitations in the RS model produced in the process e+e− → µ+µ−. From the most narrowto widest resonances the curves are for c in the range 0.01 to 0.2. (Right) Scan of the resonance (7 points) and χ2 fit tothe measured spectrum for models with different values for c.FIG. 2: (Left) G3(3200GeV) → µµ decay and (Right) G3(3200GeV) → γγ decay in a detector at CLIC, with γγbackground events overlaid (one bunch crossing).The resonance spectrum was chosen such that the first resonance G1 has a mass around 1200 GeV, justoutside the reach of a TeV class LC, and consequently the mass of the third resonance G3 will be around 3200GeV, as shown in Fig. 1. The CMS energy for the e+e− collisions of CLIC was taken to be 3.2 TeV in this study.Mainly the muon and photon decay modes of the graviton have been studied. The events used to reconstructG3 resonance signal were selected either via two muons or two γ’s with E > 1200 GeV and | cos θ| < 0.97. Twotypical events, one decaying into muons and the other in photons, are shown in Fig. 2. The background fromoverlaid two photon events – on average four events per bunch crossing –is typically important only for anglesbelow 120 mrad, i.e. outside the considered signal search region.First we study the precision with which we can measure the shape, i.e. the c and M parameters, of theobserved new resonance. A scan similar to the one at the Z at LEP was made for an integrated luminosity of1 ab−1. An example of the cross section measurements and the χ2 fit through the points for spectra generatedwith different c and M values is shown in Fig. 1b. The precision with which the cross sections are measuredallows one to determine c to 0.2%, and M to better than 0.1%.Next we determine some key properties of the new resonance: the spin and the ratio of decay modes. Thegraviton is a spin-two object. Fig. 3 shows the decay angle of the fermions G→ µµ for the G3 graviton, usingPYTHIA/SIMDET, for 1 ab−1 of data, including CLIC machine background. The typical spin-two structure3cos(theta)0255075100125150175200225-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1JJ Inv. Mass (GeV)Evts/40 GeV010203040506070600 800 1000 1200 1400FIG. 3: (Left) Decay angle distribution of the muons from G3(3200GeV) → µµ; (Right) Invariant jet-jet mass ofG1(1200GeV) produced in G3 → G1G1 and G1 → jet jet.FIG. 4: Two events in a CLIC central detector with decay G3 → G1G1 → four jetsof the decay angle of the resonance is clearly visible.For gravitons as proposed in [7, 8] one expects BR(G→ γγ)/BR(G→ µµ) = 2. With the present SIMDETsimulation we get efficiencies in mass peak (±200 GeV) of 84% and 97% for detecting the muon and photondecay modes, respectively. With cross sections of O(pb), σγγ and σµµ can be determined to better than a percent. Hence the ratio BR(G→ γγ)/BR(G→ µµ) can be determined to an accuracy of 1% or better.Finally, if the CMS energy of the collider is large enough to produce the first three resonances states, one hasthe intriguing possibility to measure the graviton self-coupling via the G3 → G1G1 decay [8]. The dominantdecay mode will be G1 → gluon-gluon or qq¯ → two jets. Fig. 4 shows the resulting spectacular event signature offour jets of about 500 GeV each in the detector (no background is overlaid). These jets can be used to reconstructG1. Fig. 3b shows the reconstructed G1 invariant mass. The histogram does not include background while thedata points include 10 bunch crossings of background overlaid on the signal events. Hence the mass of G1 canbe well reconstructed and is not significantly distorted by the γγ background.In summary a multi-TeV collider, such as CLIC, will allow for a precise determination of the shape and ofmass of the new resonance(s), and of its spin.4√s (GeV)s (fb)11010 210 310 410 51000 2000 3000 4000 5000 6000 7000 800011010 210 31000 1250 1500 1750 2000 2250 2500 2750 3000 3250 350011010 210 31000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500FIG. 5: (Left) The σµµ cross section for different models for TeV scale extra dimensions. (Middle and Right) The σµµcross section before (solid line) and after (dashed line) smearing by the CLIC luminosity spectrum, for two models.III. TEV SCALE MODELSAnother class of models, which leads to a resonance structure in the energy dependence of the two-fermioncross section, are those with a TeV scale extra dimension [10]. In the simplest versions of these theories, onlythe SM gauge fields are in the bulk whereas the fermions remain at one of the two orbifold fixed points; Higgsfields may lie at the fixed points or propagate in the bulk. In such a model, to a good approximation, themasses of the KK tower states are given by Mn = nMc, where Mc = R−1c is the compactification scale, Rc isthe compactification radius. The mass of the lowest lying KK state is constrained to be rather large, i.e. a fewTeV, due to bounds arising from precision measurements[11].The masses and couplings of the KK excitations are compactification scheme dependent and lead to a rathercomplex KK spectrum. Examples of models are shown in Fig. 5. The position of the peaks and the dips andtheir corresponding cross sections and widths can be used to uniquely identify the extra-dimensional model.As an example two of these models were taken and the production cross section was folded with the CLICluminosity spectrum. The results are shown in Fig. 5 for two dip positions, since the peaks are likely to bebeyond the reach of a 3 TeV collider. The structure of the dips is largely kept, but it is smeared out andsomewhat systematically shifted. In any case also here CLIC data will be sensitive to the model parameters,and will allow to disentangle different scenariosIV. CONCLUSIONSThe direct production of KK excitations in the TeV range was studied for CLIC, using examples of modelsbased on RS and TeV scale extra dimensions. The backgrounds at CLIC and its smeared luminosity spectrumare not preventive to make precision measurements of the model parameters. In particular, for the RS model itwas shown that the key discriminating properties of these resonances can be reconstructed and the underlyingmodel parameters can be determined precisely. Hence if KK excitations appear in the two-fermion processescross sections in the TeV range, CLIC will be an ideal tool to study in detail the properties of these resonances.[1] T.G. Rizzo, hep-ph/0108235.[2] The CLIC Study Team, A 3 TeV e+e− linear collider based on CLIC technology, CERN 2000-008.[3] D. Schulte, see http://clicphysics.web.cern.ch/CLICphysics/.[4] M. Pohl and H.J. Schreiber, SIMDET - A parametric Monte Carlo for a TESLA detector, DESY 99-030.[5] T. Sjo¨strand, Comp. Phys. Comm. 82 (1994) 74;PYTHIA 6.2: Physics and Manual Torbjorn Sjostrand, Leif Lonnblad (Lund U.), Stephen Mrenna (UC, Davis),hep-ph/0108264.[6] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).[7] For an overview of the Randall-Sundrum model phenomenology, see H. Davoudiasl, J.L. Hewett and T.G. Rizzo,Phys. Rev. Lett. 84, 2080 (2000); Phys. Lett. B493, 135 (2000); and Phys. Rev. D63, 075004 (2001).[8] H. Davousdiasl and T. Rizzo, Phys. Lett. B512, 100 (2001.)5[9] For a review of new gauge boson physics at colliders and details of the various models, see J.L. Hewett and T.G.Rizzo, Phys. Rep. 183, 193 (1989); A. Leike, Phys. Rep. 317, 143 (1999).[10] See, for example, I. Antoniadis, Phys. Lett. B246, 377 (1990); I. Antoniadis, C. Munoz and M. Quiros, Nucl. Phys.B397, 515 (1993); I. Antoniadis and K. Benalki, Phys. Lett. B326, 69 (1994)and Int. J. Mod. Phys. A15, 4237(2000); I. Antoniadis, K. Benalki and M. Quiros, Phys. Lett. B331, 313 (1994).[11] See, for example, T.G. Rizzo and J.D. Wells, Phys. Rev. D61, 016007 (2000); P. Nath and M. Yamaguchi, Phys.Rev. D60, 116006 (1999); M. Masip and A. Pomarol, Phys. Rev. D60, 096005 (1999); L. Hall and C. Kolda, Phys.Lett. B459, 213 (1999); R. Casalbuoni, S. DeCurtis, D. Dominici and R. Gatto, Phys. Lett. B462, 48 (1999);A. Strumia, Phys. Lett. B466, 107 (1999); F. Cornet, M. Relano and J. Rico, Phys. Rev. D61, 037701 (2000); T.G.Rizzo, Phys. Rev. D61, 055005 (2000) and Phys. Rev. D64, 015003 (2001); C.D. Carone, Phys. Rev. D61, 015008(2000).

Graviton Production at CLIC

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