We show that the LHC will be able to differentiate between a four-dimensional
model with quantum gravity at ~1 TeV where the (massless) graviton becomes
strongly coupled to standard model particles at 1 TeV and brane world type
models with a large extra-dimensional volume and massive Kaluza-Klein
gravitons. We estimate that the 14 TeV LHC could put a limit of the order of ~5
TeV on the four dimensional Planck mass in a model independent way.Comment: 9 page

Antoniadis

Arkani-Hamed

Calmet

Cheung

Dimopoulos

Dvali

Georgi

Giudice

Larsen

Mirabelli

Nadolsky

Priscila de Aquino

Randall

Rizzo

Thomas G. Rizzo

Vacavant

Xavier Calmet

English

arXiv

We show that the LHC will be able to differentiate between a four-dimensional
model with quantum gravity at ~1 TeV where the (massless) graviton becomes
strongly coupled to standard model particles at 1 TeV and brane world type
models with a large extra-dimensional volume and massive Kaluza-Klein
gravitons. We estimate that the 14 TeV LHC could put a limit of the order of ~5
TeV on the four dimensional Planck mass in a model independent way.
 Comment: 9 page

Calmet, Xavier

de Aquino, Priscila

Rizzo, Thomas G.

DIAL UCLouvain

arXiv:0910.1535v1  [hep-ph]  8 Oct 2009SLAC-PUB-13771CP3-09-45Massless versus Kaluza-Klein Gravitons at the LHCXavier Calmet1a, Priscila de Aquino2b,c and Thomas G. Rizzo 3da Physics and Astronomy, University of Sussex,Falmer, Brighton, BN1 9QH, UKb Universite´ Catholique de Louvain, CP3,2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgiumc Katholieke Universiteit Leuven, ITP,Celestijnenlaan 200D - Bus 2415, B-3001 Leuven, Belgiumd SLAC National Accelerator Laboratory,2575 Sand Hill Rd., Menlo Park, CA, 94025, USAAbstractWe show that the LHC will be able to differentiate between a four-dimensional modelwith quantum gravity at ∼ 1 TeV where the (massless) graviton becomes stronglycoupled to standard model particles at 1 TeV and brane world type models with alarge extra-dimensional volume and massive Kaluza-Klein gravitons. We estimate thatthe 14 TeV LHC could put a limit of the order of ∼ 5 TeV on the four dimensionalPlanck mass in a model independent way.1x.calmet@sussex.ac.uk2priscila@itf.fys.kuleuven.be3rizzo@slac.stanford.eduIt is now well understood that the energy scale at which quantum gravitational effectsbecome strong could be much lower than naively estimated using dimensional analysis argu-ments. For example in models with a brane world and a large extra dimensional volume [1,2]or in four dimensional models with a large hidden sector of some 1033 particles [3]4 , thePlanck mass could be near 1 TeV and thus in reach of colliders such as the Tevatron or theLHC. In this paper we compare the phenomenology of the extra-dimensional brane worldmodels (i.e., ADD type models) with that of the four-dimensional one. In particular weshow that the LHC can differentiate between the two scenarios. Here we follow the strat-egy developed in [6] to differentiate the phenomenology of Kaluza-Klein gravitons in ADDmodels from that of unparticles [7, 8].The specific four-dimensional model discussed in [3] is rather different at the theoreticallevel from the well known ADD model. Gravity can become strong in four dimensions ifthere is a large hidden sector that only interacts gravitationally with the standard model.This large hidden sector will contribute to the renormalization group running of Newton’sconstant. If the new particles in this sector have spin 0 and/or 1/2 the running of Newton’sconstant is such that it becomes significantly larger at lower energy. For 1033 new particlesone getsMP (1 TeV) ∼ 1 TeV. The masses of these new particles determine the energy scale atwhich the running of Newton’s constant starts, for example one could choose mi ∼ 100 GeV.In such a case most of the running of the Planck mass (equivalently of Newton’s constant)occurs close to 1 TeV. One can thus approximate the running of the reduced Planck massby a step function: for µ < 1TeV, M(µ) = 2.4 × 1018 GeV, while for µ ≥ 1TeV, M(µ) ∼ 1TeV. The phenomenology of this model is then found to be rather different from that ofADD since strong gravity cuts off at the TeV scale. For example, there are no Kaluza-Kleinexcitations of the graviton and virtual gravitons will decay massively to the hidden sectorand are thus leading to a missing energy signal. It has been suggested in [9] to search fora monojet plus missing energy as a signature of this model at the LHC. This is, however,also one of the familiar smoking gun signals of the ADD scenario and thus it is importantto establish that the LHC could differentiate between the two models. Furthermore, in caseof non-observation of the monojet + missing energy signals, one could use data from theLHC to place a corresponding lower bound on the value of the Planck mass (i.e. the scale atwhich quantum gravitational effects become important). It is the aim of the present paperto establish these two points.54See also [4] for another discussion of the value of the Planck mass in models with a large hidden sector.In their approach it is not clear how the value of the Planck mass depends on the spin of the particles in thehidden sector. However, reliable perturbative calculations [5] clearly show a spin dependence: spin 0 and1/2 particles lower the Planck mass, while spin 1 particles increase it.5Also, unlike in the ADD case, the exchange of these massless gravitons does not lead to effective dim-8contact interactions with an associated characteristic TeV scale. Furthermore, there will be no observable1The production of jets with large ET recoiling against a massless graviton G can arisefrom the parton subprocesses q+q¯ → G+g, q+g → q+G, q¯+g → q¯+G, and g+g → g+G ina manner similar to that in ADD. However, the expressions for the corresponding subprocesscross-sections are different from those found in the ADD model.The leading order contributions at the parton level for this four dimensional model havebeen calculated and presented in [9]. The polarization and color averaged cross section forq + q¯ → g +G is given bydσd cos θ=172pig2sM¯(µ)2(s2 + 2t2 + 2tss2), (1)where g2s = 4piαs is the usual strong coupling constant, hereafter evaluated at the scale ofthe jet ET , M¯(µ) is the reduced Planck mass such that Newton’s constant is given by GN =(4piM¯2)−1 and where s and t are the subprocess Mandelstam variables: t = −1/2s(1−cos θ).The cross sections for q + g → q +G and q¯ + g → q¯ +G are given bydσd cos θ= −g2s(2s2 + 2st+ t2)192piM¯(µ)2st. (2)The corresponding matrix element can be obtained using crossing symmetry from thatof the transition q + q¯ → G+ g. Finally we also obtain the cross section for g + g → g +Gwhich is given bydσd cos θ= − 3g2s(s2 + st+ t2)2128piM¯(µ)2s2t(s+ t). (3)Note that all quarks are treated as massless in these expressions. Recall that these crosssections are essentially zero below the√s = MP threshold. In the case of ADD, the partonlevel cross-sections have been given in [10] and we quote them here for comparison purposesfor KK gravitons of mass m. The cross section q + q¯ → g + GKK where GKK is an ADDKaluza-Klein graviton is given by:dσd cos θ(q + q¯ → g +GKK) = 1144pig2sM¯211−m2/s[(2− 4ut(s−m2)2 )(1 +(m2s)4)(4)+(2(s−m2)24ut− 5 + 4 4ut(s−m2)2)m2s(1 +(m2s)2)++6(u− ts−m2)2 (m2s)2],alteration in Newtonian Gravity observable in table top experiments as may be possible with ADD in thecase of 2 extra dimensions.2where here s, t, u are the Mandelstam variables where we have: t, u = −1/2s(1−m2/s)(1∓cos θ). The cross section for q + g → q + GKK can be obtained from this expression bycrossing s↔ t:dσd cos θ(q + g → q +GKK) = g2s384piM¯2(−t/s)(1−m2/s)(1−m2/t)2 × (5)×[(2− 4us(t−m2)2 )(1 +(m2t)4)+(2(t−m2)24us− 5 + 4 4us(t−m2)2)m2t(1 +(m2t)2)++6(s− ut−m2)2 (m2t)2].As in the massless case, the cross section for q¯ + g → q¯ + GKK is also the same as thatof q + g → q +GKK . For the process g + g → g +GKK, one findsdσd cos θ(g + g → g +GKK) = 316piαsGN(1−m2/s)(1− cos2 θ) × (6)[(3 + cos2 θ)2(1 +(m2s)4)− 4(7 + cos4 θ)m2s(1 +(m2s)2)+6(9− 2 cos2 θ + cos4 θ)(m2s)2].It is easy to see that one recovers the massless graviton case by taking the mass of the KKgraviton to zero. Note that in the ADD case, to obtain the collider cross sections, one has toalso perform an integration over the KK-mass distributions as well as the usual integrationover the parton densities. Of course in the case of the four dimensional model no KK sum isrequired. To be specific we will employ the CTEQ6.6 parton distributions [11] in obtainingthe results obtained below.Using the partonic cross sections above we can employ a modified version of the codedeveloped for [6], and can then generate events for the 14 TeV LHC for both the ADD and thefour dimensional models as well as for the the standard model background. Here, followingRef. [12], we expect this background to be dominated by the production of Z plus a singlejet with the Z decaying into pairs of neutrinos. This background can be much reduced byrequiring a missing energy and/or jet energy cut of at least 500 GeV and demanding that thejet to be central |ηj| < 3. The results of our direct comparison of the ADD predictions withthose of the four dimensional model assuming, e.g., that MP = 1 TeV can be found in Fig.1. Here we see that the two new physics models predict monojet ET distributions which arereasonably dissimilar in overall shape. The falling four dimensional model monojet spectrum3above the√sˆ = MP threshold is seen to be somewhat softer than the corresponding ADDmodel prediction for any number of extra dimensions.From Figs.2 and 3 we can obtain an estimate of the search reach for the four dimensionalmodel at the 14 TeV LHC of ≃ 5 TeV assuming an integrated luminosity of 100 fb−1. Herewe also see some unusual features in these distributions associated with the four dimensionalmodel which are absent from the case of ADD which are due to the cross section threshold at√sˆ = MP . Unlike for the ADD case, whose ET and EcutT distributions fall monotonically, thethreshold in the four dimensional model cross section naturally leads to structure in thesecorresponding distributions. This added kink-like structure is a clear aid in distinguishingthe predictions of these two classes of models at the LHC as can easily be seen from thesefigures. For the case of the EcutT distribution we see that it is essentially flat until the valueEcutT = 0.5MP is reached and then falls monotonically. On the otherhand, the ET distributionrises below the value of ET = 0.5MP at which point a peak occurs. At higher values of ETthe distribution fall monotonically. These are quite distinctive indications of a cutoff in thecross section at a fixed value of√sˆ and would allow us to extract this value directly fromthe LHC experimental data.Here we have focussed on one aspect of quantum gravity phenomenology at the LHC.Other interesting signatures are small semi-classical black holes [13] or small non-thermalblack holes [14]. Although small black holes would be easier to observe than the missingenergy signals discussed above, the theoretical framework typically used to discuss the for-mation of small holes at the LHC is less reliable than the one used here for the emissionof gravitons which relies on the well understood expansion of the Hilbert-Einstein actionaround the Minkowski metric. This approach thus assumes very little about the nature ofquantum gravity and the bounds derived that way will therefore be much more reliable thanusing small black holes.The LHC will start to operate in the coming months. Although it may take time to reachits design energy and luminosity, it is quite remarkable to realize that once does it will beable to probe not only whether the solution to the hierarchy problem is based on low scalequantum gravity, but it will also give us the possibility to learn whether a low Planck mass isdue to large extra-dimensions or a large hidden sector with only four space-time dimensions.The results presented in this work will be useful even if the solution to the gauge hierarchyproblem is not based on gravity. In that case, the LHC will be able to set the tightest limit todate on the value of the energy scale at which quantum gravitational effects become strongand this in a model independent way.Acknowledgments: The work of TGR was supported in part by the Department of Energy,4Figure 1: This figure shows the shape of the EminT distribution counting the number ofmonojet events at the 14 TeV LHC assuming a luminosity of 100 fb−1 above a EminT cut of500 GeV and requiring a central jet |ηj| < 3. The yellow histogram is the expected standardmodel background as discussed in the text while the red and higher histograms are for theADD model with the number of extra dimensions being 2,3,4, etc. The lower solid blackhistogram is for the four dimensional model with MP=1 TeV. The ADD results were in eachcase adjusted by varying their associated Planck scale to produce the same result as does thefour dimensional model at EminT = 500 GeV in order to show the relative shapes for thesedistributions.5Figure 2: This figure for the 14 TeV LHC shows the event rate for the standard modeljet+missing energy background as a function of the cut on the jet ET in yellow as well as thefour dimensional model predictions for the cases MP=1(2,3,4,5,6) TeV from top to bottomin red, green, blue,... and requiring that the existence of a threshold at√sˆ = MP . From thisfigure, one can deduce that the search reach for the four dimensional model at the LHC is ≃5 TeV for a luminosity =100 fb−1. The shape of the signal histograms with the requirementabove are quite different than those for ADD due to the vanishing of the cross section atsmall sˆ. Note the shape change at EminT = 0.5MP which is a result of this cross sectionthreshold that is absent in the ADD model.6Figure 3: This figure shows the monojet ET distributions at the 14 TeV the LHC assuminga luminosity of 100 fb−1. The histograms are as labeled as in the previous figure. Note thekink-like structure in the four dimensional model distributions at ET = 0.5MP which is aresult of the cross section threshold that is absent in the ADD model.7Contract DE-AC02-76SF00515.References[1] N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 429, 263 (1998)[arXiv:hep-ph/9803315];[2] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) [arXiv:hep-ph/9905221].[3] X. Calmet, S. D. H. Hsu and D. Reeb, Phys. Rev. D 77, 125015 (2008) [arXiv:0803.1836[hep-th]].[4] G. R. Dvali, G. Gabadadze, M. Kolanovic and F. Nitti, Phys. Rev. D 65, 024031 (2002)[arXiv:hep-th/0106058]; G. Dvali, arXiv:0706.2050 [hep-th]; G. Dvali and M. Redi, Phys.Rev. 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Massless versus Kaluza-Klein Gravitons at the LHC

We show that the LHC will be able to differentiate between a four-dimensional model with quantum gravity at ~ 1 TeV where the (massless) graviton becomes strongly coupled to standard model particles at 1 TeV and brane world type models with a large extra-dimensional volume and massive Kaluza–Klein gravitons. We estimate that the 14 TeV LHC could put a limit of the order of ~ 5 TeV on the four-dimensional Planck mass in a model independent way.status: publishe

Rizzo, Thomas G

Lirias

Physics Letters B

Massless versus Kaluza-Klein gravitons at the LHC

We show that the LHC will be able to differentiate between a four-dimensional model with quantum gravity at not, vert, similar1 TeV where the (massless) graviton becomes strongly coupled to standard model particles at 1 TeV and brane world type models with a large extra-dimensional volume and massive Kaluza-Klein gravitons. We estimate that the 14 TeV LHC could put a limit of the order of not, vert, similar5 TeV on the four-dimensional Planck mass in a model independent way

Xavier Calmet (4462561)

Priscila de Aquino (16061114)

Thomas G Rizzo (16079051)

Sussex Research Online

Crossref

http://dx.doi.org/10.1016/j.physletb.2009.11.045

Massless versus Kaluza-Klein Gravitons at the LHC

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DIAL UCLouvain

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