Investigating gluino production at the LHC
aa r X i v : . [ h e p - ph ] M a y Investigating gluino production at the LHC
C. Brenner Mariotto a and M.C. Rodriguez a a Departamento de F´ısica, Funda¸c˜ao Universidade Federal do Rio GrandeCaixa Postal 474, CEP 96201-900, Rio Grande, RS, Brazil
Gluinos are expected to be one of the most massive sparticles (supersymmetric partners of usualparticles) which constitute the Minimal Supersymmetric Standard Model (MSSM). The gluinos arethe partners of the gluons and they are color octet fermions, due this fact they can not mix with theother particles. Therefore in several scenarios, given at SPS convention, they are the most massiveparticles and their nature is a Majorana fermion. Therefore their production is only feasible at avery energetic machine such as the Large Hadron Collider (LHC). Being the fermion partners of thegluons, their role and interactions are directly related with the properties of the supersymmetricQCD (sQCD). We review the mechanisms for producing gluinos at the LHC and investigate thetotal cross section and differential distributions, making an analysis of their uncertainties, such asthe gluino and squark masses, as obtained in several scenarios, commenting on the possibilities ofdiscriminating among them.
PACS numbers: 12.60.Jv; 14.80.Ly, 13.85.Qk
Although the Standard Model (SM) [1], based on thegauge symmetry SU (3) c ⊗ SU (2) L ⊗ U (1) Y describes theobserved properties of charged leptons and quarks it isnot the ultimate theory. However, the necessity to gobeyond it, from the experimental point of view, comesat the moment only from neutrino data. If neutrinos aremassive then new physics beyond the SM is needed.Although the SM provides a correct description of vir-tually all known microphysical nongravitacional phenom-ena, there are a number of theoretical and phenomeno-logical issues that the SM fails to address adequately [2]: • Hierarchy problem; • Electroweak symmetry breaking (EWSB); • Gauge coupling unification.The main sucess of supersymmetry (SUSY) is in solvingthe problems listed above.SUSY has also made several correct predictions [2]: • SUSY predicted in the early 1980s that the topquark would be heavy; • SUSY GUT theories with a high fundamental scaleaccurately predicted the present experimental valueof sin θ W before it was mesured; • SUSY requires a light Higgs boson to exist.Together these success provide powerful indirect evidencethat low energy SUSY is indeed part of correct descrip-tion of nature.Certainly the most popular extension of the SM is itssupersymmetric counterpart called Minimal Supersym-metric Standard Model (MSSM) [3]. The main motiva-tion to study this models, is that it provides a solutionto the hierarchy problem by protecting the electroweakscale from large radiative corrections [4, 5]. Hence the mass square of the lightest real scalar boson has an up-per bound given by M h ≤ ( M Z + ǫ ) GeV (1)where M Z is the Z mass. Therefore the CP even, lightHiggs h , is expected lighter than Z at tree level ( ǫ = 0).However, radiative corrections rise it to 130 GeV [6].In the MSSM [3], the gauge group is SU (3) C ⊗ SU (2) L ⊗ U (1) Y . The particle content of this modelconsists in associate to every known quark and leptona new scalar superpartner to form a chiral supermulti-plet. Similarly, we group a gauge fermion (gaugino) witheach of the gauge bosons of the standard model to forma vector multiplet. In the scalar sector, we need to in-troduce two Higgs scalars and also their supersymmetricpartners known as Higgsinos. We also need to impose anew global U (1) invariance usually called R -invariance,to get interactions that conserve both lepton and baryonnumber (invariance).Other very popular extensions of SM are Left-Rightsymmetric theories [7], which attribute the observed par-ity asymmetry in the weak interactions to the sponta-neous breakdown of Left-Right symmetry, i.e. gener-alized parity transformations. It is characterized by anumber of interesting and important features [8]:1. it incorporates Left-Right (LR) symmetry whichleads naturally to the spontaneous breaking of par-ity and charge conjugation;2. incorporates a see-saw mechanism for small neu-trino masses.On the technical side, the left-right symmetric modelhas a problem similar to that in the SM: the masses ofthe fundamental Higgs scalars diverge quadratically. Asin the SM, the Supersymmetric Left-Right Model (SU-SYLR) can be used to stabilize the scalar masses andcure this hierarchy problem.Another, maybe more important raison d’etre for SU-SYLR models is the fact that they lead naturally to R-parity conservation [9]. Namely, Left-Right models con-tain a B − L gauge symmetry, which allows for this pos-sibility [10]. All that is needed is that one uses a versionof the theory that incorporates a see-saw mechanism [11]at the renormalizable level.The supersymmetric extension of left-right models[12, 13] is based on the gauge group SU (3) C ⊗ SU (2) L ⊗ SU (2) R ⊗ U (1) B − L . On the literature there are two dif-ferent SUSYLR models. They differ in their SU (2) R breaking fields: one uses SU (2) R triplets [12] (SU-SYLRT) and the other SU (2) R doublets [13] (SU-SYLRD). Since we are interested in studying only thestrong sector, which is the same in both models, the re-sults we are presenting here hold in both models.As a result of a more detailed study, we have shownthat the Feynman rules of the strong sector are the samein both MSSM and SUSYLR models [14]. The relevantFeynman rules for the gluino production are:- Gluino-Gluino-Gluon: − g s f bac ;- Quark-Quark-Gluon: − ıg s T ars γ m (usual QCD);- Squark-Squark-Gluon: − ıg s T ars ( k i + k j ) m , where k i,j are the momentum of the incoming and outcomingsquarks, respectively;- Quark-Squark-Gluino: − ı √ g s ( LT ars − RT ars ) ,where L = (1 − γ ) , R = (1 + γ ) . The “Snowmass Points and Slopes” (SPS) [15] are a setof benchmark points and parameter lines in the MSSMparameter space corresponding to different scenarios inthe search for Supersymmetry at present and future ex-periments. The aim of this convention is reconstructingthe fundamental supersymmetric theory, and its breakingmechanism, from the data. The points SPS 1-6 are Mini-mal Supergravity (mSUGRA) model, SPS 7-8 are gauge-mediated symmetry breaking (GMSB) model, and SPS9 are anomaly-mediated symmetry breaking (mAMSB)model ([15, 16, 17]). Each set of parameters leads todifferent gluino and squark masses, wich are the only rel-evant parameters in our study, and are shown in Tab.(I).Scenario m ˜ g ( GeV ) m ˜ q ( GeV )SPS1a 595.2 539.9SPS1b 916.1 836.2SPS2 784.4 1533.6SPS3 914.3 818.3SPS4 721.0 732.2SPS5 710.3 643.9SPS6 708.5 641.3SPS7 926.0 861.3SPS8 820.5 1081.6SPS9 1275.2 1219.2
TABLE I: The values of the masses of gluinos and squarks inthe SPS scenarios. qq ggk k p p qq ggk k p p qq ggk k p p (a) gg ggk k p p gg ggk k p p gg ggk k p p (b) qg qgk k p p qg qgk k p p qg qgk k p p (c)FIG. 1: Feynman diagrams for single (a,b,c) and double (a,b)gluino pair production. Gluino and squark production at hadron colliders oc-curs dominantly via strong interactions. Thus, their pro-duction rate may be expected to be considerably largerthan for sparticles with just electroweak interactionswhose production was widely studied in the literature[18, 19]. Since the Feynman rules of the strong sector arethe same in both MSSM and SUSYLR models, the dia-grams that contribute to the gluino production are thesame in both models.In the present contribution we study the gluino pro-duction in pp collisions at LHC energies. To make aconsistent comparison and for sake of simplicity, we re-strict ourselves to leading-order (LO) accuracy, where thepartonic cross-sections for the production of squarks andgluinos in hadron collisions were calculated at the Bornlevel already quite some time ago [20]. The correspond-ing NLO calculation has already been done for the MSSMcase [21], and the impact of the higher order terms ismainly on the normalization of the cross section, whichcould be taken in to account here by introducing a Kfactor in the results here obtained [21].The LO QCD subprocesses for single gluino productionare gluon-gluon and quark-antiquark anihilation ( gg → ˜ g ˜ g and q ¯ q → ˜ g ˜ g ), and the Compton process qg → ˜ g ˜ q ,as shown in Fig. 1. For double gluino production onlythe anihilation processes contribute, obviously. Thesetwo kinds of events could be separated, in principle, byanalysing the different decay channels for gluinos andsquarks [18, 19].Incoming quarks (including incoming b quarks) are as-sumed to be massless, such that we have n f = 5 lightflavours. We only consider final state squarks correspond-ing to the light quark flavours. All squark masses aretaken equal to m ˜ q . We do not consider in detail topsquark production where these assumptions do not holdand which require a more dedicated treatment [22].The invariant cross section for single gluino productioncan be written as [20] E dσd p = X ijd Z x min dx a f ( a ) i ( x a , µ ) f ( b ) j ( x b , µ ) x a x b x a − x ⊥ (cid:16) ζ +cos θ θ (cid:17) d ˆ σd ˆ t ( ij → ˜ gd ) , (2)where f i,j are the parton distributions of the incomingprotons and d ˆ σd ˆ t is the LO partonic cross section [20] forthe subprocesses involved. The identified gluino is pro-duced at center-of-mass angle θ and transverse momen-tum p T , and x ⊥ = p T √ s . The kinematic invariants of thepartonic reactions ij → ˜ g ˜ g, ˜ g ˜ q are thenˆ s = x a x b s, ˆ t = m g − x a x ⊥ s (cid:18) ζ − cos θ θ (cid:19) , ˆ u = m g − x b x ⊥ s (cid:18) ζ + cos θ θ (cid:19) . (3)Here x b = 2 υ + x a x ⊥ s (cid:16) ζ − cos θ sin θ (cid:17) x a s − x ⊥ s (cid:16) ζ +cos θ sin θ (cid:17) ,x min = 2 υ + x ⊥ s (cid:16) ζ +cos θ sin θ (cid:17) s − x ⊥ s (cid:16) ζ − cos θ sin θ (cid:17) ,ζ = m g sin θx ⊥ s ! / ,υ = m d − m g , (4)where m ˜ g and m d are the masses of the final-state partonsproduced. The center-of-mass angle θ and the differentialcross section above can be easilly written in terms of thepseudorapidity variable η = − ln tan( θ/
500 1000 1500 2000 m gl (GeV) σ (f b ) m sq =m gl , µ =m gl m sq =2m gl , µ =(m +m )/2 Gluino production at LHC g g -> gl + gl, q qb -> gl + gl, q g -> gl + sq, CTEQ6L PDF
FIG. 2: The total LO cross section for gluino production atthe LHC as a function of the gluino masses. Parton densities:CTEQ6L, with two assumptions on the squark masses andchoices of the hard scale. p T (GeV) -2 -1 d σ / dp T d η (f b / G e V ) SPS 1aSPS 6SPS 5SPS 4SPS 2SPS 8SPS 3SPS 1bSPS 7SPS 9
Double gluino production at the LHC g g -> gl gl, q qb -> gl gl
FIG. 3: The LO p T distributions for gluino production at theLHC for the different SPS points [15, 16]. We use CTEQ6Lparton densities, and µ = m g + p T as a hard scale. process) is done in a more detailed publication[14]. Theresults obtained will show the possibility of discriminat-ing among the different SPS scenarios.In Figs.3 and 4 we present the transverse momentumand pseudorapidity distributions for double gluino pro-duction at LHC energies. The results show a similarbehavior of the p T and η dependencies in all scenar-ios, but a huge diference in the magnitude for differ-ent scenarios - SPS1a gives the bigger values, SPS9 thesmallest one. Also, we find very close values for SPS1b,SPS3 (mSUGRA) and SPS7 (GMSB), which makes diffi-cult to discriminate between these mSUGRA and GMSBmodels. The same occurs for SPS5 and SPS6 (bothmSUGRA). -3 -2 -1 0 1 2 3 η d σ / dp T d η (f b ) SPS 1aSPS 6SPS 5SPS 4SPS 2SPS 8SPS 3SPS 1bSPS 7SPS 9
Double gluino production at the LHC g g -> gl gl and q qb -> gl gl
FIG. 4: The LO pseudorapidity distributions for gluino pro-duction at the LHC for the different SPS points [15, 16]. Weuse CTEQ6L parton densities, and µ = m g + p T as a hardscale. To conclude, we have investigated gluino productionat the LHC, which might discover supersymmetry overthe next years. Gluinos are color octet fermions and playa major role to understanding sQCD. Because of theirlarge mass as predicted in several scenarios, up to now the LHC is the only possible machine where they couldbe found.Regarding the strong sector, the Feynman rules are thesame for both MSSM and SUSYLR models. Therefore,our results for gluino production are equal in both mod-els. Besides, our results depend on the gluino and squarkmasses and no other SUSY parameters. Since the massesof gluinos come only from the soft terms, measuring theirmasses can test the soft SUSY breaking approximations.We have considered all the SPS scenarios and showed thecorresponding differences on the magnitude of the pro-duction cross sections. From this it is easy to distinguishmAMSB from the other scenarios. However, it is not soeasy to distinguish mSUGRA from GMSB depending onthe real values of masses of gluinos and squarks (if SPS1band SPS7, provided the gluino and squark masses are al-most similar in these two cases). For the other cases,such discrimination can be done.
Acknowledgments
This work was partially financed by the Brazil-ian funding agency CNPq, CBM under contract num-ber 472850/2006-7, and MCR under contract number309564/2006-9. [1] S. L. Glashow,
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