SUSY at the LHC without Missing P_T
SSUSY at the LHC without Missing P T A. S. Belyaev , , D. I. Kazakov , , , A. Sperling School of Physics & Astronomy, University of Southampton, UK Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, OxonOX11 0QX, UK Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna, Russia. Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia Moscow Institute of Physics and Technology, Dolgoprudny, Russia
Abstract
We consider a specific class of events of the SUSY particle production at theLHC without missing p T . Namely, we discuss the chargino pair production with afurther decay into the W-boson and the neutralino when the masses of the charginoand neutralino differ by 80-90 GeV. In this case, in the final state one has two Wsand missing E T but no missing P T . The produced neutralinos are just boostedalong Ws. For a demonstration we consider the MSSM with non-universal gauginomasses. In this case, such events are quite probable in the region of parameter spacewhere the lightest chargino and neutralino are mostly gauginos. The excess in theW production cross-section reach about 10% over the Standard Model background.We demonstrate that the LHC experiments, which presently measure the W W production cross section at the 8% level can probe chargino mass around 110 GeVwithin the suggested scenario, which is not accessible via other searches. If theprecision of
W W cross section measurement at the LHC will achieve the 3% level,then it would probe chargino masses up to about 150 GeV within the no missing P T scenario. Keywords: super partners, missing energy and momentum, LHC.
Search for R-parity conserving Supersymmetry (SUSY) at colliders is traditionally basedon the events with missing transverse momenta, (cid:54) P T , which naturally appear due tothe escape of the stable lightest supersymmetric particle - LSP. If the mass gap betweendecaying SUSY particles (either strongly or weakly produced) and the LSP is large enough,then the LSP, usually neutralinos, carry considerable momenta. The triggers which aresensitive to (cid:54) P T at the level of hundred GeV will illuminate this signature. Unfortunately,1 a r X i v : . [ h e p - ph ] F e b here is no evidence for signals with (cid:54) P T so far. There are, however, two special cases fordifferent SUSY signals coming from the long-lived particles and events with no missingtransverse momentum.The first case is related to charged particles like charginos which live long enoughto produce the secondary vertex or even to escape the detector before decaying into theStandard Model (SM) particle(s) plus neutralino. In the framework of the MSSM with theSUGRA motivated SUSY breaking this might happen when the masses of the charginoand neutralino are degenerate [1]. The closer the masses the longer is the life time. Tohave the secondary vertex at a few mm or more, one needs the degeneracy smaller thanfew hundreds of MeV. The gauge mediated models are more favourable for the long-livedparticles, and one can easily get the particle to escape the detector undecaying [2]. Bothscenarios, however, require the proper fine-tuning of parameters especially in the SUGRAscenario.The second case is less constrained. If the masses of, say, chargino and neutralinodiffer by 80-90 GeV, then the decay of the chargino into W and the neutralino is possibleand goes with 100% probability. Due to the conservation of energy in the rest frameof the chargino, the decay products are produced almost at rest and in the laboratoryframe they are boosted along W. As a result, the chargino pair production gives rise toan additional W pair production accompanied by boosted neutralinos. These neutralinos,being essentially back to back (at the leading order) along the direction of each W-bosoncarry the energy but do not contribute to missing transverse momentum of the event.Instead, one has the excess of the produced W boson pairs as compared to the StandardModel. Contrary to the usual case, here there will be virtually no contribution to (cid:54) P T from SUSY particles.In this note, we study how probable these events are, how big the parameter spaceis where it happens, and what kind of excess in the W production one might expectfor a reasonable interval of chargino masses. As an example, we consider the MSSMwith non-universal gaugino masses. We would like to note that these events, where (cid:54) P T from SUSY particles does not occur at the tree level, in general could acquire a non-negligible (cid:54) P T in case of an extra hard jet radiated from the initial state quarks. In thiscase, two neutralinos will not be balancing each other and would give a contribution tomissing energy. This W + W − jet + (cid:54) P T signature, which eventually will be suppressed incomparison with the W + W − one, could be still potentially interesting in exploring theSUSY parameter space but is not in the scope of the current paper.One should note that the LHC potential to probe the R-parity conserving SUSYwithout using the missing transverse momenta information has been discussed previouslybut in aspects different from the current study. For example, in [3] the authors haveshown that high lepton multiplicity events coming from the cascade decays of the colouredSUSY partners could provide constraints on the SUSY parameter space without using (cid:54) P T information. In paper [4], which is closer in spirit to our study, the authors usedthe W + W − signature to improve the limit on the light stop quarks production at the2HC. Finally, one should mention the case when the mass gap between the LSP and thenext-to-lightest particle (NLSP) is small, the NLSP still decays promptly in the detectorand the pair production of the NLSP leads to the signature without (cid:54) P T ; actually such aprocess leads to no signature in the detector at all. To probe such a scenario, it becametraditional now to consider the monojet signature , when high- P T jet is radiated from theinitial state quark or gluon and provides a monojet and (cid:54) P T . In our paper we studyconceptually different scenario with no (cid:54) P T signature as a key to probe SUSY at the LHC. (cid:54) P T MSSM sce-nario
In this section, we study the MSSM scenario when m χ ± − m χ ≈ M W and considerchargino production at the LHC with a subsequent decay into W and a neutralino in thewhole relevant parameter space. As an example we take the MSSM with non-universalSUSY breaking parameters [5]. This does not limit our analysis since we do not rely onparticular properties of the MSSM but just try to demonstrate that the advocated eventsare quite probable and the parameter space is not that much fine-tuned.In what follows we impose the following constraint: m χ ± − m χ ≈ M W + 0 ÷ GeV. (1)It can be easily satisfied if both the lightest chargino and neutralino are higgsinos. Thentheir masses are given essentially by µ and are close. However, in this case their interactionwith the light quarks in a proton is suppressed by the smallness of the Yukawa couplings,and the production cross-section is small. Therefore, we choose the other option andconsider the case when both the lightest chargino and neutralino are gauginos. In thiscase their masses are defined by M and M , respectively, and one needs the latter to beclose. This practically excludes the universal scenario where M = M at the GUT scaleand run down to the EW scale reaching the ratio 2:1. For this reason we consider thenon-universal gaugino masses and treat them as free parameters at the EW scale.All together we have the following set of parameters at the EW scale which are essentialfor our analysis: M , M , µ and tan β . We are interested in the region of parameter spacewhere the constraint (1) is satisfied. Besides, we check the chargino production cross-section in comparison with the W production in the SM and look for the regions, wherethe former one gives a few percent enhancement.We compare two processes of the W production: the direct SM one and the onevia chargino decay. The corresponding Feynman diagrams are shown in Fig.1. Theleading order (LO) SM cross-section for the W pair production at the LHC with the cmenergy of 8 TeV and 13 TeV is equal to 35.7 and 67.7 pb, respectively. To evaluate ittogether with the χ + χ − production, we use the CalcHEP 3.6.15 code [9] with the partondistributions MRST2008lo68cl [10] linked to CalcHEP via LHAPDF6 [11] framework. For3 qq_ WW + + −− qq_ WWZ + + − A q qq_ WW+ − ~ qq_ WWZ + − qq_ WW + − A + − q qq_ WW Figure 1: The W production at the LHC: the direct one (top) and the one via the charginodecay (bottom)this evaluation, the renormalisation and factorisation scales were set to µ R = µ F = M W and the EW parameters were set to reproduce G F = 1 . × − GeV − . Our LOresults for the W W production agree with those from [12], where the authors went up tothe NNLO level. They found out that at the LHC energies the NLO order K-factor forthe W production is about 1.5, while the NLO K-factor for chargino pair production forchargino masses of the order of 100 GeV is about 1.35 [13] . Hence, at the NLO the ratioof σ χ + χ − /σ W W will be slightly reduced by a factor of 1 . / . . σ χ + χ − σ W W ≡ σ NLOχ + χ − σ NLOW W = σ LOχ + χ − σ LOW W × K NLOχ + χ − K NLOW W (cid:39) σ LOχ + χ − σ LOW W × . http://hepmdb.soton.ac.uk/hepmdb:0611.0028 . One should note that the present theoretical accuracy of pp → W + W − production at the LHC as defined by its NNLO results (59.84pb +2 . − . [12])is at about 2%, while ATLAS (71 . ± . . ± . σ excess in W W production. Eventually, thisexcess is not conclusive; however, it provides us with some source of speculation. Inparticular, we would like to verify if MSSM could provide enough contribution from χ +1 χ − with no (cid:54) P T kinematics to explain this excess quantitatively.To calculate the cross-section in the case of chargino decay, we actually calculatethe chargino production cross-section and assume that the chargino is produced on shell4nd subsequently decays into W and the neutralino provided m χ ± ≥ m W + m χ . Indoing so we perform the scan of the whole relevant parameter space mentioned above: M [ − −
500 GeV], M [10 −
500 GeV], µ [10 − β [10 − (cid:54) P T (see e.g. [16]).
100 120 140 160 180 200 M χ ± (GeV) σ χ + χ − / σ WW × % M W +10 GeV >M χ ± − M χ >M W M ( G e V )
100 120 140 160 180 200 M χ ± (GeV) σ χ + χ − / σ WW × % M W +10 GeV >M χ ± − M χ >M W µ ( G e V ) Figure 2: σ χ + χ − σ WW at the LHC@8TeV versus chargino mass as a colour map of M (left)and µ (right).The results of the scan are shown in Fig. 2, where we present the ratio σ χ + χ − σ WW at theLHC@8TeV versus chargino mass as a colour map of M (left) and µ (right). One can seethat the chargino can contribute up to about 10% to the W + W − production at the LHCif chargino mass is of the order of 100 GeV and just above the LEP2 constraints. Onecan also see from this figure that σ χ + χ − achieves its highest value (for a given charginomass) for minimal M around 100 GeV and high values of µ parameter, µ (cid:38)
400 GeV.In this parameter space chargino has a large wino component and, respectively, largecoupling to the Z-boson, the main mediator of the chargino pair production. The largestwino component of the chargino defines the upper band of its production cross section.On the contrary, when µ is small and M is large, the chargino has a dominant higgsinocomponent, suppressed coupling to Z-boson and, respectively, a low production crosssection indicated by the lower band in Fig. 2.In Fig. 3, we present the ratio M /M versus M as a scatter plot from our scan withthe colour map indicating the ratio σ χ + χ − σ WW . One can see from this plot that the value ofthe ratio σ χ + χ − σ WW above a few percent is achievable only for M /M > M /M (cid:39) − m χ + is just above the LEP2 constraints and m χ isabout 20 GeV. It is clear that such a scenario cannot be realized for universal gaugino5
00 50 0 50 100 M (GeV) M / M M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × % Figure 3: The ratio M /M versus M with the colour map of σ χ + χ − σ WW , assuming theconstraint (1) is satisfied.masses at the GUT scale which gives M /M (cid:39) µ andtan β ; however, if one wants to increase the cross-section one is pushed to the edges ofparameter space towards smaller values. These regions are favoured by small chargino andneutralino masses since the cross section of chargino production is inversely proportionalto the latter. Note, however, that the ratio of M χ + /M χ is constrained to the narrowband where their mass difference satisfies the constraint (1). This band is linear but doesnot give the fixed mass ratio since it does not go through the origin of the coordinateplane. For small masses one finds that the neutralino mass is very small, which is stillnot excluded by modern data.There is no real preference for any particular values of tan β coming from constraint (1).This preference will appear if one considers the other constraints, in particular, the amountof the Dark matter [6]. The µ parameter might also vary in a wide range but is typicallybigger than M and even M that provides the gaugino origin of the lightest charginoand neutralino. Thus, one can see that the fulfillment of the requirement (1) is not thatrestrictive and does not require much fine-tuning. One has at least 4 free parameters whichcan be used to get into the desired region. Even more possibilities appear in extendedmodels. We use here the MSSM as an illustration of the most constrained model. Ofcourse, if one wants to apply more constraints, they might get into contradiction withthis one. For instance, the LHC limits already excluded a large part of the parameter6
00 50 0 50 100 M (GeV) M ( G e V ) M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × % M χ (GeV) M χ ± ( G e V ) M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × %
100 50 0 50 100 M (GeV) µ ( G e V ) M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × %
100 120 140 160 180 200 M (GeV) µ ( G e V ) M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × %
100 50 0 50 100 M (GeV) t a n β M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × %
100 120 140 160 180 200 M (GeV) t a n β M W +10 GeV >M χ ± − M χ >M W − − σ χ + χ − / σ WW × % Figure 4: The 2-dimensional scatter plots for various pairs of the model parameters andphysical masses from the scan of the low energy MSSM parameter space assuming thatconstraint (1) is satisfied. The colour map indicates the ratio of the cross-sections ofchargino production in the MSSM to the cross-section of W production in the SM [email protected]. However, on the other hand, the LHC limits are based on the events with (cid:54) P T and might miss some opportunities. One can think of a model free case and just look for7M β M M µ m χ m χ + σ T eVχ + χ − ( pb ) σ T eVχ + χ − ( pb )1 20 20 100 400 19.02 105.1 3.73 7.192 40 22 100 1000 21.65 110.0 3.23 6.223 10 26 105 1400 25.33 115.0 2.74 5.324 10 32 110 1000 31.12 119.6 2.34 4.595 20 40 115 800 39.23 125.2 1.96 3.876 10 44 120 1000 43.00 130.4 1.68 3.357 10 48 125 800 46.80 135.0 1.47 2.948 20 54 130 600 52.85 140.0 1.27 2.55Table 1: The cross-section of the chargino production at various benchmark points at theLHC at 8 and 13 TeV. The masses of the chargino and the neutralino as well as valuesfor M , M and µ parameters are given in GeV
105 110 115 120 125 130 135 140 145 σ χ + χ − σ WW ( % ) m χ + (GeV) 1 2 3 4 5 6 7 8BM LHC@8TeVLHC@13TeV
Figure 5: The ratio of the W production cross-section via the chargino decay to the SMcross-section at the LHC for the cm energy of 8 and 13 TeV for various benchmark pointsfrom Table 1.advocated events. The chargino production cross-section in its turn depends on its massand the mixings. As an illustration, we calculate it for several benchmark points shown inTable 1 for the LHC energies of 8 and 13 TeV. The ratio σ χ + χ − σ WW for the benchmark pointsfrom Table 1 is visualised in Fig. 5, where one can see that the W production cross-sectionvia the chargino decay varies between 9 and 4% for the chargino mass range between 105and 140 GeV. The cross-section σ χ + χ − is close to its maximum when µ > M . In this8ase the σ χ + χ − σ WW is defined mainly by the chargino mass and its decrease is caused mainlyby the parton distributions. Thus, taking higher masses one gets a smaller cross-sectionand hence a smaller excess in the W production.We would like to stress once more that our calculations within the MSSM serve as anillustration of the possibility of the SUSY production process without missing P T . Precisevalues of the cross section and the position of the benchmark points in parameter spaceare not essential. In a more complicated model these numbers may change but the verypossibility of the advocated process remains. We have explored the contribution of SUSY particles to the
W W production with no (cid:54) P T signature. We demonstrate that the LHC experiments which presently measure the W W production cross section at the 8% level can probe chargino masses around 110 GeVwithin the suggested scenario, which is not accessible via other searches. If the precisionof the
W W cross-section measurement at the LHC will achieve 3% level, then it wouldprobe the chargino masses up to about 150 GeV within the no missing P T scenario.This excess of Ws produced via the chargino decay might be noticeable. The recentdata on the diboson production with a subsequent decay into muons has shown that allresults are compatible with the theoretical expectation within the statistical and system-atic uncertainties though some excess with respect to the SM expectations at the level oftwo σ is observed by the ATLAS collaboration [14]. This might be the usual fluctuationbut equally might indicate the manifestation of a new physics. The detailed analysis ofthese data as well as the new run results will clear the case. However, this kind of pro-cesses is precisely the one where one can expect the new physics to show up. PossibleSUSY interpretation of this excess was considered in a sequence of papers [17] and itwas shown that the data from both experiments can be better fitted with the inclusionof electroweak gauginos with masses of O(100) GeV. We have demonstrated that in thecase of low energy supersymmetry, these processes are quite natural. The mass range ofthe electroweak gauginos might be even higher being well within the limits of the LHCsearches. They might come with as well as without missing p T . The latter possibility,which is the main concern of our paper, is less probable but is quite possible and shouldbe taken into account in analysis. Acknowledgements
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