Signatures of Resonant Super-Partner Production with Charged-Current Decays
aa r X i v : . [ h e p - ph ] S e p RU-NHETC-2011-07
Signatures of Resonant Super-PartnerProduction with Charged-Current Decays
Can Kilic and
Scott Thomas
New High Energy Theory CenterDepartment of PhysicsRutgers UniversityPiscataway, NJ 08854
Abstract
Hadron collider signatures of new physics are investigated in which a primary res-onance is produced that decays to a secondary resonance by emitting a W-boson, withthe secondary resonance decaying to two jets. This topology can arise in supersym-metric theories with R -parity violation where the lightest supersymmetric particlesare either a pair of squarks, or a slepton - sneutrino pair. The resulting signal canhave a cross section consistent with the W jj observation reported by the CDF collab-oration, while remaining consistent with earlier constraints. Other observables thatcan be used to confirm this scenario include a significant charge asymmetry in thesame channel at the LHC. With strongly interacting resonances such as squarks, pairproduction topologies additionally give rise to 4 jet and W + W − + 4 jet signatures,each with two equal-mass dijet resonances within the 4 jets. Introduction
In the overwhelming majority of the literature on supersymmetric extensions of the stan-dard model, R -parity is imposed as an ad-hoc symmetry to avoid phenomena such as protondecay which has been very strongly constrained by experiment. However, the proton canremain exactly stable even in the presence of a restricted set of R -parity violating interac-tions. In fact, one needs to break both baryon and lepton number for the proton to decay,because the proton is the lightest fermion that carries zero lepton number but nonzerobaryon number. Various low energy constraints on R -parity violating couplings have beenstudied in depth (see [1] and references therein), however certain aspects of collider phe-nomenology in the presence of R -parity violating couplings have not received the sameamount of attention compared to the case of exact R -parity [2]. In particular, there aretwo major differences between R -parity conserving and R -parity violating supersymmet-ric models that we wish to focus on in this paper that relate to the signatures at hadroncolliders.Firstly, R -parity violation affects production mechanisms by allowing for supersymmet-ric partner particles to be resonantly produced [3, 4]. Secondly, the lightest supersymmetricparticle need no longer be stable, and can decay promptly. Since most experimental searchesfor supersymmetry focus on the presence of missing transverse energy carried off by a neu-tral lightest superpartner, this requires a major change in search strategies. Naturally, inorder to account for dark matter, a supersymmetric theory with R -parity violation wouldneed to have additional matter content with a symmetry that can stabilize the lightestparticle in the dark sector. Finally, the fact that the lightest supersymmetric particle isno longer stable allows for spectra that are phenomenologically disfavored in models withexact R -parity and a colored superpartner can be the lightest one in the spectrum[5]. In therest of this paper we wish to study some of the phenomenological consequences associatedwith R -parity violation with relatively light scalar superpartners, such as the stop.UV motivated models of R -parity violation have been studied in the context of mSUGRAand grand unified theories [6–17]. There also exist motivated models of new physics thatare qualitatively different than the MSSM, in which R -parity is violated. An example isprovided by the setup of ref. [18], where supersymmetry is broken at high energies butreemerges as an accidental symmetry at low energies, and R -parity violation is unavoidable[19].Very recently, the CDF collaboration has announced an interesting observation of aresonance in dijets produced in association with a W boson [20]. The significance of thisobservation is 3 . σ using data with 4 . − of integrated luminosity, and the mean value forthe resonant dijet mass distribution is around 145 GeV. In this paper we will investigate1he possibility that the CDF observation arises from the production and decay of newparticles, and explore how this final state can arise in models of supersymmetry with R -parity violation. The topology we consider is characterized by the production of aprimary resonance that undergoes a charged-current transition to a secondary resonanceby emitting a W-boson, with the secondary resonance subsequently decaying to two jets.For a supersymmetric realization of this topology, we will concentrate on the possibilityof squarks or sleptons and sneutrino being the lightest (s)particles in the spectrum. Wegive a representative model in which the primary resonance is a bottom squark (sbottom),and the secondary resonance a top squark (stop), the production and decay of which occurthrough R -parity violating interactions respectively. We will show that only one or twocouplings beyond the MSSM are needed for this topology to be consistent with the CDFobservation. We will also show that the required couplings can have large enough valueswithout causing conflict with any existing constraints, and we will furthermore argue thatthe W jj channel is in fact naturally the first place for the new physics to be observed inthis scenario.In the next section we present our sbottom-stop model, estimate the size of the necessary R -parity violating couplings and show that these are not in conflict with any existingbounds. We will then go through various production and decay possibilities and arguewhy the new physics would appear first in the W jj channel, and evaluate the discoverypotential in other final states for the Tevatron as well as the LHC. In section 3 we givean alternative setup with sleptons instead of squarks that can give rise to similar collidersignatures and highlight the differences in phenomenology compared to the stop-sbottommodel.It should be emphasized that the most important aspect of the scenarios presentedhere are the production and decay topologies. While the language of supersymmetry isutilized throughout, the topologies and signatures may be more widely applicable to otherframeworks for the underlying physics, including ones with particles of different spin andgauge quantum numbers.
The R -parity violating terms in the superpotential are typically parameterized as W RP V = µ i H u L i + 12 λ ijk L i L j E ck + λ ′ ijk L i Q j D ck + 12 λ ′′ ijk U ci D cj D ck (1)where i, j, k are flavor indices. The first three types of terms violate lepton number whilethe U DD type terms violate baryon number.2mong the available R -parity violating couplings, U DD type terms are generically lessconstrained than
LQD or LLE terms, since searches for new physics involving leptonstypically have higher sensitivity. The main constraints on
U DD type terms come fromneutron-antineutron oscillations and flavor violation in the quark sector[1]. These con-straints can be avoided however, as we will outline below, and for certain choices of ijk , λ ′′ ijk can be of order one. For resonant production we will need at least one coupling to bereasonably large, and this coupling should preferably involve two light quarks in order togive rise to interesting production cross sections.Note that the U DD type terms are antisymmetric in the indices j and k . Therefore iftwo of the indices are to be 1, the only choices are λ ′′ and λ ′′ , both of which are severelyconstrained from nuclear decays involving two neutrons[1]. The next best possibility forresonant production is to make use of a strange quark PDF in the proton, and the there areseveral couplings of this type that are essentially unconstrained. Note however that thereare many additional constraints on products of couplings and therefore the safest choiceis to turn on as few R -parity violating terms as possible. Below, we will outline a modelwhere the stop and sbottom are the main players for the phenomenology, and where only λ ′′ ∼ O (0 .
1) and λ ′′ is nonzero (but need not be large). At the end of this section wewill point to an alternative choice with only λ ′′ turned on and argue that given a similarspectrum, the collider signatures are very similar.With λ ′′ turned on, sbottoms can be resonantly produced according to u + s → ˜ b ∗ R . Thecross section for this process is plotted in figure 1 for a value of λ ′′ = 0 .
1. If the sbottomhappens to be the lightest state, then it will decay back through the R -parity violatingcoupling to a pair of jets. Depending on the sbottom mass, this process is constrained bydijet resonance searches from UA2 [21] (light sbottoms), at the Tevatron [22] (intermediatemass sbottoms) and recent constraints from the LHC [23, 24] for heavy sbottoms. In figure2 we use the cross section constraints to derive bounds on λ ′′ , or equivalently on Γ jj , thepartial width of the sbottom to u + s . The exact relation between Γ jj and λ ′′ is given inequation (2). In terms of λ ′′ we find that the constraint from resonant production nevergoes below λ ′′ = 0 .
00 300 400 500 m b (GeV) ~ σ ( pb ) TevatronLHC 7 TeVLHC 14 TeV
Figure 1: Resonant production cross section for sbottom with λ ′′ = 0 . b R . λ ′′ below the bound. The presence of a neutralino below the mass of the sbottom does notlead to much improvement. The sbottom would decay as ˜ b → b + χ , the neutralino thendecaying through an off-shell sbottom as χ → bjj , thus populating the bbjj final state,which has a large background. If there are charginos significantly lighter than the sbottom,this can lead to top quarks in the final state, which is potentially a more optimistic scenario,however the large mass gap necessary for decaying to on-shell tops forces the sbottoms tobe heavier, reducing the cross section as a function of the lightest superpartner mass.A possibility that is much more interesting collider-wise, and the one we wish to considerin the rest of this section is the presence of a stop below the sbottom mass. In this casethe sbottom can decay as ˜ b → ˜ t + W . This mass spectrum is favored by the RG evolutionof the squark masses, as the large Yukawa couplings tend to drive the stop mass lighter.Note that since it is ˜ b R that is resonantly produced, for the W channel to dominate thereneeds to be some mixing between ˜ b R and ˜ b L . As long as the left handed squarks are notdecoupled however, the W decay mode can be dominant. The partial widths of the sbottom4
00 300 400 500 m b (GeV) ~ Γ jj m a x / m UA2CDF
Figure 2: The bound on Γ jj from the dijet resonance searches at UA2 and CDF. Thenumbers plotted here are conservative in the sense that we assume perfect acceptance andno suppression from left-right sbottom mixing. In terms of λ ′′ , the bound is always above0.4.into dijets and into ˜ t + W are given byΓ( e b → W − e t ) = g cos θ t cos θ b m e b πm W f / (1 , m e t /m e b , m W /m e b )Γ( e b → us ) = | λ ′′ | sin θ b m e b π (2)where f (1 , x, y ) = 1 − x + y ) + ( x − y ) is the triangle function and cos θ ˜ b, ˜ t denote themixing angles in the squark sector (for cos θ ˜ b = 0, ˜ b = ˜ b R and likewise for the stop). Infigure 4 we plot the branching fraction of ˜ b → ˜ t + W for cos θ ˜ b, ˜ t = 1 / m ˜ t = 150GeV.With only λ ′′ nonzero, the stop will have a three-body decay through on off-shellsbottom. Note however that the stop can also have two-body decays if there are additionalnonzero R -parity violating couplings, specifically a nonzero value of λ ′′ ij . Note howeverthat neutron-antineutron mixing constrains λ ′′ and λ ′′ to be of order 10 − while theconstraints are much weaker on λ ′′ [1]. Note that the product of λ ′′ and λ ′′ is also notfurther constrained, and that stop production from a small value of λ ′′ is unobservabledue to the PDFs for a s - b initial state. The decay modes of the stop are illustrated in figure5 sus ˜ b us ˜ b W ˜ t Figure 3: Resonant sbottom production and decay modes with a lighter stop in the spec-trum.5. With λ ′′ turned on, the two-body decay of the stop into jets can dominate, and thefirst signal to be seen would appear in the p ¯ p → ˜ tW → W jj channel. This is the channelwhere CDF recently reported observing an interesting signal[20]. For this specific choiceof couplings, one of the jets from the decay of the stop would be a b-jet. Currently theCDF analysis states that the heavy flavor content of the excess region is consistent with thesideband. However the analysis does not provide a quantitative measure for whether theexistence of a single b-jet is disfavored. As we will describe in section 2, the same topologycan be realized with a different choice of nonzero λ ′′ ijk such that the final state has no heavyflavor jets. The CDF analysis reports no significant deviation from the Standard Modelexpectation in an analogous channel with a dijet resonance produced in association with aZ-boson. Note that in our minimal setup, this channel is expected to be absent.In order to study the acceptance of the CDF analysis for the ˜ b → W ˜ t → W jj signal wehave performed a Monte Carlo study. It is not trivial to generate Monte Carlo events for thissetup due to the completely antisymmetric way that the color indices are contracted in the R -parity violating vertex. While certain programs such as HERWIG incorporate aspectsof R -parity violating physics, this is not adequate for our purposes and we have generated2 → R = 0 .
00 250 300 350 400 450 500 m b (GeV) ~ B r a n c h i ng F r ac ti on ( t - W ) ~ Figure 4: The branching fraction of the ˜ b to ˜ t + W . For this plot m ˜ t = 150GeV, andcos θ ˜ t = cos θ ˜ b = 1 / • The presence of an electron (muon) with E T ( p T ) >
20 GeV and | η | < . • Missing transverse energy in excess of 25 GeV. • The presence of exactly two jets with E T >
30 GeV and | η | < . • A minimum ∆ R of 0.52 between the lepton and the nearest jet. • A minimum p T of 40 GeV for the dijet system. • A transverse mass in excess of 30 GeV for the lepton-neutrino system, where theneutrino is taken to be the only source of missing transverse energy in the event. • An azimuthal angle in excess of 0.4 radians between the missing energy and eitherjet. • ∆ η < . b ∗ W + ¯ u ¯ s ˜ t ˜ t ¯ s ¯ b Figure 5: Decay modes for the stop.Taking m ˜ b = 300GeV, m ˜ t = 150GeV and cos θ ˜ t = cos θ ˜ b = 1 /
2, we find that the numberof events observed at CDF in the e + µ channels is consistent with λ ′′ = 0 .
16, giving atotal production cross section of 3 . . × − which includes a52% branching fraction for ˜ b → W + ˜ t (we take the branching fraction of ˜ t → jj to be 1).This value of λ ′′ is far below the bound from dijet resonance searches. We plot the dijetinvariant mass distribution from the stop decay in our sample in figure 6.Another interesting question that is reported to be consistent with the backgroundhypothesis but not ruled out by the CDF analysis is whether a primary resonance can bepresent in the W jj system. In the topology considered here, this system will reconstructthe sbottom mass. In figure 7 we plot the reconstructed sbottom mass in our model for atrue value of m ˜ b = 300GeV using both solutions for the neutrino rapidity in reconstructingthe W-mass (and discarding the event if no real solutions can be found). Note that whilethe stop mass is determined by the position of the observed dijet excess, the sbottom massis an adjustable parameter in this model, and for lighter sbottom masses, the excess in m W jj may be difficult to resolve on top of background. A definitive comparison of the primaryresonance aspect of this topology with the CDF observation would require a full detectorsimulation of both signal and backgrounds, as well as the CDF data-driven estimates ofbackground.
Additional Collider Signatures
While in our topology the resonant production of any up-type squark is strongly suppresseddue to the smallness of the couplings λ ′′ k , the pair production of the stop is determinedby QCD and can be an interesting production channel. In figure 8 we show the stop pairproduction cross section as a function of its mass calculated by using the batch mode ofCalcHEP[29]. This production channel would manifest itself in the four jet channel, with8
50 100 150 m jj (GeV) E v e n t s Figure 6: The invariant mass distribution of the two jets from the stop decay ( e and µ channels combined) using the same cuts as the CDF analysis, with m ˜ b = 300GeV and m ˜ t = 150GeV. λ ′′ = 0 .
16 and cos θ ˜ t = cos θ ˜ b = 1 / − of integrated luminosity.two pairs of jets reconstructing narrow resonances of the same mass. Ref. [30] studiedthis channel with the conclusion that stops with up to m ˜ t = 210 GeV can be discovered.References [31–35] also studied the same event topology at the Tevatron and the LHC forvarious scenarios of underlying physics, and showed that there is strong discovery potential.Currently no search for new physics has been performed in this channel. Note that for astop mass of 150GeV, a search in the four jet channel analysis will be difficult at the LHCbecause of the larger trigger thresholds which will have low efficiency on the signal. TheTevatron has a unique advantage for the case of light stops, and an analysis of existingdata could be used to explore this possibility.The initial state for resonant anti-squark production through R -parity violating interac-tions is quark–quark (rather than quark–anti-quark). In the scenario described here, withproduction through the λ ′′ coupling, one of the initial state quarks is a strange-quark.At the Tevatron with p - ¯ p collisions, as well as at the LHC with p - p collisions, the partondistribution functions for the leading resonant production are therefore of the valence–seatype. Aside from the relative center of mass energies, there is no qualitative difference forthe overall production rates between the Tevatron and LHC for such a resonance. How-9
00 200 300 400 m Wjj (GeV) E v e n t s Figure 7: The invariant mass of the
W jj system from the sbottom decay ( e and µ channelscombined) using the same cuts as the CDF analysis, with m ˜ b = 300GeV and m ˜ t = 150GeV.Both solutions for the neutrino momentum are included in the distribution. λ ′′ = 0 . θ ˜ t = cos θ ˜ b = 1 / − of integrated luminosity.ever, the relative rates for sbottom versus anti-sbottom are significantly different. At theTevatron sbottom and anti-sbottom are produced at equal rates because of the chargesymmetry of the colliding particles. In contrast, at the LHC, production of anti-sbottomarising from valence–sea quark collisions is enhanced compared with sbottom productionarising from sea–sea anti-quark collisions. This leads to a significant charge asymmetry inthe W jj signal at the LHC, as shown in figure 9. A charge asymmetry is also present inthe W+jets background due to the difference between the u and d valence quark partondistribution functions. However, the W+jets background asymmetry arises predominantlyfrom an order one difference in the relative magnitude of two types of valence–sea quarkcollisions, whereas the signal asymmetry is much larger since it arises from a difference be-tween valence–sea versus sea–sea collisions. The enhanced charge asymmetry of the W jj signal may provide an additional handle at the LHC to isolate this supersymmetric scenariofor the topology of a primary and secondary resonance with a charged-current transition.Finally, one can also consider the pair production of the sbottom through QCD. In thescenario with a lighter stop, this channel will go to W + W − + 4 j . While the combinatoric10
00 200 300 400 500 m q (GeV) ~ σ (f b ) TevatronLHC 7 TeVLHC 14 TeV
Figure 8: Cross section (QCD only) for pair production of a single squark as a function ofits mass.background can be reduced by reconstructing the stops as well as demanding equal sbottommasses, the cross section is small compared to the irreducible standard model backgroundsof t ¯ t +jets and W W +jets in the dileptonic decay channel, and the additional backgroundof W+jets for the semileptonic case. As one can see in figure 8, even for moderately lightsbottom masses, the cross section for this process is too low at the Tevatron. The leptonicbranching fraction of W bosons and acceptance effects make it unlikely that a statisticallysignificant excess can be observed at the 7 TeV LHC as well (assuming a total integratedluminosity of 5 fb − ). This channel may become interesting for the 14 TeV LHC with highstatistics however. Squark Mixing
We wish to briefly comment on the stability of the choice of nonzero λ ′′ ijk that we use.For instance, the 1-loop diagram in figure 10 shows how an existing U DD coupling mayinduce additional R -parity violating couplings in the presence of neutralinos that couple off-diagonally in flavor space. This can be avoided however if all three generations are nearly-degenerate. For the model we outlined in this paper, one can imagine a mass spectrumsuch that all three generations are present, with m ˜ u R < m ˜ d R < m ˜ q L . The presence of11
00 300 400 500 m b (GeV) ~ σ b / σ b ~ * ~ LHC 7 TeVLHC 14 TeV
Figure 9: Ratio of the anti-sbottom to sbottom resonant production cross sections throughthe λ ′′ R -parity violating interaction at the LHC.the additional squarks does not significantly change the phenomenology that we discussed.With only λ ′′ and λ ′′ turned on, the ˜ u iR are not resonantly produced at observable rates.They are pair produced, enhancing the cross section by a factor of three compared tothat of a single stop in the four jet channel. Resonant production of the additional ˜ d iR is also suppressed by the PDF’s. Therefore the phenomenology is essentially identical tothe minimal scenario with only a sbottom and a stop. If the left-handed squarks are lightenough to be produced, new decay channels with on-shell Higgs or Z bosons may openup. Other operators induced by a diagram similar to figure 10 but with a W in the looprather than a neutralino are nonrenormalizable, and are small for our choice of nonzero λ ′′ since they are suppressed by quark masses and CKM angles. We do not consider operatorsinduced at higher loops. An Alternative Choice of Couplings
There is a second choice for which nonzero λ ′′ can give rise to the CDF excess. If λ ′′ isturned on, then both ˜ s and ˜ c can be resonantly produced from d - c and d - s initial states,respectively. This choice has the advantage that λ ′′ will also induce decays of both the ˜ s and the ˜ c , so no second λ ′′ ijk need be turned on. There are several disadvantages however.12 u iR χ u jR ˜ d lR d mR d kR Figure 10: How additional
U DD type couplings may be induced at 1-loop from existingones. The black box denotes a λ ′′ coupling that is nonzero at tree level and the circlesrepresent off diagonal couplings in flavor space.Since both ˜ s and ˜ c are now resonantly produced through the same coupling, the UA2 dijetresonance bound on the lighter state (assumed to have a mass of 150 GeV) will directlyapply to the production cross section of the heavier state, and therefore on the cross sectionfor the W jj decay mode. Furthermore, the branching fraction for the W-mode depends onthe left-right squark mixing and may be much smaller for the second generation squarkscompared to ˜ b and ˜ t . Finally, the production cross section for a d - s initial state is lowerthan that of the u - s initial state by a factor of order one. Since this affects the bounds fromdijet resonances in the same way as the production cross section however, one can simplycompensate by using a larger value of λ ′′ as long as one is not already at the upper limit. R -parity violation through U DD -type terms is not the only possibility to resonantly pro-duce superpartners at a hadron collider. One can also consider the resonant production ofleft-handed sleptons through a
LQD type coupling. The λ ′ ijk couplings necessary in thisscenario are generically more constrained that the U DD couplings [1]. While we will notattempt to build a detailed model as in the squark case, we remark that a similar finalstate can be obtained. Resonant production of a left-handed slepton, with charged-currentdecay through an off-shell W ∗ to the sneutrino, which subsequently decays back throughthe R -parity violating coupling, gives an ℓ ¯ ν jj signature. The main difference with a left-handed SU (2) L doublet only, is that the mass splitting between the slepton and sneutrinoarises only from electroweak symmetry breaking and is parametrically small. The leptonsin this scenario are then significantly softer than those arising from an on-shell W topology.13
00 300 400 500 m (GeV) σ ( pb ) l ~ ν ~ Figure 11: Resonant production cross section for a slepton and a sneutrino for λ ′ = 0 . λ ′ ijk are constrained through lepton flavor violating processes, there are fewchoices in which couplings can be turned on to match the CDF W jj observation. Onepossibility is resonant stau production from a nonzero value of λ ′ . Scenarios of R -parityviolation with ˜ τ and ˜ ν τ LSP have been considered in mSUGRA scenarios (see for example[36], [37] and references therein). As in the squark case, there is a charge asymmetry in theresonant production of the slepton vs. the anti-slepton. Unlike the squark case however,the origin of this asymmetry is the difference between the u and d valence quark PDF’s.Therefore the asymmetries of the signal and the W+jets background will be of the samesize. Additionally, unlike in the case of squarks, sleptons are only pair produced throughelectroweak interactions, so pair production cross sections will be much smaller, and only q -¯ q initial states can contribute, which is a disadvantage for the LHC compared to thesquark case where the g - g initial state contributes.If both right- and left-handed sleptons are light enough to be produced, then the sameproduction and decay topology discussed above can arise with resonant production of the14
00 300 400 500 m (GeV) Γ jj m a x / m l ~ ν ~ Figure 12: The bound on Γ jj for resonant slepton and sneutrino production from UA2 andCDF with only λ ′ turned on. The numbers plotted here are conservative in the sensethat we assume perfect acceptance and we neglect left-right mixing. The bound on λ ′ never goes below 0.3 for the sneutrino and below 0.2 for the slepton.heavier states that charged-current decay through an on-shell W-boson to the lighter stateswhich subsequently decay back to two jets. Since in LQD -type R -parity violation both res-onant production as well as the charged-current coupling involve the left-handed componentof sleptons, significant left-right mixing is required in order for both the cross section aswell as the W branching fraction to be sizeable in this case. If kinematically open, decaymodes with on-shell Higgs and Z -bosons also arise in this scenario. We have explored a production and decay topology for hadron colliders in which a primaryresonance undergoes a charged-current transition to a secondary resonance that subse-quently decays to dijets. Supersymmetric scenarios with R -parity violation where a lightsbottom is resonantly produced and decays to a W-boson and stop, which decays to a pairof jets through the R -parity violating coupling, give a concrete realization of this topology.Other possibilities for underlying theoretical frameworks that could give topologies of thistype include technicolor [38] (for reviews of phenomenology see [39–41]), two-Higgs-doublet15odels (for a detailed overview see [42]), and excited quarks [43–45]. We have argued thatwith such a topology, the new physics may be observed first in the W jj channel, possiblyconsistent with the recent CDF observation in this channel. We have also pointed to otherfinal states that would be associated with this scenario. In particular, for strongly inter-acting resonances, other important topologies are pair production of the secondary stategiving rise to a 4 jet signature, as well as pair production of the primary state giving rise toa W + W − + 4 jets signature, both with two equal mass dijet resonances within the 4 jets.We argued that due to the smallness of the mass of the secondary state, the former wouldmost effectively be searched for at the Tevatron, while the latter has better prospects atthe upgraded LHC. We have outlined how a less minimal supersymmetric model can be setup with all three generations of squarks present, without significantly changing the colliderphenomenology, but forbidding additional R -parity violating couplings to be induced atloop-level from existing ones.We have also shown that there is an alternative choice of couplings for the squarkscenario, where the phenomenology is focused on the second generation squarks ratherthan the third. This alternative model needs only one R -parity violating coupling to benonzero, however the branching fraction for the W mode may be small unless there issignificant left-right mixing in the squark sector. Finally we have outlined an alternativesupersymmetric scenario with the same production and decay topology, but where the newparticles are sleptons rather than squarks. Many additional production channels such aspair production through QCD are absent in this case.To conclude, we believe that even if the CDF W jj observation proves not to be due tonew physics, that collider signatures of R -parity violating supersymmetric models shouldbe further explored by both theorists and experimental searches. Note Added:
After this paper was submitted, several developments took place. CDFupdated their analysis with a 7 . − data set in which the significance of the excesswas reported as 4 . σ after accounting for systematic uncertainties [46]. In this analysis,various other consistency checks were performed on the analysis, such as using differentMonte Carlo generators, making the jet cuts inclusive (rather than demanding exactly twojets), varying the jet energy scale and some of the analysis cuts. The excess was reportedas being robust under these variations. This is true of the signal in our scenario as well,the effect of these variations to the acceptance of our Monte Carlo sample is mild. Thereis however a result in the updated CDF analysis that has a larger impact on our scenario,namely the heavy flavor content in the jets accompanying the W -boson has been reportedquantitatively. This result is difficult to reconcile with one of the two jets being a b-jetin each event, and therefore disfavors our sbottom-stop benchmark. Note however that16oth the second generation squark benchmark as well as the slepton benchmark which weproposed produce light jets in the final state and are therefore still consistent with the CDFupdate.Another dramatic development was the release of a DØ search for new physics in thesame final state [47]. This analysis reports that DØ does not observe an excess consistentwith the CDF result, and for a Gaussian centered at the same mass they obtain a best fitfor the cross section of 0 . +0 . − . pb. Considering that the DØ analysis uses cuts very similarto the CDF analysis, it is not at the moment clear why the two experiments obtain suchdrastically different results. While this development casts doubt on the existence of newphysics in this final state, it is also possible that there is a signal with a cross section smallerthan the one reported by CDF but still consistent with the DØ result, for example around1 . R -parity violating couplings. As we remarked at the end of our conclusions, astheorists we believe this topology for the resonant production of supersymmetric particlesto be an interesting one that should be studied further even if the eventual resolution ofthe discrepancy between CDF and DØ results disfavors a new physics explanation.We also wish to mention a variety of other new physics explanations that were proposedto explain the CDF excess after the submission of this paper. These include technicolormodels [48], new gauge bosons [49], extended Higgs sectors [50] and other possibilities [51].Since technicolor is arguably the most commonly associated type of new physics associatedwith the W jj final state, we want to point to a few phenomenological differences betweenour scenario and a technicolor model, which could be used in order to distinguish the twosignals. For one, since a techni-pion is expected to couple to SM fermions proportionally totheir mass, it is expected to decay preferentially to b ¯ b pairs. In our scenario, the alternativesquark and slepton benchmarks would only give rise to light jets in the final state whereasthe sbottom-stop benchmark would produce a single b -jet. As mentioned earlier in thisnote, the CDF update appears to disfavor the existence of b -tagged jets in the excess.Another possibility that can distinguish between our scenario and a technicolor model isto look for pair production of the primary resonance. In both our sbottom-stop as wellas our alternative squark benchmarks, both the heavier as well as the lighter squarks areexpected to be pair produced from QCD processes, giving rise to a 4 j final state for thelighter squark and a W W + 4 j final state for the heavier squark, as we mentioned at theend of section 2, whereas techni-rhos and techni-pions in minimal technicolor models donot carry color charge and will not be pair produced in the same way. Note however thatpair production is not a good discriminant if the resonantly produced superpartners are17leptons which also do not carry color. Acknowledgments
The work of C.K. and S.T. is supported by DOE grant DE-FG02-96ER40959.
References [1] R. Barbier et al. , Phys. Rept. , 1 (2005) [arXiv:hep-ph/0406039].[2] S. Dawson, E. Eichten, C. Quigg, Phys. Rev.
D31 , 1581 (1985); H. Baer, X. Tata,Cambridge, UK: Univ. Pr. (2006) 537 p; K. Nakamura et al. [ Particle Data GroupCollaboration ], J. Phys. G
G37 , 075021 (2010).[3] S. Dimopoulos, R. Esmailzadeh, L. J. Hall and G. D. Starkman, Phys. Rev. D ,2099 (1990).[4] H. K. Dreiner and G. G. Ross, Nucl. Phys. B , 597 (1991).[5] U. Sarid and S. D. Thomas, Phys. Rev. Lett. , 1178 (2000) [arXiv:hep-ph/9909349].[6] N. Sakai and T. Yanagida, Nucl. Phys. B , 533 (1982).[7] L. J. Hall and M. Suzuki, Nucl. Phys. B , 419 (1984).[8] D. E. Brahm and L. J. Hall, Phys. Rev. D , 2449 (1989).[9] R. Hempfling, Nucl. Phys. B , 3 (1996) [arXiv:hep-ph/9511288].[10] A. Y. Smirnov and F. Vissani, Nucl. Phys. B , 37 (1996) [arXiv:hep-ph/9506416].[11] K. Tamvakis, Phys. Lett. B , 251 (1996) [arXiv:hep-ph/9604343].[12] K. Tamvakis, Phys. Lett. B , 307 (1996) [arXiv:hep-ph/9602389].[13] R. Barbieri, A. Strumia and Z. Berezhiani, Phys. Lett. B , 250 (1997)[arXiv:hep-ph/9704275].[14] G. F. Giudice and R. Rattazzi, Phys. Lett. B , 321 (1997) [arXiv:hep-ph/9704339].[15] H. K. Dreiner, arXiv:hep-ph/9707435.[16] M. A. Diaz, J. C. Romao and J. W. F. Valle, Nucl. Phys. B , 23 (1998)[arXiv:hep-ph/9706315]. 1817] B. C. Allanach, A. Dedes and H. K. Dreiner, Phys. Rev. D , 115002 (2004) [Erratum-ibid. D , 079902 (2005)] [arXiv:hep-ph/0309196].[18] R. Sundrum, JHEP , 062 (2011) [arXiv:0909.5430 [hep-th]].[19] R. Sundrum, private communication.[20] T. Aaltonen et al. [CDF Collaboration], arXiv:1104.0699 [hep-ex].[21] UA2 Collaboration, Nucl. Phys. B , 3 (1993) ISSN 0550-3213, DOI: 10.1016/0550-3213(93)90395-6.[22] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. D , 112002 (2009)[arXiv:0812.4036 [hep-ex]].[23] G. Aad et al. [ATLAS Collaboration], arXiv:1103.3864 [hep-ex].[24] V. Khachatryan et al. [CMS Collaboration], Phys. Rev. Lett. , 211801 (2010)[arXiv:1010.0203 [hep-ex]].[25] J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. M. Nadolsky and W. K. Tung,JHEP (2002) 012 [arXiv:hep-ph/0201195].[26] E. Boos et al. , arXiv:hep-ph/0109068.[27] T. Sjostrand, S. Mrenna and P. Z. Skands, “PYTHIA 6.4 Physics and Manual,” JHEP , 026 (2006) [arXiv:hep-ph/0603175].[28] J. Conway et al. , “PGS 4: Pretty Good Simulation of high energy collisions,” 2006, ∼ conway/research/software/pgs/pgs4-general.htm [29] A. Pukhov et al. , arXiv:hep-ph/9908288; A. Pukhov, arXiv:hep-ph/0412191.[30] D. Choudhury, M. Datta and M. Maity, Phys. Rev. D , 055013 (2006)[arXiv:hep-ph/0508009].[31] R. S. Chivukula, M. Golden and E. H. Simmons, Nucl. Phys. B , 83 (1991).[32] B. A. Dobrescu, K. Kong and R. Mahbubani, Phys. Lett. B , 119 (2008)[arXiv:0709.2378 [hep-ph]].[33] C. Kilic, T. Okui and R. Sundrum, JHEP , 038 (2008) [arXiv:0802.2568 [hep-ph]].[34] C. Kilic, S. Schumann and M. Son, JHEP , 128 (2009) [arXiv:0810.5542 [hep-ph]].1935] Y. Bai and B. A. Dobrescu, arXiv:1012.5814 [hep-ph].[36] K. Desch, S. Fleischmann, P. Wienemann, H. K. Dreiner and S. Grab, Phys. Rev. D , 015013 (2011) [arXiv:1008.1580 [hep-ph]].[37] H. K. Dreiner and S. Grab, Phys. Lett. B , 45 (2009) [arXiv:0811.0200 [hep-ph]].[38] L. Susskind, “Dynamics Of Spontaneous Symmetry Breaking In The Weinberg-SalamTheory,” Phys. Rev. D , 2619 (1979); S. Weinberg, “Implications Of DynamicalSymmetry Breaking,” Phys. Rev. D , 974 (1976); S. Weinberg, “Implications OfDynamical Symmetry Breaking: An Addendum,” Phys. Rev. D , 1277 (1979).[39] E. Farhi and L. Susskind, “Technicolor,” Phys. Rept. , 277 (1981); C. T. Hill andE. H. Simmons, “Strong dynamics and electroweak symmetry breaking,” Phys. Rept. , 235 (2003) [Erratum-ibid. , 553 (2004)] [arXiv:hep-ph/0203079].[40] K. Lane and S. Mrenna, “The Collider phenomenology of technihadrons in the tech-nicolor straw man model,” Phys. Rev. D , 115011 (2003) [arXiv:hep-ph/0210299].[41] G. H. Brooijmans et al. , “New Physics at the LHC: A Les Houches Report. Physicsat Tev Colliders 2007 – New Physics Working Group,” arXiv:0802.3715 [hep-ph].[42] J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson, Front. Phys. , 1 (2000).[43] H. Terazawa, M. Yasue, K. Akama and M. Hayashi, Phys. Lett. B , 387 (1982).[44] F. M. Renard, Nuovo Cim. A , 1 (1983).[45] A. De Rujula, L. Maiani and R. Petronzio, Phys. Lett. B , 253 (1984).[46] [47] V. M. Abazov [ D0 Collaboration ], Phys. Rev. Lett. , 011804 (2011).[arXiv:1106.1921 [hep-ex]].[48] E. J. Eichten, K. Lane, A. Martin, Phys. Rev. Lett. , 251803 (2011).[arXiv:1104.0976 [hep-ph]].[49] M. R. Buckley, D. Hooper, J. Kopp, E. Neil, Phys. Rev. D83 , 115013 (2011).[arXiv:1103.6035 [hep-ph]]; F. Yu, Phys. Rev.
D83 , 094028 (2011). [arXiv:1104.0243[hep-ph]]; X. -P. Wang, Y. -K. Wang, B. Xiao, J. Xu, S. -h. Zhu, Phys. Rev.
D83 ,117701 (2011). [arXiv:1104.1161 [hep-ph]]; K. Cheung, J. Song, Phys. Rev. Lett.20 , 211803 (2011). [arXiv:1104.1375 [hep-ph]]; A. E. Nelson, T. Okui, T. S. Roy,[arXiv:1104.2030 [hep-ph]]; S. Jung, A. Pierce, J. D. Wells, [arXiv:1104.3139 [hep-ph]];P. Ko, Y. Omura, C. Yu, [arXiv:1104.4066 [hep-ph]]; P. J. Fox, J. Liu, D. Tucker-Smith,N. Weiner, [arXiv:1104.4127 [hep-ph]]; D. -W. Jung, P. Ko, J. S. Lee, [arXiv:1104.4443[hep-ph]]; S. Chang, K. Y. Lee, J. Song, [arXiv:1104.4560 [hep-ph]]; K. S. Babu,M. Frank, S. K. Rai, [arXiv:1104.4782 [hep-ph]]; Z. Liu, P. Nath, G. Peim, Phys.Lett. B701 , 601-604 (2011). [arXiv:1105.4371 [hep-ph]]; J. L. Hewett, T. G. Rizzo,[arXiv:1106.0294 [hep-ph]]; A. E. Faraggi, V. M. Mehta, [arXiv:1106.5422 [hep-ph]].[50] Q. -H. Cao, M. Carena, S. Gori, A. Menon, P. Schwaller, C. E. M. Wagner, L. -T. Wang,[arXiv:1104.4776 [hep-ph]]; B. Dutta, S. Khalil, Y. Mimura, Q. Shafi, [arXiv:1104.5209[hep-ph]]; C. -H. Chen, C. -W. Chiang, T. Nomura, Y. Fusheng, [arXiv:1105.2870 [hep-ph]].[51] X. -P. Wang, Y. -K. Wang, B. Xiao, J. Xu, S. -h. Zhu, Phys. Rev.
D83 , 115010(2011). [arXiv:1104.1917 [hep-ph]]; R. Sato, S. Shirai, K. Yonekura, Phys. Lett.
B700 , 122-125 (2011). [arXiv:1104.2014 [hep-ph]]; L. A. Anchordoqui, H. Goldberg,X. Huang, D. Lust, T. R. Taylor, Phys. Lett.