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Heavy Squarks at the LHC

The LHC, with its seven-fold increase in energy over the Tevatron, is capable of probing regions of SUSY parameter space exhibiting qualitatively new collider phenomenology. Here we investigate one such region in which first generation squarks are very heavy compared to the other superpartners. We find that the production of these squarks, which is dominantly associative, only becomes rate-limited at mSquark>4(5) TeV for L~10(100) fb-1. However, discovery of this scenario is complicated because heavy squarks decay primarily into a jet and boosted gluino, yielding a dijet-like topology with missing energy (MET) pointing along the direction of the second hardest jet. The result is that many signal events are removed by standard jet/MET anti-alignment cuts designed to guard against jet mismeasurement errors. We suggest replacing these anti-alignment cuts with a measurement of jet substructure that can significantly extend the reach of this channel while still removing much of the background. We study a selection of benchmark points in detail, demonstrating that mSquark= 4(5) TeV first generation squarks can be discovered at the LHC with L~10(100)fb-1.


Introduction
The Large Hadron Collider (LHC) has commenced operation and is already producing collisions at energies far above the scale of electroweak symmetry breaking (EWSB). Thus one can be hopeful that soon the particle responsible for EWSB (e.g. the Higgs) will be discovered, as well as any physics beyond the standard model (BSM) responsible for setting the scale at which this breaking occurs. Supersymmetry (SUSY) is perhaps the most promising candidate for BSM physics, and as such its phenomenology has been studied extensively. However, the SUSY parameter space is so complicated that most collider studies confine themselves to studying a restrictive subset of models or simple benchmark points (e.g. mSURGRA [1] and the SPS points [2], respectively). In general though, it is useful to look at other regions of parameter space to make sure no signals are missed [3,4].
Here we will focus on one such understudied region in which first generation squarks are very heavy compared to the other SUSY superpartners 1 . This scenario deserves attention not only because it yields a viable SUSY spectrum, but also because it is motivated by many interesting SUSY scenarios [5,6] including more recent work in split SUSY [7,8,9], PeVscale SUSY [10], and single sector SUSY breaking [11,12]. Intuitively, it is reasonable to anticipate heavy first generation squarks because they play a minimal role in solving the hierarchy problem (i.e. stabilizing the electroweak scale) -only the third generation really needs to be light if SUSY plays the role we expect of it. In any case, here our main goal is to determine an optimal search strategy for discovering heavy squarks and to assess the reach of the LHC in finding them. Now, when squarks are very heavy it becomes too costly to create them in pairs and so heavy squarks are dominantly produced in association with a different superpartner. This associated particle is usually the gluino, due to its large color charge. Furthermore, once produced the squark usually decays into a gluino and a jet, again because of the gluino's large color charge, yielding the topology: Since, in most plausible SUSY spectra, all superpartners decays yield a stable neutral particle (i.e. the LSP, labeledχ 0 1 ) squark associated production would seem to yield the classic new physics signal: jets +E / T . However, for heavy squark scenarios, new challenges appear in this well-studied final state.
Difficulties arise because the gluino from the decaying squark will be be very energetic (assuming mg mq), and so all of its decay products become collimated, confined to a cone of opening angle In practice, this means that the boosted gluino's decay products will often be resolved as a single jet (henceforth the gluino jet). Furthermore, although there are two sources of E / T in this process, theχ 0 1 from the boosted gluino is much harder than that of the associated gluino, and so the E / T in this process tends to be aligned with the gluino jet. Thus, what is really a complicated SUSY process is resolved as two back-to-back jets with E / T aligned along one of them -the telltale signature of a mismeasured QCD dijet event. Indeed, precisely because our signal events look so much like QCD dijets they are often vetoed by standard pre-selection cuts. Traditionally one requires a separation in azimuthal angles between the E / T and any nearby jets in order to remove mismeasurement backgrounds: D0 requires ∆ φ (E / T , j) > 0.8 in its jets + E / T search [13], while the LHC experiments require ∆ φ (E / T , j) 0.3 [14]. We therefore expect to run into trouble using standard analyses when mg/mq 0.3.
It is clear that to resolve heavy squarks at the LHC the cut on ∆φ(E / T , j) should be relaxed and some other tool must be used to remove mismeasured QCD. Here we propose using jet substructure 2 for this purpose. This approach is motivated by the fact that while the four-momenta of a gluino jet could be similar to that of a QCD jet, the distribution of the constituent four-momenta inside the jet (i.e. the calorimeter cells inside of it) will be very different. Gluino jets contain many hard, widely seperated subclusters of energy, evidence of a decay chain, while the depositions within a QCD jet assume a hierarchical structure, evidence for emissions governed by the showering of partons within QCD. The variables of jet substructure allow one to distinguish between these two cases, as we will soon see.
The paper is structured as follows. In Sec. 2 we discuss squark production rates and decay channels. Sec. 3 studies the basic kinematic cuts necessary to discover heavy squarks over the SM backgrounds and discusses jet substructure observables helpful in reducing mismeasurement errors. Finally, we conclude in Sec. 4.

Production Rates and Branching Ratios
In determining the reach of the LHC in probing heavy squarks the place to start, of course, is with production rates. As mentioned in the introduction, heavy squarks are dominantly produced in association with one of the lighter superpartners simply because pair production would require a very high energy, the probability of which is suppressed by the fast-falling nature of the proton's parton distribution functions (PDFs). Furthermore the state produced in association with the squark is almost always a gluino because of its large coupling.
In Fig. 1 we plot the leading order 3 cross section for the process pp →q +g over a range of (mq, mg) and at different LHC energies. These results are obtained using Pythia v6.423 [18] assuming the first generation squarks are all degenerate in mass and any mixings are negligible. If we require S/ √ B > 5 with at least 10 signal events [19] for discovery, then one can see that for L ∼ 10(100) fb −1 a 14 TeV LHC is in principle capable of discovering squarks up to mq ∼ 4(5) TeV.
Once heavy squarks are produced they will dominantly decay through the QCD channel q → qg which will be the focus of our study, although some squarks will decay into neutralinos or charginos 4 . Of course, once gluinos have been produced they too decay. Fortunately, gluino decays in models with heavy squarks have been well studied in the literature [20,21]. In general, there are three major decay chains for the gluino: 1. Via an off-shell squark to two quarks and the LSP:g → qq +χ 0 1 .
The explicit formulae of the decay widths can be found in Ref. [20]. A few remarks are in order: • We note that the qq pair formed from the decay of the gluino can, if kinematically allowed, be composed of top quarks. This results in an even richer jet substructure than the decay to light quarks. In fact, as one expects the stop squark to be relatively light (as it plays a large role in stabilizing the Higgs mass), and the decay widths scale as 1/m 4 q , the branching ratio to the ditop channelg → tt +χ 0 1 can often dominate. • In the limit whereχ 0 1 is purely a Bino, the squark mass matrices are flavor-diagonal, and left-right mixings are negligible, the branching ratio between the 2-body and 3-body ratios R 2/3 ≡ Γ(g → 2 body)/ Γ(g → 3 body) is In this limit, the loop-induced decayg → g +χ 0 1 is suppressed by the mass splitting between the left-and right-handed squarks m 2 L − m 2 R . This is becauseg → g +B, governed by the magnetic operatorχ 0 1 σ µν γ 5g G µν , is a C-violating process. It vanishes for pure strong interactions with degenerate squark masses as these preserve C-parity. Any such C-violating decay channel can only be generated by the weak interactions which generate the mass splittings between squarks of different handedness.
• Finally, another interesting limit emphasized in [20] is when the gluino is kinematically allowed to decay into Higgsinos. Here the radiative decay is enhanced by (log(mt/m t )) 2 due to the stop and top loop.
For our study, we will take the mass differences between m 2 L − m 2 R to be negligible compared to the squark mass, and we will posit that gluino decays to Higgsinos are kinematically forbidden. Thus, in what follows we will be considering only gluino three-body decays. The three benchmark SUSY models we will consider. In the last column, where we have listed the branching ratio for the decay of the squark into a gluino, the number outside of parenthesis is for mq = 4 TeV and the number inside is for mq = 5 TeV.

Analysis
To study the phenomenology of the different gluino decay possibilities discussed in Sec. 2 we choose the three benchmark models presented in Table 1. We will study each of these points at mq = 4 TeV and 5 TeV. These points include the decay of the gluino into two light jets+χ 0 1 , the cascade decay into heavy electroweak particles along with two jets and aχ 0 1 , and the decay into top pairs with aχ 0 1 . All of these points are consistent with existing studies which place bounds on mg and mχ0 1 using Tevatron data on jets +E / T [22].

Pre-selection cuts and backgrounds
To begin we define a set of pre-selection cuts which roughly characterize the kinematic features of the signal. This will allow us to focus on the most relevant backgrounds. Since we study benchmark models with heavy squarks at mq = 4 TeV and 5 TeV, which then decay into an ordinary QCD jet and a gluino jet, our signal is characterized by jets and missing energy. We therefore require: where we use j i to denote the i-th hardest jet. With these pre-selection cuts there are three major sources of background: 1. The most obvious background given the pre-selection cuts above is Z/W + jets where Z → νν or W → lν 5 . It is worthwhile to emphasize that the effects of this background are somewhat non-standard for heavy-squark signals. Normally the Z/W + jets background can be significantly reduced via a cut on how dijet-like an event is (e.g. the α variable of Ref. [25]) as SUSY events, which usually have two or more sources of E / T , look less dijet-like than SM events 6 . Here however, because the BSM events we study appear dijet-like, such a cut cannot be imposed without removing a significant portion of the signal.
2. Another important background comes from boosted tt production. Here E / T can arrise when one top decays semi-leptonically and the resulting lepton becomes difficult to distinguish from the b-jet (due to their collimation). Just as with the leptonic decays of the W in W + jets production, here the lepton can become collimated with a jet.
As discussed in Ref. [27], the lepton and the b quark from a boosted top decay will be within ∆R = 0.4 of each other roughly 50% of the time when p T ∼ 1 TeV, and nearly 100% of the time when p T ∼ 2 TeV. Due to this collimation, the resulting leptons will not pass isolation cuts and the events could be resolved as simply jets + E / T . As with the W + jets background, here we will take a conservative approach and cluster non-isolated leptons into jets.
3. Finally, QCD multijet events can contribute to our background in two ways. Dijet events can contribute real missing energy when they fragment into b-hadrons, which can decay semi-leptonically. Furthermore, dijet events can yield fake missing energy when they are mismeasured. Here we will simulate the effects of the first type of contribution (semi-leptonic b-hadron decays) and provide efficiency estimates for methods to reduce the second type of decay 7 .
Before proceeding, we note that in what follows our signal events are generated at parton level using Madgraph v4.4.49 [28], showered in Pythia v6.422 [18], and matched using the MLM procedure [29]. Some of our backgrounds (multi-jets and Z + jets) are simulated in Sherpa 1.2.3 [30] using the package's automated CKKW matching [31], while others (tt and W + jets) are simulated using the same Madgraph/Pythia flow with MLM matching that we used to generate our signal. When we have run checks comparing Madgraph with MLM matching to Sherpa with CKKW, we find they agree with each other within roughly 20% for most distributions. After generation, all events are clustered into jets by Fastjet v2.4.2 [32,33] using the anti-k T algorithm [34] with R = 0.7.

E / T -jet alignment cuts
The initial signal cross sections (after accounting for the gluino branching ratio), as well as the signal and background rates resulting from the pre-selection cuts introduced earlier, are 6 It is also worth mentioning that the cross section for Z + jets can be surprisingly large when the Z is allowed to be collinear with a jet [26]. For configurations like these the events are, morally speaking, dijet QCD events where a jet radiates a Z, leading to a ln 2 pT /mZ enhancement. 7 In the kinematic region we are considering, where E /T is large compared to jet pT s, any mismeasurement error is non-gaussian and would require a more detailed detector simulation than we can confidently provide. Therefore, we do not attempt to simulate this sort of mismeasured event -instead, later we only provide efficiency estimates.  shown in Table 2. Using the pre-selection cuts we see that the signal rates are reduced by roughly 60%, but the background are brought to the fb level. Furthermore, as can be seen in Fig. 2, the signal and background are both primarily dijet like (since ∆φ(j 1 , j 2 ) ∼ π) and E / T is mostly aligned with the second hardest jet.
As discussed earlier, in addition to the cuts already imposed it is customary to apply a cut on jet-E / T alignment requiring ∆φ(j, E / T ) 0.3. However, as can be seen on the right hand side of Fig. 2, and in Table 2, such a cut would reduce signal rates by 60 − 70%. While the ∆φ(j, E / T ) cut does reduce background (especially the QCD background, which goes down by ∼ 96%), such a cut is impractical and we must relax it, replacing it with something else. A.U.  : ∆φ(j 1 , j 2 ) and ∆φ(E / T , j 2 ) distributions on the left and right after the pre-selection cuts have been applied. The distribution labeled "SUSY" is for a mq = 4 TeV squark decaying to light flavor:q → qqχ 1 0 (Model 1). However, we note that the distributions using other gluino decay modes are quite similar. Note that all histograms are normalized to the same area.

Jet substructure variables
As emphasized in the introduction, the gluino jets in our signal events have a rich substructure. Here we will investigate observables sensitive to this substructure and use them to replace cuts on ∆φ(E / T , j).
A particularly simple observable sensitive to jet substructure is the z variable of Ref. [47]. To calculate z for a jet, one takes its constituents, reclusters them using the k T -algorithm [60,61], and unwinds the clustering one step so that there are two subjets, A and B. Then, z is defined as where E A and E B are the energies of the two subjets. When the k T -algorithm acts on the constituent four-momenta (e.g. calorimeter cells) of a jet, it does so by computing a distance between each pair of four-momenta using the metric for ∆R the angular distance between two jets and R 0 a constant. The smallest of these distance measures is chosen, and the four-momenta associated with it are combined together. In this way a jet is built up in stages, from soft to hard and in angle from near to far. Now, the angle and energy sharing of the radiation emitted by quarks and gluons has a soft/collinear singularity 8 and thus z, which measures this energy sharing is ∼ 0 for ordinary QCD jets, while boosted heavy objects, which have no such singularity 9 , yield z ∼ 1/2. The distributions of z for our signal and background processes are shown in Fig. 3. Here we see that, as expected, the hard splitting present in the signal processes can be distinguished from the soft/collinear splitting of QCD.
However, it is possible to do better. The z variable measures only the energy sharing of the subjets when a jet is broken in two -it only provides minimal information about the for d 1→2 the scale at which the initial jet is broken into two (see Eq. 3.2) contains this information.
The resulting efficiency curves obtained from cuts using this variable are presented in Fig. 4. One can see a marked improvement over the results obtained with the 10 The kT algorithm makes use of angular information when constructing the two subjets.
z variable. Using y 1→2 it is possible to obtain over 90% background rejection with greater than ∼ 40% signal acceptance (and even 60% signal acceptance forg → tt). Finally, we note that it is possible to detect jet substructure without directly constructing subjets. Ref. [62] introduced a jet shape variable termed girth: where the sum is taken over all jet constituents and r i is the distance from each to the jet center. By making the replacements E → p T and θ → r, one can see girth is analogous to the 'jet broadening' [63] shape used at e + e − colliders. The efficiencies obtained through the application of girth are shown in Fig. 4. They are even better than the efficiencies obtained with the y variable (although in what follows we will make use of the y variable, as it is more widely used). Before closing, we note that while these are not completely independent variables, they have different sensitivities and sensitivities to contamination, and thus a more detailed experimental study is needed to optimize a cut on substructure. In closing, we note that the recently introduced N -subjettiness [64,65] variables might be also be useful for this purpose.

Final cuts
We now apply a substructure cut (y 1→2 > 2 · 10 −3 ) in addition to the pre-selection cuts used earlier to find the efficiencies listed in Table 2. From these efficiencies we see that the substructure cut removes a significant amount of the background (the QCD rate drops 79%) while much of the signal is retained (only dropping 20 − 30%). However, the background levels are still worrisome, in particular for W + jets. Fortunately, we can still cut on the subleading jets. Even though our signal is dominantly dijet like, the gluino produced in association with the squark decays largely into jets which are harder than those characteristic of the background. This can be seen in Fig. 5, where we show the p T of the third hardest jet in the events. After imposing a cut on the third hardest jet (we use p T (j 3 ) > 100 GeV) we find the background has been reduced to the point where all three mq = 4 TeV models can be seen at 5σ in 10 fb −1 of data (see Table 2 and Table 3). It is interesting to note that that after all of these cuts the three backgrounds contribute comparably.
Finally, we observe that while the cuts so far are insufficient to see mq = 5 TeV squarks in 100 fb −1 of data, this can be remedied by increasing the jet p T cuts slightly to account for the higher squark mass. Indeed, we find that simply increasing the cut on p T (j 1 ) from 1.5 to 2 TeV we reduce the background enough (by 86%) to see the heavier squarks 11 . The final cross sections and LHC sensitivity can be see in Table 3.  Table 3: Signal cross section and significance for mq = 4(5) TeV at L = 10(100) fb −1 . To arrive at these numbers we use the preselection cuts defined earlier (increasing the cut on p T (j 1 ) to 2 TeV for mq = 5 TeV) and required p T (j 3 ) > 100 GeV and y 1→2 (j 2 ) > 2 · 10 −3 . Note that, after applying these cuts we found background cross sections of σ B = 0.37(0.05) fb.

Conclusion
Here we have considered a relatively unstudied region of SUSY parameter space exhibiting interesting collider phenomenology. In the region we investigated first generation squarks are very heavy, leading to signal events which appear dijet like with E / T aligned with a jet. We found that while we were able to go far in reducing the background to this channel via cuts on jet p T s and E / T , much of our signal was removed by jet/E / T anti-alignment cuts used by LHC experiments to guard against jet mismeasurement errors. We suggested replacing these cuts by a measurement of jet substructure. This allowed us to still remove much of the background while retaining a substantial portion of the signal.
After applying this and the aforementioned cuts, we demonstrated heavy squarks could be seen at mq = 4(5) TeV in L ∼ 10(100) fb −1 of data. Interestingly, in the end all of our background contributed equally, motivating the need for a careful experimental study of the relevant efficiencies (so as to avoid an unfortunate Altarelli cocktail).
In closing, we note that it would be interesting to see if other signals could be enhanced by replacing anti-alignment and similar cuts on jet quality cuts by measurements of jet substructure. In addition, the backgrounds we encountered could potentially be reduced even more through cuts on non-isolated leptons. We hope this serves as further motivation for experimental study of this interesting configuration.