Search for Top Squarks at Tevatron Inspired by Dark Matter and Electroweak Baryogenesis

The search for the top squark ($\widetilde{t}_{1}$) within the kinematic reach of Tevatron Run II is of great contemporary interest. Such a $\widetilde{t}_{1}$ can explain the baryon asymmetry of the universe provided $120 ~GeV/c^{2} \leq m_{\widetilde{t}_{1}} \leq m_t$. Moreover if $\Delta m \equiv m_{\widetilde{t}_{1}}$ - $m_{\widetilde\chi_1^0}$ is small, where $\widetilde\chi_1^0$ is the LSP, the dark matter relic density as obtained from the WMAP data may be explained via $\widetilde{t}_{1}$- LSP coannihilation. In this scenario the decay $\widetilde{t}_{1} \to c \widetilde\chi_1^0$ is likely to occur with 100 % branching ratio but for small $\Delta m$ the conventional di-jet + $\not E_T$ signal becomes unobservable. We propose a new search strategy based on the $2j + \not E_T$ signature accompanied by an isolated cluster of energy which arises from a decaying heavy particle with characteristic decay length. Our preliminary simulations with PYTHIA indicate that for $100 ~GeV/c^{2} \le m_{\widetilde{t}_{1}} \le 130 ~GeV/c^{2}$ this signal may be observable while somewhat lager $m_{\widetilde{t}_{1}}$ may still provide hints of new physics.


Introduction
In the Minimal Supersymmetric Standard Model (MSSM) [1] there are two scalar superpartners t L and t R , of the top quark which are the weak eigenstates. The mass eigenstates the lighter top squark ( t 1 ) and the heavier top squark ( t 2 ) are linear combinations of the weak eigenstates. Due to mixing effects in the top squark mass matrix in the weak basis driven by the top quark mass (m t ) there may be a significant mass difference between t 1 and t 2 . In fact the former could very well be the next-to-lightest supersymmetric particle (NLSP), the lightest neutralino ( χ 0 1 ) being the lightest supersymmetric particle (LSP) by the standard assumption in R-parity conserving MSSM. This happens in a wide region of the MSSM parameter space. In this scenario, henceforth referred to as the t 1 -NLSP scenario, the t 1 may be the only strongly interacting superpartner within the kinematic reach of Tevatron Run II experiments with a relatively large production cross-section.
Additional interest in the light top-squark scenario stems from the observation that the MSSM can explain the baryon asymmetry of the universe via electroweak baryogenesis (EWBG) provided 120 GeV /c 2 ≤ m t 1 ≤ m t [2]. The search for t 1 is, therefore, a high priority program for the on going experiments at the Tevatron.
The search for t 1 -NLSP at Tevatron Run I and LEP and, more recently, at Tevatron Run II produced negative results and lower bounds on m t 1 . Most of the analyses [3,4,5] are based on the assumption that t 1 decays via the Flavor Changing Neutral Current (FCNC) induced loop decay, t 1 → c χ 0 1 [6] with 100 % branching ratio (BR). We also employ this assumption which is by and large valid if tanβ ≥ 7 where tan β is the ratio of the vacuum expectation values for the two neutral Higgs bosons present in the MSSM [7,8]. For lower values of this parameter the four body decay of the t 1 may be a competing channel [7,8,9] There are decay modes of the t 1 -NLSP other than the above two channels. They are the tree-level two body decay, t 1 → t χ 0 1 and the three body decay, t 1 → bW χ 0 1 . The last modes are kinematically forbidden for small values of the mass difference ∆m = m t 1 − m χ 0 1 which is the main concern of this paper.
The search for t 1 -NLSP are based on the jets plus missing E T channel [4,5]. Some of the more recent works employed c-jet tagging by a lifetime based heavy flavour algorithm.
These jets become softer if ∆m is small. As a result the efficiency of the kinematical cuts for suppressing the background as well as that of c-jet tagging decreases. This weakens the limit on m t 1 from Tevatron. At Tevatron Run I the largest m t 1 excluded was 122 GeV /c 2 for m χ 0 1 = 55 GeV /c 2 . The most recent analysis by the D0 collaboration at Run II [5] with c-jet tagging obtained the limit 150 GeV /c 2 for m χ 0 1 = 65 GeV /c 2 for the most conservative cross-section after including the next to leading order (NLO) corrections [10].
On the other hand the LEP lower-bounds on m t 1 are restricted mainly due to kinematics and are around 100 GeV /c 2 [3]. However, much smaller values of ∆m can be probed in the cleaner environment of an e + − e − collider.
The prospect of t 1 -NLSP search via this decay channel at Run II was investigated in [11]. It was observed that a large region of the m t 1 -m χ 0 1 parameter space corresponding to small ∆m is beyond the reach of Run II. For a given m t 1 there is a minimum value of ∆m that can yield an observable signal.
A modified strategy for t 1 -NLSP searches in the limit of small ∆m is important in its own right. The current interest in this search, however, is further strengthened by one of the cornerstones of the interface between particle physics and cosmology. A very attractive feature of the R-parity conserving MSSM is that the LSP ( χ 0 1 ), is a very good candidate for the dark matter (DM) in the universe required, e.g, by the Wilkinson Microwave Anisotropy probe (WMAP) data [12]. The DM relic density depends on the annihilation cross-section (thermally averaged) of a LSP pair. The coannihilation of the LSP with any other supersymmetric particle(sparticle)is another important mechanism for relic density production.
This mechanism is, however, efficient only when the two coannihilating particles have approximately the same mass. Thus in the small ∆m scenario t 1 -LSP coannihilation may indeed be an important mechanism for producing appropriate relic density [13].
The region of the parameter space of MSSM consistent with the DM relic density is severely constrained by the WMAP data. Nevertheless even in more restricted versions of the MSSM like the minimal supergravity model(mSUGRA) [14] one finds a narrow region of the parameter space where t 1 -LSP coannihilation is an important relic density producing mechanism [15].
The search for t 1 -NLSP with a small ∆m is, therefore, important irrespective of the question of EWBG. However, it is certainly worthwhile to check whether t 1 with mass in the quoted range preferred by EWBG can also produce an acceptable DM relic density. This was investigated in [6]. It was found that in a significant region of the allowed parameter space ∆m is indeed small ( see figure 7 of [6]).
The results of [6] were illustrated by specific choices of other MSSM parameters. In particular EWBG in the MSSM requires certain CP violating (CPV) phases. In a certain phase convention the relative phase(φ µ ) between the higgsino mass parameter µ and the SU(2) gaugino mass M 2 is the most important one. EWBG usually requires 0.05 ≤ φ µ ≤ 1. However, various uncertainties in the calculation does not rule out a much smaller magnitude of this phase. Thus calculations by neglecting this phase seems to be a reasonable approximation [16].
It should, however, be emphasized that the signal proposed by us is fairly model independent and does not depend on the CPV phase or many of the other MSSM parameters at all as long as the BR( t 1 → c χ 0 1 ) is close to 100%. Under this assumption the size of the signal depends on m t 1 through the production cross-section of the t 1 pair via the standard QCD processes and on m χ 0 1 through the efficiency of the kinematical cuts. The starting point of our work is the observation that when mass difference ∆m is small, in most of the signal events, one of the c-quarks from t 1 pair decay is not energetic enough to produce a jet which may pass jet selection criteria of the experiments at Tevatron. It may be seen as an isolated energy deposit in the calorimeter coming from the decay of a heavy particle. We call it isolated cluster (IC). Thus the proposed signal consists of a c-jet of modest E T accompanied by missing energy and an isolated cluster. In order to reduce the background we require another hard jet in the signal which in most cases comes from QCD radiation. Our simulations show that a set of selection criteria based on the above features of the signal can isolate it from the SM background.
In this work we do not consider the prospect of fully identifying the flavour of the heavy, isolated, decaying object because of the rather small statistics. This leads to inevitable backgrounds from, e.g., bb events and W/Z + jets events. However, we shall analyze at the generator level some important characteristics of this object which has the potential of reducing the SM backgrounds to a manageable level. At the same time we emphasize that this work is only suggestive of a new approach to t 1 search at the Tevatron and needs detailed detector simulation for a more definitive statement and that is beyond the scope of this work.
We have used Pythia (v 6.206) [17] for generation of both signal and background events which includes generation of the parton level events followed by the decay of the partons hadronization and decay of their daughters. Generation of both signal and background events take into account initial state radiation (ISR) and final state radiation (FSR). The cross-sections σ bb and σ cc are very large and most of these events generated with low √ŝ are not relevant for our analysis. To sample the bb and cc events better for our purpose and save 1. The calorimeter coverage is |η| ≤ 3.

A cone algorithm with ∆R =
√ ∆η 2 + ∆φ 2 = 0.5 has been used for jet finding with E jet T,min ≥ 10 GeV and |η jet | ≤ 3 and jets have been ordered in E T .
3. We consider leptons (ℓ = e, µ) with E ℓ T ≥ 5 GeV , |η ℓ | ≤ 3. The lepton should be isolated from jets (∆R(jet, ℓ) ≥ 0.5).  A quark or a gluon from (mainly) FSR is seen as a jet and in most cases this jet appears to have the highest E T . This prompts us to consider a rather unusual signature for the signal events as mentioned below.
The backgrounds, particularly bb and cc events have very large cross-sections and hence we need to generate a large number of events and retain only a small fraction of them which pass pre-selection for detailed analysis. We have used the following pre-selection criteria: 1. Event should have only two jets: N jet = 2 (see figure 1) 2. Events with isolated leptons are rejected.
3. One of the jets should contain a long lived particle (B or, D hadron) and henceforth called matched-jet (MJ). 4. Event should have an isolated cluster resulting from the decay of a B or D hadron such that ∆R(jet, IC ) ≥ 0.5. The direction of the isolated cluster is defined to be the direction of the decaying B or D hadron. In the final selection this cluster has to be identified as the signature of a long lived particle, the criteria for which are discussed in detail later. 5. We assume that a b-jet with 30 GeV < E jet T < 50 GeV is tagged with a probability ǫ b = 0.4 and for E jet T > 50 GeV , ǫ b = 0.5 where ǫ b is the single b-jet tagging efficiency (i.e., the ratio of the number of tagged b-jets and the number of taggable b-jets).
The largest background comes from Z+jets production. The variation of the cross-section of this process with the QCD scale is not very severe.      rejects background, particularly W+jets and Z+jets events. The matched-jet is most likely to be the leading jet in W+jets and Z+jets events whereas it is the 2nd jet in the signal events. We therefore select events whose E MJ T < 40 GeV (see figure 5).
We also partially reconstruct invariant mass of the matched-jet ( M M J inv ) using the charged tracks associated with it. Similarly M IC inv is reconstructed for the isolated cluster. The cuts M M J inv ≤ 4.5 GeV /c 2 and M IC inv ≤ 2 GeV /c 2 , reject the bb events and also reduce W+jets and Z+jets backgrounds (see figure 6). The combined effect of these cuts (Cut 5) for the signal and the dominant backgrounds is shown in column 8 of table 1.
In table 1 the selection efficiencies for each cut (1 -5) includes the effects of pre-selection.
The eighth column shows the efficiency for the final selection. Although a very high rejection factor of (10 −7 ) is achieved for the bb events and no event in the simulated sample survives, this may still be dangerous as σ bb is very large. Since the signal events do not have spectacular signatures, it is not possible to apply more stringent criterion on any of the features and still retain a good signal. It may be required to exploit the subtle features of the matched-jet and the isolated cluster to get rid of the bb events. There are a few features which may be exploited to this end although it may be experimentally challenging: • Number of charged tracks associated with the isolated cluster.
• Upper cut on the lifetime related observables for the matched-jet, expected to be a c-jet and the isolated cluster, expected to come from the decay of a D hadron in the signal.
• presence of a K ± in the isolated cluster which carries a significant fraction of its p T .
• More reliable reconstruction of the invariant masses using full detector information. Since these observables are rather delicate, they may be simulated only using detailed detector modelling and estimation of the effects of criteria based on these observables is beyond the scope of this analysis. However it may be said with some degree of confidence that bb and other background events may be further suppressed by using judicious choice of such criteria.
Our final results are presented in table 2. In view of the LEP limits [3] we have looked into signals with m t 1 ≥ 100 GeV /c 2 and we have chosen m t 1 − m χ 0 1 (in GeV /c 2 ) = 10, 15 and 20. The significance is defined as S = N sig / N bkg where N sig ( N bkg ) is the number of signal ( background ) events passing the selection criteria for an integrated luminosity of L = 8 f b −1 . For m t 1 ≤ 130 GeV /c 2 we may hope for a discovery while beyond that it may be restricted to the level of a hint. The parameter space probed by us contains a part of the region interesting in the context of EWBG.
Again, it should be emphasized that this very preliminary analysis is designed to provoke the experimentalists to scan the region interesting from the point of view of dark matter relic density and EWBG.