Prospects of Searches for Gauge Mediated Supersymmetry with h^0 ->{\chi}_1^0 {\chi}_1^0 production in the Time-Delayed Photon + MET Final State at the Tevatron

We propose a search for direct production and decay of the lightest supersymmetric Higgs boson to two neutralinos in gauge mediated models at the Fermilab Tevatron. We focus on the final state where each neutralino decays to photon and light gravitino with a lifetime of order O(ns). In the detector this will show up as a photon with a time-delayed signature and missing E_T. We estimate that using the photon timing system at CDF, and the full 10/fb data sample, that the sensitivity can be within a factor of three in some regions of parameter space for direct production of the Higgs.


I. INTRODUCTION AND OVERVIEW
The Higgs potential in the standard model (SM) provides a simple description of the dynamics of electroweak symmetry breaking. An explanation of why the electroweak scale is hierarchically smaller than the Planck scale is provided by embedding the Higgs potential in the minimal supersymmetric standard model (MSSM). The MSSM predicts the existence of a variety of new supersymmetric (SUSY) particles. If SUSY breaking is communicated to the MSSM via gauge interactions [1][2][3][4][5][6], so-called gauge mediation supersymmetry breaking (GMSB), it is possible that the fundamental scale of SUSY breaking can be low, O(100 TeV), in which case the messenger and SUSY breaking scales are similar in magnitude [7][8][9]. In the most general framework [10][11][12][13][14][15][16], so-called general gauge mediation (GGM), a variety of superpartner spectra are possible. Since many explicit models fall into this broader class, it is important to consider them. In particular, GGM allows for the lightest and next-tolightest sparticles to be the gravitino (G) and lightest neutralino (χ 0 1 ) respectively and have masses less than 1 keV/c 2 and 50 GeV/c 2 , respectively. In the case that theχ 0 1 mass is near or below M Z 0 we expect BR(χ 0 1 → γ +G) ≈100%. These scenarios lead to interesting γ + E / T final states if sparticles are produced at colliders [17][18][19][20][21][22][23][24][25][26][27][28].
Current experimental results from searches for GMSB at LEP, the Tevatron and the LHC [29][30][31][32] are not sensitive to scenarios where theχ 0 1 andG are the only sparticles with masses that are kinematically accessible. The standard GMSB searches are focused on minimal gauge mediation (MGM) which is typically encapsulated using the SPS-8 relations [33], and often assume the lifetime of theχ 0 1 (τχ0 1 ) is ≪1 ns. The reason most experiments are sensitive to MGM models is that they allow for the production of the heavier sparticles at a high rate, each of which decay down toχ 0 1 -pairs which in turn decay to γγ + E / T in association with other high energy SM particles. For low lifetimes, both photons can be observed in the detector as they are promptly produced. Other searches that assume a nanosecond or longer τχ0 1 , favored when the SUSY breaking scale is low [17], have also been done at both LEP [29] and the Tevatron [31], but they also assume SPS-8 type relations, which keep the production cross sections high. If the mass relationships in SPS-8 are released, then it is possible that only theχ 0 1 andG have masses low enough to be kinematically allowed in collider experiments and the large direct sparticle production rate previously considered essentially vanish. In this case then the LEP, Tevatron and LHC limits no longer cover the low massχ 0 1 scenarios [34]. We will refer to this case as the Light Neutralino and Gravitino (LNG) scenario.
In this paper we discuss the potential for sensitivity to LNG models by focusing on the production of the lightest Supersymmetric Higgs (h 0 ) at the Tevatron and its subsequent decay toχ 0 1 -pairs. If we consider the Electroweak fits and SUSY favored mass region 115 GeV/c 2 < m h 0 < 160 GeV/c 2 [35,36] and assume a favorable mass relationship between the h 0 and theχ 0 1 , (m h 0 ≥ 2 · mχ0 1 ), then the production cross section for photon+E / T final states via pp → h 0 →χ 0 1χ 0 1 → (γG)(γG) can be in the picobarn range at the Tevatron and be a factor of 1,000 over production that proceeds via Z * /γ diagrams [34]. While single Higgs production is always a challenge because it will not produce many final state particles, the long-lifetime of theχ 0 1 can provide a smoking gun signature of exclusive photon+ E / T with a delayed arrival time of the photon at the calorimeter. Using the CDF photon timing system [37] and the techniques in [31] we can identify these delayed photons, γ delayed .
We propose a search for exclusive production of pp → h 0 →χ 0 1χ 0 1 → γ delayed + E / T ; the so-called exclusive γ delayed + E / T final state. We take advantage of the high production cross section of the h 0 , the nanosecond lifetime of theχ 0 1 , old phenomenology methods/results for pp → Z * /γ →χ 0 1χ 0 1 → γ delayed + E / T [38], as well as improvements in the understanding of the EMTiming system at CDF [37] and the SM backgrounds to the exclusive γ delayed + E / T final state searches [39]. As we will see, this search opens the exciting possibility of a simultaneous discovery of both the Higgs and low-scale SUSY using the full 10 fb −1 data set at the Tevatron.
The outline of the paper is as follows, in Section II we briefly describe both the framework we consider for general forms of gauge mediation as well as how it couples to the Higgs sector. We then describe the assumptions and the experimental results used to constrain the parameter space we consider in the search. As we will see, sparticle production rates are well described by m h 0 and its branching ratio toχ 0 1 -pairs. In Section III we describe the analysis methods. Using existing tools and data, as well as simple analysis assumptions, we find that the sensitivity is determined solely by m h 0 , mχ0 1 and τχ0 1 . Each plays an important role in the kinematics of the events and the amount of delay of the photon. In Section IV we give our results, and in Section V we conclude that even with our simple assumptions, and no particular optimization, that we are within a factor of three of being sensitive to single Higgs production in a scenario that no one else is sensitive to.

II. GAUGE MEDIATED SUPERSYMMETRY AND THE HIGGS SECTOR
We will consider the LNG scenario where only theχ 0 1 and theG have masses that are accessible at the Tevatron, as is allowed in GGM scenarios [10] and not excluded by current searches for GMSB. In GGM models the bino mass (M 1 ), wino mass (M 2 ), and gluino mass (M 3 ) are free parameters. By way of contrast, in MGM models there is a rigid relation, , where g and g ′ are the SU(2) L and U(1) Y gauge coupling strengths. This forces the chargino to be light if theχ 0 1 is also; current limits would imply mχ 0 Since there is no reason these relationships must hold in Nature, a lighterχ 0 1 can easily be achieved in this context due to a general soft mass spectrum for superpartners which still preserves the flavor-blind mechanism of communicating SUSY breaking to the MSSM. In this case, it is possible that mχ0 1 is of the order 50 GeV/c 2 , the gravitino is less than a keV/c 2 , and all other sparticles are too heavy to be produced at the LEP, Tevatron or the LHC. Exclusive searches at LEP [29] can place very restrictive limits on a low massχ 0 1 but are only applicable for situations with large directχ 0 1 -pair production cross sections as in MGM models [34] which do not occur in this scenario.
In addition to the sparticle spectrum of the MSSM, the two-higgs doublets provide five separate physical Higgs particles. We note that most of SUSY parameter space is such that the h 0 is SM-like in its couplings to SM particles. For this reason, it is reasonable to work in the decoupling limit [40]. Furthermore, if 2·mχ0 1 < m h 0 the branching fraction of the Higgs toχ 0 1 pairs, BR(h 0 →χ 0 1χ 0 1 ), can become significant. In this case, the LEP and Tevatron bounds on the SM Higgs mass are applicable to m h 0 , but must be modified in order to take into account the inclusion of the h 0 →χ 0 1χ 0 1 decay mode. The SM Higgs mass bound from LEP, m Higgs > 114.4 GeV/c 2 at 95% C.L. [41], is only slightly modified by the inclusion of our new decay process since, as we will show, BR(h 0 →χ 0 1χ 0 1 ) < 0.7. The Tevatron 95% C.L. exclusion region for the SM Higgs, 153 GeV/c 2 < m Higgs <173 GeV/c 2 [42], will also be slightly reduced. For the scope of this paper we consider the Higgs mass as a free parameter [43] and consider the range 120 GeV/c 2 < m h 0 < 160 GeV/c 2 , favored by electroweak fits. For this mass region, the Higgs's production cross-section is dominated by the gg fusion diagram and is in the picobarn range and effectively determined by m h 0 alone [44]. 1 is very different than that produced in SPS-8 scenarios [33]. In the LNG scenario, spartice production is dominated by h 0 events which yieldsχ 0 1 -pairs; in SPS-8χ 0 1 -pairs are produced at the end of decay chains, and thus are associated with large amounts of high energy final state particles from the cascades which makes them easier to separate from SM backgrounds. While W ± h 0 and Z 0 h 0 processes can occur, their rate will be much smaller. New discovery methods will be needed at the Tevatron.
A crucial issue for any new search in LNG scenarios is that τχ0 1 of order O(1 ns) is favored for models with a low fundamental scale of SUSY breaking. Theχ 0 1 lifetime is given [17] by: where |P 1γ | = |N 11 c W + N 12 s W | and N is the unitary rotation that diagonalized the neu-  χ 0 1 -pairs can be produced at the Tevatron, different final states must be considered for the lifetime regimes τχ0 1 ≪ 1 ns, 1 ns < τχ0 1 < 50 ns and τχ0 1 > 50 ns [38]. For τχ0 1 ≪ 1 ns the photons will be produced promptly. The prospects of searches for pp →h 0 →χ 0 1χ 0 1 → (γG)(γG) → γγ+E / T are described in [34] with corresponding versions from Z * /γ described in [38]. In the case τχ0 1 > 50 ns, bothχ 0 1 -pairs will leave the detector and SUSY is largely undetectable using direct methods at the Tevatron. In the case 1 ns < τχ0 1 < 50 ns, the final cascade ofχ 0 1 → γ +G happens at a spatial location that is significantly displaced from the primary collision event that produced the h 0 . While this can produce the γγ+E / T , the γ + E / T and the E / T final states, in each case the arrival time of the photon can be delayed relative to expectations than if it were promptly produced. This is known as a delayed photon or γ delayed . As shown in [38], having a long-enough lifetime to produce a delayed photon also typically produces the case where a significant fraction of the events have oneχ 0 1 escaping the detector entirely, making the γ delayed +E / T final state more sensitive than γ delayed γ delayed +E / T [38]. Finally, since onlyχ 0 1 -pairs are produced we must search in the exclusive γ delayed + E / T final state. While there has been a search for long-livedχ 0 1 → γG at the Tevatron using the delayed photon final state [31], there is no Tevatron analysis of exclusive γ delayed +E / T final state. LEP has performed a search in exclusive γ delayed +E / T [29], but in the LNG scenario at LEP the production rates of sparticles would be negligible.

III. ANALYSIS
Our proposal is to use the photon timing system at CDF to search for an excess of exclusive γ delayed + E / T events above background expectations with the full Tevatron dataset of 10 fb −1 . A similar idea was proposed in 2004 [38], but was based on the kinematics of χ 0 1 -pair production through Z * /γ and only crude analysis methods were employed. Since then the CDF EMTiming system has been installed and commissioned [37], delayed photon searches have been shown to be viable at the Tevatron [31] and CDF has completed a sophisticated Run II version of the search for γ + E / T events with a jet veto to enforce the exclusive final state, but without the timing requirement [39]. While we are sure that any actual exclusive γ delayed +E / T search will be more sophisticated than what we are proposing, we use the current published results as well as Monte Carlo (MC) simulation methods to reliably estimate a sensitivity. We will use simple requirements to define our signal regions to estimate the backgrounds and acceptance to the search. Our primary emphasis is on robustness, so we will not introduce additional requirements where we cannot confidently model the backgrounds.
The estimate of our sensitivity requires a number of elements. This includes the expected production cross sections, the branching ratios, the backgrounds for the proposed cuts (with associated uncertainty), the acceptances for the signal (with associated uncertainty), and the luminosity. For simplicity, we define the sensitivity as the expected 95% confidence level (C.L.) cross section times branching ratio upper limit in the no-signal assumption scenario [45]. This allows for a comparison to various production cross section predictions that can be model or parameter choice dependent. We also choose to make our predictions based on the results of a straight-forward counting experiment where we compare the number of events in a signal region to background expectations as these are readily converted into an expected cross section limit. Thus, to estimate the sensitivity we simply require an estimate of the number of background events that pass all the final event selection requirements and the acceptance, which we define to be the fraction of the h 0 →χ 0 1χ 0 1 → (γG)(γG) events passing those same requirements. In addition, we take into account some reasonable expectations for uncertainties as well as assume the full Tevatron run dataset with a 6% luminosity uncertainty. For the event selection requirements we will use a combination of selection requirements from the published CDF papers.
We walk through these elements systematically. Since we assume the h 0 is SM-like in its couplings to SM particles, its production cross section is the same as for the SM Higgs and is determined solely by m h 0 . The largest production mechanism of a Higgs is through gg → h 0 and is the only one we will consider. This production cross section receives large enhancements from radiative corrections at NLO and are calculated using the HIGLU program [44]. NNLO corrections, as calculated in [46], are incorporated using k-factors.
The background and acceptance estimates are based on a combination of published results and MC simulation. For simplicity, for the backgrounds we follow the available data from the CDF search for new physics in the exclusive γ+E / T final state in Ref. [39] and use these cuts as our baseline selection requirements. We then use a simple set of additional requirements.
The baseline requirements from the paper include a single isolated photon with |η| < 1.1, such as an extra lepton or jet using a jet veto. Since the data is well described as a function of E T in [39], we can consider raising the E T requirement. Table I lists the final set of requirements as well as the event reduction. We scale the results from 2 fb −1 to 10 fb −1 .
Since the kinematics of the backgrounds are assumed to be independent of the timing of the photon [37], we consider them to be uncorrelated and follow the recommendations of [31,38]. The photon timing variable at CDF compares the time of arrival of a photon candidate at the calorimeter relative to expectations. We define "t corr " as, where (t i , x i ) is the space-time location of the primary collision vertex and (t f , x f ) is the space-time location of the photon when it deposits energy into the EM calorimeter. For a promptly produced photon with perfect measurements we would have t corr =0. Due to measurement uncertainties, for photons with a correctly identified vertex, the distribution is well described as a Gaussian with a mean of zero, and an RMS of 0.65 ns [37]. However, for this sample, where there is a jet veto, there are likely to be only a small amount of charged particles available to produce the vertex. In addition, the high luminosity running at the Tevatron is likely to produce multiple min-bias collisions which can be incorrectly selected as the vertex. This produces random values of t i and x i , where each is distributed according to the beam parameters which can each be described as a Gaussian with an RMS of 1.28 ns and 28 cm respectively. This scenario has been studied in [37] which describes the "wrong vertex" background as being well modeled as a Gaussian with a mean of zero, and an RMS of 2.05 ns. Because there is a high probability of picking the wrong vertex, we conservatively assume that 25% of all background events will have an incorrectly assigned vertex. Putting this together, we take the background timing distribution to be uncorrelated with the kinematics of the event, double Gaussian, with both Gaussians's centered at zero, but 25% having an RMS of 2.05 ns, and the rest with an RMS of 0.65 ns. The standard timing requirement is t corr >2 ns [31], although this could, in principle, be optimized. This requirement rejects about 95% of the backgrounds. We take an uncertainty on the final background estimate to be 30%.
To estimate the acceptance for the signal we model pp → h 0 →χ 0 1χ 0 1 → (γG)(γG) using the pythia 6.4 MC event generator [47] and the PGS4 [48] detector simulation. We have modified PGS4 to recalculate the calorimeter cell in which a photon deposits energy for the case that the photon arises from the decay of aχ 0 1 . This properly takes into account the fact that theχ 0 1 decays at a position that can be different than location of the primary vertex. Similarly, we modified PGS4 to calculate the t corr for signal events. We measure the acceptance by counting the fraction of events that pass each of the final event-level reduction requirements in Table 1. To correct for the fact that we are comparing to the NNLO production, but using a LO MC simulation, we reduce the acceptance accordingly. Taking Cut Signal Acceptance Background Events = 55.5 GeV/c 2 and τχ0 1 = 5 ns. The acceptance is the fraction of events passing all the requirements, and takes into account the 75% jet-veto efficiency starting in that row. We take a 20% uncertainty on the acceptance. The backgrounds are scaled to expectations for 10 fb −1 and we assume a 30% uncertainty.
the ratio of the 0-jet production cross section, σ (N LO) 0−jet (gg → h 0 ), to the ≥ 1-jet cross section we take an additional 75% jet veto efficiency which we use in the final acceptance [46]. The final acceptance, as a function of the cuts, is displayed explicitly in Table I for our baseline scenario. Following the recommendations of Ref. [31,38] we assume a 20% uncertainty on the acceptance.
Given the background, acceptance, luminosity and uncertainties we use a modification of the Corlim program [49] in order to compute the expected 95% C.L. cross section upper limit. In addition to the baseline selection requirements and the t corr > 2 ns requirement, we found that raising the E γ T to be E γ T > 50 GeV was helpful. We considered raising the t corr and the E γ T requirements further, but found either similar or lower sensitivity. Seeing no gain, we find a final background estimate of 52 ± 16 events.

IV. RESULTS
We next consider the expected sensitivity as a function of m h 0 , mχ 0 1 and τχ0 1 . We begin by looking at the sensitivity as a function of  Figure 2. We find that the optimal sensitivity occurs for a lifetime of 5 ns. This is readily understood in terms of kinematic arguments, and is consistent with the results of [31,38]. For low lifetimes, τχ0 1 ≪1 ns, theχ 0 1 does not travel long enough within the detector to produce a γ delayed with t corr > 2 ns. Said differently, the acceptance for the t corr >2 ns requirement goes to zero and the expected limit gets far worse. On the other side, as τχ0 1 gets large, for example τχ0 1 >10 ns, a larger and larger fraction of theχ 0 1 will leave the detector before decaying so the acceptance goes down as well. It is also useful to consider how the sensitivity varies as a function of m h 0 and mχ0 1 for a fixed τχ0 1 = 5 ns. The acceptance is sensitive to both masses individually, as well as in combination. In particular, the larger the value of m h 0 the more energy there is available for the photon and E / T -producing objects to go above the selection requirement thresholds in Table I. Similarly, the mass difference affects the kinematics as well. Equally important, as shown in Ref. [38], is the boost of theχ 0 1 which has an important effect on t corr since it also affects both the path length difference between the arrival position in the calorimeter and the original direction of theχ 0 1 . To study this latter variation we consider a m h 0 fixed at its baseline value (and τχ0 1 = 5 ns), and map out the sensitivity as a function of mχ 0 1 . This is shown in Fig. 3. The minimum of the distribution optimizes the expected limit. Repeating the results for all Higgs masses and picking the mχ 0 1 that minimizes the cross section, see This optimal relationship arises for a number of reasons. On one side is the E γ T > 50 GeV cut. Intuitively, the h 0 is mostly produced at rest in the lab frame and theχ 0 1 must carry some kinematic "kick" so that the photon it emits has enough energy to pass these hard cuts. The lighter the m h 0 the more of a kick theχ 0 1 needs. This favors small values of mχ0 1 . However, if theχ 0 1 becomes very boosted, then the emitted photon travels in the same direction as theχ 0 1 in the lab frame and this reduces the value of t corr . This effect favors larger values of mχ 0 1 . The minimal value of the expected limit value reflects this balance.  To compare our expected cross section limits to the production cross section and branching ratio predictions we consider two branching ratio scenarios. For the expected limit on GeV. This is shown in Fig. 5 as the black curve. Note that the expected sensitivity gets better and better for higher m h 0 as more and more events pass can pass the kinematic thresholds. We first compare this to the expected σ · BR for tan β = 1.5 and µ = 300 GeV/c 2 (red line) where both σ and BR(h 0 →χ 0 1χ 0 1 ) depend on m h 0 . The second comparison is to the prediction for σ · BR where BR ≤ 0.5. This is shown as a yellow band. While our sensitivity is clearly dependent on m h 0 , mχ 0 1 , τχ0 1 as well as µ and tan β, we see our sensitivity is often within a factor of 5 of the expected production cross section times branching ratio. At some locations it is as close as a factor of 3.

V. CONCLUSION
We have investigated the sensitivity of a proposed search in the exclusive γ delayed + E / T final state at CDF for direct production and decay of h 0 →χ 0 1χ 0 1 in gauge mediated models at the Fermilab Tevatron. While we have picked a fairly restricted regime, in many ways we are picking the favored regions of parameter space, and regions which are not yet covered by existing experiments. We find that within these assumptions we have optimal sensitivity when τχ0 1 of the order of 5 ns and when the mass of theχ 0 1 is slightly less than half the mass of the h 0 . While it is possible to consider lower lifetime searches, τχ0 1 ≪ 1 ns [34,38], we note that similar searches have not found any evidence of new physics [30]. We estimate that using the photon timing at CDF, and a data sample of 10 fb −1 that the sensitivity can be within a factor of three of some regions of parameter space for direct production of the Higgs.