I Introduction and Overview
###### Abstract

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 . In the detector this will show up as a photon with a time-delayed signature and missing . We estimate that using the photon timing system at CDF, and the full 10  data sample, that the sensitivity can be within a factor of three in some regions of parameter space for direct production of the Higgs.

Prospects of Searches for Gauge Mediated Supersymmetry with  production in the Time-Delayed Photon +  Final State at the Tevatron

John D. Mason111E-mail: jdmason@physics.harvard.edu and David Toback222E-mail: toback@tamu.edu

Harvard Center for the Laws of Nature, Harvard University, Cambridge, Massachusetts 02138, USA

Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station TX 77843-4242

July 14, 2019

## 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 Dine:1981za (); Dimopoulos:1981au (); Dine:1981gu (); Nappi:1982hm (); AlvarezGaume:1981wy (); Dimopoulos:1982gm (), so-called gauge mediation supersymmetry breaking (GMSB), it is possible that the fundamental scale of SUSY breaking can be low, , in which case the messenger and SUSY breaking scales are similar in magnitude  Dine:1993yw (); Dine:1994vc (); Dine:1995ag (). In the most general framework Meade:2008wd (); Carpenter:2008wi (); Buican:2008ws (); Komargodski:2008ax (); Rajaraman:2009ga (); Intriligator:2010be (); Dumitrescu:2010ha (), 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-to-lightest sparticles to be the gravitino () and lightest neutralino () respectively and have masses less than 1 and 50 , respectively. In the case that the  mass is near or below we expect 100%. These scenarios lead to interesting +  final states if sparticles are produced at colliders Dimopoulos:1996vz (); Ambrosanio:1996zr (); Ambrosanio:1996jn (); Dimopoulos:1996va (); Dimopoulos:1996yq (); Lopez:1996gd (); Baer:1996hx (); Ambrosanio:1997rv (); Kawagoe:2003jv (); Shirai:2009kn (); Meade:2009qv (); Meade:2010ji ().

Current experimental results from searches for GMSB at LEP, the Tevatron and the LHC LEPGMSB (); TeVGMSB (); CDFLongLived (); LHCGMSB () are not sensitive to scenarios where the  and  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 SPS8 (), and often assume the lifetime of the  () 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 to  -pairs which in turn decay to 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 , favored when the SUSY breaking scale is low Dimopoulos:1996vz (), have also been done at both LEP LEPGMSB () and the Tevatron CDFLongLived (), 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 the  and  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 mass  scenarios PromptHiggsGMSB (). 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 () at the Tevatron and its subsequent decay to -pairs. If we consider the Electroweak fits and SUSY favored mass region 115     160  Inoue:1982ej (); Carena:2002es () and assume a favorable mass relationship between the  and the , (  ), then the production cross section for photon+ final states via can be in the picobarn range at the Tevatron and be a factor of 1,000 over production that proceeds via diagrams PromptHiggsGMSB (). While single Higgs production is always a challenge because it will not produce many final state particles, the long-lifetime of the  can provide a smoking gun signature of exclusive photon+   with a delayed arrival time of the photon at the calorimeter. Using the CDF photon timing system EMTNIM () and the techniques in CDFLongLived () we can identify these delayed photons, .

We propose a search for exclusive production of + ; the so-called exclusive +  final state. We take advantage of the high production cross section of the , the nanosecond lifetime of the , old phenomenology methods/results for +  TobackWagner (), as well as improvements in the understanding of the EMTiming system at CDF EMTNIM () and the SM backgrounds to the exclusive +  final state searches CDFLED (). 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  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  and its branching ratio to -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 ,  and . 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 the  and the  have masses that are accessible at the Tevatron, as is allowed in GGM scenarios Meade:2008wd () and not excluded by current searches for GMSB. In GGM models the bino mass (), wino mass (), and gluino mass () are free parameters. By way of contrast, in MGM models there is a rigid relation, , where and are the and gauge coupling strengths. This forces the chargino to be light if the  is also; current limits would imply 150 . Since there is no reason these relationships must hold in Nature, a lighter  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  is of the order 50 , the gravitino is less than a , and all other sparticles are too heavy to be produced at the LEP, Tevatron or the LHC. Exclusive searches at LEP LEPGMSB () can place very restrictive limits on a low mass   but are only applicable for situations with large direct -pair production cross sections as in MGM models PromptHiggsGMSB () 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  is SM-like in its couplings to SM particles. For this reason, it is reasonable to work in the decoupling limit Gunion:2002zf (). Furthermore, if 2 the branching fraction of the Higgs to  pairs, , can become significant. In this case, the LEP and Tevatron bounds on the SM Higgs mass are applicable to , but must be modified in order to take into account the inclusion of the  decay mode. The SM Higgs mass bound from LEP, 114.4  at  Barate:2003sz (), is only slightly modified by the inclusion of our new decay process since, as we will show, . The Tevatron 95% C.L. exclusion region for the SM Higgs, 153  173  TeVHiggsLimits (), will also be slightly reduced. For the scope of this paper we consider the Higgs mass as a free parameter HiggsNote () and consider the range 120   160 , favored by electroweak fits. For this mass region, the Higgs’s production cross-section is dominated by the fusion diagram and is in the picobarn range and effectively determined by  alone HIGLU ().

The branching fraction can often be as large as 50%. The width of  is determined by  as well the full widths to other modes such as and , if kinematically accessible, and the values , , and . We note that and , like and , are independent parameters in GGM Komargodski:2008ax (). As long as the other superparticles remain kinematically inaccessible at the Tevatron, only these four parameters affect the Higgs branching ratio. The is largest for small values of and and fall as either or grow. Results for are shown in Figure 1 for   and   but as a function of and , and can be bigger than 50%. Since these parameters do not significantly affect other properties of the ,  or  the values of and can be thought of as being implicit in a choice of . While the BR is fairly insensitive to , it is sensitive to  and   also shown in Figure 1. This result, in conjunction with the large  production cross section shows why the production and decay of  at the Tevatron can easily be a thousand times larger than for appropriate choices of  HIGLU ().

The final state phenomenology of  is very different than that produced in SPS-8 scenarios SPS8 (). In the LNG scenario, spartice production is dominated by  events which yields -pairs; in SPS-8 -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 and 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  of order is favored for models with a low fundamental scale of SUSY breaking. The  lifetime is given Dimopoulos:1996vz () by:

 cτ~χ01 =48πm23/2M2Plm~χ0151|P1γ|2, (1)

where and N is the unitary rotation that diagonalized the neutralino mass matrix (), and . The value of F (or equivalently ) is related to the value of the superpartner masses through the dynamics of SUSY breaking. In known calculable models, the fundamental scale of SUSY breaking is typically bounded by: . For squark masses of () this bounds (), which corresponds to a lifetime range of 0.4 ns   180 ns.

Previous studies of GMSB phenomenology at the Tevatron indicate that even if only -pairs can be produced at the Tevatron, different final states must be considered for the lifetime regimes   1 ns, 1 ns    50 ns and   50 ns TobackWagner (). For   1 ns the photons will be produced promptly. The prospects of searches for + are described in PromptHiggsGMSB () with corresponding versions from described in TobackWagner (). In the case   50 ns, both  -pairs will leave the detector and SUSY is largely undetectable using direct methods at the Tevatron. In the case 1 ns    50 ns, the final cascade of  happens at a spatial location that is significantly displaced from the primary collision event that produced the . While this can produce the +, the and the  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 . As shown in TobackWagner (), having a long-enough lifetime to produce a delayed photon also typically produces the case where a significant fraction of the events have one  escaping the detector entirely, making the + final state more sensitive than + TobackWagner (). Finally, since only -pairs are produced we must search in the exclusive +  final state. While there has been a search for long-lived at the Tevatron using the delayed photon final state CDFLongLived (), there is no Tevatron analysis of exclusive + final state. LEP has performed a search in exclusive + LEPGMSB (), but in the LNG scenario at LEP the production rates of sparticles would be negligible.

To summarize, we have outlined an important and uncovered scenario where only the  and  are kinematically accessible at the Tevatron in GGM models. In this model, production of    can be large and is well described by  and alone. For the favored nanosecond lifetime region, we expect the best sensitivity to be in exclusive + if the Higgs is more that twice as heavy as . We next turn to the sensitivity of this search which, as we will see, is dependent on , , and . For the reasons above we considered a number of different mass and lifetime combinations in the phenomenologically favored regions: 120   160 , 30   80  and . For simplicity we choose a baseline scenario with = 135 , = 55.5  and = 5 ns since it is near the central values of our parameters.

## Iii Analysis

Our proposal is to use the photon timing system at CDF to search for an excess of exclusive +  events above background expectations with the full Tevatron dataset of 10 . A similar idea was proposed in 2004 TobackWagner (), but was based on the kinematics of -pair production through and only crude analysis methods were employed. Since then the CDF EMTiming system has been installed and commissioned EMTNIM (), delayed photon searches have been shown to be viable at the Tevatron CDFLongLived () and CDF has completed a sophisticated Run II version of the search for +  events with a jet veto to enforce the exclusive final state, but without the timing requirement CDFLED (). While we are sure that any actual exclusive + 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 Boos (). 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 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  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 . The largest production mechanism of a Higgs is through 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 HIGLU (). NNLO corrections, as calculated in NNLOXsec (), are incorporated using -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 + final state in Ref. CDFLED () 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 , , and the requirement of  50 . In addition, to reduce the large SM backgrounds, the event is rejected if there are any extra high energy objects in the event, such as an extra lepton or jet using a jet veto. Since the data is well described as a function of in CDFLED (), we can consider raising the requirement. Table 1 lists the final set of requirements as well as the event reduction. We scale the results from 2  to 10 .

Since the kinematics of the backgrounds are assumed to be independent of the timing of the photon EMTNIM (), we consider them to be uncorrelated and follow the recommendations of TobackWagner (); CDFLongLived (). The photon timing variable at CDF compares the time of arrival of a photon candidate at the calorimeter relative to expectations. We define “” as,

 tcorr=(tf−ti)−|→xf−→xi|c, (2)

where is the space-time location of the primary collision vertex and 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 =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 EMTNIM (). 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 and , where each is distributed according to the beam parameters which can each be described as a Gaussian with an RMS of and respectively. This scenario has been studied in EMTNIM () 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 2 ns CDFLongLived (), 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 using the pythia 6.4 MC event generator PYTHIA () and the PGS4 PGS () 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 a . This properly takes into account the fact that the  decays at a position that can be different than location of the primary vertex. Similarly, we modified PGS4 to calculate the  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 the ratio of the 0-jet production cross section, , to the 1-jet cross section we take an additional jet veto efficiency which we use in the final acceptance NNLOXsec (). The final acceptance, as a function of the cuts, is displayed explicitly in Table 1 for our baseline scenario. Following the recommendations of Ref. TobackWagner (); CDFLongLived () we assume a 20% uncertainty on the acceptance.

Given the background, acceptance, luminosity and uncertainties we use a modification of the Corlim program WalkerCorlim () in order to compute the expected 95% C.L. cross section upper limit. In addition to the baseline selection requirements and the 2 ns requirement, we found that raising the  to be 50 GeV was helpful. We considered raising the  and the  requirements further, but found either similar or lower sensitivity. Seeing no gain, we find a final background estimate of events.

## Iv Results

We next consider the expected sensitivity as a function of ,  and . We begin by looking at the sensitivity as a function of  for fixed values of the  and  at their baseline values of = 135  and = 55.5 . The results are shown in 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 TobackWagner (); CDFLongLived (). For low lifetimes, 1 ns, the  does not travel long enough within the detector to produce a  with   2 ns. Said differently, the acceptance for the 2 ns requirement goes to zero and the expected limit gets far worse. On the other side, as  gets large, for example 10 ns, a larger and larger fraction of the  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  and  for a fixed = 5 ns. The acceptance is sensitive to both masses individually, as well as in combination. In particular, the larger the value of  the more energy there is available for the photon and -producing objects to go above the selection requirement thresholds in Table 1. Similarly, the mass difference affects the kinematics as well. Equally important, as shown in Ref. TobackWagner (), is the boost of the  which has an important effect on  since it also affects both the path length difference between the arrival position in the calorimeter and the original direction of the . To study this latter variation we consider a  fixed at its baseline value (and = 5 ns), and map out the sensitivity as a function of . 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  that minimizes the cross section, see Figure 4, we see a clear relationship which is well approximated by = 2   + 24 GeV. This optimal relationship arises for a number of reasons. On one side is the   cut. Intuitively, the  is mostly produced at rest in the lab frame and the  must carry some kinematic “kick” so that the photon it emits has enough energy to pass these hard cuts. The lighter the  the more of a kick the  needs. This favors small values of . However, if the  becomes very boosted, then the emitted photon travels in the same direction as the  in the lab frame and this reduces the value of . This effect favors larger values of . 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 , we show the result as a function of  where we have fixed = 5 ns and taken  according to = 2   + 24 GeV. This is shown in Fig. 5 as the black curve. Note that the expected sensitivity gets better and better for higher  as more and more events pass can pass the kinematic thresholds. We first compare this to the expected for and (red line) where both and depend on . The second comparison is to the prediction for where BR 0.5. This is shown as a yellow band. While our sensitivity is clearly dependent on , ,  as well as and , 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 +  final state at CDF for direct production and decay of  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  of the order of 5 ns and when the mass of the  is slightly less than half the mass of the . While it is possible to consider lower lifetime searches, 1 ns TobackWagner (); PromptHiggsGMSB (), we note that similar searches have not found any evidence of new physics TeVGMSB (). We estimate that using the photon timing at CDF, and a data sample of 10   that the sensitivity can be within a factor of three of some regions of parameter space for direct production of the Higgs.

Acknowledgements

The authors would like to thank the Harvard Center for the Fundamental Laws of Nature and the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University. We would like to thank Joel Walker for the use of his customized limit setting tools. DT would like to thank Jonathan Asaadi, Adam Aurisano, Bhaskar Dutta, Daniel Goldin, Eunsin Lee, Jason Nett and Peter Wagner for helpful discussions. JDM would like to thank David Poland for useful discussions and would like to acknowledge the generous support of NSF Grant PHY-0855591, and the Aspen Center for Physics for their hospitality during the preparation of this manuscript

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