A Measurement of Neutralino Mass at the LHC in Light Gravitino Scenarios

We consider supersymmetric (SUSY) models in which a very light gravitino is the lightest SUSY particle. Assuming that a neutralino is the next-to-lightest SUSY particle, we present a measurement of the neutralino mass at the LHC in two photons + missing energy events, which is based on the MT2 method. It is a direct measurement of the neutralino mass itself, independent of other SUSY particle masses and patterns of cascade decays before the neutralino is produced.

Among various supersymmetric (SUSY) models, those with an ultralight gravitino of mass m 3/2 < ∼ O(10) eV are very attractive, since they are completely free from notorious gravitino problems [1]. In this letter, we assume a neutralino is the next-to-lightest SUSY particle (NLSP), and present a measurement of its mass at the LHC. It is based on the so-called M T2 method [2]. We show that this method can directly determine the neutralino mass, independently of other SUSY particle masses, and it does not rely on specific patterns of cascade decays before the neutralino is produced.
In the scenario considered here, essentially all the SUSY events will end up with two neutralino NLSPs, 1 each of which then dominantly decays into a gravitino and a photon. 2 We assume that the decay length of the NLSP neutralino is so short that the decay occurs inside the detector and the photons' momenta are measured well. Therefore, the main signature at the LHC will be two high transverse momentum photons and a large missing transverse momentum. If such a signal will indeed be discovered, one of the most natural candidates for the underlying model is a SUSY model with a gravitino LSP and a neutralino NLSP.
Furthermore, from the prompt decay of the neutralino, we can assume that the gravitino is very light, essentially massless for the following discussion. This is because the NLSP decay length is proportional to the gravitino mass squared as and a heavier gravitino (m 3/2 > O(1) keV) would make the neutralino decay outside the detector. 3 This indirect information of the massless LSP plays a crucial role in the NLSP mass determination.
Let us start by briefly explaining the M T2 method [2]. Suppose that there is a particle A which promptly decays by the process A → B + X, where B is a visible (standardmodel) particle and X is a neutral and undetected particle. When two A s are produced in a collider, we can measure the two Bs' transverse momenta p B,1 T , p B,2 T and the missing We consider two gauge mediation models for a demonstration. In the following, mass spectrums are calculated by ISAJET 7.72 [5] and we use programs Herwig 6.5 [6] and AcerDET-1.0 [7] to simulate LHC signatures.
The first example is a strongly interacting gauge mediation (SIGM) model [8], in which the NLSP is a neutralino. We take the same SIGM parameters as the example in Sec. 4 of Ref. [8]. The mass spectrum is shown in Fig. 1. The masses of the lightest neutralino and gravitino are 356 GeV and 10 eV, respectively.
We take the events cuts as follows: • ≥ 4 jets with p T > 50 GeV and p T,1,2 > 100 GeV.
• p miss Under these cuts, we see that the standard-model backgrounds are almost negligible.
In Fig. 2-(a), a parton level distribution of M T2 is shown for an integrated luminosity of 10 fb −1 . Here, we take the sum of gravitino and neutrino transverse momenta as the parton level missing p T . As discussed in Ref. [8], very little number of leptons are produced in the SIGM. Therefore, missing p T is due to almost only gravitinos and the assumption that p miss There is a clear edge at M T2 ≃ mχ0 1 = 356 GeV. In Fig. 2-(b), we show a distribution of M T2 after taking account of detector effects.
In order to extract the point of the edge, we use a simple fitting function; where θ(x) is the step function and a, b, c, d and M are fitting parameters. We fit the data with f (x) over 300 ≤ M T2 ≤ 500 GeV and find Here, the estimation of the error is done by 'eye' because of lack of information on the shape of the M T2 distribution. The estimation that mχ0 1 = 357 ± 3 GeV is very good agreement with the true value mχ0 1 = 356 GeV. Next we show another example. We study the Snowmass benchmark point SPS8 [9], which is a minimal gauge mediation model with a neutralino NLSP. In Fig. 3, SPS8 mass spectrum is shown. The masses of the lightest neutralino and gravitino are 139 GeV and 4.8 eV, respectively.
In Fig. 4-(a), a parton level distribution of M T2 is shown for an integrated luminosity of 10 fb −1 . The event cuts are the same as in the previous SIGM case. The blue and dashed line represents the case that p miss T = gravitino p T and the red and solid line p miss T = gravitino p T + neutrino p T . In SPS8, there are many neutrino production sources. Hence, we cannot see a clear edge as in the SIGM case. However, there is a cliff at M T2 ≃ mχ0 1 = 139 GeV.
In Fig. 4-(b), detector level distribution of M T2 is shown. To get the value of mχ0 1 , we fit the data with f (x) in Eq. (8) over 110 ≤ M T2 ≤ 180 GeV. Then we get In summary, we have presented a determination of the neutralino mass for the SUSY models with an ultralight gravitino LSP and a neutralino NLSP, which may work in the early stage of the LHC.
Though we have considered GMSB models with a neutralino NLSP, our method is applicable to any model in which the signal events will lead to a pair of cascade decays that result in where B is a visible (standard-model) particle and X is a missing particle that is almost massless. The mass of A is then determined by the two Bs' momenta and the missing transverse momentum.
For example, let us consider GMSB models with a slepton NLSP. In this case, the slepton, lepton and gravitino correspond to A, B and X in Eq. (11), respectively. In addition to leptons from the sleptons' decays, many other leptons are produced in this scenario. However, we may see which of observed leptons is produced through the slepton decay by measuring lepton's momentum, or by detecting a kink of its track for a long-lived slepton. In such a case, we can measure the slepton mass with the M T2 method as discussed above. Furthermore, the present method may work in an axino LSP scenario.
and for other values of c 1 and c 2 , (M T2 ) 2 is given by (M (ii) m X = 0 case: Generalization of the above result for the case with massive X, i.e., m X = 0, is straightforward. In this case, the M T2 variable is defined by Eq. (2) with m B = 0. The same argument as above shows that Eq. (13) holds also in this case.
Calculating in the same way as above, it can be shown that with z being the solution of Eq. (30) with a = 1