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In one class of models explored, Gauge Mediated Supersymmetry Breaking (GMSB) [55–62] models, the supersymmetry is broken in a secluded sector not directly accessible to Standard Model particles (the visible sector) and at the collider. The breaking is communicated to the Standard Model via messenger particles or mediators, generally through loops. This introduces two key scales to

the theory M, the messenger scale, and √F,the SUSY breaking scale. There are some GMSB

mechanisms that produce a125 GeV Higgs boson consistent with current measurements [63–67].

In model-independent SUSY frameworks, the spontaneous breaking of global supersymmetry will provide a Goldstone fermion, in this case the goldstino. This is analogous to how spontaneous EWK symmetry breaking provides a Goldstone bosons. When SUSY is promoted to a local symmetry, the goldstino is “eaten” by the spin 3/2 gravitino and becomes its longitudinal component; giving the gravitino mass [68, 69]. This is referred to as the “super-Higgs” mechanism. In GMSB models, the lightest supersymmetric particle is generally this gravitino, with a mass proportional to the SUSY breaking scale over the Planck mass:

m_G˜ =

F

√

3MP

. (2.10)

The gravitino is stable in R-parity conserving models1_{and does not couple to SM particles. Therefore} the next-to-lightest supersymmetric particle (NLSP) will decay to a gravitino (Lightest Supersym- metric Particle (LSP)) and another SM particle. Moreover, the phenomenology of GMSB models is mainly driven by the next-to-lightest supersymmetric particle properties. For instance, if the NLSP is a Bino-like neutralino there can be a significant branching fractions of NLSPs to a photon and gravitino.

In these models the gravitino is generally very light as the SUSY breaking scale and messenger scale is on the order of hundreds of TeV. The gravitino can also be heavier in more generalized models, but this leads to non-prompt signatures at the LHC. The signature which is sought after in this dissertation is under the assumption of a mostly Bino NLSP neutralino with a Higgsino compo- nent allowing couplings to the SM Higgs. Since gravity is weak, only the longitudinal components

(goldstino) of the spin 3/2 gravitino will interact, allowing for effective couplings of the SM Higgs to neutralinos and gravitinos.

NLSP compositions and masses are mostly constrained by searches for direct production of charginos or neutralinos at the Large Electron-Positron Collider (LEP), Tevatron, and the LHC. In order for the lightest neutralino to be an allowed Higgs decay product, it must be mostly Bino. This is in part due to bounds for significantly Wino or Higgsino NLSPs being more constrained by LEP’s bounds on couplings to gauge bosons, which exclude charginos lighter than103.5 GeV[70,71]. Some of the strongest constraints on light neutralinos decaying to photons come from direct searches at LEP for photons and missing transverse momentum, which limits σ(e+e− → γγ+Emiss_T ) to less than∼10−2pb [72, 73]. In the Standard Model without the Higgs, this signature would arise from t-channel W exchanges with radiated photons (from the electrons or W) or a Z decaying to ν¯ν

with photons radiated from the incoming electrons. Any enhancement can arise from intermediate particles (like neutralinos or Higgs) decaying to invisible particles and photons. One vital part of this model is the neutralino mixing matrix contains only one Higgsino mixing factor, which allows for couplings to the SM Higgs. Two Higgsino or Wino mixing factors are required for the Bino-like neutralino to couple to theZboson and thus this allows the model to escape LEP constraints [74,75]. For this reason, the mostly Bino NLSP would have little to couple to ine+_e− _{andppcolliders and}

direct production would be greatly suppressed.

In minimal MSSM GMSB models the lightest neutralino is constrained to be heavier than half of the Higgs mass, but this is not the case for general GMSB models. With these assumptions in the mind, there can be significant branching fractions of Higgs boson decays to neutralinos and gravitinos in decays paths such as h → χ˜0

1χ˜01 → γGγ˜ G˜ or h → χ˜01G˜ → γG˜G˜. For example, in one simplified model for theh→χ˜0_1G˜ _→γG˜_G˜ _{decay path, the BSM terms in the Lagrangian can} contain: LBSM ⊃ m2 √ 2F g_χ˜0 1G˜h ˜ χ0_1G˜₊gχ˜01γ m ˜ GσµνFµνχ˜ 0 1 +h.c.; (2.11)

where h is the Higgs boson, G˜ is the gravitino, χ˜01 is the Bino-like neutralino, σµν are the Pauli matrices,Fµν is the photon field strengths,g are the coupling parameters, andm is a scale related to soft SUSY soft parameters. This can lead to the decay width of the Higgs to a single gravitino and neutralino as:

Γ(h→χ˜0_1G˜_{) =} mh 16π g_χ2_˜0 1G˜ m4 F2 1− m2_χ˜0 1 m2 h 2 . (2.12)

2. Theoretical Framework 18

and subsequent decays of the neutralino to photon + gravitino with partial widths of:

Γ( ˜χ01→γG˜) = m2 ˜ χ0 1 16π g2 ˜ χ0 1γ m2 F2 . (2.13)

Note the neutralino mass scale is one of the controlling parameter for the neutralino to photon decay width. In order for this process to be physically meaningful, the SUSY breaking scale cannot

be too far away from m. From the literature, the Higgs branching fraction of this process can

range from sub percent levels up to 15% depending on model assumptions [76, 77]. Similar models can be constructed with the decay paths of Higgs bosons to two neutralinos in the case when

m_χ˜0

1 < mh/2in generalized MSSM GMSB models. In this case the event may have the decay chain

of h→χ˜0

1χ˜01 → γGγ˜ G˜ where in the final state there will be two photons and two gravitinos [78]. These models are the inspirations of the search performed in Chapter 7.