Gravitino production in the GMSB scenario

Supersymmetry (SUSY) is the most popular among the scenarios beyond the SM. For each SM fermion this theory predicts a bosonic “super-partner”, and viceversa for the SM bosons. The introduction of this symmetry is particularly appealing for solving several issues of the SM. First of all, SUSY eliminates the hierarchy problem because divergent corrections to the Higgs mass from fermions and their bosonic super-partner are automatically cancelled out (see figure 2.11). Additionally, this theory includes valid DM candidates and provides a framework in which the unification of gravity and the SM interactions can be more easily pursued.

Figure 2.11: Corrections to the Higgs self-energy with SUSY. The term with a top loop is compensated by a stop loop.

SUSY needs to be a broken symmetry since no SUSY particle has been observed until now, and the masses of the superpartners are therefore different from those of their SM partners. Such a symmetry breaking needs to happen at a relatively low energy scale (10-100 TeV) in order to still provide a solution for the hierarchy problem.

Typically, it is assumed that a spontaneous symmetry breaking is induced by a hidden sector, and it is due to “soft breaking” terms added to the Lagrangian:

L = L_{SU SY} + L_{sof t} . (2.24)

The breaking is communicated from the hidden to the visible sector either through gravity or electroweak and QCD gauge interactions. These two possible mechanisms for SUSY breaking lead to Minimal Supergravity (mSUGRA) [43,44] and Gauge Mediated SUSY Breaking (GMSB) [45,46,47]. In the latter, messenger fields at mass scale M_mess are supposed to share the gauge interaction, and to provide the soft breaking terms in loop diagrams. The coupling of the messenger fields to the hidden sector produces in the fields a supersymmetric mass of order M with mass-squared splittings of order F, with√

F being the scale of SUSY breaking. In its minimal version, GMSB models are described by six fundamental parameters, that define the mass hierarchy of all particles, and therefore the phenomenology:

• √

F: the scale of the SUSY breaking. SUSY masses are proportional to√ F.

• M_mess: the mass scale of the messengers.

• N5: number of messenger fields. Gaugino ¹ masses depend linearly on N5.

• tan(β): ratio of the two vacuum expectation values of the SUSY Higgs doublets.

• sign(µ): sign of the Higgsino mass term. Gaugino masses are dependent on this parameter.

In GMSB, the super-partner of the spin-2 graviton, the spin-3/2 gravitino ˜G, is the lightest supersymmetric particle (LSP). The gravitino does not necessarily couple to matter with gravitational strength only, but its coupling can be enhanced to electroweak strength once SUSY is broken through the super-Higgs mechanism and the associated Goldstone fermion, the spin-1/2 goldstino, is absorbed to give the gravitino its mass.

An important feature of this mechanism is that the gravitino mass gives direct access to the scale of the SUSY breaking:

*F+=√

3 m_G˜ M¯_pl , (2.25)

where ¯M_pl =M_pl/√ 8π.

In the following, the production of gravitinos in association with a squark or a gluino

2 at hadron colliders is described. Here a simplified scenario is considered, depending

1Gauginos are combinations of the SUSY electroweak and Higgs fermionic fields.

2The squark and the gluino are the superpartner of the squark and gluon, respectively.

only on the gravitino, squark and gluino masses. In the case of very light gravitino, the productions (pp→ G+˜˜ g) and (pp→ G+˜˜ q) dominates over the strong production of squarks and gluinos, and the dominant squark and gluino decays are ˜q → qG˜ and

˜

g → gG, respectively. Therefore, the final state is characterized by two gravitinos˜ escaping detection and a jet, leading to a mono-jet final state.

Figure 2.12: Some of the LO diagrams for ˜G+˜q/˜g production at LHC.

The ˜G+˜gassociated production is driven by two competing initial states, i.e. quark-antiquark or gluon-gluon scattering, while the production ˜G+˜q can only be produced in quark-gluon scattering (see figure2.12). Predictions for ˜G+˜g/˜q are calculated at LO in pQCD, neglecting the gravitino mass everywhere apart in the coupling constants. The differential cross section, expressed in terms of the usual Mandelstam variables takes the form:

dσ dt = 1

2s 1

8πs|M| , (2.26)

with

|M|(gg→G˜˜g) = g²_sm²_˜g 6C_FM_pl²m²_˜

G

F_A(u, t, s, m_˜g) , (2.27)

|M|(qq¯→G˜˜g) = g_s²C_F 3NCM_pl²m²_˜

G

F_B(u, t, s, m_g˜, m_q˜) , (2.28)

|M|(qg→G˜˜q) = g_s² 12N_CM_pl²m²_˜

G

FC(u, t, s, mq˜, m˜g) , (2.29) where the explicit expression ofFA,FB, andFC is reported in reference [48]. It can be noticed that the cross sections depend m²_˜

G as σ ∼ 1/m²_˜

G, and therefore lower bounds on m_G˜ can be deduced from the cross section constraints. It can also be noticed that the ˜G+˜gproduction has a dependency onm_q˜, coming from diagram contributions with squark exchange in thet channel. (see diagrams in figure2.12). In the same way, the G+˜˜ q production cross section depends on the gluino massm_˜g.

As previously mentioned, for a light gravitino the ˜q → qG˜ and ˜g → gG˜ decays dominate. This assumption is studied in reference [48], showing that the branch-ing ratios BR(˜q → Gq) and˜ BR(˜g → Gg) are larger than 0.9, for gravitino masses˜ mG˜ !10⁻⁴ GeV.

Figure 2.13: LO diagrams for the decays ˜q→qG˜ (left) and ˜g→gG˜ (right).

The branching ratios of squark or gluino decays are included in the cross sections using the Narrow Width Approximation (NWA). In this procedure, intermediate par-ticles are set on shell (Γ =0) in order to simplify the calculation. In our case, the width of squarks and gluinos are neglected so that the cross section can be factorized in the following way.

σ(pp→G˜Gq)˜ ,σ(pp→G˜˜q)×BR(˜q→Gq)˜ , (2.30) Typically, this approximation is considered valid if the width of the particle does not exceed 25% of its mass.

The ATLAS experiment at LHC

This chapter introduces the main aspects of the ATLAS detector at the LHC collider.

The reconstruction procedures of the physics objects that are relevant for the analyses described in this thesis (jets, electrons, muons and missing energy) are also discussed.

The appendix A describes dedicated studies carried out during the commissioning of the Tile hadronic calorimeter (TileCal), while appendixB details the measurement of the instantaneous luminosity using the TileCal data.

3.1 Large Hadron Collider

The Large Hadron Collider (LHC) [49] is a particle accelerator designed to collide protons at a center of mass energy √

s=14 TeV. On the accelerator ring (∼27km in circumference) four detectors (ALICE [50], ATLAS [51], CMS [52] and LHCb [53]) have been built around the four interaction points to reconstruct and study the collisions delivered by the LHC.

Since 2010, the LHC has delivered proton-proton (p-p) collisions at center of mass energies of 7 TeV and 8 TeV, about half of its nominal energy. The LHC has pro-duced also lead ions (Pb-Pb) collisions with a per-nucleon center of mass energy

√s_{N N} =2.76 TeV and proton-ion (p-Pb) collisions with√s_{N N} =5.02 TeV. More details about the delivered luminosity will be given below.