2.7 Stable Massive Particles
2.7.1 Interaction with matter
Figure2.20: Stopping power as a func- tion ofβγ=β/
p
1−β2whereβ=v/c
and the momentum p for antimuons propagating through copper. The stop- ping power translates to ionization en- ergy losses dE/dx. The figure was taken from [136].
The possible interactions of SMPs depend on the kind of long- lived particle. While all SMPs interact through electromagnetic ef- fects, hadron-like SMPs likeR-hadrons can also interact via the strong interaction. In comparison to electromagnetic effects they are sig- nificantly less understood. Because of their large masses all SMPs
have in common that their propagation velocity can be significantly smaller than the speed of lightβ<1, whereβ=v/c. Since all light
SM particles are expected to propagate with the speed of light it is possible to detect SMPs by performing time-of-flight measurements. The following chapter gives a summary of the possible interactions within the detector. For a more complete overview [137] is recom- mended.
Figure2.21: Elastic scattering of an R- hadron and a proton. TheRstands for theR-hadron. Figure taken from [128].
Lepton-like SMPs The main electromagnetic effects are Coulomb scat- tering and continuous energy losses through ionisation in the de- tector material. The scattering processes influence the trajectory of the particle. Since the scattering angle is proportional to 1/pβone
can at first assume a large effect because of the small β. However,
since most SMPs exhibit a considerable momentum, the slow veloc- ity is compensated for and the deflection angle is in fact small. The ionisation-energy losses dE/dx23
are well described by the Bethe-
23
In a rigorous notation one would write −dE/dx to describe the energy losses. However, the ’minus’ sign is omitted here and throughout the re- mainder of this thesis
Bloch equation and proportional to 1/β2in the relevant energy regime,
as can be judged from figure2.20. It can therefore be expected to ob- serve largedE/dxfor SMPs [138]. The passage of particles through matter and the resulting ionisation-energy losses are well under- stood [29,139]. The main background in this study originates from muons. Since they are light compared to the SMP and thus travel close to the speed of light, the dE/dx can be used to discriminate between signal and background.
For HIPs the ionization energy losses are enormous and can even lead to the particle stopping in the detector creating unique signa- tures [140,141].
Figure 2.22: Conversion of an R- meson into anR-baryon. Figure taken from [128].
Hadron-like SMPs In addition to Coulomb scattering and ionization energy losses, heavy R-hadrons can undergo scattering processes with nuclei resulting in parton exchange. The interaction probability of a specific parton with massmp and another parton in a nucleus is proportional to 1/m2p and consequently very low for the heavy supersymmetric parton considered here, which also carries most of the momentum. The majority of interactions are executed by the lighter SM constituents which are dragged along by the heavy spar- ton as shown exemplary in figure2.21. Every time a parton looses some energy through scattering it is "replenished" from the vast en- ergy carried by the massive constituent. The energy losses are thus determined by the kinetic energy of the parton cloud. A back-of-the- envelop calculation reveals that the energy scales which need to be considered are indeed low24
[142].
24
Consider anR-hadron with an energy of 1.5 TeV and a mass of the heavy con- stituent of 1000 GeV. This gives theR- hadron a kinetic energy of 500 GeV and results in a Lorentz-factor ofγ = 1.5.
Assuming now further the remaining constituents are auand adquark yields a kinetic energyEqq¯ = mqq¯(γ−1) ≈
0.3 GeV for the interacting system.
By scattering off a nucleus an R-meson can convert into an R- baryon. A possible interaction is shown in figure2.22where a neutral R-meson exchanges one quark for two quarks from a proton result- ing in a neutral pion and a charged R-baryon. The reverse of this process, however, is suppressed kinematically and by the absence of pions in the detector material [137]. It is therefore valid to assume most detectable R-hadrons to be of baryonic character. This is im-
portant to consider since baryons carry the larger scattering cross sections. The present study is mainly interested in gluino, sbottom and stopR-hadrons. From the SM quark mass hierarchy it can be de- rived that the squark R-hadrons will predominantly end up in ˜qud states. This results in a neutral sbottomR-hadron and a charged stop R-hadron. The present analysis can therefore be predicted to have a slightly larger sensitivity to stop based R-hadrons than to sbottom R-hadrons.
Figure2.23: Inelastic scattering of anR- hadron resulting in a charge flip. Figure taken from [128].
The experimentally most challenging feature of figure2.22, how- ever, is the change of electric charge of the R-hadron. While it was produced neutral and therefore invisible to the searches presented here, it becomes charged and visible at some point in the detector. A similar process is depicted in figure 2.23, where a gluinoR-hadron scatters inelastically with a proton resulting in a change of the elec- tric charge of the system from neutral to positive. Obviously the reverse of the reaction is possible as well and a formerly charged R-hadron performs a charge flip and becomes invisible, mimicking the signature of a decay to invisible particles in the detector. It can be estimated that charge-flip reactions contribute substantially to all interactions [128]. This can lead to peculiarR-hadron signatures in the detector with segmented tracks and (possibly several) changes of sign25
. 25
It has also been speculated about the observability of mesino-antimesino os- cillations in which a neutral R-meson oscillates into its own antiparticle [143, 144]
Different models have been developed to correctly model the R- hadron behaviour in matter [137, 138,145–147]. In this study two different models have been used: the generic and the Triple-Regge model.
Figure2.24: Cross sections for interac- tions of a stop (top) and gluino (bottom) R-hadron with a stationary nucleon for the Triple-Regge model (solid lines) and the generic model (dashed lines). Fig- ure taken from [145].
The generic model assumes a flat geometric scattering cross sec- tion of 12 mb per light quark and a heavy spectator constituent. This is the pragmatic approach given the fundamental uncertainty regard- ing R-hadron interaction. ForR-meson to R-baryon conversion pro- cesses phase-space factors are considered. The generic model pre- dicts most R-baryons to be electrically charged. In this work, the generic model is used to describe the interaction of gluinoR-hadrons within the detector. For this it is also necessary to specify the fraction of gluinos which hadronise into agg˜-system. This fraction is referred to as the f-parameter.
The Triple-Regge model employs insights gained from low-energy hadron–hadron scatterings and estimatesR-hadron interaction cross sections and energy losses from the Triple-Regge formalism [146]. Contrary to the generic model, this results in interaction rates de- pending on the Lorenz factorγ, as can be seen in figure2.24, where the interaction cross sections of stop and gluino R-hadrons with a nucleon that is part of a nucleus consisting of an equal number of protons and neutrons, are plotted. The model was initially for- mulated for squark-based R-hadrons, but later extended to include gluino R-hadrons. It predicts a larger fraction of neutralR-hadrons than the generic interaction model. The Triple-Regge model is used in the present study to describe sbottom- and stop-based R-hadron interaction in the detector.
In principle it is also possible to form resonant R-hadron states as depicted in figure2.25. Such processes are currently not imple- mented in any model and thus constitute a source for uncertainty on the interaction model. In [137] it is argued that the negligence of such possible resonances does not have a significant impact.
Figure2.25: Formation of anR-hadron resonance. Figure taken from [128].
Because the energy lost through hadronic interactions is small, the passage of an SMP through a detector will not be accompanied by hadronic showers in the calorimeter systems. It follows that an SMP mimics the experimental signature of a muon, albeit with a much larger mass.
Because the interaction of R-hadrons in matter is highly uncer- tain, there exist also models predicting the SMP to loose almost all their momentum mainly though ionisation-energy losses and come to a stop within the detector. Such stopped particles can be found by detecting out-of-time decays. Such scenarios are not within the scope of the present work but are well covered by other analysis ef- forts [148–150].