Figure 7.3: Feynman diagrams (leading-order) for electroweak production of supersymmetric particles from quark-antiquark annihilation, taken from Ref. [39].
7.2 Production and Decay Processes at the LHC
This section gives a brief overview of the expected patterns of supersymmetric production and the subsequent decay chains, at the LHC. Here and in the following, exact R-parity conservation is assumed. As discussed, supersymmetric particles are therefore produced in pairs. The coupling of two sparticles to SM partons can either be of electroweak or QCD strength.
The supersymmetric particles interact similarly to their SM superpartners (since they belong to the same supermultiplet). The mass eigenstates, however, can mix and thus receive couplings belonging to several sparticles. For example, the charginos and neutralinos couple to light squarks primarily due to their gaugino content (the coupling due to the Higgs component is negligible for nearly massless initial-state quarks).
The second important rule is that every interaction vertex must have an even number of sparticles.
With these concepts in mind, it is straightforward to find the leading-order Feynman diagrams that constitute the sparticle production at hadron colliders. Fig. 7.3shows the processes that involve an electroweak interaction. All reactions obtain contributions from electroweak vector bosons in thes-channel. Additionally, the processes leading toχe+i χe−j ,χe0iχe0j, andχe−i χe0j sparticles also have t-channel squark-exchange contributions (bottom three diagrams).
Fig. 7.4shows the leading-order Feynman diagrams for strong gluino and squark production at hadron colliders from gluon-gluon and gluon-quark fusion. The remaining diagrams for strong gluino and squark production from quark-antiquark annihilation and quark-quark scattering are shown in Fig.7.5. All processes (leading tog˜˜g,q˜qe∗, andq˜q˜sparticle pairs) get contributions from
g
Figure 7.4: Feynman diagrams (leading-order) for gluino and squark production from gluon-gluon and gluon-quark fusion, taken from Ref. [39].
thet-channel exchange of an appropriate squark or gluino, and all but the quark-quark scattering also haves-channel contributions.
Note that in Figs.7.3–7.5the charged conjugated and crossed diagrams are omitted in favour of clearness.
The production cross sections of the various channels shown above depend on the parton density functions (PDFs) evolved to the appropriate Q2-scale at the hadron collider, and on the super-symmetric particle spectrum. To a first approximation, the Tevatron is a quark-antiquark collider, while the LHC is a gluon-gluon and gluon-quark collider (due to the higher center-of-mass energy at the LHC).
At the Tevatron, the electroweak production of neutralinos and charginos is expected to have the largest cross section. This is because in typical supersymmetry models the sleptons are consid-erably lighter than squarks and the gluino. At the LHC, the situation is expected to be reversed:
the strong production of squarks and gluinos from gluon-gluon and gluon-quark fusion dominates, unless the gluino and squarks are heavier than about1TeV.
The decay of a sparticle is expected to typically proceed through numerous chains of decays into gradually lighter sparticles and SM particles. This is called a cascade decay. For the following discussion of possible sparticle decays, the usual assumption is made that the lightest neutralino (χ˜01) is the LSP. Consequently, every sparticle decay eventually ends with oneχ˜01, and several SM particles. Another possibility for the LSP is the gravitino. This, however, is not discussed here.
Neutralinos and charginos can decay into lepton+slepton or quark+squark, through their elec-troweak gaugino admixture (Be0, fW0, fW±). Secondly, a neutralino or chargino may also decay
7.2. PRODUCTION AND DECAY PROCESSES AT THE LHC 95 Figure 7.5: Feynman diagrams for strong gluino and squark production from quark-antiquark annihilation and quark-quark scattering, taken from Ref. [39].
e
Figure 7.6: Neutralino and chargino decays with χ˜01 in the final state, taken from Ref. [39]. The inter-mediate scalar or vector boson in each case can be either on-shell (so that actually there is a sequence of two-body decays) or off-shell, depending on the sparticle mass spectrum.
into any lighter neutralino or chargino plus a Higgs scalar or an electroweak gauge boson. This is because of the inherited gaugino-higgsino-Higgs andSU(2)Lgaugino-gaugino-vector boson cou-plings. If all two-body decays for a given chargino or neutralino are kinematically forbidden, then the decay can proceed through a three-body process with an off-shell gauge boson or gaugino.
The Feynman diagrams for the neutralino and chargino decays withχ˜01in the final state that seem most likely to be important are shown in Fig. 7.6, where f denotes a fermion, and f and f0 are distinct members of oneSU(2)L multiplet (and one of thef orf0 is an antifermion in each decay). To the extent that sleptons are probably lighter than squarks, the lepton+slepton decays can dominate. Theτ˜1 is often the lightest slepton, because of the commonly found enhanced mixing of staus. This results in larger branching fractions into final states with taus, rather than electrons or muons.
Sleptons can decay into a SM lepton and a neutralino or chargino, because of the gaugino content of the latter two. These weak two-body decays are:
`e±→`±χe0i, `e±→νχe±i , νe→νχe0i, eν→`±χe∓i .
In particular the decays with aχ˜01 in the final state are kinematically allowed, if theχ˜01is the LSP.
The right-handed sleptons do not couple to the SU(2)L gauginos (winos) but only to the bino.
Thereby, they prefer the decay to the bino-likeχ˜01.
Squarks inherit the strong and electroweak interaction couplings of their superpartners. If kine-matically allowed, then the dominating squark decay is into a gluino+quark (of QCD strength).
Otherwise, a squark will decay weakly into a quark + neutralino or chargino. In the neutralino and chargino final states, left-handed and right-handed squarks have different preferences: in an analogous way to sleptons right-handed squarks are expected to decay into the bino-like χ˜01, while the left-handed squarks decay preferentially into heavier and more wino-like neutralinos and charginos.
An interesting feature might be the decay of the lightest stop (˜t1). If both decayst˜1 → t˜g and
˜t1 → tχ˜01 are kinematically forbidden, then the decay into a chargino ˜t1 → beχ±1 dominates. If this decay is also closed due to kinematics, then the lightest stop can only decay to a charm quark
˜t1 → cχ˜01(which is flavour-suppressed) or through a four-body process. These decays might be very slow resulting in a quasi-stablet˜1.
The decay of coloured gluinos can only proceed through squarks, either on-shell or virtual. In typical models, the gluino is heavier than the squarks, thus the two-body decayg˜ → qq˜is open and dominates.
The production of supersymmetric particles and the subsequent cascade decays are illustrated using two examples in AppendixB.