7.1.1 Light Neutralinos in R-Parity Conserved Supersymmetry at Colliders To understand the difficulty to find light neutralinos at colliders, let us start the discussion under the assumption thatR-parity is conserved. We already discussed some limits on supersymmetric particle masses derived from LHC results in Chapter 6. If all supersymmetric particles had comparable masses, strongly coloured particles, i.e. squarks and gluinos, would have the largest cross section (see e.g. Ref. [162]) and thus out of all SUSY particles would be expected to be produced at the highest abundance. These are then expected to produce SUSY decay chains which in most phenomenological SUSY models end with the lightest neutralino as the stable LSP inR-parity conserving supersymmetry (see our discussion in Section2.4.3). Searches for these decay chains, which typically expect a significant amount of missing transverse momentum, then yield combined limits in the potentially high-dimensional mass plane spanned by the produced coloured SUSY particle, the neutralino LSP and all intermediate particles in the SUSY spectrum. Clearly, if the mass of the first is set high enough such that the production cross section falls below the inverse of the integrated luminosity of the experiment, no BSM events are expected in the first place and thus no limits on the neutralino LSP can be set. We encountered this effect in the results of the natural NMSSM scenario in Section 6.4.2, where a massless neutralino could not be constrained if the gluino had mass beyond 1.5 TeV and the naturally light third generation squarks were heavier than about 700 GeV.
In such a scenario, even though the corresponding production cross sections are small, some sensitivity can be expected through direct production of charginos and neutralinos [331]. How-ever again the bounds on m
χe01 critically depend on the mass of the produced mother particle.
Only direct pair production of χe01 could be used to bound the neutralino mass independently of the remaining SUSY spectrum by for example looking for monojet signatures inpp→χ01χ01j [91]. However, to be truly independent from the remaining SUSY spectrum the production of such a neutralino can only occur via Standard Models-channelZ(∗) and h(∗)-boson exchange.
Since a very light neutralino should be mostly B, c.f. Sectione 2.4.3, it does not couple toZ or hat tree level and thus generally the production cross section for these neutralinos is expected to be very small. For the same reason, measurements of theZ-boson width [265] or the invisi-ble Higgs branching ratio (see our discussion in Section 5.2.1) do not constrain Bino-like light neutralinos either.
If the neutralino has sub-GeV mass — which in an R-parity conserving scenario automati-cally means it must have sub-eV mass according to our discussion in Section2.4.3 — another production scenario could be thought of via new decays of Standard Model particles. For ex-ample, see e.g. Ref. [332], pairs of χe01 can be produced via decays of e.g. π, K or B mesons.
Unfortunately, the maximal possible branching ratios within R-parity conserving MSSM are typically very small. Also, since mesons at colliders are typically produced in association with large hadronic activity, it might be extremely hard to identify such a new partially invisible meson decay.
Hence, from the collider perspective, nearly massless neutralinos in an R-parity conserving setup do not render a problem with existing bounds as long as the remaining SUSY spectrum is beyond the TeV scale and thus invisible. This generally holds for collider neutralino searches and thus also applies to analogous limits from LEP [333] and the Tevatron [334].
7.1 Experimental Situation
7.1.2 Motivation for Searches with Broken R-Parity
If R-parity is broken by any of the operators in Eq. (2.100) with a sufficiently large coupling constant, the neutralino is not stable any more on collider scales and thus the above standard signatures which include missing tranverse momentum often become invalid. Instead, searches target events with high final-state multiplicity (for an extensive review, see Ref. [335]) or dis-placed vertices for neutralinos withO(mm) lifetimes (see exemplary searches at CMS [336] and ATLAS [337]). This can affect mass limits derived from stable neutralino searches. However, if the production rate still depends on an abundantly created mother particle, these limits can still easily be avoided if the remaining SUSY spectrum is set to sufficiently high values1.
In the special case of very light neutralinos, the consideration of rare meson decays as men-tioned above in Section 7.1.1turns out to be more promising in anR-parity violating scenario thanks to the following reasons:
1. If the neutralino is unstable on cosmological scales, the corresponding mass bounds in Eq. (2.98) are avoided and the neutralino can have mass of similar order of Standard Model mesons, i.e. O(few hundred MeV).
2. Through R-parity violation, meson decays can produce single neutralinos whereas R-parity conservation required them to be produced in pairs. This increases the phase space and the kinematic range for decays to be possible.
3. The newR-parity violating coupling can contribute to the meson branching ratio into the neutralino and hence increase the overallχe01 production rate sizably.
4. Not only can mesons decay into neutralinos but also neutralino decays into mesons are possible which opens new interesting experimental channels.
It is the combination of all these arguments which motivates the search for neutralinos at a long-baseline experiment as we propose it here, as it is only the presence of R-parity violation which allows for a long-lived neutralino with O(GeV) mass which can be abundantly produced via Standard Model meson decays.
7.1.3 General Bounds on R-parity Violating Couplings
In Section 2.4.3 we briefly mentioned the constraints which can be put on R-parity violating operators by low-energy experiments. We now follow with a more complete list of existing bounds on various operators, most importantly those on the couplings λ0iab which we analyse within this thesis. Exhaustive summaries of exiting bounds on individual and products of couplings can be found in Refs. [96, 338, 339]. In the following summary we make use the explanations and results in Ref. [96, 339] and refer to this source and references therein for more details on calculations and used observables.
Numerical bounds onλ0couplings which we use in our study are summarised in Table7.1. We briefly explain the respective experimental observables which are responsible for these bounds:
1 It should be mentioned at this point that strictly speaking the neutralino signatures via meson decay rates discussed in this chapter are also not truly independent of the remaining SUSY spectrum either. We derive effective operators by integrating out heavy sfermons from the spectrum which results in decay rates that strongly depend on the sfermion massmf˜. However, it will turn out that our expected bounds are sensitive to multi-TeV sfermion masses which are significantly beyond direct collider production reaches.
CKM unitarity: Couplingsλ0 which lead to an effective (¯uγµPLd)·(¯eγµPLν) operator2 con-tribute to the Standard Model Fermi interaction and thus change the predicted value of the CKM matrix elementVCKMud (c.f. Eq. (2.18)). The unitarity ofVCKM paired with the unchanged values forVCKMus and VCKMub can then be translated into bounds on λ0.
leptonic π decay rates: Any contribution of a couplingλ0to the low-energy operator (¯uγµPLd)· (¯µγµPLν) changes the ratioRπ of the pion branching ratios into electrons and muons.
τ-to-π decay rates: Analogously toRπ, a change of the effective operator ( ¯dγµPLu)·(¯νγµPLτ) affects the predicted ratio of Br(τ− →π−ν) and Br(π−→µ−ν).
D decay rates: Again very similar to Rπ, a change of the effective operators ( ¯dγµPLc) · (¯νγµPLe) or (¯sγµPLc)·(¯νγµPLe) affects the relative branching ratios ofDand Dsmesons into kaons and muons or electrons, respectively.
Cs atomic charge: Due to the parity violating nature of weak interactions, the mediation of Z bosons between electrons and nucleus in an atom leads to a small perturbation and thus a misalignment of energy and parity eigenstates. This can be measured by e.g.
measuring the transition rate of equal-parity energy eigenstates (in the unperturbed basis) by applying an external electric field for which such a transition would be forbidden if parity was conserved. From this measurement one can induce the weak chargeQW which is directly related to vector-axial current interactions of type (¯eγµγ5e)(¯qγµq) between electrons and valence quarks. Any BSM operator contributing to the latter hence changes the prediction of the former and since QW of the cesium atom is measured to a good precision, tight bounds on these BSM operators can be derived.
νµ deep inelastic scattering: BSM contributions to effective operators ( ¯νµγµPLd)·( ¯dγµPLν) affect the predicted rates for muon-neutrino induced deep inelastic scattering νµ+p → νµ+X.
K−K mixing: Higher order box diagrams with sfermions and W± bosons can give sizable contributions toK−K mixing via operatos of type (¯sγ5d)( ¯dγ5s).
K →πνν¯: The rate of this decay is strongly suppressed in the Standard Model due to the absence of tree-level flavour changing neutral currents (c.f. Section2.1.3). It can however easily be enhanced inR-parity violating supersymmetry via sfermion mediation.
Note that all these constraints originate from low energy effective operators resulting from integrating out heavy scalar fermions (see also below in Section 7.3.1) and thus depend on the mass of the respectively heavy sfermion. Also, some combinations of operators are more constrained than individual operators as the presence of two couplings might open new low energy interactions. We quoted bounds on those combinations in Table 7.1 which surpass bounds on the respective individual couplings.
2 Throughout this chapter, if we talk about neutrinos or antineutrinos whose flavour is irrelevant for the discus-sion, we simply refer to them viaν, ν.