R-Parity Violation and Light Neutralinos at Ship and the LHC
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BONN-TH-2015-12 R-Parity Violation and Light Neutralinos at SHiP and the LHC Jordy de Vries,1, ∗ Herbi K. Dreiner,2, y and Daniel Schmeier2, z 1Institute for Advanced Simulation, Institut f¨urKernphysik, J¨ulichCenter for Hadron Physics, Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany 2Physikalisches Institut der Universit¨atBonn, Bethe Center for Theoretical Physics, Nußallee 12, 53115 Bonn, Germany We study the sensitivity of the proposed SHiP experiment to the LQD operator in R-Parity vi- olating supersymmetric theories. We focus on single neutralino production via rare meson decays and the observation of downstream neutralino decays into charged mesons inside the SHiP decay chamber. We provide a generic list of eﬀective operators and decay width formulae for any λ0 cou- pling and show the resulting expected SHiP sensitivity for a widespread list of benchmark scenarios via numerical simulations. We compare this sensitivity to expected limits from testing the same decay topology at the LHC with ATLAS. I. INTRODUCTION method to search for a light neutralino, is via the pro- duction of mesons. The rate for the latter is so high, Supersymmetry [1{3] is the unique extension of the ex- that the subsequent rare decay of the meson to the light ternal symmetries of the Standard Model of elementary neutralino via (an) R-parity violating operator(s) can be particle physics (SM) with fermionic generators [4]. Su- searched for [26{28]. This is analogous to the production persymmetry is necessarily broken, in order to comply of neutrinos via π or K-mesons. with the bounds from experimental searches. To solve For a neutralino in the mass range of about 0.5 - 5 GeV, the hierarchy problem [5, 6], the masses of the super- the newly proposed SHiP experimental facility [29] seems symmetric partners of the SM ﬁelds should be lighter ideal. It will consist of a high intensity 400 GeV pro- than 1-10 TeV, with a clear preference for lighter ﬁelds, ton beam from the CERN SPS incident on a ﬁxed tar- see for example [7{11]. All experimental searches for su- get. 63.8 m down beam line there will a detector for persymmetric particles have hitherto been unsuccessful. long-lived heavy neutral particles. Two of us (HKD, The LHC sets limits on the strongly interacting spar- DS) have performed a preliminary analysis in [30], for ticles, the squarks and gluinos, of order 1 TeV, see for a small set of R-parity violating operators: the decay + 0 + 0 ¯ example [12, 13]. However the limits on the only elec- D ! χ~1 `i via the operator λi21LiQ2D1, and the de- 0 0 ∓ ± 0 troweak interacting particles, such as the sleptons, the caysχ ~1 ! (K ν; K `i ) via λi21;i21. It is the purpose neutralinos and the charginos, are signiﬁcantly weaker of this paper to extend this to all possible production [14, 15]. In fact, as has been discussed in the literature modes and decay channels, and to determine the search there is currently no lower mass bound on the lightest su- sensitivity of the SHiP experiment. As an example, in persymmetric particle (LSP) neutralino, which is model earlier work [26], the production of B-mesons at NuTeV 0 0 independent [16, 17]. The limits from LEP can easily be was considered. The mesons could decay as Bd;s ! χ~1 ν ± 0 ± 0 avoided, and in particular, a massless neutralino is still or B ! χ~1 `i via λi13. The neutralinos could decay via allowed, for suﬃciently heavy selectrons and squarks [18]. the LiQ1D¯ 3 operators, or purely leptonically via LiLjE¯k We discuss this in more detail below, in Sec. III. operators. These scenarios can also be tested at SHiP, We are here interested in the possibilities of searching where a suﬃciently large number of B-type mesons is ex- arXiv:1511.07436v1 [hep-ph] 23 Nov 2015 for a light neutralino, up to masses of about 10 GeV. pected and we will show the sensitivity reach to the LQD¯ Already for a slepton mass of 150 GeV there is no sen- operators here. + − 0 0 sitivity via the process e e ! χ~1χ1γ from LEP data This paper is organized as follows. In Sec. II, we brieﬂy [19], see also [20, 21]. Since mass reach is not a factor, review supersymmetry with broken R-parity. We also one might suspect that the high intensity facilities used discuss the bounds on the operators relevant to our anal- as B-factories, would be more sensitive, but this is also ysis. Constraints on the neutralino mass and motiva- not the case [19]. tions for the possibility of a very light neutralino follow In order to avoid over-closing the universe [22{24], a in Sec. III. In Sec. IV we discuss the relevant neutralino 10 GeV or lighter neutralino must decay via R-parity production and decay channels we expect to be most rele- violating operators [25]. If the R-parity violating cou- vant for SHiP observations of R-parity violation (RPV). plings are not too small, in this case, the most promising In Sec. V we set up the eﬀective ﬁeld theory need to compute the relevant meson and neutralino decays and compute the latter in general fashion. With these re- ∗ [email protected] sults at hand, we specialize to the SHiP set-up in Sec. VI y dreiner@uni{bonn.de and discuss under what circumstances a neutralino could z [email protected]{bonn.de be detected. In Sec. VII we explain the methodology of 2 our numerical study. The discussion of the sensitivity of B. Bounds on R-parity Violating Couplings the SHiP experiment to the existence of light, but unsta- ble, neutralinos in several benchmark scenarios is given The operators LiQjD¯ k which we investigate here all vi- in Sec. VIII. In Sect. IX, we discuss an estimate for pos- olate lepton number; thus there are strict bounds on the sible eﬀects of our benchmark scenarios at the LHC. We 0 coupling constants λijk, see for example the reviews [46{ conclude in Sect. X. 50]. We brieﬂy summarize here the existing bounds on the speciﬁc operators which we investigate in our bench- mark scenarios in Sec. VIII. For our results on the sensi- 0 II. R-PARITY VIOLATION tivity reach of SHiP, we focus on the cases λ1jk, involving 0 ﬁnal state electrons, and λ31k, which produces tau lep- A. Introduction tons. However, experimentally ﬁnal state muons should be testable at least as well as electrons. We thus also 0 present the corresponding bounds on the couplings λ2jk, The minimal supersymmetric extension of the SM re- which are typically weaker. We take most of the numbers quires the introduction of an additional Higgs doublet. from the most recent review [50]. The minimal set of pure matter couplings are then en- 0 ms~r 0 ms~R coded in the minimal supersymmetric SM (MSSM) su- λ112 < 0:03 ; λ212< 0:06 : (5) perpotential 100 GeV 100 GeV m m ~ ¯ ¯ λ0 < 0:2 c~L ; λ0 < 0:1 dR ; (6) WMSSM = (hE)ijLiHdEj + (hD)ijQiHdDj 121 100 GeV 221 100 GeV +(h ) Q H U¯ + µH H : (1) U ij i u j d u m m λ0 < 0:2 c~L ; λ0 < 0:1 s~R ; (7) 122 100 GeV 222 100 GeV Here hE;D;U are dimensionless 3 × 3 coupling matrices. The Higgs mixing µ has mass dimension one. This su- m~ 0 mt~L 0 bL perpotential is equivalent to imposing the discrete Z λ131 < 0:03 ; λ231< 0:18 ; (8) 2 100 GeV 100 GeV symmetry R-parity [31], or the Z6 proton hexality [32], and results in a stable proton. Both are discrete gauge ms~R λ0 < 0:06 ; (9) anomaly-free, ensuring stability under potential quantum 312 100 GeV gravity corrections [33]. A model restricted to the super- m~ potential W is called R-parity conserving. The ad- 0 tL MSSM λ313 < 0:06 ; (10) vantage is that the LSP, usually the lightest neutralino, is 100 GeV 0 an automatic WIMP dark matter candidate [34]. How- The bound on λ231 is from [48], as there is no bound ever, no such dark matter has been observed to-date, quoted in [50]. Assuming an experimental neutrino mass motivating the search for other forms of supersymmetry. bound mν < 1 eV results in a bound of approximately 0 Instead in R-parity violating models, there are further λ122;222 < 0:01 m=~ 100 GeV [40, 48, 51]. This is how- possible terms in the superpotential ever model dependent, as we know there must be further, possibly oﬀ-diagonal,p contributions to the neutrino mass WRPV = WLV + WBV ; (2) matrix. ¯ 0 ¯ WLV = λijkLiLjEk + λijkLiQjDk + κiLiHu ; (3) 00 ¯ ¯ ¯ WBV = λijkUiDjDk : (4) III. A LIGHT NEUTRALINO Imposing the discrete Z3 symmetry baryon triality [32, The best lower mass limit on the lightest supersym- 35], the lepton-number violating terms in WLV remain. metric particle (LSP) neutralino is from LEP [17] The proton remains stable, since baryon-number is con- served, however the neutralino LSP is unstable and is m 0 > 46 GeV: (11) χ~1 no longer a dark matter candidate. This can be solved by introducing the axion to solve the problem of CP- This uses the LEP-II chargino search to restrict the range violation in QCD. The supersymmetric partner, the ax- of µ and the SU(2) soft breaking gaugino mass parameter ino, is then automatically a good dark matter candidate M2 and then assumes the supersymmetric GUT relation [36{39] and light neutrino masses are also generated auto- 5 2 1 matically [40{44].