Decaying light particles in the SHiP experiment. II. Signal rate estimates for light neutralinos D. Gorbunov∗ Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia and Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia I. Timiryasovy Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia and Physics Department, Moscow State University, Vorobievy Gory, Moscow 119991, Russia Considering the supersymmetric models with light neutralino and R-parity violation, we perform estimates of the signal rate expected at the recently proposed fixed target SHiP experiment exploiting the CERN SPS beam of 400 GeV protons. We extend the existing studies by introducing new production channels (in particular through the beauty mesons) and decay modes. We also constrain the model parameter space from analysis of negative results of the CHARM experiment. I. INTRODUCTION Higgs sector) have Rp = +1, while their superpartners have Rp = −1. If R-parity is conserved, superpartners Supersymmetric (SUSY) extensions of the standard may only be created in pairs. R-parity guarantees stabil- model of particle physics (SM) provide taming of the ra- ity of the lightest supersymmetric partner (LSP) which diative corrections to the Higgs boson mass (for a review becomes a candidate to form the dark matter component see [1]). The crucial role is played by the superpartners of of the Universe. the SM particles, whose contributions cancel the quadrat- However, the theoretical grounds of R-parity have been ically divergent quantum corrections of the SM particles. questioned (see, e.g., Refs [10, 11]), and one can introduce Therefore, one naturally expects to observe (some of) the R-parity violating (RPV) terms in the Minimal Super- superpartners at the TeV mass scale. Testing this pre- symmetric extension of the SM (MSSM). These terms diction is one of the main tasks of run 2 at the LHC. trigger decays of superpartners into SM particles, in par- However, there can be renegades in the SUSY world ticular, decays of the LSP. The latter may be the light- with masses (much) below the TeV scale and suffi- est mass eigenstate in the sector of neutral fermion su- ciently suppressed interactions with the SM fields, so they perpartners called neutralinos. If the neutralino is suf- are missed by numerous previous searches and are be- ficiently light, it is an example of the renegades to be yond the reach of the LHC. The renegade hunting can searched for at the SHiP experiment. There, the neu- be performed at a beam-dump experiment, where the tralinos can be produced either directly in proton scat- high statistics of proton(electron)-proton collisions might tering off the target material or indirectly via decays of compensate for smallness of the couplings, so the new secondary hadrons, and they later decay into SM parti- light particles can be produced. Recently a proposal has cles exhibiting signatures very similar to those of sterile been submitted [2, 3] to build the new experiment at neutrinos [4]. Thus, the procedures applied in data anal- CERN with a 400 GeV SPS proton beam. Originally mo- ysis to probe both models are very similar. The differ- tivated as a facility to search for sterile neutrinos (heavy ence between the two models is expected in the produc- neutral leptons) of O(1) GeV mass [2, 4, 5], lately it has tion channel pattern and in decay channel patterns, so been recognized as a universal tool to probe various mod- that the momentum spectra of each final state and the els predicting light, sufficiently long-lived, neutral parti- weights of the different final states (K±µ∓, µ+µ−ν, etc) cles; it has been named SHiP (Search for Hidden Parti- are generically not the same in the two models. arXiv:1508.01780v2 [hep-ph] 27 Oct 2015 cles) [3]. The SHiP physics case is presented in a separate Light neutralino phenomenology has previously been paper [6], including a number of the SUSY renegades. studied in the SHiP physics paper [6]. Here, we consid- In this work, we consider the light unstable neutralino erably extend this study by including more production in supersymmetric models with R-parity violation (for (from neutral charm mesons and from beauty mesons) reviews, see [7{9]). R-parity is a discrete multiplicative and decay (π±l∓, l±l∓ν) channels and by obtaining lim- symmetry ascribing factor, its on the model parameter space from analysis of the 3B+L+2S published results of the CHARM experiment [12, 13]. Rp = (−1) ; (1) The paper is organized as follows. In Sec. II we intro- to any particle of baryon charge B, lepton charge L, and duce the model and calculate the neutralino production spin S. All SM fields (including scalars of the extended rates and decay rates for a number of channels. In Sec. III we give the estimate of the number of signal events ex- pected in the SHiP fiducial volume. In Sec. IV we present ∗ [email protected] the sensitivity of the SHiP experiment to the model pa- y [email protected] rameters (assuming zero background) and find new limits 2 on the model parameters from the published results of the Neutralinos as the LSPs could be created in decays CHARM experiment. We summarize in Sec. V. of heavier sparticles. Missing momentum carried out by the LSP, which escaped from a detector, remains one of the main signatures in collider searches of supersymme- II. SUPERSYMMETRY WITH RPV: try. The proposedp center-of-mass energy of the SHiP PRODUCTION AND DECAYS OF LIGHT experiment s = 27:4 GeV is too low to create heavy NEUTRALINOS superpartners with masses above the electroweak scale, as we anticipate from LEP-II, Tevatron, and LHC run I. One can check that the neutralino direct production R-parity is explicitly violated by the following terms in the proton-proton scattering is negligibly low. There- in the MSSM superpotential fore, here we study an indirect production of neutralinos in decays of heavy mesons via R-odd couplings λ0 in (2). W = λ LaLbEC + λ0 LaQbDC (2) 6Rp ijk ab i j k ijk ab i j k These R-odd couplings also lead to neutralino decays into 00 C α C β C γ a a +λijkαβγ Ui Dj Dk + µiabLi HU ; (3) the ordinary SM particles. where dimensionless couplings λijk and mass parameters A. Neutralino production in decays of heavy µi (i; j; k run over the three matter generations) charac- terize violation of R-parity, the superscript C refers to the mesons charge conjugated fields, indices a; b = 1; 2 indicate the 0 SU(2)W doublet components (L and Q are lepton and Light enough neutralinosχ ~1 can be produced in decays quark doublets; E, D, and U are lepton , down-type, of heavy mesons (charm D and beauty B) provided that and up-type quark singlets, respectively), while α; β; γ we have R-parity-violating coupling λ0 as shown in Fig. 1. count SU(3)C triplet components; ab and αβγ are fully λi′13 λi′13 ¯ antisymmetric 2 × 2 and 3 × 3 × 3 tensors. Now, if all the d ν¯i ¯b ν¯i b ν¯i terms (2), (3) are present, they initiate the fast proton ˜bR d˜L λi′13 decay. This process can be forbidden with some discrete ν˜i remnant of R-parity. In particular, the baryon triality ¯ 1 1 1 b χ˜0 d χ˜0 d χ˜0 [14] forbids the first term in (3) and hence keeps the proton stable. In what follows we concentrate on the FIG. 1. Typical Feynman graphs of neutralino production in phenomenology of the RPV terms in Eq. (2) and neglect meson decay via R-parity-violating couplings λ0. the terms in Eq. (3). Whereas the lightest neutralino should be heavier than 46 GeV in the constrained MSSM + with five parameters [15], the authors of Ref. [16] show Expressions for the partial widths of B0 and B meson that this bound can be relaxed and, even a massless neu- decays can be found in Ref. [17] (for details and derivation tralino is possible. In this study we consider models with of similar expressions see also Ref. [18]). For a neutralino the mass of the lightest neutralino in a GeV range. being a pure bino state, they read " #2 λ02 g02f 2 M 2 p ∗ 0 0 i13 B B0 cm Yνi Yd Yb 2 2 Γ Bd ! ν¯iχ~1 = 2 2 − 2 + 2 MB0 − Mχ~0 ; (4) 128π(md + mb) M M M 1 ν~i d~L ~bR " #2 λ02 g02f 2 M 2 p ∗ + + 0 i13 B B+ cm Yli Yu Yb 2 2 2 Γ B ! ` χ~ = − + M + − m − M 0 ; (5) i i 2 2 2 2 B `i χ~ 64π(mu + mb) M M M 1 ~li u~L ~bR where pcm is the 3-momentum of outgoing particles in 30 MeV [15] is the B-meson decay constant. Note that the rest frame of decaying meson, mu, md, mb are quark definition of the constant fB in [17] differs from that by masses, m`i is mass of the final state lepton (electron the Particle Data Group [15]. Therefore, formulas from or muon), M , M , M , . are sfermion masses, Y , [17] should be multiplied by 1=2 for our choice of f . ν~ d~L ~bR νi B Yd, Yb, . are corresponding hypercharges (coming from Without loss of generality, hereafter we assume the 0 neutralino couplings in the pure bino limit), g is U(1)Y common mass scale of sfermions M ≡ M = M = f~ ν~i d~L gauge coupling constant, M 0 is neutralino mass, MB+ , ··· = M This assumption simplifies further phe- χ~1 ~bR + 0 MB0 are B and B masses, respectively, and fB = 204± nomenological treatment since Eqs.