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Decaying light 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. Timiryasov† 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 . We extend the existing studies by introducing new production channels (in particular through the beauty ) 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 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 physics (SM) provide taming of the ra- ity of the lightest supersymmetric partner (LSP) which diative corrections to the Higgs mass (for a review becomes a candidate to form the dark 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 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 scat- high statistics of proton()-proton collisions might tering off the target material or indirectly via decays of compensate for smallness of the couplings, so the new secondary , 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 [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 ) 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 charge B, charge L, and duce the model and calculate the neutralino production 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- † [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. WITH RPV: try. The proposed√ 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 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 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 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 [15]. Therefore, formulas from or ), M , M , M , . . . are 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 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. (4) and (5) turn into: 3

2 0 ! 02 2 2 0 0 λi13 9g fBmB0 pcm  2 2  Γ Bd → ν¯iχ˜1 = MB0 − Mχ˜0 , (6) M 2 512π(m + m )2 1 f˜ d b 2 0 ! 02 2 2 + + 0 λi13 9g fBmB+ pcm  2 2 2  Γ B → ` χ˜ = M + − m − M 0 (7) i i B `i χ˜ M 2 256π(m + m )2 1 f˜ u b

and the production rates of neutralinos are proportional three-body leptonic decay via λijk, two-body semilep- to the squared combination λ0 /M 2. Note that our as- tonic decay into a charged via the coupling λ0 , i13 f˜ i11 sumption is not related to any particular pattern of mass and two-body semileptonic decay into a charged via 0 spectrum of RPV SUSY. In a more general case of differ- λi12. These states yield the detectable at SHiP signature ent masses of superpartners, the dominant contribution of two charged particles originated from a single vertex. will come from the intermediate sfermion with the high- The amplitude of the leptonic neutralino decay est value of λ0/M 2, e.g., from the lightest sfermion, if all f˜ through a virtual slepton or sneutrino was calculated in RPV couplings are of the same order. Ref. [19]. The decay width in the pure bino limit (ne- Expressions similar to (6) and (7) can be obtained for glecting masses of the final-state particles) reads decays of D mesons with obvious replacement of cou- 0 0 plings λi13 → λi21 and replacement of the corresponding quark flavors. !2 02 5 λ 3g Mχ˜0 Γ(˜χ0 → ν¯ `+`−) = ijk 1 . (8) 1 i j k M 2 4096π3 f˜ B. Decay pattern

We study three different decay channels of light neu- The rate of semileptonic decay can be calculated analo- tralinos with two charged particles in the final state: gously to Eq. (4). In the pure bino limit one has [6]

  !2 02 2 4 2 2 i 2 0 g fK mK+ M 0 − mK+ − m` pcm 0 − + 9 λi12 χ˜1 Γ(˜χ1 → K `i ) = 2 2 2 (9) 256π M ˜ M 0 (ms + mu) f χ˜1

0 − + 0 0 and the expression analogous to (9) forχ ˜1 → π `i , there is one additional decay channelχ ˜1 → K νi.A 0 2 which is proportional to |λi11| . One can see from special study is needed to understand whether it can be Eqs. (8) and (9) that the decay rates of a neutralino, as distinguished from background since there are no charged well as its production rates [Eqs. (6) and (7)], are pro- particles in the final state [20] but it affects the neutralino  2 lifetime. Hence we take into account the decay rate portional to the factor λ/M 2 . f˜ 0 0 Ifχ ˜1 is produced in decays of D mesons via λi21 then

  !2 02 2 4 2 2 0 g fK mK0 M 0 − mK0 pcm 0 0 1 λi21 χ˜1 Γ(˜χ1 → K ν¯i) = 2 2 2 (10) 512π M ˜ M 0 (ms + md) f χ˜1

0 0 and a similar one forχ ˜1 → π νi (which is proportional III. SIGNAL EVENT RATES 0 2 to |λi11| ) in further investigations. The goal of the present paper is to estimate the event rate of light neutralino decays within the SHiP detec- tor. We consider the light neutralinos created in decays 4

0 of heavy mesons. These heavy mesons are produced, in The probability ofχ ˜1 decay inside the fiducial volume turn, by 400 GeV protons scattering off the target mate- of the SHiP detector is rial. −lsh/lχ˜0 −lfid/lχ˜0 lfid For the production cross section of a particle (a neu- wdet = e 1 (1 − e 1 ) ' , (15) l 0 tralino in our case) with 3-momentum ~p created in a de- χ˜1 cay of the heavy meson H (H = D,B) with 3-momentum p lχ˜0 = , ~ 1 M 0 Γ k, one has: χ˜1 3 Z 3 with l denoting the muon shielding length (the distance d σ 3 ~ d σH sh = B d kf(~p, k) , (11) between the collision point and the detector, 63.8 m for dpdθpdφp dkdθkdφk SHiP [3]) and lfid referring to the length of the detector where p ≡ |~p|, k ≡ |~k|, B is the branching ratio of H fiducial volume (60 m); the second equality in (15) is valid when lsh  l 0 . two-body decay to neutralino, f(~p,~k) is the momentum χ˜1 distribution of a neutralino, and dσH is the differen- The proposed geometry of the SHiP detector [3] is a dkdθkdφk tial production cross section of meson H in pp collisions. 60 m length cylindrical vacuum tank with an elliptical All the momenta in Eq. (11) are given in the labora- section of x and y semiaxes 2.5 m and 5 m long, respec- tory frame. In the rest frame of the meson H (denoted tively. In the following estimates of the signal event num- by an asterisk), neutralino 3-momentum is uniformly dis- bers, we utilize a more conservative fiducial volume that tributed and one finds: is a cone formed by the vertex in the target and the 5 m × 10 m ellipse at the very end of the fiducial volume. 1 f(~p ∗, 0) = δ(p∗µp∗ − m2), (12) It covers part of the elliptical section. We argue that this 2πp ∗ µ choice is quite reasonable since neutralino decay prod- ucts should be tracked by the detector placed at the end ∗µ where p is the 4-momentum of the neutralino in the 0 of the vacuum tank. We select only neutralinosχ ˜1 with rest frame of the decaying meson. Note that the value of 3-momenta inside the cone region described above. ∗ ∗ p ≡ |~p | is fixed by kinematics of the two-body decay. The number of neutralino decays within the detector In order to boost expression (12) to the laboratory frame, is given by one should multiply it by the appropriate Jacobian and ∗ ∗ express ~p = ~p (~p,~k) in terms of the 3-momenta of the Z dσ 0 NPOT χ˜1 3 neutralino (~p) and the decaying meson (~k) in the labora- N = wdet d p (16) σpp,total cut dpdθdφ tory frame. The differential cross section of D-meson production√ where the distribution of neutralinos over the 3- in pp interactions at the center-of-mass energy s = momentum is defined in (11) and “cut” refers to the con- 27.4 GeV, which is relevant for the SHiP setup, was mea- straint on the neutralinos’ 3-momenta described above 20 sured by the LEBS-EHC Collaboration [21]. It has been and NPOT = 2 × 10 is the number of protons on target found that the differential production cross section is well during 5 years of operation [6]. represented by the empirical form [21] We consider the four production channels of light neu- tralinos described in Sec. II : D±, D0 decays via coupling dσD 1 ¯  n 2 λ0 and B±, B0 decays via coupling λ0 . According 2 = σ(D/D)(n + 1)b (1 − |xF |) exp(−bpT ) i21 i31 dxF dpT 2 to the SHiP technical proposal [3], at least two charged (13) particles are required to distinguish the signal from a −2 with n = 4.9 ± 0.5, b = (1.0 ± 0.1) GeV . We adopt the background. Hence we consider three decay channels: same value of the inclusive D/D¯ cross section σ(D/D¯) = 0 + − 0 − + 0 − + χ˜1 → `i ν¯j`k , χ˜1 → K `i , χ˜1 → π `i , driven by 18µb [6]. The differential cross section in (13) depends 0 0 λijk, λi12, λi11 correspondingly. As a result, we have on transverse pT and longitudinal√ pL components of 3- six combinations of couplings that can be tested by SHiP. momenta through xF = 2pL/ s and can be related to Resulting event rates for neutralinos produced in D0 that used in Eq. (11) as follows: and B0 decays are shown in Fig. 2. Plots for the D+ and + 3 2 3 B channels are very similar to those in Fig. 2. At small d σD 4k sin θk d σ couplings the number of events drops due to poor pro- = √ 2 . (14) dkdθkdφk s dxF dkT dφk duction, while at relatively large couplings the number of events also drops because of fast neutralino decay; thus, The beauty production cross section has not been mea- one has lχ˜0  lsh and the neutralino flux in the detector sured in the interesting energy region. Therefore, fol- 1 lowing the SHiP Collaboration [6] we extrapolate ex- is exponentially suppressed [see Eq. (15)]. The num- ber of events depends both on combination (λ/M 2)2 and isting data [22] to estimate the number of produced B f˜ mesons. To estimate the angular distribution of pro- on neutralino mass. To demonstrate this dependence we solve Eq. (16) with N ≡ 3 and find (λ/M 2)2 as a func- duced B mesons, we employ the theoretical results from f˜ Ref. [23] together with the Lund fragmentation model tion of M 0 . As one can see from Fig. 2, there are two χ˜1 [24]. solutions to this equations: one corresponding to small 5

���� ���� -�

�� 0 ˜0 -� 0 ˜0 �� D → νi χ ;M ˜0  1 GeV 1 χ1 ��×�� D → νi χ1

��� -� ��� -� � � ��� ����

� -� ∼

�� � ��×�� -� ��� λ�

�

���� -� -�� -� -� -� -� -� ��×�� �� �� �� �� �� �� ��� ��� ��� ��� ′ � -� �˜� λ λ/� ∼ � ��� χ� ��� � -� ���� ��×��

�� 0 ˜0 -� + + ˜0 �� B → νi χ ;M ˜0  4 GeV ��×�� D → μ χ1 1 χ1

��� -�

��� -� � ���

� ���� -�

� ∼ �� � ��×�� -� λ� ���

�

���� ��×�� -� ��-�� ��-� ��-� ��-� ��-� ��-� ��� ��� ��� ��� ˜� ′ � -� �χ λ λ/� ∼ � ��� � ��� � ��×�� -�

FIG. 2. Number of signal events for neutralinos produced in 0 ˜0 ��×�� -� B → ν χ D0 decay (upper panel) and in B0 decay (lower panel). De- i 1 + − + − cays of the neutralino to e νie (solid line), to π ` (dashed -� line), and to K+`− (dotted line) are considered. λ stands for -� the appropriate RPV couplings. The horizontal line repre- � ��� ��×�� -� ∼ sents three events: their absence implies an upper limit on � ��×�� -� the model parameters placed at 95% confidence level within λ� the Poisson statistics.

��×�� -� � � � � � � couplings and slow decay and another corresponding to ˜ �χ� relatively large couplings and fast decay. Since large cou- � plings are excluded by different searches (see, e.g., Ref. ��×�� -�

[7] for details), we show in Fig. 3 a solution corresponding -� + + ˜0 ��×�� B → μ χ1 to small couplings. Note that for the small couplings the

probability of neutralino decay inside the fiducial volume -� (15) and, consequently, the number of events is propor- -� � ��� ����

tional to the decay width. Therefore, one can use Eqs. -� ∼ � (4) – (7) and Eqs. (8) – (10) (see also expressions from ��×�� -� λ� Ref. [19]) in order to rescale λ0/M 2 dependence for the f˜ generic case of a nondegenerate mass spectrum and any pattern of RPV couplings. ��×�� -� 0 � � � � � � One can see from Fig. 3 that the decay channelχ ˜ → ˜ 1 �χ� 0 � K νi sufficiently affects the lifetime and, subsequently, the event rate of neutralinos created in D-meson decays 0 FIG. 3. Expected sensitivity of the SHiP experiment to a light via the coupling λi21. neutralino with RPV. The solid line refers to leptonic decay, the dashed line is for decay to e+π−, and the dotted line is for decay to e+K−. λ stands for the appropriate combination IV. SHIP SENSITIVITY TO AND CHARM of RPV couplings. BOUNDS ON RPV

Absence of the events, while the three signal events are ground is negligible, which is true in our case [3]). Lim- expected, implies 95% confidence level bounds (if back- its on RPV couplings that could be placed by the SHiP 6 experiment depend both on the common sfermion mass adapting the whole procedure described above for the scale and on the neutralino mass. Exclusion limits on var- CHARM geometry [12]. The CHARM experiment has ious combinations of RPV couplings are shown in Fig. 4. exploited the same 400 GeV beam as the SHiP plans. Dark shaded regions are excluded by previous stud- The detector was located at 480 m downstream from the 0 0 ies. Namely, the constraints on λ121, λ113, λ121, λ122, λ123 beam dump. Therefore, it covers a sufficiently smaller have been obtained from charged current universality, solid angle compared to the SHiP. The length of the de- 0 and the constraint on λ111 has been obtained from neutri- cay region was 35 m and the radius of the calorimeter noless double beta decay (see Refs. [25], [7] for details). placed at the end of decay volume was 1.5 m. The total 18 Note that these constraints scale as ∝ λ/Mf˜, while in our amount of protons on target equalled 2.4 × 10 [12]. To 2 the best of our knowledge there was no special investiga- case of the SHiP sensitivity the scaling goes as ∝ λ/M ˜. f tion of the CHARM sensitivity to RPV SUSY, but very Vertical lines in Fig. 4 at M = 1 TeV show the mass f˜ similar signatures of heavy neutral lepton decays to the scale that is excluded by the LHC searches in the case SM leptons were studied in Refs. [12], [13]. of approximately equal sfermion and masses [26]. Note, however, that for some particular RPV spectra this V. CONCLUSION bound can be as low as 800 GeV [27]. We list our estimates of SHiP bounds on these cou- To summarize, we have estimated the sensitivity of the plings in Table I. As one can see from Fig. 3 the bounds recently proposed SHiP experiment to the supersymmet- ric extensions of the SM with light neutralinos and R- parity violation. For the R-parity violating couplings λ TABLE I. Estimates of SHiP sensitivity to and CHARM of order one, the SHiP will allow us to probe the super- bounds on combinations of RPV couplings. In the first three partner mass scale as high as 30 TeV (see Fig. 3), which rows we set M 0 = 1 GeV and M 0 = 4 GeV for the last three χ˜1 χ˜1 is in agreement with previous estimates in Ref. [6]. The rows. Indices j, k = 1, 2 and i = 1, 2, 3 indicate flavor of the 0 2 4 number of signal events scales as ∝ (λ /M ˜) . As a by- final-state leptons. f product we have obtained limits on the model parameters from nonobservation of anomalous events in the CHARM Expected sensitivity Upper limit experiment. With respect to the CHARM, the SHiP will λ SHiP, M 2/TeV2 CHARM, M 2/TeV2 f˜ f˜ improve the sensitivity to R-parity-violating couplings by pλ0 λ 2.4 × 10−3 2.5 × 10−2 121 ijk an order of magnitude. q 0 0 −3 λ121λj11 1.2 × 10 – Several remarks are in order. First, other final states q 0 0 −3 such as the mentioned neutral must be considered λ121λj21 1.4 × 10 – as well. Second, the light neutralinos can be produced in p 0 −3 −2 λ113λijk 2.4 × 10 2.5 × 10 pairs due to R-parity-conserving couplings, and the cor- q 0 0 −3 λ113λj11 3.9 × 10 – responding new production channels can also be studied. q Third, not only heavy meson but also heavy can λ0 λ0 4.0 × 10−3 – 113 j21 decay into light neutralinos, which gives additional pro- duction channels. Fourth, secondary hadrons, produced in the showers initiated by 400 GeV proton scat- listed in Table I are valid for a wide range of kinemati- tering off target materials, can contribute to the light cally allowed region (with phase-space corrections at the neutralino production. Fifth, τ leptons produced mostly boundaries) of M 0 . in decays of D mesons allow us to probe other R-parity- χ˜1 s In order to illustrate advantages of the SHiP facility, violating couplings λijk, which is also worth investigat- we also present in Fig. 4 our estimates of the bounds on ing. RPV couplings that follow from the absence of signal in This work has been supported by Russian Science the CHARM experiment. These bounds are obtained by Foundation Grant No. 14-22-00161.

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at Mf˜ = 1 TeV is generally disfavored as the mass scale due to searches at the LHC (see discussion in the main text).