Looking forward to test the KOTO anomaly with FASER
Felix Kling∗ SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA Sebastian Trojanowski† Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield, S3 7RH, UK and National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland
The search for light and long-lived particles at the LHC will be intensified in the upcoming years with a prominent role of the new FASER experiment. In this study, we discuss how FASER could independently probe such scenarios relevant for new physics searches at kaon factories. We put an emphasis on the proposed explanations for the recently observed three anomalous events in the KOTO experiment. The baseline of FASER precisely corresponds to the proposed lifetime solution to the anomaly that avoids the NA62 bounds on charged kaons. As a result, the experiment can start constraining relevant models within the first few weeks of its operation. In some cases, it can confirm a possible discovery with up to 104 spectacular high-energy events in FASER during LHC Run 3. Further complementarities between FASER and kaon factories, which employ FASER capability to study γγ signatures, are illustrated for the model with axion-like particles dominantly coupled to SU(2)W gauge bosons.
I. INTRODUCTION or FASER [3–5]. The FASER experiment will search for LLPs abundantly produced in the far-forward direction The quest for beyond the Standard Model (BSM) of the Large Hadron Collider (LHC) during its upcom- physics is undoubtedly among the biggest challenges in ing Run 3. Several features of its setup make it an ideal contemporary physics. It has typically been driven by probe for light LLPs produced in kaon decays: i) Given the lack of answers to some fundamental questions, such a large expected boost factor of light particles traveling as understanding the unification of the forces of nature towards FASER, and the location of the detector, the or the mechanism of baryogenesis, as well as by hints of experiment’s sensitivity is optimal for the precise combi- new physics appearing in anomalous experimental obser- nation of the lifetime and mass that are required to fit vations. The latter become especially intriguing when the anomaly. In particular, for high-energy LLPs with the known Standard Model (SM) background (BG) can E ∼ 1 TeV that are produced at the ATLAS IP, the be reduced to negligible levels so that even the observa- sensitivity reach of FASER is maximized for tion of a few events can be attributed to BSM effects. The flavor-changing rare decays of kaons are excep- τLLP 0.1 ns ∼ , (best FASER reach). (1) tionally promising examples of such discovery channels mLLP 100 MeV given their highly suppressed SM rates. In particular, the KOTO collaboration has recently reported a possible ii) The FASER sensitivity additionally benefits from the observation of three anomalous events in the search for O(150 m) long part of the LHC beam pipe, in which 0 KL → π νν¯ [1], in which no SM signal was expected at forward-going neutral kaons can travel and decay before the current level of the experimental sensitivity. If taken being absorbed, as well as the presence of additional LLP as a signal, this observation would indicate that the rel- production modes at the LHC. iii) The FASER detector evant branching fraction exceeds the SM prediction by has the capability to not only detect LLP decays into about two orders of magnitude [2]. It has been quickly arXiv:2006.10630v2 [hep-ph] 2 Dec 2020 charged particles but also into photon pairs, due to its noticed that the discrepancy could be resolved by intro- dedicated pre-shower detector. As a result, during Run ducing a new light long-lived particle (LLP) with mass 3 of the LHC, FASER can turn the three currently ob- of order 100 MeV, light enough to be produced in kaon served anomalous events at KOTO into up to O(104) decays. By properly adjusting the lifetime of the LLP, spectacular high-energy LLP decay events with expected one can explain the neutral kaon anomaly while avoid- negligible BG. ing stringent bounds on such models from searches for The rest of this paper is organized as follows. In Sec.II charged kaon decays. and Sec.III we provide more details about the KOTO In this study, we illustrate how such proposed solu- anomaly and the FASER experiment, respectively. The tions to the KOTO anomaly could be thoroughly probed FASER sensitivity reach in several selected BSM scenar- by the recently approved ForwArd Search ExpeRiment, ios is presented in Sec.IV. In Sec.V, we further illustrate the possible interplay between FASER and searches for LLPs in kaon factories. We conclude in Sec.VI. Sev- ∗ [email protected] eral useful expressions for BSM meson decay branching † s.trojanowski@sheffield.ac.uk fractions are listed in AppendixA. 2
II. KOTO EXPERIMENT AND THE with the corresponding branching fraction measured to ANOMALY be at the 68% CL [13], B (K+ → π+νν¯) = 0.47+0.72 × 10−10, (6) The KOTO experiment [6] has been designed to study NA62 −0.47 decays of kaons into neutral pions and a neutrino/anti- and the upper bound at the 95% CL given by neutrino pair, K → π0νν¯. The kaons are produced + + −10 L BNA62,bound(K → π νν¯) < 2.44 × 10 . The mea- in collisions of 30 GeV protons from the Japan Proton surements of the charged kaon decay branching fraction, Accelerator Research Complex [7] (J-PARC) main ring together with the GN bound Eq. (5), lead to (2 − 3)σ accelerator with the target made out of gold. A high- tension with the anomalous observation by the KOTO intensity beam of neutral kaons produced at an angle of collaboration, cf. Eq. (4), depending on how the possible ◦ 16 with respect to the proton beam line is created with impact of new physics is taken into account [2]. A num- the use of dedicated collimators. At a distance of about ber of BSM scenarios have been proposed to explain this 24 m away from the target, the ∼3 m long vacuum cham- discrepancy [2, 14–31]. ber of the KOTO detector begins. Here, kaon decays are Among these scenarios, a prominent role is played by identified by detecting photons produced in prompt neu- models predicting the existence of a new LLP with the tral pion decays. mass mX ∼ 100 MeV, which can be produced in rare The data collected by the KOTO collaboration in 2015 0 kaon decays, KL → π X [2]. In particular, if such a light allowed them to obtain the leading bound on the branch- BSM particle has a lifetime of order τX ∼ 0.1 ns, it can ing fraction of the aforementioned decay process. At the be effectively stable and invisible in the search performed 90% confidence level (CL) it reads [8] by the KOTO collaboration. At the same time, X will
0 −9 typically decay inside the E949 and NA62 detectors, and BKOTO,bound(KL → π νν¯) ≤ 3 × 10 . (2) it does not contribute to the measured branching fraction + + of KL → π νν¯. This leads to an apparent violation of Notably, Eq. (2) is consistent with the SM prediction the GN bound when the results of these experiments are which remains about two orders of magnitude lower, 0 −11 compared with each other, which is further referred to as BSM(KL → π νν¯) = (3.4 ± 0.6) × 10 [9]. A simi- 0 0 the lifetime solution to the anomaly. lar bound on the two-body decay K → π X has also A very long-lived X can also explain the anomaly while been obtained, where X is a stable or long-lived BSM avoiding the bounds from past beam-dump searches. In bosonic particle, addition, if its mass is close to the pion mass, it can es- cape detection in E949 and NA62 experiments by hiding B (K → π0 X) 2.4 × 10−9. (3) KOTO,bound L . in the SM BG [32]. Another distinct possibility is to allow In the subsequent analysis of the data from 2016-18 [1], KL decays into neutral dark states, KL → X1 X2. Sub- however, a total of four candidate events were found, only sequent Xi decays that produce photons can be detected one of which had the properties of BG. If taken as a in the KOTO electromagnetic calorimeter and resemble signal, the remaining three anomalous events point to a neutral pion signature [26]. In this case, charged kaon the branching fraction which significantly exceeds the SM three-body decays can be suppressed or even kinemati- prediction. At the 95% CL it is given by [2] cally forbidden. Below, we analyze the prospect of probing such se- 0 +4.1 −9 lected BSM scenarios in the FASER experiment at the BKOTO,anom.(KL → π νν¯) = (2.1 ) × 10 . (4) −1.7 LHC. Importantly, in the SM the aforementioned neutral kaon decay mode is also related by the isospin symme- try to the value of the branching fraction of a charged III. FASER AND FASER 2 EXPERIMENTS kaon decay into a pion π+ and a neutrino/anti-neutrino pair, which proceeds via the same parton level process The FASER experiment [3–5] has been proposed to s → dνν¯. The relevant so-called Grossman-Nir (GN) search for LLPs [33, 34] produced in the forward region bound [10] reads of the LHC [35–41], as well as to study interactions of high-energy neutrinos [42–44]. It utilizes the fact that 0 + + B(KL → π νν¯) < 4.3 B(K → π νν¯). (5) light and high-energy particles produced in pp collisions at the LHC and e.g. subsequent decays of light mesons The current upper limit on the K+ decay branching M, will typically travel in the forward direction, as dic- fraction is obtained from the results of the E949 ex- tated by their estimated angular spread around the beam periment, which observed several charged kaon decay collision axis, θX ∼ mM /EX 1. As a result, even a + events [11, 12], and it is given by BE949,bound(K → small detector placed along the beam collision axis can π+νν¯) < 3.35 × 10−10 at 90% CL. This is consistent search for displaced decays of LLPs, provided that it is + + with the SM expectation BSM(K → π νν¯) = (8.4 ± shielded to suppress the SM BG. The FASER detector 1) × 10−11 [9]. An improved analysis has also recently will operate during the LHC Run 3 in the former ser- been preliminarily presented by the NA62 collaboration vice tunnel TI12 located at a distance L = 480 m away 3 from the ATLAS IP. Below, we also show the sensitiv- Additionally, LLP decays into photons could also be ity reach for the same detector with continued operation proved in the single photon channel. Importantly, single during the High-Luminosity LHC phase (HL-LHC). We high-energy BG photons with Eγ & 100 GeV at FASER refer to this version of the experiment as FASER HL. We location are typically associated with time-coincident also present the results obtained for a possible larger ver- muons activating veto layers. Hence, a large number sion of the detector to operate during HL-LHC, dubbed of very energetic photon pairs produced in LLP decays FASER 2. In particular, we assume a cylindrical decay even closer to the pre-shower detector, which could be volume with length ∆, radius R, and an integrated lu- misidentified as a single EM shower, would still be in- minosity L for each of the three aforementioned cases: dicative of new physics. b. Forward going kaons at the LHC It is also impor-
−1 tant to stress that forward-going kaons produced at the FASER: ∆ = 1.5 m,R = 10 cm, L = 150 fb , ATLAS IP will not be immediately absorbed. Instead, FASER HL: ∆ = 1.5 m,R = 10 cm, L = 3 ab−1, they can travel a long distance through the LHC beam pipe, which allows them to decay with a sizable probabil- FASER 2: ∆ = 5 m,R = 1 m, L = 3 ab−1. ity. In particular, for neutral kaons produced within the angular coverage of FASER, θ < θ ≈ 0.2 mrad, Our main focus in this study is to highlight possible com- K FASER the closest element of the LHC infrastructure that they plementarity between FASER searches for LLPs and kaon hit is the TAN neutral particle absorber placed at a dis- factories, with a particular emphasis on the recently ob- tance 140 m away from the ATLAS IP. We take this into served KOTO anomaly. It is then useful to briefly sum- account in our modeling along with the TAS absorber marize the main advantages of FASER that make it an placed 20 m away from the IP that affects neutral kaons ideal tool to study related BSM scenarios predicting a produced with larger θ . The TAS also marks the end new unstable light species: K of the region where charged kaons are not deflected away • FASER has the capability to study di-photon final by strong LHC magnets. states in LLP decays, on top of more often considered Below, we also illustrate how in specific models addi- electron-positron pairs. tional production modes of LLPs, for example in heavy meson decay, can further improve FASER sensitivity. • Forward-going kaons produced in pp collisions at the c. Lifetime regime Last but not least, it is worth ATLAS IP can travel about 140 m, and hence de- highlighting that in order for the LLP with mX ∼ cay with sizable probability, before they are absorbed. 100 MeV and energy EX ∼ TeV to reach FASER, the Additional production modes can further improve de- required lifetime is of order τX ∼ L/(γX c) ∼ 0.1 ns. tection prospects. This precisely corresponds to the sweet spot between the KOTO and NA62 searches discussed in Sec.II. Therefore, FASER’s sensitivity is optimal for typical LLP mass • as we will see below, it is not a surprise that FASER and lifetime proposed to explain the KOTO anomaly, can effectively exclude many such explanations of the cf. discussion in Sec.II. anomaly even with the first 10 fb−1 of data. Instead, in The signatures that we focus on consist of LLP X de- the case of discovery, FASER can confirm the anomaly cays into mainly γγ or e+e− pairs that can be resolved in with large statistics of related LLP decay events. This 4 the detector. For sufficiently large energy, which we take can reach up to O(10 ) events in FASER during LHC Run 3, while it could grow even larger for FASER HL to be EX & 100 GeV, the search at the FASER location can be considered BG-free [4,5]. In the following, we and FASER 2. assume a 100% detection efficiency. Notably, the prelim- inary efficiency studies show that it typically has a minor impact on the sensitivity reach plots [4]. IV. FASER SENSITIVITY REACH a. FASER capabilities to study the γγ final state As far as the γγ final state is concerned, a very good separa- As discussed in Sec.II, if the anomalous neutral kaon tion efficiency between the photons is achieved thanks decay events observed in the KOTO experiment are con- to a dedicated pre-shower detector placed in front of firmed, this would require a BSM explanation. In the the FASER calorimeter, i.e. 2 m after the end of the following, we illustrate how such models can be indepen- FASER decay vessel. A preliminary relevant discussion dently probed in FASER. To this end, we focus on several can be found in Ref. [37] in the context of FASER search scenarios predicting LLPs. for axion-like particles with the dominant di-photon cou- pling. As shown there, taking into account a finite sepa- ration resolution between the two γs of order δ ∼ 200 nm, which is achievable in FASER, has a negligible impact A. Generic LLP and the lifetime solution on the sensitivity reach. Instead, the substantial effect was expected only if the resolution was worse than about The simplest BSM scenario proposed to explain the 1 mm. anomaly and to avoid stringent bounds on rare decays of 4
101 E949 FASER CHARM NA62
10 2 0 E137 10 10 Orsay
NA62 E949 CHARM 10 1 NA62 03 ] E949 ] 1 m m
[ 1 [ 10 NA62 4 x x NuCal 10 NuCal (g c c KTEV 2 KTEV 5 ) 10 2 0X) > 1% 6 KTEV BR(KL KTEV 10 10 2 K 2 1% K 2 0 X) > BR(KL FASER - 3 events FASER2 - 1000 events FASER (HL) - 3 events SHiP - 1000 events 10 3 10 2 0.05 0.10 0.15 0.20 0.25 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 mX [GeV] mX [GeV]
FIG. 1. Results for the lifetime solution to the KOTO anomaly (white regions in the plots) presented in the (mX , cτX ) plane, where mX and τX correspond to the LLP mass and lifetime, respectively. The current bounds are shown as gray-shaded regions. Left: Reach for the generic X scenario in which a new light and unstable particle is produced specifically in the KL and K+ decays, cf. discussion in Sec.IVA. From top to bottom, dark and light red solid lines correspond to the upper limit in cτX of the sensitivity reach of the FASER HL and FASER experiments, respectively. The experiments can probe scenarios relevant for the entire white region in the plot below the sensitivity lines. Also shown, are the lines with a fixed number of events Nev = 1000 expected for the FASER 2 (orange dotted line) and SHiP (blue dashed line) experiments. The number of events in both cases grow for lower values of cτX in the white region of the plot. At the bottom of the plot, the dark red solid 0 line marks the region of the parameter space which is excluded by the untagged KL → π X branching fraction. Right: Event contours (from top to bottom: 10 (solid), 102 (dash-dotted), 103 (dashed), 104 (dotted), 105 (solid) and 106 (dash-dotted)) at FASER at the LHC Run 3 for the dark Higgs boson model with non-universal couplings to the SM leptons and quarks, as discussed in Sec.IVB. The green-shaded band corresponds to the 2 σ fit to the (g − 2)µ anomaly. charged kaons, employs a new unstable X particle pro- γγ final state.1 0 + + duced in kaon decays, KL → π X, and K → π X. The anomalous KOTO events can be fitted within the In particular, if the lifetime of X and its mass are of or- remaining portion of the parameter space shown in Fig.1. der τX ∼ 0.1 ns and mX ∼ 100 MeV, respectively, then Notably, the reconstructed transverse momentum of the X typically decays within the volume of the E949 and pion can more easily resemble the observed such distri- NA62 detectors and does not contribute to the measured bution by KOTO when mX . 180 MeV [2], or even + + value of B(K → π νν¯). On the other hand, the proba- mX . mπ [23]. bility for X to escape the KOTO decay volume without In order to obtain the FASER sensitivity reach, we decaying remains larger [2]. generate the meson spectra using EPOS-LHC [50] as im- In the left panel of Fig.1, we show the FASER and plemented in the simulation package CRMC [51] and subse- FASER HL sensitivity reach contours in a generic sce- quently decay the mesons using the branching fractions nario, in which X is produced only in kaon decays. We as- obtained as discussed above. As can be seen, already sume that the real branching fraction of a two-body neu- the FASER experiment operating during the LHC Run tral kaon decay is of order B(K0 → π0X) ∼ 10−8 −10−6. 3 can already cover the entire region of the parameter Its precise value is chosen depending on mX and τX , as space corresponding to the anomaly. The relevant ex- well as the KOTO detector efficiency [8], as detailed in pected number of events can be as large as O(102) for Ref. [2, 18]. This is done by requiring that the mea- FASER, and grow by an additional factor of 20 and a sured branching fraction fits the KOTO anomaly, cf. few hundred for FASER HL and FASER 2, respectively. Eq. (4), after correcting for finite escape probability from Notably, thanks to the use of the dedicated pre-shower the detector. In the plot, it is also assumed that the detector, FASER can probe this scenario even for lep- charged kaon decay branching fraction saturates the GN bound, cf. Eq. (5). The gray-shaded region is excluded by the constraints from the aforementioned searches for K+ → π+νν¯ at E949 [12] and NA62 [13], the untagged 1 In particular, the NuCal bounds shown in Fig.1 have been ob- K → π0X branching fraction [45], beam-dump searches tained following a “conservative” approach discussed in Ref. [15] L and by taking into account X production in decays of kaons (left at CHARM [46] and NuCal [47, 48] experiments that panel) or all the relevant mesons (right panel). We note that the we implement following Refs. [15, 18], and the mea- bounds from hadronic beam dumps are subject to uncertainties 0 surement of the branching fraction for KL → π γγ by in modeling of the high-energy tail of the meson spectrum in the KTEV [49], assuming that X decays dominantly into a target. 5 tophobic X which decays dominantly into a di-photon Assuming a hierarchy between the couplings, ` q, pair, as assumed in the bounds shown in the left panel allows one to reduce the lifetime of X, which is gov- of Fig.1. erned by the leptonic coupling `. Thanks to this, strin- The lifetime solution to the KOTO anomaly can also gent bounds from hadronic beam-dump searches can be be explored by other experiments dedicated to LLP avoided and the kaon decay branching fraction into X −3 −2 searches, although this can be limited by the lack of di- can be kept low, as it depends on q ∼ 10 − 10 . photon signal detection capabilities. We illustrate this In particular, for ` ∼ O(1) the most important bounds in the left panel of Fig.1 for the proposed SHiP experi- on long-lived X come from electron beam-dump experi- ment [52] to operate in a similar time frame to FASER HL ments E137 [54] and Orsay [55]. However, they do not and FASER 2. The sensitivity of SHiP is analyzed by exclude scenarios with τX ∼ 0.1 ns. conservatively requiring that the kaons decay within one The dominant decay mode for X in the considered nuclear interaction length in the SHiP target made out mass regime is into the e+e− final state, although a loop- of molybdenum, λ = 15.25 cm. We show the relevant induced decay into the γγ pair can take values of up to contour line corresponding to a fixed number of expected O(10%) of the decay branching fraction of X. The addi- 0 + − events, Nev = 1000, similarly to the FASER 2 line also tional bounds from the KTEV search for KL → π e e shown in the plot. The number of events grows larger decays exclude a part of the region of the parameter space for lower values of the LLP lifetime within the allowed of the model with mX & 140 MeV [56], although they are region in the (mX , cτX ) plane. Interestingly, although not relevant for lighter X. We employ the decay width kaon absorption in the target at distances greater than of X following Ref. [18]. λ could limit SHiP sensitivity, a large number of protons A relative smallness of q is consistent with only a few 20 on target (POT), NPOT = 2 × 10 , as well as the size events currently observed in KOTO. However, as far as of the decay volume, ∆ ' 50 m, sufficiently compensate FASER is concerned, additional production modes of X for this effect. The number of expected events in SHiP can become more important than rare kaon decays, there- could be further enhanced once more detailed modeling fore increasing the expected number of signal events. In of the kaon propagation in the target is performed. particular, when obtaining the FASER sensitivity reach, we take into account the following production channels:
Meson decays: In our modeling, we include rare two- B. Specific example employing 2HDM body decays of charged and neutral long-lived kaons that propagate in the LHC beam pipe, as discussed Once a specific model of the LLP that corresponds to in Sec.III. We also analyze the impact of short-lived 0 the aforementioned lifetime solution is considered, typ- kaon decays, KS → π X. Notably, the relevant BSM ically more production and decay modes appear for X branching fraction of KS is suppressed with respect −4 that should be taken into account. This has an impact to KL by an additional factor of order O(10 ) due on present constraints on such X, but can also signif- to a larger value of the total decay width of KS. On icantly increase the expected number of events in the the other hand, short-lived kaons can more easily de- future detectors. We illustrate this below for FASER cay prior to hitting any element of the LHC forward employing the model with a leptophilic dark scalar dis- infrastructure. cussed in Ref. [18]. Interestingly, such a scalar with On top of kaons, a number of other mesons can be 40 MeV m 70 MeV and τ ∼ 0.1 ns could simulta- . X . X abundantly produced in the forward direction of the neously explain the recently observed KOTO events and LHC. In particular, we study prompt rare two-body the measurement of the anomalous magnetic moment of decays η → π0X and η0 → ηX, as well as inclusive de- the muon, (g − 2) [53]. µ cays of B mesons into final states containing strange The model of our interest can effectively be described hadronic states, b → sX, where the light meson spec- by three parameters corresponding to the LLP mass, as tra were obtained using EPOS-LHC, while the b-quark well as its coupling constants to leptons, , and quarks, ` spectrum was obtained using Pythia 8 [57, 58]. We . The relevant Lagrangian reads q implement the kaon and B-meson branching fractions following Ref. [35], while for η mesons we employ the 2 2 X mq X m` ¯ L ⊃ − m X + q Xqq¯ + ` X`` results from Ref. [15]. We give the relevant expres- X v v (7) sions for the branching fractions in AppendixA. m2 + W XW +W µ−, W v µ The dominant contribution to the K and B decay widths into X corresponds to a top-W loop. Unlike where the SM Higgs boson vev is equal to v ' 246 GeV for kaon decays, the relevant branching fractions of and we set W = q. The couplings ` and q can arise as B mesons do not suffer from a strong CKM suppres- 2 2 the mixing angles in the scalar sector of the type-X two sion, Vtb Vtd, which makes this channel the domi- Higgs doublet model (2HDM). In particular, the model nant production mode despite the suppressed b-quark allows one to disjointly treat interactions of X with the production rate and the broader pT spectrum. In- SM leptons and quarks. stead, the decays of η mesons are suppressed for small 6
Experiment Benchmark X prod. in meson decays and decay in FASER Proton brem 0 + + 0 0 mX [MeV] cτX [cm] KL → π X K → π X η, η ,KS → π X b → sX pp → X + ... FASER 150 50 650 2000 135 50 1.5 FASER 2 80k 30k 250k 11M 16k
TABLE I. The number of X decay events in FASER (FASER 2) and the integrated luminosity of L = 150 fb−1 (L = 3 ab−1) for various production modes of the LLP. The number of events for FASER HL are 20 times larger than for FASER during LHC Run 3. The results correspond to the model discussed in Sec.IVB and to the benchmark values of the model parameters given in the text and indicated in the table. The scenario can explain both the KOTO and (g − 2)µ anomalies.
Yukawa-like couplings of X to the first-generation of X is shown in tableI for the benchmark scenario with quarks and for a loop-induced coupling to gluons. mX = 50 MeV, q = 0.016 and ` = 1.22. The values Similarly to KS, however, prompt decays of η mesons of the parameters of the model have been chosen so that make them a non-negligible production mode of X. both the KOTO and (g − 2)µ anomalies can be fitted to their central values [18]. The dominant production mode Scalar bremsstrahlung: Another production mode of in FASER, in this case, is due to rare B meson decays, light and high-energy scalar BSM particles produced although decays of lighter mesons give a contribution of in the forward direction of the LHC is through their order 30% in total. This is dominated by rare decays of bremsstrahlung in proton-proton collisions. We study η mesons. Instead, the kaon decays give only a few % this process following the discussion in Ref. [59] and contribution. find that the relevant contribution to the event rate in FASER is typically of order a few % or smaller.
Lepton-induced production: We have also analyzed C. A very long-lived dark scalar a number of production modes that depend on the lep- ton coupling, ` ∼ O(1). These include loop-induced If a new LLP is produced in rare kaon decays with the Primakoff production from high-energy photons hit- mass close to the pion mass, mX ∼ mπ, and the relevant ting the TAN, cf. Ref. [37], as well as various sec- branching fraction fitting the anomaly, cf. Eq. (4), the ondary processes employing electrons and muons pair- stringent NA62 and E949 bounds on K+ decays can be produced in the absorber material or traversing the avoided even for a very long-lived or effectively stable X. rock shielding of FASER. However, since the differ- This is due to increased BG in the respective searches for ence in ` and q is typically not sufficient to com- K+ decays (see the discussion in Ref. [2] and references pensate for a large Yukawa suppression of the corre- therein). In addition, such scenarios can also escape con- sponding coupling constants, as well as due to addi- straints from beam-dump searches provided that τX is tional suppression factors relevant for these produc- large enough and the LLPs typically overshoot the de- tion modes, we have found that they play a subdom- tector. inant role for high-energy scalars of our interest. An interesting example of such a scenario that can fit In the right panel of Fig.1, we show the contours with the KOTO anomaly is a dark Higgs boson X with a uni- the different number of events in FASER, N = 10, 102 ..., versal mixing angle with the SM species, cf. Eq. (7) with that correspond to the total integrated luminosity of ` = q = W and Ref. [15] for further discussion. In L = 150 fb−1 for the LHC Run 3. In the white region of this scenario, the lifetime of the LLP is typically large, the plot, the KOTO anomaly can be explained without cτX ∼ 100 km. As a result, probing this model goes violating current bounds shown as the gray-shaded re- beyond the capabilities of FASER and FASER 2 exper- gion, following Ref. [18]. In addition, we have added the iments, which are designed to focus on more short-lived constraint from the NuCal experiment following Ref. [15]. BSM species. The green-shaded band in the plot indicates the region On the other hand, in the long-lifetime regime relevant in the parameter space of the model in which the (g −2)µ here, the sensitivity reach in searches for displaced decays anomaly can be resolved. As can be seen, FASER can of X can be improved by increasing the size of the de- detect up to O(104) LLP decays in the region of the pa- tector and its angular coverage. We illustrate this in the rameter space corresponding to both the anomalies. In left panel of Fig.2, where we show the expected reach this case, even a few weeks of the operation of the ex- of proposed future Codex-b [60], MATHUSLA [61] and periment would be enough to test such scenarios. Once SHiP [52] experiments in their searches for dark Higgs more data are accumulated, the entire allowed region of boson decays into electron-positron pairs, X → e+e−, the parameter space will be covered with at least a few following Ref. [33]. hundred expected events. For comparison, we also present the expected sensitiv- The breakdown of the number of the expected events ity of the enlarged FASER 2 detector assuming the total in FASER and FASER 2 for different production modes integrated luminosity of L = 3 ab−1 relevant for HL- 7
LHC. As can be seen, probing the region in the param- anomaly is indicated by a green-shaded band in the plot. eter space of the model that corresponds to the KOTO The current bounds on the model from the CHARM ex- 0 anomaly would require a quite substantial increase in the periment, the previous KOTO search for KL → π νν¯, detector radius, R & 5 m, or its length, ∆ & 50 m, with cf. Eq. (2), atomic parity violation (APV) [64], and the respect to the design discussed in Sec.III. On the other Belle-II search for B → Kνν¯ [65] are shown as the gray- 2 hand, for lower values of τX , even a much smaller and shaded region following Ref. [26]. properly placed detector can have very good detection The region of the parameter space of the model in prospects, as we show for other scenarios discussed in which the KOTO anomaly can be explained by rare de- this study. cays KL → ψ1ψ2 corresponds to 350 MeV . m2 . 450 MeV. Here, one requires that ψ2 decays within the KOTO detector volume so that it can mimic neutral pion D. KL decays into dark sector particles decays. However, such decays that are too fast lead to larger production rates that are already excluded by pre- A different approach to the BSM explanation of the vious KOTO studies. As a result, the anomalous events
KOTO anomaly has been proposed in Refs [25, 26]; this can be best fitted for τψ2 ∼ (0.01 − 0.1) ns and such approach employs two-body decays of neutral kaons into scenarios can be well tested in FASER. In particular, as dark species, KL → ψ1ψ2. The relevant three-body de- shown in Fig.2, one expects O(100) of high-energy visible + + cay processes of charged kaons, e.g. K → π ψ1ψ2, can ψ2 decay events in the detector for LHC Run 3. then be kinematically suppressed or even forbidden de- pending on the masses of the ψis. The anomaly can be fitted if at least one of the dark species is unstable and V. BEYOND THE ANOMALY – ALP can mimic the di-photon decay signature of neutral pions COUPLING TO SU(2)W GAUGE BOSONS inside the KOTO detector. In the following, we focus on the model in which a non- The complementarity between FASER and kaon fac- diagonal coupling of kaons to two dark fermionic states tories extends beyond possible explanations to the cur- ψi arises due to a vector portal and a new gauge field Xµ rently observed anomalous events in the KOTO experi- that mixes with the SM Z boson [62–64] ment. In particular, more general BSM scenarios leading to two-body kaon decays, K → π0X and K+ → π+X, 1 2 µ 2 µ L ⊃ mX XµX − Z mZ XµZ , (8) can be constrained in searches for detector-stable X act- 2 ing as neutrino impostors, as well as in studies focused −3 −2 + where Z ∼ 10 − 10 denotes the relevant mixing on displaced decays X → γγ leading to 4γ or π + 2γ parameter. After the electroweak symmetry breaking, a signatures observed in the detector. Some examples of 0 2 2 2 2 new Z gauge boson acquires a mass mZ0 = mX −Z mZ . such studies have recently been discussed in Ref. [25] for The interactions of Z0 with the dark fermions can then models with axion-like particles (ALPs), X ≡ a, which be described by couple dominantly to gluons or SU(2)W gauge bosons. The sensitivity reach of FASER in the former scenario 0 ¯ µ ¯ 5 µ L ⊃ gX Zµ (cV ψ2γ ψ1 + cAψ2γ γ ψ1) + h.c. (9) has been studied in Ref. [38]. In the following, we will focus on the latter model in In particular, an effective operator which couples ψis to s and d quarks is induced at a loop level with W boson which the ALP couples to the SM field strength tensor W a of the SU(2) group exchange [64]. In the following, we set gX = 1, cV = 0, µν cA = 1, mZ0 = 10 GeV, and m2 = 11 m1, where mi ≡ 1 2 2 gaW W a a mψi . L ⊃ − m a − aW Wf . (10) 2 a 4 µν µν The ψ2 decay width and branching fractions for ψ1ψ2- pair production in various meson decays can be found The coupling to W bosons in Eq. (10) gives rise to both in Ref. [26]. In particular, as discussed therein, the as- kaon decays, s→d a, and B-meson decays, b→s a, via the sumption about a relatively large mass splitting between usual loop diagrams. We implement the relevant branch- the dark species, m1 m2 − mπ0 , allows one to ob- ing fractions following Ref. [25, 66, 67] as discussed in tain about an 80% branching fraction of two-body decays 0 AppendixA. ψ2 → ψ1π . The subsequent prompt decays of high- After the EWSB, additional couplings of a to γγ, Zγ, energy neutral pions with Eπ0 & 100 GeV generate a and ZZ arise with the relative strength dictated by the di-photon signature inside the FASER detector. In the right panel of Fig.2, we show the contours with the expected number of events in FASER in the parameter space spanned by m and G /G param- 2 X F 2 As discussed in Ref. [26], a more detailed simulation of the eters, where GF is√ the Fermi coupling constant and CHARM and NuCal experiments is needed to refine the lower 2 GX = (Z ggX )/(2 2cW mZ0 ) with g corresponding to part of the gray-shaded region in Fig.2. This, however, is ex- the weak coupling constant. The region of the parame- pected to have a small impact on the upper part of the plot ter space in which a 2σ fit can be obtained to the KOTO corresponding to the KOTO anomaly. 8
101 Belle 2
3 Belle 2 10 CHARM
103 APV W F
= NA62
NA62 G / 100 CODEX-b X G = E949 KOTO q KOTO 2 SHiP 102
KOTO 2 4 10 10 FASER2 MATHUSLA CHARM FASER with R=5m, =5m 3 FASER with R=1m, =50m FASER 10 1 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.15 0.20 0.25 0.30 0.35 0.40 0.45 mX [GeV] m2 [GeV]
FIG. 2. The results for the models discussed in Sec.IVC and Sec.IVD. In both panels, the 2 σ regions of the parameter space in which the KOTO anomaly can be explained are shown as the green-shaded bands. Left: Reach for the dark Higgs boson model discussed in Sec.IVC. The sensitivity contour for FASER 2 is shown with the orange solid line, while purple and yellow solid lines correspond to larger versions on FASER 2 with the radius R = 5 m or length ∆ = 50 m, respectively. The current bounds are shown as gray-shaded regions following Ref. [15]. The blue dashed lines correspond to the expected sensitivity of other proposed future experiments (from top to bottom): CODEX-b, SHiP and MATHUSLA. Right: Event contours (from outside to inside: 3 (solid red line), 10 (dash-dotted), 100 (dashed), 1000 (dotted)) at FASER at LHC Run 3 for the model with pure dark sector decays of kaons, KL → X1X2, discussed in Sec.IVD. The current bounds are shown as gray-shaded regions following Ref. [26]. weak mixing angle. As a result, the ALP can also be pro- prompt decay inside the detector, e+e− → γ + (a → 2γ). duced through the Primakoff process, γN → aγ, employ- We show the relevant reach for 50 fb−1 in Fig.3 following 2 ing the di-photon coupling gaγγ = gaW W sW , cf. Ref. [37] Ref. [69]. Similarly, future ATLAS and CMS searches for for relevant discussion for FASER, providing a sublead- Z → γ + (a → 2γ) signature can also cover an important ing contribution to the ALP event rate. In contrast, a part of the parameter space of the model corresponding −5 −1 production in rare Z decays is more isotropic and can be to gaW W & 10 GeV , as shown in the plot based on neglected. For the low-mass ALPs of our interest, the Ref. [70]. dominant decay mode is into two photons, a → γγ [68]. Both FASER HL and FASER 2 experiments will be We present the FASER, FASER HL, and FASER 2 able to further improve the detection prospects, as well sensitivity reach lines for this model in Fig.3. Ad- as constrain scenarios with ma up to 1 GeV or even close ditional dashed contours in the plot correspond to the to the limit ma . mB − mK , respectively. In a similar expected future sensitivity in searches in KOTO and time frame, additional bounds on the model can come NA62 for the aforementioned two-body BSM kaon de- from e.g. the SHiP experiment (not shown in the plot). cays, K(+) → π0(+)a. Depending on whether the ALP escapes the detector without decaying or decays inside to two photons, the searches focus on 2γ or 4γ signatures in VI. CONCLUSION AND OUTLOOK KOTO, and π+ +0γ or π+ +2γ signal in NA62. We show these searches following Ref. [25]. The current bounds on A long-awaited definite experimental discovery of new the model are taken from Refs. [25, 69]. The most impor- physics effects should first manifest itself as a clear devi- tant constraints in the region of the parameter space of ation from the SM predictions and excess over expected our interest come from the beam-dump experiment E137 BG. In this study, we have focused on recently observed and past searches in kaon factories. and intriguing anomalous neutral kaon decay events in As can be seen, FASER will cover the entire region of the KOTO experiment. The current KOTO observation the parameter space corresponding to KOTO and NA62 corresponds to a striking excess over the expected SM 0 searches for detector-stable a. It will also independently branching fraction of the decay process KL → π νν¯, probe scenarios relevant for unstable ALP decaying inside while it awaits further dedicated analyses to be per- these detectors. In addition, FASER reach extends to- formed by the KOTO collaboration and other experi- wards lower values of the gaW W coupling and larger mass ments before it can be fully confirmed. In particular, we of the ALP. The larger values of the coupling constant have analyzed the prospects of independently probing the will, instead, be probed by e.g. Belle-II searches for the relevant BSM scenarios proposed to explain the anomaly 3γ signature from the ALP production and subsequent in the upcoming FASER experiment at the LHC [3–5]. 9
3 Ref. [29] for a recent discussion. 10 CDF LEP KTEV NA62 Last but not least, FASER complementarity to BSM KOTO 4 +NA48/2 KOTO 2 Belle2 3 searches in kaon factories extends beyond the current 10 4 E949 NA62 2 anomaly. We have illustrated this for a simplified model FASER with ALPs coupled to SU(2)W gauge bosons that dom- FASER (HL) ] KOTO 1 NA62 0 FASER2 inantly decay to γγ pairs. FASER will probe regions of
V 5 e 10 NA62 the parameter space relevant for several distinct searches G [ LHC Z 3
W E949 for LLPs decaying either inside or outside the KOTO and W a
g NA62 detectors. It will, therefore, provide an indepen- 6 E137 10 dent probe of such scenarios. In a longer term, improved bounds can be obtained by FASER HL or FASER 2 de-
10 7 SN1987 tectors operating during the HL-LHC phase. The upcoming run of the LHC will push the limits of intensity-frontier exploration of new physics to the next 10 1 100 level. The FASER experiment will play a vital role in this m [GeV] a endeavor toward potentially groundbreaking discoveries. FIG. 3. Sensitivity reach of the FASER (red solid line), FASER HL (brown) and FASER 2 (orange) experiments in ACKNOWLEDGMENTS the model with axion-like particles coupled to SU(2)W dis- cussed in Sec.V. The currently excluded gray-shaded region and the dashed blue lines corresponding to the future sensi- We would like to thank Jonathan Feng, Sam Homiller tivity reach in the KOTO and NA62 searches for promptly de- and Ben Lillard for useful discussions and comments on caying and detector-stable ALPs are taken from Ref. [25, 69]. the manuscript. We are also grateful to the authors The expected reach of the Belle-II search for the 3γ signature and maintainers of many open-source software packages, is shown following Ref. [69]. The future ATLAS/CMS reach including CRMC [51], EPOS [50] Jupyter notebooks [71], in the Z → 3γ signature from production and prompt decays Matplotlib [72], NumPy [73], pylhe [74], Pythia 8 [58], of the ALP to a di-photon pair is shown following Ref. [70]. and scikit-hep [75]. FK is supported by the De- partment of Energy under Grant DE-AC02-76SF00515. ST is supported by the Lancaster-Manchester-Sheffield We have shown that FASER could start probing such Consortium for Fundamental Physics under STFC grant models, which predict light and unstable new particles, ST/P000800/1. ST is partially supported by the Pol- immediately after the beginning of its operation. The ish Ministry of Science and Higher Education through pp collisions at the LHC produce large numbers of kaons its scholarship for young and outstanding scientists (de- that typically hit elements of the infrastructure before cision no. 1190/E-78/STYP/14/2019). decaying unless they go down the beam pipe i.e. towards FASER. This can lead to a large flux of forward-going LLPs produced in rare kaon decays and in other produc- Appendix A: Meson decay branching fractions to tion modes. The FASER baseline compatible with the dark Higgs boson and ALP predicted lifetime cτX of such LLPs, and its excellent di- photon detection capabilities, will then result in up to O(104) high-energy LLP decay events observed during Below, we list the branching fractions of the dominant LHC Run 3. meson decay modes to produce light scalar and pseu- Our results are presented for selected distinct BSM doscalar particles in the models discussed in Sec.IVB, scenarios corresponding to the lifetime solution to the Sec.IVC and Sec.V. KOTO anomaly, as well as for some other models that Scalar decay: For a light scalar, as defined in Eq. (7), either predict very long-lived LLPs with a mass close to the dominant production modes are rare decays of ηs, the pion mass or employ purely dark sector decays of neu- η0s, kaons and b-quarks, with the following branching tral kaons. Interestingly, even in the less promising case fractions adapted from Refs. [15, 35] and references of large τX , FASER can also be indirectly sensitive to therein KOTO-related models that predict a larger set of LLPs 1 and simultaneously address a number of outstanding ex- + + −3 2 2 B(K →π X) ' 2.0 · 10 × q λ (mK , mπ, ma), perimental and theoretical issues. An example of such 1 0 −3 2 2 a scenario with below GeV-scale heavy neutral leptons B(KL →π X) ' 7.0 · 10 × q λ (mK , mπ, ma), 1 within the reach of FASER 2 [36, 38] has recently been 0 −6 2 2 B(KS →π X) ' 2.2 · 10 × q λ (mK , mπ, ma), discussed in Ref. [20]. Although in this study we focus on 1 0 −5 2 2 collider searches for new physics, it is important to note B(η →π X) ' 3.4 · 10 × q λ (mη, mπ, ma), that the KOTO anomaly can also have profound cosmo- 0 −5 2 1 B(η →ηX) ' 7.2 · 10 × λ 2 (m 0 , m , m ), logical consequences that would have to be thoroughly q η η a 2 2 22 investigated, especially if the observed excess persists, cf. B(b→sX) ' 5.7 × q 1 − mX /mb , 10
with branching fractions taken from Ref. [66] 2 2 (m2 +m3) (m2 −m3) 4 2 1 2 B(B →Ka) ' 2 · 10 × g λ 2 (m , m , m )F , λ(m1, m2, m3)= 1− 2 1− 2 . B K a K m1 m1 3 ∗ 4 2 2 2 B(B →K a) ' 2 · 10 × g λ (mB, mK∗ , ma)FK∗ ,
ALP with the SU(2)W couplings: For an ALP, as where the relevant form factors are given by [76, 77] defined in Eq. (10) and with g =gaW W · GeV, the rel- evant branching fractions for kaon decays read [25], 0.33 F = K 2 2 1 − ma/(38 GeV ) + + 2 1 B(K →π a) ' 10.5 × g λ 2 (mK , mπ, ma), 0 2 1 and B(KL →π a) ' 4.5 × g λ 2 (mK , mπ, ma). 1.35 1 FK∗ = − . In the case of B-mesons, we follow the data-driven 1 − m2/(28 GeV2) 1 − m2/(37 GeV2) approach discussed in Ref. [67] and use B(b → sa) ≈ a a 5 × [B(B → Ka)+B(B → K∗a)] with the individual
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