Sensitivity of the FACET experiment to Heavy Neutral Leptons and Dark Scalars

We analyze the potential of the recently proposed experiment FACET (Forward-Aperture CMS ExTension) to search for new physics. As an example, we consider the models of Higgs-like scalars with cubic and quartic interactions and Heavy Neutral Leptons. We compare the sensitivity of FACET with that of other proposed"intensity frontier"experiments, including FASER2, SHiP, etc. and demonstrate that FACET could probe an interesting parameter space between the current constraints and the potential reach of the above mentioned proposals.


Introduction
Despite its success in describing accelerator data, the Standard model (SM) fails to explain several observed phenomena constituting beyond the Standard model problems: neutrino masses, dark matter, and the matter-antimatter asymmetry.These problems may be resolved by extending the SM particle content with some new particles.One class of extensions is where new particles interact with SM via renormalizable operators suppressed by very small couplings, the so-called portals.Depending on the spin of the mediator field entering the portal operator, there are three types of portals -scalar, vector, and fermion [1,2].
To search for portal particles, many experiments have been proposed during the last few years.Examples include dedicated beam experiments such as SHiP [3], DUNE [4], SHADOWS [5], NA62 [6]; LHC-based experiments, such as MATH-USLA [7], Codex-b [8], ANUBIS [9], AL3X [10].There is a class of LHC-based experiments that have decay volume covering large pseudorapidities, which is called the far-forward experiments.The particles produced in the far-forward direction have large energies, E = O(1 TeV), which means that their lifetime is increased by γ ∼ 10 3 (1 GeV/m).Therefore, as compared with the off-axis experiments located at the same distance, the far-forward experiments may probe particles with shorter lifetimes.
The representatives of this class are already running FASER [11,12], FASERν [13,14] and SND@LHC [15] experiments.Their proposed upgrades, FASER2/FASERν2 and AdvSND, would be installed at the Far Forward physics facility and work during the High Luminosity phase of the LHC [16].Recently, a new far-forward experiment FACET has been proposed [17].Apart from covering 4 times larger solid volume and having longer decay volume, it would be located in 100 meters downwards the CMS interaction point -5 times closer than SND@LHC/FASER, and in this way allows to probe even shorter lifetimes [18,19].
In this work, we estimate the sensitivity of the FACET experiment to models of scalar and fermion portals, making a qualitative comparison of its sensitivity with FASER2.The final results are shown in Fig. 1, where we also show the sensitivities of other proposed experiments such as SHiP, MATHUSLA, Belle II, and LHC, to demonstrate the possible synergy between these searches.We see that due to larger decay volume and closer distance from the interaction point, FACET allows to significantly extend the probed parameter space as compared to FASER2.shows the sensitivity of FACET including the production of scalars from h and B, while the dashed line denotes the sensitivity to scalars from h only.We also include the sensitivity of Belle II from [20] (see also [21]).Right panel: HNLs that mix predominantly with ν e .For comparison, we also show the sensitivity of SHiP and MATHUSLA experiments from [2], as well as the optimistic estimate of the sensitivity of HL-LHC from [22].The region excluded by the previous experiments is given from [23] for HNLs and from [2] for Higgs-like scalars.
The content of the paper is as follows.In Sec. 2, we briefly describe the scalar and neutrino portals.In Sec. 3, we describe the FACET experiment.In Sec. 4, we compare the reach of the FACET and FASER2 experiments based on semi-analytic estimates, considering scalars and heavy neutral leptons produced by decays of B mesons and Higgs bosons.In Sec. 5, we discuss the obtained results and make their comparison with the literature.Finally, in Sec.6, we make conclusions.

Scalar portal with the quartic coupling
The general form of the Lagrangian of the scalar portal below the electroweak scale [1] is where h is the Higgs boson field, S is a new scalar particle (also called the Higgs-like scalar, or dark scalar), θ is the mixing angle, and α is the quartic coupling constant.
Current constraints on α are not very restrictive for the model of scalars.Indeed, the strongest bound on α comes from searches for invisible decays h → inv at ATLAS and CMS, constraining Br(h → inv) < 0.15 [46,47].During the high luminosity phase of the LHC, it would be possible to probe the branching ratio down to the values Br(h → inv) = 0.05 [48].
The number of Higgs bosons that would be produced during the High Luminosity phase of the LHC is N h 2 • 10 8 .Therefore, given the current constraints on Br(h → inv), the production channel h → SS allows to significantly extend the reach of the LHC and LHC-based experiments, making it possible to search for the scalars with masses up to m S m h /2.
The parameter space of dark scalars excluded by past experiments and probed by proposed LHC experiments (we choose FASER2 and MATHUSLA as a representative example), assuming Br(h → SS) = 0.05, is shown in the left panel of Fig. 1.In the paper [49], it has been demonstrated that FASER2 has a limited potential to probe this model, mainly due to the suppressed small angular coverage and short length of the decay volume.

Heavy Neutral Leptons
The Lagrangian of the fermion portal is where N I , i = 1, 2, . . . is a massive fermion (that may be either Dirac or Majorana depending on the N mass term), H = iσ 2 H * is the Higgs doublet in the conjugated representation, L α is the SM lepton doublet (α = e, µ, τ ), and F αI are complex couplings.Below the scale of the electroweak symmetry breaking, the first term in (2.2) induces a mass mixing between the N and active neutrinos.The mixing is parametrized by the mixing angle , where v is the Higgs VEV.As a result, the combination of active neutrinos α F αI and the fermion N I are a combination of two mass eigenstates -a very light neutrino and a heavy neutral lepton N I (HNL).
The mass mixing determines the way how HNLs interact with SM particles.Similarly to the interaction of the SM active neutrinos, it is with other neutrinos and charged leptons via W and Z bosons.The only difference is that the HNL couplings are suppressed by U αI .
The parameter space of HNLs is shown in the right panel of Fig. 1.We show SHiP, FASER2, MATHUSLA, and high luminosity LHC among the proposed experiments.At the LHC, HNLs heavier than kaons may be produced in decays of D, B mesons, and W bosons.The last channel allows extending the maximal HNL mass reach from m N = m B 5 GeV to m N m W as compared to the dedicated beam experiments such as SHiP.However, this is not the case for either MATHUSLA or FASER2, since they are located too far from the HNL production point, and the HNLs produced from W bosons in the accessible parameter space are too short-lived to reach the decay volume [50].

FACET experiment
FACET (Forward Aperture CMS ExTension) [17] is a recent proposal of a subsystem of CMS to be added to search for long-lived particles during the High Luminosity (HL) phase of the LHC.
The schematic layout of FACET is shown in Fig. 2. Given z as the distance from the CMS experiment along the beam axis, FACET will be located between the 35 T•m superconducting beam separation dipole D1 at z = 80 m and the TAXN absorber at z = 128 m.The decay volume is an enlarged proton beam pipe with radius r = 0.5 m located from z = 101 m to z = 119 m.
The detector part is located right after the decay volume.It has shape of the annulus with the inner radius r in = 18 cm and outer radius r out = 50 cm.The detector covers polar angles 1.5 < θ < 4 mrad and consists of 3 m of silicon tracker with the transversal resolution of σ x,y = 30 µm, the timing layer with Low-Gain Avalanche Detectors (LGAD) having resolution σ t ∼ 30 ps, and a high granularity EM and hadronic calorimeter.
The background is greatly reduced because of 200-300 λ int of magnetized iron in the LHC quadrupole magnets Q1-Q3.Detailed FLUKA simulations predict 30 charged particles with momentum p > 1 GeV and 1 light neutral hadron (K 0 S , K 0 L , Λ) per bunch crossing [17].Charged particles and decays of neutral hadrons may mimic decays of new physics particles.The combination of the precision hodoscope (with the inefficiency of 10 −5 ) and precision tracking reduces the background for most of the new physics decay channels down to a negligible level for the mass of a new physics particle m X 0.8 GeV.Nevertheless, decays of neutral hadrons create a background in the region m X 0.8 GeV, making searching for new particles in this mass range complicated.
However, given the specific model, the background may be greatly reduced.First, one may utilize specific final states of decays of the HNLs and dark scalars, see [25,51] for detail.In particular, the neutral SM particles do not decay (or decay very rarely) into solely a dilepton pair [52].In contrast, these may be the main decay modes of light scalars (the decay S → l + l − ) and the HNLs (decays N → l + l − ν, N → π + l − ).The only caveat is the situation when the decay product would be falsely reconstructed (in particular).In addition, in the case of dark scalars and HNLs with masses up to O(1 GeV), most of their decays (into l + l − , π + π − , N → π + l − ) -are fully reconstructable.Therefore, the invariant mass distribution is peaked at the true scalar/HNL mass.Collecting even a few of such events would be enough to distinguish them from similar events from decays of neutral particles, for which the distribution is peaked at m K 0 (a very rare process K → π + π − ) or is continuous (the decay K → π − l + ν).

FACET vs FASER2: qualitative comparison of the sensitivity
In this section, we compare the sensitivities of the FACET and FASER2 experiments.
For this purpose, we will use semi-analytic estimates similar to the ones presented in [50].
We estimate the number of events with decays of a particle Y = S, N at the FACET and FASER2 experiments (see Table 1) in the following way: Here, X corresponds to the decaying particle that produces scalars, with N X being the total number of SM particles produced during the high luminosity phase of the LHC.We assume N h = 1.7 • 10 8 from [53], take N B = 2.4 • 10 15 , N D = 5 • 10 16 , from FONLL [54][55][56][57] at the upper bound of uncertainties (see a discussion in [50]), and = 1 or 2 is the number of particles Y produced per decay of X.The integration in (4.1) is performed over Y energies E Y , polar angles θ Y , and the distance from the collision point along the beam axis z within l min < z < l min + l fid , where l min is the distance to the beginning of the decay volume, and l fid is the decay volume length.
θ Y ,E Y is the angle-energy distribution of Y produced by decays of X.To derive it, we have followed the semi-analytic approach summarized in [49]; namely, we have integrated the differential distribution dBr(X → Y ) multiplied with the distribution of the mother particle X over X energy and angles.The mother particle distributions have been obtained from FONLL [54][55][56][57] (B, D), by the method described in [49] (for h), and from [59] (for W ).
decay (γ S , θ S , z) is the decay acceptance -the fraction of decay products from Y intersecting the front plane of the detector.We estimate it using a simple Monte Carlo simulation by approximating the decay of scalars into two massless particles, and of HNLs into three massless particles via the charged current. 1urther, we will assume that both FACET and FASER2 are background-free experiments.Taking into account considerable background from neutral hadron decays on FACET for m Y 0.8 GeV, discussed in Section 3, the obtained results for FACET are only valid above this mass.Parameters of the experiments are summarized in Table 1. Let given ≈ 5 times smaller l min at FACET and γ Y FACET ≈ γ Y FASER2 .At the lower bound, e −z/cτ Y γ Y ≈ 1, and the ratio of the probed mixing angles is Here, κ = 1/2 in the case when both Y production and decay are controlled by θ, and κ = 1 in the case when the production is controlled by different couplings.geom is the averaged geometric acceptance at the lower bound:

Scalar portal
The production processes of scalars at the LHC are h → S + S for the Higgs bosons, and B +/0 → S + S + X s , B s → S + S, B +/0 → S + X s , for the B mesons [25], see also Fig. 3.The first three processes are mediated by the quartic coupling α, while the process B +/0 → S + X s by the mixing angle θ.

Geometric acceptance
Let us discuss the geometric acceptance.For the moment, we will drop the decay acceptance.
The solid angle distribution df /d cos(θ) ∼ df /dΩ of Higgs bosons, B mesons, and light scalars produced in their decays is shown in Fig. 4. The distribution of B, h remains constant in the angular coverage of FASER2 and gradually drops by a factor 1.5-2 for the angular coverage of the FACET experiment.While the distribution of scalars with mass close to the kinematic threshold is the same as for their mother particles, the distribution of light scalars m S m B , m h /2 gets broadened due to acquiring transverse momentum, of order of p T m B/h /2.Given that the typical B, h energy in the far-forward direction is O(1 TeV), the smearing is ∆θ ∼ p T /1 TeV -smaller than the angular coverage of FACET and FASER2 for scalars from B mesons, and much larger for scalars from h.As a result, the angular distribution of light scalars from B remains very similar to the distribution of B, while in the case of scalars from h it is isotropic up to the angles 30 mrad.This in particular suggests that FACET already has an optimal placement and size to search for particles from B mesons.Therefore, if not including the decay acceptance in Eq. (4.4), for the geometric acceptance of scalars from X = h, B one has Let us now discuss the effect of the decay acceptance.It becomes important   if the characteristic angle between the decay products in a 2-body decay, α 1 arcsin(2/γ S ), exceeds the angle covered by the detector as seen from the beginning of the decay volume, which is 0.4 rad for FASER2 and 0.1 rad for FACET.
Given the typical scalar energies E S = O(1 TeV), for light scalars with m S m h/2 , m B the decay acceptance is 1.However, with the increase of the scalar mass, more and more decay products produced in the beginning of the decay volume fly in directions outside the detector coverage.This feature effectively shrinks l det .For FACET, this effect is much more important than for FASER2.As a result, in dependence on the scalar mass, the geometric acceptance at FACET drops even below the geometric acceptance at FASER2 for h and becomes very close to the geometric acceptance at FASER2 for B, see Fig. 5 and Table 2.
Given the ratio l FASER2 det /l FACET det ≈ 4 and the behavior of the geometric acceptances (see Fig. 5), we conclude that the overall increase of the number of events in the regime of the lower bound at FACET as compared to FASER2 reaches a factor 2−15 and 5 − 15 for the case of the production from h and B respectively, in dependence on the scalar mass.

Maximal number of events
In the case of the production from Higgs bosons, it is also useful to compare the maximal possible number of events at FACET and FASER2.An estimate with an accuracy in a factor of two is given by where geom is given by Eq. (4.4), while P decay,max is the maximal value of the decay probability as a function of l decay,S = cτ S γ S , which depends only on l min , l max :2  From Eq. (4.8), we see that N events,max at FASER2 is very close to the number of events required at 95% C.L. to observe one event in background free regime.More accurate estimates [49] that included the energy distribution of scalars (which decreases the value of P decay,max ) showed that it is even lower, dropping below 3.This explains why FASER2 has no sensitivity to scalars from Higgs bosons in the domain m S 45 GeV.

Comparison for HNLs
Consider now the case of HNLs.The interaction vertices of HNLs with SM particles are similar to the vertices of active neutrinos ν α , but are suppressed by the mixing angle U α 1 [60,61].At the LHC, the HNLs may be copiously produced in decays of D, B mesons and W bosons [51].In this Section, we consider HNLs that mix predominantly with ν e , keeping in mind that the results for the other mixings are similar.
For the qualitative comparison, we will consider the following production channels: D s → N + e, B c → N + e, W → N + e, which respectively dominate the production of HNLs from D mesons above m N 0.5 GeV, from B mesons above m N 3 GeV, and from W bosons.The angular distributions for these particles, as well as for light HNLs with mass m N = 50 MeV produced by their decays, are shown in Fig. 7.
The values of the geometric acceptances are given in Table 3.

Results and discussion
Using Eq. (4.1) and requiring N events > 3, corresponding to 95% C.L. in the background free-regime of observing 1 event, we obtain the sensitivity of FACET and FASER2 to HNLs and Higgs-like scalars shown in Fig. 1.
The results agree with the estimates from Sec. 4. Namely, as compared to FASER2, detectors of FACET covers 3 larger solid angle, while the decay volume of FACET is 4 times longer and located 5 times closer.Because of this, for dark scalars, FACET may probe the whole mass range m S < m h /2, while at FASER2 it is impossible to search for scalars in the mass range m B − m π < m S 45 GeV due to the suppression of the geometric acceptance (see the discussion in Sec.4.1.2).For HNLs, FACET may probe masses up to m N 6 GeV, while FASER2 only up to 4 GeV, which is again due both to better sensitivity of FACET at the lower and upper bounds.
As a cross-check of our results, we compare the sensitivity to dark scalars obtained in this work with [17], which used FORESEE package [59].Namely, we compared the sensitivities of FASER2 to scalars with zero quartic coupling, and the sensitivities of FACET assuming Br(h → SS) = 0.05, see Fig. 8.The sensitivities agree well for low masses m S 10 GeV, but disagree by a factor of 2-3 at higher masses.The differences may be due to smaller decay width in [17] (which explains the discrepancy at the upper bound) and the absence of the decay acceptance in their estimates.An important feature shown in Fig. 1 is that the sensitivity of FACET at the upper bound is better than the sensitivity of other experiments.The reason is the following: the upper bound is controlled by the ratio p /l min , where p is the mean momentum of decaying particles, and l min is the distance from the production point to the decay volume.While FACET has l min comparable to experiments such as

2 Figure 1 .
Figure1.Sensitivity of FACET and FASER2 to the models of HNLs and Higgs-like scalars.Left panel: Higgs-like scalars, assuming Br(h → SS) = 0.05.The solid red line shows the sensitivity of FACET including the production of scalars from h and B, while the dashed line denotes the sensitivity to scalars from h only.We also include the sensitivity of Belle II from[20] (see also[21]).Right panel: HNLs that mix predominantly with ν e .For comparison, we also show the sensitivity of SHiP and MATHUSLA experiments from[2], as well as the optimistic estimate of the sensitivity of HL-LHC from[22].The region excluded by the previous experiments is given from[23] for HNLs and from[2] for Higgs-like scalars.

Figure 2 .
Figure 2. The schematic layout of the FACET experiment (see text for details).The figure is taken from [17].

Figure 3 .
Figure 3. Diagrams of the production of the scalar S in the model (2.1): meson decay X → X + S (a) mediated by the mixing θ; and the Higgs boson decay h → S + S (b), the mesons decays X → S + S, X → X + S + S (c) mediated by the quartic coupling α.

1 FACET 1 Figure 5 .
Figure 5.The behavior of the geometric acceptance (4.4) for scalars produced in decays h → SS and B → X s + S. The solid lines are obtained with taking the decay acceptance, decay , into account, whereas the dashed lines correspond to decay = 1.

Figure 6 .
Figure 6.The maximal possible number of events (eq.(4.8)) at FASER2 and FACET as a function of the scalar mass.The dashed gray line denotes 3 events defining the sensitivity domain of the experiments.

Figure 8 .
Figure 8.Comparison of the sensitivity of FACET to dark scalars obtained in our work and in[17], assuming Br(h → SS) = 0.025 (for FACET) and Br(h → SS) = 0 (for FASER2).

Table 1 .
us compare the sensitivity of FACET and its modification at the lower bound (the regime cτ Y γ Y l max ) and the upper bound (regime cτ Y γ Y l min ) with the Experiment l min , m l fid , m θ min , θ max , mrad Parameters of FASER2 and FACET configurations: the distance to the beginning of the decay volume l min , the length of the decay volume l fid , the polar angle coverage of detectors θ min , θ max , and the solid angle Ω covered by the detectors.sensitivity of FASER2.The lifetime scales as τ Y ∝ g −2 Y , where g Y is the mixing angle.The production branching ratio scales as Br At the upper bound, the number of events behaves as N events ∝ g 2 Y ×exp[−l min /cτ Y γ Y ].

Table 2 .
Geometric acceptances (Eq.(4.4) for scalars produced by decays of Higgs bosons and B mesons, for various choices of the scalar mass.