NICA prospects in searches for light exotics from hidden sectors: the cases of hidden photons and axion-like particles

We present first estimates of NICA sensitivity to Standard Model extensions with light hypothetical particles singlet under the known gauge transformations. Our analysis reveals that NICA can explore new regions in the parameter spaces of models with a hidden vector and models with an axion-like particle of masses about 30-500\,MeV. Some of these regions seem unreachable by other ongoing and approved future projects. NICA has good prospects in discovery ($5\sigma$) of the new physics after 1 year of data taking.

Hence, in this Letter we consider models with hypothetical light vectors (hidden photons) and models with axion-like particles (ALPs), both exhibiting direct interactions with photons.Physical motivation for these models, various concrete realisations, present constraints on the model parameters along with prospects of future experiments in testing their predictions can be found in e.g.recent reviews [7][8][9].Here we identify the dominant mechanisms of production of these hypothetical particles at NICA, their promising signatures, check them against the relevant background and finally estimate the NICA sensitivity to the model parameters.
2. Both hidden photon and ALPs can travel macroscopic distances before decaying into visible particles.Given this fact we propose to search for the corresponding displaced vertex signature.The noticeable displacement reduces the otherwise too high background down to a negligible level.In recent MPD TDR an upgrade of Inner Tracking System (ITS) was proposed [10].This upgrade will allow one to determine the displaced vertex position with resolution up to ∼ 10 µm.The position of the ion collision (the actual point of each collision) can be fixed within a region of about 100 µm.To compare different possible outcomes we perform our calculations for three different minimal travel distances of new physics (NP) particles: L min = 100 µm, L min = 500 µm and L min = 1000 µm.The probability of a particle to travel a distance larger than L min and nevertheless decay inside the detector is given by where L max ∼ 1 m is the detector size, and d = τ γβ is the mean travel distance of NP particle.
In our estimations we inferred d max ∼ 1 mm that yields L max ≫ d, exp − Lmax d ≈ 0, hence the probability (1) approaches In our work for the signal of A ′ we consider only its electronic decay (i.e.A ′ → e + e − ), because in the present configuration the MPD is not equipped with muon detector, while the hadronic decay modes of A ′ are undistinguished given the huge pion background.In the model with axion-like particle only the radiative decay (i.e. a ′ → γγ) is accounted as the potential signal source.However, there are other decays to SM particles.In each model we sum up all of them to the total decay width to SM particles denoted as Γ SM .Moreover, in a particular model of the hypothetical particle there can be decay modes to particles from the hidden sector.Such unexplored decays can give sizeable contribution to the total decay width of the hypothetical particle 1/τ ≡ Γ tot and consequently d and relevant branchings.To take into account these possible decays we additionally discuss the Half Hidden case (HH) with total width Γ tot = 2Γ SM and the Half Hidden/5 case (HH/5) with Γ tot = 10Γ SM .The first case corresponds to models where the couplings to hidden sector are of the same order as the couplings to SM.The second case corresponds to models where the hidden sector decays dominate.The numbers of signal events then read where N A ′ and N a are the numbers of produced hidden vectors A ′ and ALPs a.
Light long-lived mesons like K-mesons are the main source of possible background, because these mesons also can travel macroscopic distances in the detector before their decay into visible particles.However, the maximum reach for NP mass at NICA appears to be less than kaon mass m K = 498 MeV even in the background-free case.Another source of background is conversion of photons inside the detector volume.However, the current design of the ITS positions the initial elements of the detector at a distance of 20-30 mm from the beam axis [10].And dark photons are expected to decay well before reaching this distance, typically within a few millimeters from the beam axis.Given the high-vacuum conditions inside beam-pipe, which has approximately the same radii of 20-30 mm, we consider the contribution from photon conversion within inner region to be negligible.Still, pions from kaon semileptonic decays may be misidentified with electrons, which interferes with the suggested signature of A ′ .To avoid this type of background we follow the special procedure which singles out only pure (almost 100%) electrons at the cost of 60%-reduction of the expected electron statistics [1].Consequently, the background-free identification of the signal e + e − pair will be allowed only for 0.4 × 0.4 = 0.16 of the total signal statistics.In what follows we adopt this procedure and to estimate the 95% CL sensitivity of NICA to the model parameters we ask for the NICA operation time large enough to collect not 3 (as typically required by the Poisson statistics in the background free case) but 3/0.16=18 signal events.
3. First, we investigate models with light vector hypothetical particle A ′ coupled to the SM fields through the vector portal [11] where A µ stands for the SM photon field.This mixing with photon (5) yields A ′ direct production in heavy ion collisions, where the big electric charge highly amplifies the production cross section with respect to A ′ production in e + e − collisions at similar energies, e.g. at future c-τ factories [12][13][14][15].Likewise, one can take advantage of the multiple production inherent in hadronic scattering: the hidden photon can also emerge in photonic decays of mesons produced in heavy ion collisions.The most promising decays for the interesting previously unexplored range of A ′ masses and mixing ϵ < 10 −3 are π 0 → γA ′ , η → γA ′ and ω → π 0 A ′ .The corresponding branchings are [16] Br Br Since the parent mesons above are short-lived, all the hidden particles appear in the small vicinity of the ion collision point.The momentum distribution of the produced in this way A ′ is obtained by boosting the isotropic distribution over 3-momenta in the meson decay frame to the laboratory frame.The boost parameters are determined by the transverse momentum p T and rapidity y of the parent mesons, which we obtain by making use of the simulations of 10 5 Bi Bi collisions at central mass energy √ s NN = 9.2 GeV per nucleon.
The simulations are performed with generator PHSD for pseudoscalar mesons [17] and with generator UrQMD for vector mesons [18].In 1 year (50 weeks) of the MPD data taking at the differential luminosity of L = 10 27 cm −2 s −1 we get N π ∼ 10 13 neutral pions, N η ∼ 10 12 η-mesons and N ω ∼ 10 11 ωmesons [19].Each channel contributes to the number of produced hidden photons The produced hidden vector can potentially decay into the SM particles among which we recognize lepton and meson pairs with decay rates [20] Γ where R( √ s) = σ(e + e − → hadrons)/σ(e + e − → µ + µ − ) is the energy dependent R-ratio [21].Then we must account for the fact that the initial meson 3-momentum affects the decay length of A ′ via non-unity boost factor.We integrate (p T , y) distributions obtained by simulations to get the normalized to unity dn X /dp X distributions over meson 3-momentum p X .Then we transform Eq.( 3) accordingly and get for the number of signal events, these are electron-positron pairs coming from the vertex displaced from the ion collision region, Here d ≡ 1/Γ tot × p A ′ /m A ′ and p A ′ is the A ′ 3-momentum in the laboratory frame.Since MPD can only detect photons with energies exceeding 50 MeV, we accordingly constrain the momenta in the integral (10).Within this approach we arrive at the results presented in Figs.1, 2, 3, where black lines correspond to 18 signal events (lepton pairs) consistent with limits at 95% CL in the background free case according to our procedure explained above.2).Right plot shows results for different values of Γ tot .The existing limits (colored and outlined) are taken from BaBar at 90% CL [22], KLOE at 90% CL [23], accelerator experiments (NA64 at 90% CL [24], E141 at 95% CL [25], NuCal at 95% CL [26]) and expected reaches of the ongoing experiments (colored) are given for FASER at 95% CL [27], Belle-II at 90% CL [28], LHCb D * at 95% CL [29], LHCBµ at 95% CL [30].
On these plots we illustrate the NICA sensitivity to model parameters ϵ, m A considering separately the three sources of A ′ production.We also investigate the impact of the total decay width Γ tot of A ′ on the NICA sensitivity.To this end for the plots on left panels  2).Right plot shows results for different values of Γ tot .The existing limits (colored and outlined) are taken from BaBar at 90% CL [22], KLOE at 90% CL [23], accelerator experiments (NA64 at 90% CL [24], E141 at 95% CL [25], NuCal at 95% CL [26]) and expected reaches of the ongoing experiments (colored) are given for FASER at 95% CL [27], Belle-II at 90% CL [28], LHCb D * at 95% CL [29], LHCBµ at 95% CL [30].
we assume Γ tot to be a free parameter, but constrained in such a way, that Γ tot ≳ Γ SM and corresponding particle decay length defined below Eq. ( 10) is large enough to avoid the suppression (2) due to minimal recognizable decay length L min = 100, 500, 1000 µm.The latter suppression guarantees, that the decay vertex is displaced from the ion collision point at the distance sufficient to be recognizable, and no any background is expected at such distances.For the plots on right panels we assume particular relations between the total width Γ tot and the width into SM modes Γ SM and constrain the decay length d from below by choosing the minimal displacement as L min = 100 µm.
One concludes, that new regions of the model parameter space can certainly be explored at NICA after 1 year of operation.The production of A ′ is dominated by π 0 and η 0 decays.
To estimate the contribution of the direct production of A ′ in heavy ion collisions we consider its production in ultraperipheral collisions via A ′ -strahlung, assuming colliding ions remain intact.To calculate the cross section we make use of the CalcHEP package [31] and multiply each electromagnetic vertex with fermions by the monopole form factor [32].The obtained results show that cross section of such processes is too small to produce interesting amount of A ′ .
4. The second model we investigate is Axion Like Particle (ALP) with coupling to photons Along with effective coupling of neutral pseudoscalar mesons P = π 0 , η, η ′ to photons [33], where f = 92.4MeV, c π = 1, c η = 1.10, c η ′ = 1.34, eq. ( 11) yields decays of mesons to axions P → γγa through the diagram depicted in Fig. 4. The width of ALP decay to photons is In our analysis, calculating ALP production and ALP decays we account for only ALP coupling to photons.Generically, there also could be ALP interactions with leptons and quarks, as we have in QCD axion models.Couplings to fermions open new decays to pairs of electrons, muons and mesons (if kinematically allowed).Typically, ALP decay rates to pair of are suppressed by m 2 l /m 2 a [34].Nevertheless one may say we somehow account for them introducing HH and HH/5 cases with an additional to photon contribution to the ALP total width.Coupling to fermions could also provide with another sources of ALPs like weak decays of K-mesons [35,36].In our case, where the photon coupling dominates, we neglect all other possible additional sources of ALP production, and consider only twophoton displaced vertex as the signature of ALP decay inside the NICA detector.It implies, that together with HH and HH/5 cases we obtain conservative estimates of the NICA reach.
For ALPs we use the same simulations of ion collisions as we exploited above for the model with A ′ .The squared amplitude of process depicted in Fig. 4 is calculated using CalcHEP package [31] and then integrated over the interesting region of the phase space as explained in the case of A ′ .The achieved results are depicted in Fig. 5 and Fig. 6, where the black line refers to 3 signal events required within the Poisson statistics to exclude the corresponding outlined regions at 95% CL (there is no dangerous background for the displaced vertex of two photons from the ALP decay).We find that the pion contribution to the ALP production is negligible for the model parameters in the previously unexplored regions.
There is also a direct contribution to the ALP production in heavy ion collisions due to rescatterings of the secondary photons abundantly produced in the collisions and subsequent relaxation processes.To estimate the number of ALPs coming from that photon-photon scattering we make use of the method presented in [32] and perform calculations for Bi Bi  2).Right plot shows results for different values of Γ tot .The existing limits (colored and outlined) taken from Belle at 95% CL [37], LEP at 95% CL [38], accelerator experiments (NA64 at 90% CL [39], E137 at 95% CL [40], NuCal at 90% CL [41]) and expected reaches of the ongoing experiments (colored) are given for FASER at 95% CL [42], Belle-II at 90% CL [43].2).Right plot shows results for different values of Γ tot .The existing limits (colored and outlined) are taken from Belle at 95% CL [37], LEP at 95% CL [38], accelerator experiments (NA64 at 90% CL [39], E137 at 95% CL [40], NuCal at 90% CL [41]) and expected reaches of the ongoing experiments (colored) are given for FASER at 95% CL [42], Belle-II at 90% CL [43].
collisions at the same luminosity of L = 5•10 27 cm −2 s −1 and center-of-mass energy, √ s NN = 9.2 GeV, as we adopted for simulation of the light meson production described above.In our calculations we use the monopole approximation for equivalent photon spectrum: where ω is the photon energy, γ is the ion gamma-factor, and we set Λ = 50 MeV.Then we obtain for the cross section of N N → N N a: with photon energy ratio x ≡ ω 1 /ω 2 and ω max ≫ Λγ solving the equation n(ω max ) = 0.
Here again we require that energies of the photons from ALP decays exceed 50 MeV.The corresponding to 3 signal events contours are presented in Fig. 7.One observes from Figs. 5-Figure 7: The regions to be probed at NICA after 1 year of operation at 95% CL with ALPs produced in ultraperipheral collisions.The existing limits (colored and outlined) are taken from Belle at 95% CL [37], LEP at 95% CL [38], accelerator experiments (NA64 at 90% CL [39], E137 at 95% CL [40], NuCal at 90% CL [41]) and expected reaches of the ongoing experiments (colored) are given for FASER at 95% CL [42], Belle-II at 90% CL [43].
7, that the direct production exhibits similar to η-meson channel potential in testing the models with light ALPs. 5. To summarise, in this letter, we start the investigation of the NICA perspectives in searches for hypothetical light particles.We study models with light vectors and model with light axion-like particles.After an upgrade of MPD with ITS it becomes possible to use the displaced vertex as a signature of the light particle decays.It allows to cover yet unexplored regions of new physics model parameter space and cross check results of other ongoing experiments.Implementing HH case in our analysis we further widen the spectrum of models which NICA can actually explore.One may anticipate good prospects for NICA in testing models with light scalars and axial vectors as well.
Our results for ALPs may be improved by taking into account fermionic couplings and non radiative decays of mesons to ALP inherent in particular models.However we don't expect a significant improvement in the NICA sensitivity.Then, while the direct production is a promising source of ALPs but there are known uncertainties in calculation of the ALP production in such processes, e.g.how to determine the number of ultra-peripherial collisions and the spectrum of viable photons.Still it seems to be the most powerful source of ALPs at high collision energies with higher γ-factor for ions.In the case of A ′ it may be worth to conduct more detailed research of ultraperipheral collisions.As soon as the details (type of colliding ions, their energies, luminosity, ITS resolution and other) of MPD update are finally fixed one will refine the present analysis.

Figure 4 :
Figure 4: The Feynman diagram for the production of axion in pseudoscalar radiative decays.