Probing New Physics with Underground Accelerators and Radioactive Sources

New light, weakly coupled particles can be efficiently produced at existing and future high-intensity accelerators and radioactive sources in deep underground laboratories. Once produced, these particles can scatter or decay in large neutrino detectors (e.g Super-K and Borexino) housed in the same facilities. We discuss the production of weakly coupled scalars $\phi$ via nuclear de-excitation of an excited element into the ground state in two viable concrete reactions: the decay of the $0^+$ excited state of $^{16}$O populated via a $(p,\alpha)$ reaction on fluorine and from radioactive $^{144}$Ce decay where the scalar is produced in the de-excitation of $^{144}$Nd$^*$, which occurs along the decay chain. Subsequent scattering on electrons, $e(\phi,\gamma)e$, yields a mono-energetic signal that is observable in neutrino detectors. We show that this proposed experimental set-up can cover new territory for masses $250\, {\rm keV}\leq m_\phi \leq 2 m_e$ and couplings to protons and electrons, $10^{-11}<g_e g_p<10^{-7}$. This parameter space is motivated by explanations of the"proton charge radius puzzle", thus this strategy adds a viable new physics component to the neutrino and nuclear astrophysics programs at underground facilities.

Introduction. In recent years, there has emerged a universal appreciation for new light, weakly-coupled degrees of freedom as generic possibilities for New Physics (NP) beyond Standard Model (SM). Considerable effort in "intensity frontier" experiments is now devoted to NP searches [1]. In this Letter we argue that there is a powerful new possibility for probing these states by combining large underground neutrino-detectors with either high luminosity underground accelerators or radioactive sources.
Underground laboratories, typically located a few km underground, are shielded from most environmental backgrounds and are ideal venues for studying rare processes such as low-rate nuclear reactions and solar neutrinos. Thus far, these physics goals have been achieved with very different instruments: nuclear reactions relevant for astrophysics involve low-energy, high-intensity proton or ion beams colliding with fixed targets (such as the LUNA experiment at Gran Sasso), while solar neutrinos are detected with large volume ultra-clean liquid scintillator or water Cerenkov detectors (SNO, SNO+, Borexino, Super-K etc).
In this Letter we outline a novel experimental strategy in which light, "invisible" states φ are produced in underground accelerators or radioactive materials with O(MeV) energy release, and observed in nearby neutrino detectors in the same facilities as depicted in Fig. 1: X * → X + φ, production at "LUNA" or "SOX"(1) e + φ → e + γ, detection at "Borexino".
Here X * is an excited state of element X, accessed via a nuclear reaction initiated by an underground accelerator ("LUNA") or by a radioactive material ("SOX") 1 . In the "LUNA"-type setup a proton beam collides against 1 Our idea is very generic, not specific to any single experiment or location, which is why quotation marks are used. collisions. An on-shell A 0 is radiated and decays o↵ diagonally to 'h,`pairs. b) Inelastic up scattering of the lighter '`into the heavier state via A 0 exchange. For order-one (or larger) mass splittings, the metastable state promptly de-excites inside the detector via 'h ! '`e + e . The signal of interest is involves a recoiling target with energy ER and two charged tracks to yield a instinctive, zero background signature.
FIG. 1: Schematic figure of φ production in a "LUNA"-type underground accelerator via p+ 19 F → ( 16 O * → 16 O + φ) + α or a "SOX"-type radioactive source via 144 Ce − 144 Pr(νe) → Nd * → Nd + φ. Subsequent detection at "Borexino" proceeds via φe → eγ scalar conversion. a fixed target, emitting a new light particle that travels unimpeded through the rock and scatters inside a "Borexino"-type detector. Alternatively, in the "SOX" production scenario, designed to study neutrino oscillations at short baselines, a radioactive material placed near a neutrino detector gives rise to the reaction in Eq. 1 as an intermediate step of the radioactive material's decay chain.
We study one particularly well-motivated NP scenario with a ∼ < MeV scalar particle, very weakly O(10 −4 ) coupled to nucleons and electrons. This range of masses and couplings is not excluded by astrophysical or laboratory bounds, and is motivated by the persistent proton charge-radius anomaly. Two concrete, viable possibilities for producing light scalars are considered: • For the LUNA-type setup, we show that such light particles can be efficiently produced by populating the first excited 6.05 MeV 0 + state of 16  The subsequent detection of a mono-energetic release in a Borexino-type detector with 6.05, 2.19, or 1.49 MeV will be free from substantial environmental backgrounds. The strategy proposed in this Letter is capable of advancing the sensitivity to such states by many orders of magnitude, completely covering the parameter space relevant for the r p puzzle. Scalar particles below 1 MeV. New particles in the MeV and sub-MeV mass range are motivated by the recent 7σ discrepancy between the standard determinations of the proton charge radius, r p , based on e − p interactions [2], and the recent, most precise determination of r p from the Lamb shift in muonic Hydrogen [3,4]. One possible explanation for this anomaly is a new force between the electron(muon) and proton [5][6][7] mediated by a ∼100 fm range force (scalar-or vector-mediated) that shifts the binding energies of Hydrogenic systems and skews the determination of r p . Motivated by this anomaly, we consider a simple model with one light scalar φ that interacts with protons and leptons, and define 2 ≡ (g e g p )/e 2 . We assume mass-weighted couplings to leptons, g e ∝ (m e /m µ )g µ , and no couplings to neutrons. UV completing such a theory is challenging, so we regard this as a purely phenomenological model. The apparent corrections to the charge radius of the proton in regular and muonic hydrogen are [5][6][7] to the current discrepancy of −0.063 ± 0.009 fm 2 [4], one obtains a relation between m φ and . Thus, for m φ = 0.5 MeV, the anomaly suggests 2 1.3 × 10 −8 . For m φ > 2m e , the φ → e + e − process is highly constrained by searches for light Higgs bosons [1], so we consider the m φ < 2m e region, which is relatively unconstrained. Since g e g p , the φ − e coupling is suppressed relative to that of a massive photon-like particle, so precision measurements of α and (g − 2) e do not constrain this scenario.
The astrophysical and fixed-target constraints depend on the cross section for eφ → eγ conversion, which for m φ m e with a stationary electron target is and yield 10 signal events (> 3σ) above backgrounds [8]. The Borexino 3 MeV and SuperK 3 MeV lines assume the same setup with a 3 MeV p-accelerator 10 m away from each detector. The SuperK projection shows 100 signal events (> 3σ) above backgrounds at 6.05 MeV [9]. The SOX lines assume a radioactive 144 Ce − 144 Pr source 7.15 m away from Borexino with 50 and 165 events (> 3σ) above backgrounds for 2.19 and 1.49 MeV lines respectively. Shaded in gray are constraints from solar production [8], LSND electron-neutrino scattering [10], and stellar cooling [11], for which we assume ge = (me/mp)gp.
where E is the electron recoil energy and Q is the φ energy. At Q m e , this leads to a total cross section of which determines the in-medium φ-absorption probability. Absorption competes with the φ → γγ decay, proceeding through loops of fermions f with the width given by a standard formula, where Q f is the fermion charge, τ f ≡ m 2 φ /4m 2 f , and An approximate proportionality to particle masses ensures that couplings to neutrinos are negligible. Processes (5), (7) define the gross features of φphenomenology in cosmological and astrophysical settings. The ensuing constraints are summarized as follows: • Energy loss in stars via eγ → eφ (red giants, white dwarfs etc) is exponentially suppressed for m φ > T star . This places a strong bound for m φ ∼ < 250 keV, for the fiducial range of couplings.
• The decay of φ in the early Universe at T ∼ m φ results in a negative shift of the "effective number of neutrinos." For m φ > 250 keV the shift is moderate, N eff ∼ −0.5 [12], and can be easily compensated by the positive contributions from other light particles (e.g. sterile neutrinos).
• SN physics: Low masses and sizable couplings, g e,p ∼ 10 −4 , ensures the φ are trapped during the explosions, and neither take energy from the explosive zones nor degrade the neutrino energies on account of g ν = 0.
• Emission of φ in solar nuclear reactions can be constrained using the Borexino search for solar axions [8], and disfavors some fraction of the parameter space with 2 in between 10 −12 and 10 −10 , as shown in this work.
In addition to astrophysical constraints, bounds on from direct searches of very light scalars typically probe 2 ∼ > 10 −7 . When combined, existing constraints leave an unexplored part of the parameter space for the scalar model, 250 keV ∼ < m φ < 2m e , 10 −10 ∼ < 2 ∼ < 10 −7 , and the ∆r p -motivated range falls in the middle of this allowed territory. The existing constraints are summarized in Fig. 2.
Production of scalars in nuclear reactions. Searches of light scalar particles in nuclear reactions, such as 3 H(p, γ) 4 He and 19 F(p, α) 16 O * have been successfully implemented [13,14] on the surface, where the main background comes from cosmic events. For sub-MeV masses of φ, the latter reaction is especially advantageous as φ is produced in the de-excitation of the 0 + state: with energy release Q = 6.05 MeV. In the SM, the singleγ decay of this state is not possible due to angular momentum conservation, and the main de-excitation process is 16 O * → 16 O + e + e − with the long lifetime 96 ± 7 ps [15]; thus, the relative branching to new physics can be greatly enhanced. Following [16] for m φ Q, the NP branching ratio Γ φ /Γ e + e − is where s = (Q − 2m e )/(Q + 2m e ) and b(s) ≈ 0.92 is defined in [16]. The excited state 16 O * can be efficiently produced in ∼ 100 keV-MeV p accelerators.
To estimate the φ yield from p + 19 F → 16 O * (6.05) + α , we model the cross section below 3 MeV using [17,18] and extrapolate to the Coulomb-suppressed region. Specifically, we take σ(E) σ 0 f (E), with σ 0 = 18 mbn and model the Coulomb repulsion with in the E < E 0 ≡ 1.5 MeV range. Here E g = 2(παZ F ) 2 µ = 45.5 MeV is the Gamow energy and µ is the proton-fluorine reduced mass, E is the c.o.m. energy, and normalization ensures continuity at f (E 0 ) = 1, where repulsion can be neglected. The signal yield for a proton beam of energy E p (i.e. the probability to produce a quantum of φ per each injected proton) and target material of Fluorine numberdensity n F is |dE/dx| depends on the material that includes Fluorine, and is readily available in [19]. For example, for the C 3 F 8 material, the probability of producing one φ per injected The angular distribution of emerging φ is fully isotropic as nuclear recoil velocities are negligible, and the flux at the position of the detector is given by Φ φ = N φ (E p ) × (dN p /dt)/4πL 2 . Inside the detector, the emitted φ scatter off electrons through eφ → eγ with cross sections given by (5). Thus, the only remaining free parameters (distance L, number of accelerated protons per second dN p /dt, their energy E p as well as the number of electrons in the detector volume) are location, source, and detector-specific.
Production of light states in radioactive decays. An alternative realistic mechanism for producing light weakly coupled particles is using the high-intensity radiative sources placed near a neutrino detector. In particular, we focus on the specific radioactive source 144 Ce − 144 Pr(ν e ) motivated by the SOX proposal by the Borexino collaboration. The production of the scalar in this reaction proceeds via 144 Ce → βν + 144 Pr followed by 144 Pr→ βν + ( 144 Nd * → 144 Nd + φ). Once produced, the scalar can be detected at a neutrino detector.
Possible accelerator realizations. All the ingredients for a successful realization of our idea currently exist at the underground Laboratori Nazionali del Gran Sasso (LNGS) in Italy, home of both the LUNA accelerator and Borexino detector. In addition, there are several other facilities of interest including SNOLAB in Canada and the Kamioka Observatory in Japan. Both SNO+ and Super-K detectors in these laboratories could be sensitive to new sub-MeV states if a proton accelerator were to be placed in their vicinity. Furthermore, the Sanford Underground Research Facility (SURF) has current plans to host the Dual Ion Accelerators for Nuclear Astrophysics (DIANA), which are expected to deliver 10-100 mA 3 MeV proton beams. SURF is also home to the Large Underground Xenon (LUX) experiment, which despite its smaller volume compared to Borexino and Super-Kamiokande, could also be sensitive to new sub-MeV states.
The LUNA accelerator [20] can deliver mA currents of MeV scale proton energies [21]. Our main results and the plot with sensitivity projections assume a target which is not currently used by the LUNA experiment, (e.g. C 3 F 8 ), but can easily be installed. In Fig. 2 we show a realistic scenario assuming the existing 400 keV accelerator L = 100 m away in the canonical LUNA scenario. We also show projections for an upgraded 3 MeV beam [22] 10m away from the Borexino detector in the Gran Sasso service tunnel. For all our accelerator projections we optimistically assume 10 25 protons-on-target (POT), achievable with a 50 mA beam running for one year. Very importantly, at 6.05 MeV energy Borexino is almost background-free and has good energy resolution, so that even a handful of events (∼ 10) would show a significant excess in the corresponding energy bin, and constitute a discovery.
One practical limitation of this proposal could be a requirement of not increasing the neutron background in LNGS. In our example, the main source of neutrons is α nuclei produced in each reaction step, which yield neutrons in secondary collisions with target nuclei. Using [23], we estimate the neutron yield from 19 F (α, n) 23 Na in our setup to be ∼ O( few Hz). Such low rates are irrelevant at LNGS, which can accommodate 10 3 Hz, but might matter if alternate production methods are employed, thus requiring extra shielding.
The Super Kamiokande (SuperK) detector [24] in Kamioka, Japan contains a 50,000-ton waterČerenkov detector. In Fig. 2 we show the expected sensitivity of a high-intensity 3 MeV proton source, assuming a C 3 F 8 target 10 m away from the detector. Despite a penalty due to a relatively high threshold for the electron energy in SuperK, one can see an incredibly strong potential for the reach to new physics.
Possible radioactive source realizations. For scalar production via radioactive decays, one possibility is phase B of the SOX proposal by the Borexino collaboration [25], which intends to deploy a ∼ 2 PBq source of 144 Ce-144 Pr 7.15 m from the Borexino center. Roughly 2% of 144 Ce decays are accompanied by the γ-radiation from the decay of the metastable Nd * daughter nuclei described above. The 1.49 and 2.19 MeV transition energies are well above the Borexino threshold, so this method covers the full mass range of interest, generating ∼ 10 13 (g p /e) 2 φ-particles per second. Given the planned exposures [25], we estimate the Borexino reach in this case, and add corresponding sensitivity lines on Fig. 2.
Existing constraints. While many of the past beamdump experiments can be sensitive to sub-MeV particles, we concentrate on the one that is able to constrain the product of g p g e , namely the LSND experiment at Los Alamos. Its measurement of the elastic electron-neutrino cross section [10] is also sensitive to light scalars that induce eγ events due to scattering on electrons. This analysis has previously been used to constrain new vector particles produced in π 0 decays to dark sector states [26,27]. In our scenario, a scalar φ cannot be produced from pseudoscalar π 0 decays. Instead, the dominant process is π − absorption via π − p → nφ. The analogous SM process π − p → nγ has branching ratio ∼ 35% [28], so we approximate the φ branching as ∼ 2 × 35%. Taking the π − production rate at LSND to be roughly 10% of the π + production implies ∼ 10 22 π − for the exposure in [10]. Assuming isotropic φ emission and the scattering cross section in Eq. (5) with Q → m p + m π − − m n m π , and implementing the cuts from this analysis, we obtain a roughly flat bound 2 ∼ < 10 −8 for m φ < MeV as shown in Fig. 2. This sensitivity exceeds even the bounds from (g − 2) e from [29], which only imply 2 ∼ < 10 −7 over this mass range, assuming mass weighted couplings g p = (m p /m e )g e ; for g e = g p , the bounds from (g − 2) e are comparable to those set by LSND.
In the 100 keV -MeV mass window φ's cannot be produced thermally in the solar interior, but can be produced in nuclear reactions. A particularly relevant process is p + d → 3 He + φ (that accompanies the d(p, γ) 3 He reaction occurring for every individual pp event of energy generation). If φ is sufficiently long lived, and not absorbed in the solar interior, it will reach the Earth and deposit 5.5 MeV of energy in Borexino. The absence of such events [8] sets an important constraint on our model. The solar flux of 5.5 MeV φ particles at Borexino is approximated using the pp-neutrino flux via Φ φ,solar 2 P esc P surv Φ ppν , where Φ ppν = 6.0 × 10 10 cm −2 s −1 [8]. The probability of escaping the sun is P esc = exp(− R drn σ eφ ), the probability that the scalar does not decay between the Sun and the Earth is P surv = exp(− / φ ), where φ = Qc/m φ Γ(φ → γγ) is the boosted decay length, and is the Earth-Sun distance. The Borexino rate iṡ where n ,B are mean-solar and Borexino e − densities, V B is the Borexino volume, and the cross section off electrons is given in (6). The current limits on this process are O(5) events [8] and the constraint is depicted by the oval region in Fig. 2. For 2 ∼ > 10 −10 , scattering off electrons prevents φ from leaving the Sun and for 2 ∼ < ×10 −12 the production and scattering are insufficient to yield an appreciable signal at Borexino.
The constraints from thermal energy loss in red giants and white dwarfs follow the standard considerations. Calculating the thermal energy loss ∝ g 2 e exp(−m φ /T star ) and reinterpreting the axion constraints from [11], we exclude the m φ ∼ < 250 keV parameter space for all of interest.
To conclude, in this Letter we have proposed a novel strategy to hunt for sub-MeV particles produced in underground accelerators and radioactive sources located 10 -100 m away from large underground neutrino detectors. This experimental program offers unprecedented sensitivity to a variety of NP scenarios including those that resolve the r p puzzle.