Dark Photon Search at Yemilab, Korea

Dark photons are well motivated hypothetical dark sector particles that could account for observations that cannot be explained by the standard model of particle physics. A search for dark photons that are produced by an electron beam striking a thick tungsten target and subsequently interact in a 3 kiloton-scale neutrino detector in Yemilab, a new underground lab in Korea, is proposed. Dark photons can be produced by"darkstrahlung"or by oscillations from ordinary photons produced in the target and detected by their visible decays,"absorption"or by their oscillation to ordinary photons. By detecting the absorption process or the oscillation-produced photons, a world's best sensitivity for measurements of the dark-photon kinetic mixing parameter of $\epsilon^2>1.5 \times 10^{-13} (4.6 \times 10^{-13})$ at the 95% confidence level (C.L.) could be obtained for dark photon masses between 80 eV and 1 MeV in a year-long exposure to a 100 MeV electron beam with 100 kW (10 kW) beam power. In parallel, the detection of $e^+e^-$ pairs from decays of dark photons with mass between 1 MeV and $\sim$80 MeV would have sensitivities of $\epsilon^2>\mathcal{O}(10^{-17})$ at the 95% C.L. for the 100 kW beam power, which are comparable to those of the Super-K experiment.


Introduction
The standard model of particle physics has been very successful at explaining phenomena in the visible universe. However, it has a number of clear limitations. It provides no explanations for dark matter, the muon g-2 anomaly, the m ee = 17 MeV e + e − excess from 8 Be that is reported in refs. [1,2], etc. In order to explain these "beyond the standard model" (BSM) observations, the introduction of a hypothetical sector of new particles and interactions, the dark (or hidden) sector has been proposed. In this scheme, there are only a few portals (or mediators) that connect the dark sector to the visible universe that have significant srength and satisfy Lorentz and gauge symmetries. These are the vector, higgs, neutrino, and axion portals that can be explored with different types of experiments.
In particular, in the vector portal, a dark photon (usually denoted as A , φ, or γ ), that usually described by an extra U (1) D gauge symmetry group, is the dark sector particle that could be more readily explored than corresponding particles in the other portals because it can kinetically mix with an ordinary photon. As a result, any experiment that can produce photons and detect photons or leptons can, in principle, explore the vector portal [3].
The Lagrangian that describes the dark photon (DP) is: where F µν ≡ ∂ µ A ν − ∂ ν A µ is the DP field strength tensor, A µ is the U (1) D gauge field, is the kinetic-mixing strength between the dark and ordinary photons, and m φ is the dark photon mass.  [29]).
The 1988 SLAC beam dump experiment (E137) was the pioneering search for dark photons [4]. More recently, in the last decade, there have been numerous reports of dark photon searches  based on data from fixed target accelerator experiments, e + e − colliders, reactors and astrophysical measurements, that have set stringent limits to the dark photon parameter space. These limits could be further improved or, possibly, a dark-photon signal could discovered, by current or future experiments without huge costs. Figures 1 and  2 show the current constraints (or sensitivities) on for m φ < 1 MeV and m φ > 1 MeV, respectively; comprehensive reviews on the status of dark photon searches can be found in refs. [27,28].
Yemilab, a new underground lab that is being constructed in Handuk iron mine in Jeongseon-gun, Korea, will have a cavern that will be capable of hosting a ∼3 kiloton liquid target neutrino detector. A 100 MeV electron accelerator (100 kW or 10 kW beam power) located close to the neutrino detector, would make a dark photon search possible at Yemilab.
In the following sections, the proposed Yemilab neutrino detector 2, expected numbers of produced and detected dark photons 3, and the expected dark photon sensitivity 4 are described. These are followed by a summary 5.

A neutrino detector for Yemilab
By early 2022, the 2 nd phase construction of Yemilab (∼1000 m overburden under the eponymous Mt. Yemi) will be completed and experimental operation will commence (see Fig. 3). In addition to spaces for the upgraded COSINE [30] dark matter and AMoRE-II [31] 0νββ search experiments, a cavern suitable for hosting a ∼3 kiloton neutrino detector/target  The layout of Yemilab, including a cavern for a ∼3 kiloton neutrino detector (LSC). The laboratory will be accessed by a 600 m vertical shaft and a 730 m entrance tunnel. Adapted from [32].
will be available. The current plans for this space include a liquid scintillator (LS) or waterbased LS (WbLS) neutrino detector [32]. The ∼3 kiloton Yemilab neutrino detector be primarily dedicated to precise determinations of solar neutrino fluxes to search for signs of BSM physics, study reactor neutrinos from the Hanul nuclear power plant with a 65 km baseline, and measurements of geo-neutrinos [32]. It would be the first kiloton-scale neutrino telescope in Korea and a follow-on to the successful programs of the smaller scale RENO [33] and NEOS [34] reactor neutrino experiments at the Hanbit Nuclear Power Plant. The Yemilab neutrino detector could also be used to for a dark photon search by the addition of an electron accelerator for underground experiments, as suggested in reference [35]. Figure 4 is a schematic diagram that shows how an electron linac (100 MeV, 100 kW or 10 kW), tungsten target & radiation shield (50 cm-thick), and the neutrino detector (D: 20 m, H: 20 m cylinder) could be configured at Yemilab.

Dark photon production
In dark sector models with a vector portal there is a small mixing between dark photons and ordinary photons. As a result, dark photons could be produced via the electron bremsstrahlung process that is common for ordinary photons; i.e., when an electron beam strikes a target with atomic number Z, dark photons, A , are produced by the reaction e − + Z → e − + Z + A , as illustrated in Fig. 5. Practical calculations generally use the Weizäscker-Williams (WW) approximation to obtain the dark photon production cross-section via this reaction, in this case known as the "darkstrahlung" process, as a simplificatin of the exact result, which is quite complicated. For computer calculations an improved WW (IWW) approximation that increases the calculation speed has been also developed and widely used as well. These approximations, however, assume that the dark photon's mass is much greater than electron mass and much less than electron beam en-ergy. Recently, Liu and Miller [36] have reported an exact calculation of the darkstrahlung cross-section and, in addition, generalized versions of the WW and IWW approximations so that no restrictions on the dark photon mass apply. Liu and Miller compared their exact calculation with the generalized IWW approximation that was used by SLAC experiment E317 and found reasonable agreement for dark photon masses below 100 MeV. In this work, the generalized IWW approximation by Liu and Miller is employed to compute darkstrahlung cross-sections. This has the analytic form where x is the fraction of energy a dark photon carries away from electron energy (E), |k| is the 3-momentum of the dark photon, is the kinetic mixing parameter, and χ is the effective dark photon flux and given by Here t is the square of the four-momentum transfered to the target nucleus, which ranges in the IWW approximation where the produced dark photon is assumed to be collinear to the incident electron, and G 2,el (t) and G 2,in (t) are elastic and inelastic form factors of the target nucleus, respectively. In the following, we only consider the elastic form factor because the contribution from the inelastic one is negligibly small. The χ/Z 2 values are shown in Fig. 10 of reference [3] for 200 MeV, 1 GeV, and 6 GeV e − beams on a tungsten target. For m φ < 100 MeV with a 200 MeV e − beam, the χ/Z 2 values from ∼1 to ∼7 and we infer from the figure that the range of χ/Z 2 values for MeV-scale dark photon masses are similar for the case of a 100 MeV e − beam. For simplicity, in this work we use χ/Z 2 = 6 and found that changes in this value over a reasonable range has negligible effects on our results. Figure 6 shows the differential darkstrahlung cross-section for a 100 MeV e − beam on a tungsten target as a function of the fractional dark photon (DP) energy, x, where the crosssections of the DP masses of 1 keV, 10 keV, 100 keV, 1 MeV, and 10 MeV are compared. As the dark photon mass gets heavier, the cross-section decreases as expected from Eq.  Figure 6: The IWW differential cross-sections for DP production for a 100 MeV e − beam on a tungsten target for different DP masses. Here x is the fraction of DP energy relative to that of the e − beam energy. Note that here the differential cross-section is scaled by 1/ 2 .

Dark photon detection
If m φ > 2m e , dark photons could decay to the visible e + e − final state; if m φ < 2m e the only visible decay mode is the γγγ channel. If the DP mass is greater than 2m µ , it could also decay to µ + µ − (see top plot of Fig. 7). In this study, the e − beam energy is taken to be 100 MeV and only the e + e − (for m φ > 1 MeV) and 3γ (for m φ < 1 MeV) decay modes are considered. The expected DP decay length, taken from ref. [36], is where Γ φ is the decay width of a dark photon and given in Eqs. (3.4) and (3.5) for e + e − and γγγ decays, respectively: Dark photons can also interact with electrons in the material of the target, shield, and detector, thereby producing real photons in a process similar to Compton scattering as shown in the bottom plot of Fig. 7; this is called dark photon "absorption." The DP absorption length is given by where n e is the electron number density of the medium and σ abs is the total cross-section of the DP absorption and can be computed using Eq. (36) in ref. [36].

Expected number of dark photons
Using the DP production cross-section for the darkstrahlung process in a thick target, and detection through visible decays and absorption interactions that are discussed above, the expected number of dark photons that are either absorbed or decay in the detector is given by where N e is the total number of incoming electrons, X the radiation length of the target material (6.8 gm/cm 2 for tungsten); M is the mass of target atom; E 0 is the incoming electron beam energy; , where E cut is the measured energy cutoff depending on the detector; x max is very close to, but smaller than, 1 and is approximated to be 1 − me E if the DP and the initial and final electron states are collinear; T = ρL sh /X where ρ is the density of the target; l φ is the decay length of the DP in a lab frame; λ sh (λ det ) is the absorption length of the DP passing through target and shield (detector). Even though electrons enter the target with initial energy E 0 , DP production could occur after some energy loss of the incoming electrons as they penetrate the target. This is taken into account with an analytic function I e (E 0 , E, t) from ref. [36] that was originally reported in [3]: where b = 4/3 for a vector boson like a DP, and t represents how many numbers of radiation length traversed by the electron before "darkstrahlung" occurs, E is the e − energy after t radiation lengths and Γ is the Gamma function.

Dark Photon Sensitivity at Yemilab
Before obtaining the DP sensitivity at Yemilab, the DP decay and absorption lengths are compared to check which process is dominant for different DP masses and mixing parameters. Then DP sensitivities are obtained for decay-only, absorption-only, and both combined. For light DP (m φ < 1 MeV), oscillation between ordinary and dark photons  Table 1: Dark photon decay and absorption length scales for three different kinetic mixing parameters and for two different DP mass values. These length scales depend on the fractional of DP energy (x) and electron energy (E) at the DP point of production, while for the allowed ranges of x and E the length scale values given in the table do not change.
is discussed and separate detection sensitivities are obtained for the decay and absorption processes. Table 1 lists the DP decay and absorption lengths for = 10 −3 , 10 −5 and 10 −8 cases for 0.1 MeV and 10 MeV DP masses, which are taken as representative for the m φ < 2m e and m phi > 2m e cases corresponding to the 3γ and e + e − decay modes, respectively. Note that the 3γ decay lengths are very large while the e + e − decay lengths are more compatible with the detector size. However, for large values of (e.g., = 10 −3 ) the e + e − decay length becomes quite small (10 −5 m), and DP decays occur primarily in the shield, and well before they reach the detector. The absorption lengths in target/shield (both tungsten) and detector material (water, WbLS or LS) are similar but the length at the target/shield is an order of magnitude shorter due to its higher density. Note that the absorption lengthscales are shorter than the 3γ decay lengths and larger than those for the e + e − decays. Figure 8 shows DP decay and absorption lengths for = 10 −3 , 10 −5 and 10 −8 cases for several different DP masses. The red horizontal line indicates detector diameter (20 m) where DP can either decay or be absorbed. If the DP decay and absorption lengths are longer or shorter than the detector size, the detection probability is suppressed.

Dark photon sensitivity
The expected number of dark photon signal events are obtained from Eq. (3.7), where the energy threshold of the detector (E cut ) is set at 5 MeV in order to discriminate against all radiogenic backgrounds. Cosmic muon backgrounds can be suppressed either by using a pulsed electron beam or by the addition of a muon veto system that, for example, may be plastic scintillator modules on top of the detector plus an outer water Cherenkov veto detector that surrounds the inner detector [32]. Cosmogenic neutron backgrounds can be removed by tagging neutrons in Gadolinium-loaded water, WbLS or an LS target. Neutrinos from 8 B decays in the solar interior can contribute to the above 5 MeV background but most of these could be removed by a directional veto in a water or WbLS detector, and/or by requiring very forward vertex positions for DP signals especially for an LS detector.
Assuming zero background, the 95% C.L. sensitivity (N φ = 3) on the parameter space of DP mass (m φ ) vs kinetic mixing parameter ( ) at Yemilab is obtained as shown in Fig. 9. The gray areas represent regions that are excluded at the 95% C.L. The upper plot in Fig. 9 shows the DP sensitivity for visible decays (3γ or e + e − ) only for a 100 MeV-100 kW electron beam, where the sensitivity for m φ < 2m e decreases quickly for smaller values because the 3γ decay length exceeds the size of the detector as shown in Fig. 8; there is zero sensitivity for 2 values between 10 −6 and 10 −10 for m φ > 2m e because of the short e + e − decay length, and below 2 ∼ 10 −17 because of long e + e − decay length. The middle plot of Fig. 9 shows the DP sensitivity for the absorption-only process for the 100 MeV-100 kW e − beam.
Not shown in Fig. 9 is that the number of m φ > 2m e DP events that are detectable via the absorption process, which is found to be much smaller than that of those detected via the decay process in the overlapping region of sensitivity in the parameter space. Note also that the sensitivity for the absorption process is nearly independent of DP mass for masses lighter than 2m e . The lack of sensitivity for sub-MeV DPs for 2 values below 1.5 × 10 −12 is because of their large absorption length. The bottom plot of Fig. 9 shows the DP sensitivity including both decay and absorption processes for a year-long run with a 100 MeV-100 kW e − beam. The 95%-C.L. exclusion level for the e + e − decay mode for m φ above 1 MeV is 2 > 4.8 × 10 −17 , which is comparable to that for Super-Kamiokande (see Fig. 4 in reference [35]), and would have the world's best direct DP search sensitivity for 2m e < m φ <∼80 MeV; for sub-MeV DPs, the exclusion level is 2 > 1.5 × 10 −12 . Figure 10 shows the DP sensitivity for the combined decay and absorption processes using 100 MeV-10kW e − beam, where the 95% C.L sensitivities are 2 > 1.7 × 10 −16 for 2m e < m φ <∼80 MeV and 2 > 5.3 × 10 −12 for sub-MeV DPs.

Oscillation between ordinary and dark photons
Although it is not shown in Fig. 9, the DP sensitivity for the absorption process extends down to very low DP masses, even to the sub-eV level. However, as discussed in refs. [24,26], for m φ < 2m e , oscillations between ordinary and dark photons (similar to neutrino oscillations) dominate. The oscillation probability is given in ref. [26,37] to be where m e is effective photon mass in matter, E γ and Γ are ordinary photon energy and attenuation coefficient, respectively, and L is the length of the detector in the beam direction.
In the case of the Yemilab neutrino detector, the oscillation would have to occurs twice, one at production (γ → A ) and the other at detection (A → γ). In this case, the oscillation probability is where, m T γ (m W γ ) is an effective photon mass in tungsten (water), i.e. 80 eV (21 eV), and Γ T (Γ W ) is a photon attenuation coefficient in tungsten (water), where Γ −1 T 1 cm (Γ −1 W 45 cm) at E γ = 10 MeV according to NIST database. In the following extreme cases, the oscillation probability Eq. (4.3) becomes For m W γ < m φ < m T γ , the oscillation probability is the same as Eq.(4.3). At resonance (m φ ≈ m T γ or m W γ ), the oscillation probability is maximum. Using Eq.(4.3), the expected number of DP signal events from the oscillation is: where I (1) γ and I (2) γ are, respectively, the 1 st and 2 nd generations of photon flux in target per an incoming electron and given in the Eqs. (24) and (29) of [38]; E min γ = 5 MeV to remove radiogenic background and E max γ ≈ E 0 = 100 MeV. The 95% C.L. sub-MeV DP detection sensitivities for photon-DP oscillations determined from Eq. (4.8) are shown in Fig. 11. A comparison of Fig. 11 with Figs. 9 and 10 shows that the above 80 eV mass DP sensitivity from oscillations is better that for the absorption process; the best 95% C.L. direct DP search sensitivity, 2 > 1.5 × 10 −13 (4.6 × 10 −13 ), is obtained in a year-long data-taking run with a 100 MeV-100 kW (10 kW) e − beam on a thick tungsten target and the Yemilab neutrino detector.

Summary
Dark photon searches are the focus of a variety of experiments and have been invoked to explain a number of anomalies that have cropped up in (astro-)particle physics observations. Many of the best constraints, especially for sub-MeV dark photons, are from helioscopic or astrophysical observations. However, the helioscopic/astrophysical constraints depend, in a large part, on the choice of DP mean-free-path lengths inside stellar objects [39] and, therefore, direct search experiments at laboratories are absolutely necessary. Our study shows that a combination of a 3 kiloton-scale neutrino detector and an electron beam at Yemilab could constrain DP kinetic mixing parameters with the world's best direct search sensitivity for sub-MeV and above MeV DPs produced via darkstrahlung (e − + Z → e − + Z + A ) or oscillations (γ → A ). By detecting DPs via their absorption (A + e − → γ + e − ) or oscillations (A → γ) processes, a 95% C.L. direct search sensitivity for 80 eV < m φ < 1 MeV DP of 2 > 1.5 × 10 −13 (4.6 × 10 −13 ) could be achieved with one year of operation of a 100 MeV-100 kW (-10 kW) electron beam on a thick tungsten target. The best sensitivities for sub-MeV DPs are achieved by exploiting the oscillation between ordinary and dark photons. At the peaks of the oscillation resonances, i.e. m φ = 21 eV (in water) and 80 eV (in tungsten), the sensitivities are enhanced to 2 ∼ O(10 −15 ). The dark photon sensitivity for masses below the m φ < 21 eV resonance peak rapidly decreases as 4 ∝ m 8 φ due to the oscillation. Sub-MeV dark photon detection via decays to 3γ highly are highly suppressed because of the very long decay lengths. For 2m e < m φ <∼80 MeV DPs, the direct search sensitivity for the kinetic mixing parameters using visible decays (A → e + e − ) is 2 > O(10 −17 ) at the 95% C.L. for the 100 kW beam power; a sensitivity that is comparable to that of Super-K. With a higher energy electron beam, the sensitivity beyond 80 MeV DPs could also be explored but, it may not be practical to accommodate such a facility in the current Yemilab design configuration.      Figure 11: The dark photon sensitivity from the γ ↔ A oscillation for m φ < 2m e at the Yemilab neutrino detector for one year of data taking with a 100 MeV e − beam (100 kW: solid red line, 10 kW: dotted red line) on a tungsten target (50 cm), compared to those of other direct search experiments, TEXONO (dashed black line) [26] and NA64 (two solid black lines) [24].