COHERENT constraints after the COHERENT-2020 quenching factor measurement

Recently, an improved quenching factor (QF) measurement for low-energy nuclear recoils in CsI[Na] has been reported by the COHERENT Collaboration. The new energy-dependent QF is characterized by a reduced systematic uncertainty and leads to a better agreement between the experimental COHERENT data and the Standard Model (SM) expectation. In this work, we report updated constraints on parameters that describe the process of coherent elastic neutrino-nucleus scattering within and beyond the SM, and we also present how the new QF affects their interpretation.

Experiments looking for CEνNS and direct dark matter signals are typically based on accurate measurements of the nuclear response and are aiming to achieve keV or sub-keV threshold capabilities depending on the nuclear target.
In such measurements, most of the nuclear recoil energy is dissipated as heat and ionization, while the recorded energy for the case of scintillator detectors is in reality an electron equivalent energy whose magnitude depends on the so-called quenching factor (QF) [49]. The QF is an energy-dependent quantity that is different for a given isotope, and its calibration involves neutron scattering measurements [50]. Regarding the first observation of CEνNS at COHERENT with a 14.57 kg CsI[Na] detector, the first theoretical simulations adopted an energyindependent QF of 8.78 AE 1.66% in the search region 5-30 keV nr [51]. In this work, we employ the new energy-dependent QF resulted by the COHERENT-2020 campaign [52] from a refined analysis correcting systematic effects of previous measurements, i.e., Chicago-1, Chicago-2, and Duke. 1 We first show that the new QF measurement leads to a higher consistency between the SM expectation and the experimental data, a result that is in agreement with Ref. [53]. We then revisit various constraints on conventional and exotic parameters describing the CEνNS interaction and update their status. In the first stage, we explore the sensitivity to the weak mixing angle and to the average nuclear root-mean-square (rms) radius of CsI assuming purely SM interactions. Afterward, we reexamine the sensitivity of COHERENT to phenomenological parameters in the framework of new physics interaction channels such as vector NSIs, neutrino magnetic moments, and charge radii as well as in simplified scenarios with novel vector-Z 0 and scalar mediators. The new constraints are obtained on the basis of an improved χ 2 fit analysis that incorporates the aforementioned quenching factor effects.
We show that the new energy-dependent QF combined with the reduced uncertainty leads to stronger constraints compared to previous studies.
The paper is organized as follows: In Sec. II, we provide all necessary ingredients to accurately simulate the observed CEνNS signal. In Sec. III, we provide the numerical results of our sensitivity analysis and update the constraints on the parameters describing the studied conventional and exotic physics phenomena. Finally, in Sec. IV we summarize the main outcomes of our work.

II. SIMULATION OF THE COHERENT
CEνNS RATE During the CEνNS interaction, a neutrino with energy E ν scatters off a nuclear target (A, Z) with Z protons and N ¼ A − Z neutrons, which in turn produces a detectable nuclear recoil T A . Focusing on the COHERENT experiment, after summing appropriately over the nuclear isotopes x ¼ Cs; I and all incident neutrino flavors ν α ¼ ðν e ; ν μ ;ν μ Þ, the number of expected CEνNS events is given by 3 m is the detector distance from the SNS source, and r ¼ 0.08 denotes the number of neutrinos per flavor produced for each proton on target (POT), i.e., N POT ¼ 1.76 × 10 23 for a period of 308.1 days. Assuming SM interactions, the differential cross section with respect to the nuclear recoil energy is expressed as [55][56][57] dσ where m A denotes the nuclear mass and G F the Fermi coupling constant. The vector Q V W weak charge is given by [58] while the P-handed couplings of u and d quarks to the Z boson take the form Here,ŝ 2 Z ≡ sin 2 θ W ¼ 0.2382 is the weak mixing angle, and ρ NC [59]. Because of their tiny contributions to the CEνNS rate, axial-vector interactions, incoherent interactions, as well as contributions due to the sodium dopant of the CsI[Na] detector are neglected.
The main source of theoretical uncertainty in the SM CEνNS process arises from the nuclear form factor that takes into account the finite nuclear size and depends on the variation of the momentum transfer Q 2 ¼ 2m A T A [31]. Following the COHERENT Collaboration, in this work we adopt the Klein-Nystrand (KN) form factor parametrized as [60] where a k ¼ 0.7 fm is the range of the Yukawa potential (over a Woods-Saxon distribution) in the hard sphere approximation with radius R A ¼ 1.23 × A 1=3 . We note that regarding the old QF, slight differences from the corresponding results of Ref. [16] throughout the paper are due to the adoption of the KN form factor, the different neutrino-energy distribution considered, the different value of the weak mixing angle, as well as the binned χ 2 analysis performed here (see below). For a scintillation-based experiment, the measured quantity is the number of photoelectrons (PEs) denoted here as n PE . To account for this mechanism, the CEνNS differential rate in events vs nuclear recoil energy gets converted to an equivalent differential rate in events vs electron recoil energy through the application of the QF function Q f ðT A Þ, and that in turn gets converted to a PE spectrum via the light yield L Y ¼ 13.348 PE=keV ee measured for electron recoils as In Eq. (1), the acceptance efficiency of the CsI detector is taken into account, which in terms of the photoelectron content of the signal reads 2 [2] , and the modified Heaviside function Up to now, previous analyses adopted the energyindependent QF of 8.78 AE 1.66% recommended by the COHERENT Collaboration in Ref. [1] which carried a large uncertainty of 25%. 3 In the present work, we consider the new energy-dependent QF which came out of the refined COHERENT-2020 measurement with a reduced uncertainty by about a factor of 4 at 3.6% (for more details, see Ref. [52]). In agreement with Ref. [52], within the SM the new calculation gives a theoretical value of 158 events as compared to the 174 events corresponding to the old QF. At this point, it is rather important to emphasize that a better agreement is now reached with the 134 events observed in Ref. [1]. The corresponding results are compared in Fig. 1 as a function of the PE bins.

III. NUMERICAL RESULTS
In the present study, we perform a sensitivity analysis of the parameter set S in question (see below) that follows from a χ 2 ðSÞ fit that is relevant for the CsI detector at the COHERENT experiment and reads [1] Here, N i meas (N i theor ) represents the ith bin of the observed signal (theoretical CEνNS events), and B i 0n (B i ss ) denotes the beam-on prompt neutron (steady-state) background events taken from the COHERENT data release [2], while the analysis is restricted to the 12 energy bins corresponding to 6 ≤ n PE ≤ 30. In Eq. (10), a 1 and a 2 are the corresponding systematic parameters with fractional uncertainties σ a 1 ¼ 12.8% (5% from signal acceptance determination, 5% from form factor choice, 10% from neutrino flux, and 3.6% from the new QF) and σ a 2 ¼ 25%. Note that compared to σ a 1 ¼ 28% given in Ref. [1] and adopted by all similar studies up to now, the fractional uncertainty considered here is reduced by about a factor of 2. This is also in agreement with estimations of previous studies addressing possible future experimental setups [17,27,31] and will have a direct impact on the updated constraints presented below.

A. SM precision tests and nuclear physics
Assuming purely SM interactions, we first extract the new sensitivity to the weak mixing angle that arises from the new QF measurement. To this end, we evaluate the χ 2 ðsin 2 θ W Þ function and perform a sensitivity fit by varying around the central value sin 2 θ W ¼ 0.2382. The resultant sensitivity profiles are depicted in the left panel of Fig. 2. A comparison with the corresponding result assuming the old energy-independent QF is also shown. Indeed, this new calculation leads to reasonably improved results. From the fit, we find the following constraints at 90% C.L.
Evaluating the 1σ bands δs 2 W according to the definition given in Ref. [15], we find the values δs 2 W ¼ ð0.057; 0.042Þ for the (old, new) QF case, which yield the corresponding percentage uncertainties δs 2 W = sin 2 θ W of (29%, 20%). We then make an effort to explore the sensitivity to the nuclear rms radius that follows from the recent COHERENT measurement. To this purpose, we employ the refined QF resulting from Ref. [52], while in this case we consider the Helm form factor [62] where j 1 ðxÞ is the spherical Bessel function of the first kind. Here, hR 2 is the nuclear rms radius, R 0 ¼ 1.23A 1=3 fm is the diffraction radius, and s ¼ 0.9 fm quantifies the surface thickness (for more details, see Refs. [30,31]). The resultant sensitivity profile is presented in the right panel of Fig. 2, showing that the constraints are now stronger than previously reported [27,28,31]. In particular, at 90% C.L. we find the best fits 4 hR 2 n i 1=2 ¼ 5.6 þ1.5 −2.1 fm ðold QFÞ; In a similar manner, within 1σ error we find the bands δhR 2 n i 1=2 ¼ ð1.01; 0.76Þ and the corresponding percentage uncertainties (18%, 14%) for the (old, new) QF measurement. We finally stress that the latter results remain essentially the same when considering the Klein-Nystrand form factor.

B. Nonstandard interactions
Nonstandard interactions have been a popular subject of extensive research during the last 15 years, with interesting applications in neutrino oscillations and lowenergy neutrino physics (for a review, see Refs. [63,64]).
For a neutrino with flavor α ¼ fe; μ; τg and a quark q ¼ fu; dg, the vector-type NSI contributions that arise due to nonuniversal (NU) flavor-preserving and flavor-changing interactions are described in the NSI weak charge [65,66] In the context of NSI, the expected CEνNS rate is modified according to the substitution Q V W → Q V NSI in the SM differential cross section of Eq. (3).
Assuming a single nonvanishing NSI parameter at a time, Fig. 3 illustrates the obtained sensitivity for the NU ϵ qV ee (ϵ qV μμ ) couplings in the left (right) panel, while a useful comparison is also given for the case of the old QF. The impact of the new QF measurement on NSI constraints becomes evident. The left and right panels of Fig. 4 show the allowed regions at 90% C.L. in the ðϵ dV ee ; ϵ uV ee Þ and the ðϵ dV μμ ; ϵ uV μμ Þ parameter space, respectively. We see that the bounds are now more restrictive than the corresponding results using the old QF.

C. Electromagnetic neutrino interactions
In this subsection, we are interested in exploring the possibility of probing nontrivial neutrino electromagnetic (EM) properties [67] and to revisit existing constraints from CEνNS [16]. The two main phenomenological parameters that arise in the framework of EM neutrino interactions are the neutrino magnetic moment and the neutrino charge radius. For completeness, we mention that in the simplest Majorana neutrino case, the neutrino magnetic moment μ ν is in reality expressed in terms of the neutrino transition magnetic moments Λ i of the neutrino magnetic moment matrix [68,69], while constraints have been recently extracted from neutrino-electron scattering [70] and CEνNS [17]. Here, for simplicity, we consider the effective neutrino magnetic moment in the helicity-violating EM cross section [71] dσ In Fig. 5, we present the updated constraint on μ ν from our analysis with the new QF, which is also compared to the corresponding one that comes from the old QF. The obtained upper limits at 90% C.L. read μ ν < 3.1 × 10 −9 μ B ðold QFÞ; From the same plot, it can be deduced that this difference is more pronounced at 99% C.L. For a flavor neutrino ν α , the associated neutrino charge radius hr 2 ν α i is another interesting phenomenological quantity which arises from the helicity-conserving charge form factor of the EM neutrino current [72]. The latter leads to a shift of the weak mixing angle as follows [73]: We stress that there is not a sign flip regarding antineutrino charge radii; e.g., it holds hr 2 ν α i ¼ hr 2 ν α i as defined in Ref. [16]. 5 In this work, we follow the definition given in Ref. [16]; however, the shift considered here is smaller by a factor of 2. Neglecting transition charge radii and varying one parameter at a time, Fig. 6 shows the χ 2 profiles of the neutrino charge radii hr 2 ν α i associated with the respective SNS neutrino flux, where the left (right) panels correspond to the old (new) QF measurement. The obtained constraints differ slightly due to the old vs new QF data. The only noticeable difference is that by employing the new QF in the case of the promptν μ beam, the resultant constraint on hr 2 ν μ i is separated into two distinct regions at 90% C.L. It is now worthwhile to explore the simultaneous constraints that can be obtained. Figure 7 presents the allowed regions at 90% C.L. in the ðhr 2 ν α i; hr 2 ν β iÞ parameter space. As expected, the allowed parameter space in all cases is more restricted using the new QF data.

D. Simplified scenarios with light mediators
In addition to the NSIs discussed previously in Sec. III B, we are now interested in simplified scenarios where the NSI is generated due to the presence of novel mediators.
In the first step, we explore the case where the CEνNS rate is enhanced from contributions due to a vector-Z 0 mediator with mass M Z 0 . The relevant cross section takes the form [76] dσ dT A with the Z 0 factor defined as In the above expression, in order to reduce the number of model parameters, we consider the generalized coupling under the assumption of universal quark-Z 0 couplings (for more details, see Ref. [16]). Concentrating our attention on the case of a new scalar boson ϕ mediating the CEνNS process, the cross section takes the form [77] dσ with the corresponding scalar factor being In the same spirit of the discussion made above, for the sake of simplification our calculations involve the generalized scalar coupling g 2 ϕ ¼ g νS ϕ Q ϕ =ð14A þ 1.1ZÞ. 6 The exclusion regions in the parameter space ðM Z 0 ; g 2 Z 0 Þ and ðM ϕ ; g 2 ϕ Þ for the vector and scalar scenarios, respectively, are obtained from a two parameter analysis of the COHERENT data. For both old and new QF data, the results are presented at 90% C.L. in the left (right) panel of Fig. 8 for vector (scalar) mediators. As in all previous cases, from this plot we conclude that the new QF data lead to generally more stringent bounds.

IV. CONCLUSIONS
Focusing on the COHERENT experiment, we reexamined the results implied from CEνNS in light of a new QF measurement [52]. By using the new QF data, we came out with improved constraints regarding all the cases analyzed in this work. A full summary is given in Table I. At first, we presented updated constraints focusing on important SM parameters, namely, the weak mixing angle and the average nuclear rms radius of CsI, and we explicitly demonstrated the level of improvement. We then concentrated on interesting phenomenological parameters beyond the SM and presented updated constraints for nonuniversal NSIs as well as for electromagnetic neutrino properties including the effective neutrino magnetic moment and the neutrino charge radius. Finally, we revisited the sensitivity of COHERENT in the framework of simplified scenarios involving massive vector and scalar mediators. We concluded that a substantial improvement on SM parameters is reached, while the improvement of beyond the SM physics constraints is also evident.  [16].