Atomic Parity Violation, Polarized Electron Scattering and Neutrino-Nucleus Coherent Scattering

Available online at www.sciencedirect.com ScienceDirect Nuclear Physics B 959 (2020) 115158 www.elsevier.com/locate/nuclphysb New physics probes: Atomic parity violation, polarized electron scattering and neutrino-nucleus coherent scattering Giorgio Arcadi a,b, Manfred Lindner c, Jessica Martins d, Farinaldo S. Queiroz e,∗ a Dipartimento di Matematica e Fisica, Università di Roma 3, Via della Vasca Navale 84, 00146, Roma, Italy b INFN Sezione Roma 3, Italy c Max-Planck-Institut für Kernphysik (MPIK), Saupfercheckweg 1, 69117 Heidelberg, Germany d Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil e International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN 59078-970, Brazil Received 7 April 2020; received in revised form 22 July 2020; accepted 20 August 2020 Available online 27 August 2020 Editor: Hong-Jian He Abstract Atomic Parity Violation (APV) is usually quantified in terms of the weak nuclear charge QW of a nucleus, which depends on the coupling strength between the atomic electrons and quarks. In this work, we review the importance of APV to probing new physics using effective field theory. Furthermore, we correlate our findings with the results from neutrino-nucleus coherent scattering. We revisit signs of parity violation in polarized electron scattering and show how precise measurements on the Weinberg’s angle give rise to competitive bounds on light mediators over a wide range of masses and interactions strengths. Our bounds are firstly derived in the context of simplified setups and then applied to several concrete models, namely Dark Z, Two Higgs Doublet Model-U(1)X and 3-3-1, considering both light and heavy mediator regimes. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. * Corresponding author. E-mail addresses: [email protected] (G. Arcadi), [email protected] (M. Lindner), [email protected] (J. Martins), [email protected] (F.S. Queiroz). https://doi.org/10.1016/j.nuclphysb.2020.115158 0550-3213/© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 2 G. Arcadi et al. / Nuclear Physics B 959 (2020) 115158 1. Introduction For decades it was assumed that the laws of nature preserved parity, but the seminal paper of Lee and Yang in 1956 gave rise to a different perspective [1]. It was indeed confirmed in 1957 in the realm of weak interactions, via the beta decay in Cobalt [2] and muon decay [3]. In 1959 the possibility of observing parity violation in atomic physics and electron scattering was contemplated [4] and further investigated in the late 70’s [5–7]. Interestingly these ideas preceded the theory of electroweak interactions. The following decades were populated by experiments that aimed at probing parity violation [8]. For interesting reviews on APV see [9–14]. Our current understanding of parity and APV has greatly improved. Given the experimental precision acquired over the years, we may now test new physics models that feature parity- violating interactions. The main objects of study in this regard are the Weak Charge of the Cesium (Cs) and polarized electron scattering. Concerning the first observable, the weak charge of a nucleus, QW , is an analogous of the electromagnetic charge, where the Z boson is the key player of the atomic electron and nucleus interactions instead. QW is the sum of the weak charges of all constituents of the atomic nucleus, QW = (2Z + N)QW (u) + (Z + 2N)QW (d), where QW (u, d) accounts for the Z interactions 2 with up and down quarks and it depends on sin θW , with θW being Weinberg’s angle. To un- derstand how the Z boson can affect atomic transitions and QW is extracted from experiments, one needs to perform precise atomic physics calculations and measure the left-right asymmetry 2 2 2 ∼ −15 ALR, which is naively estimated to be ALR α me/mZ 10 . Despite atoms with a high atomic number be, in principle, better suited for experimental observation of APV [15], because of the enhancement in ALR by orders of magnitude, such high atomic number makes the theoretical determination of ALR extremely challenging. For this reason, Cesium has become a popular target because it offers a good compromise between high atomic number, necessary to have siz- able effects, and relatively simple atomic structure, required to make precise atomic calculations. Precise measurements of APV in Cesium have been presented in [16,17]. Based on them, de- exp =− ± tailed atomic physic computations yielded the following determination: QW 72.62 0.43 th =− ± [18,19], in slight disagreement with the SM prediction QW 73.23 0.01 [20,21]. Such precise measurements of the Cs weak charge can be used to constraint new physics effects. The other parity violation observable, polarized electron scattering, also constitutes an impor- tant laboratory to new physics searches. Again, the left-right asymmetry is the key observable. For deep inelastic scattering processes of the type eL,RN → eX, the left-right asymmetry can be expressed, in the quark model and in the limit of zero nucleon mass, in the relatively simple form 2 1 A/Q = a1 + a2f(y). The coefficients a1, a2 depend on the axial-vector coupling between the 2 electron and quarks, which, in turns, depends on sin θW , θW being Weinberg’s angle. y and Q represent, respectively, the fraction of energy transferred from the electron to the hadrons and the momentum transfer. Detailed expressions for a1, a2 and f can be found, for example, in [8,22]. 2 Measurement of A translates into a measurement of sin θW at a given momentum Q. It is well- known that photon exchange diagrams conserve parity but processes mediated by the Z do not as it not interact with left-handed and right-handed fermions in the same way. In a similar vein, eventual additional massive vector bosons from new physics models might also contribute to the left-right asymmetry. This kind of contribution can be conveniently parametrized as a shift on 1 In the case of electron-positron scattering or the so-called Moeller scattering (scattering on electrons), the Q2 dependence of the asymmetry is more complicated and is parametrized by a form factor. G. Arcadi et al. / Nuclear Physics B 959 (2020) 115158 3 2 Fig. 1. Scale dependence (gray curve) of sin θW [27,28] compared with measurements (colored points) from APV [29] as well as the E158 [30], Qweak [31,32], P2 [33], Mesa [34], Moller [35], Solid [36]. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.) 2 sin θW (see e.g. [23–26]for previous analyses along this line). If measurements of A translate 2 into a determination of sin θW compatible with the Standard Model (SM) prediction, one can obtain constraints on New Physics effects responsible for parity violation possibly contributing to the left-right asymmetry. 2 We show in Fig. 1 an illustration of the expected energy scale dependence of sin θW (see e.g. 2 [27,28]for details) together with different measurements of sin θW (see also [21]). The aforementioned observables depend on the couplings of the New Physics degrees of free- dom with electrons and quarks. Constraints on parity violation effects will be then translated into limits on such couplings. That has been the whole story up to now, but with the observation of neutrino-nucleus coherent scattering new information came into light. Strictly speaking, neutrino-nucleus coherent scattering and parity violation probes are sensitive to different interactions, between electron and quarks in the former case, between neutrinos and quarks in the latter. However, due to SU(2) invariance, it is reasonable to assume that new degrees of free- dom can couple with both electrons and neutrinos (one notable exception is represented by the so-called dark photon though). In this work, we will revisit this scenario and explore the possible complementarity between parity violation observables and coherent neutrino scattering [23–26]. To be as general as possible, the first part of our analysis will be carried out adopting an EFT approach as well as a simplified model in which the SM spectrum is extended by a new light spin– 1 mediator. We will apply later on our findings to some more complete models already existing in the literature. While this approach is not new by itself, we stress again that our work makes an advance concerning the existing literature in light of the considered complementarity between neutrino-nucleus coherent scattering, APV, and polarized electron scattering. At the same time, it is worth pointing out that the models investigated here might be embedded in non-trivial neutrino sectors, e.g. with the presence of sterile neutrinos, which can weaken the correlations between neutrino coherent scattering and parity violation phenomena. We will not consider this possibility here. The paper is structured as follows. In Section 2, we will review the theoretical aspects of parity violation; in Section 3 we discuss APV; in Section 4 we address the complementary aspects with neutrino-nucleus coherent scattering using effective field theory; in Section 5 we study polarized electron scattering in terms of light mediators and put into perspective with neutrino-nucleus 4 G. Arcadi et al. / Nuclear Physics B 959 (2020) 115158 coherent scattering. Lastly in Section 6 we discuss our bounds using concrete models proposed in the literature.

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