FERMILAB-PUB-21-200-T, MI-TH-218 Light, Long-Lived B L Gauge and Higgs Bosons at the DUNE − Near Detector P. S. Bhupal Dev,a Bhaskar Dutta,b Kevin J. Kelly,c Rabindra N. Mohapatra,d Yongchao Zhange;a aDepartment of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, MO 63130, USA bMitchell Institute for Fundamental Physics and Astronomy, Department of Physics and Astronomy, Texas A&M University, College Station, TX 77845, USA cTheoretical Physics Department, Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA dMaryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742, USA eSchool of Physics, Southeast University, Nanjing 211189, China E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: The low-energy U(1)B−L gauge symmetry is well-motivated as part of beyond Standard Model physics related to neutrino mass generation. We show that a light B L gauge boson Z0 and the associated − U(1)B−L-breaking scalar ' can both be effectively searched for at high-intensity facilities such as the near detector complex of the Deep Underground Neutrino Experiment (DUNE). Without the scalar ', the Z0 −9 can be probed at DUNE up to mass of 1 GeV, with the corresponding gauge coupling gBL as low as 10 . In the presence of the scalar ' with gauge coupling to Z0, the DUNE capability of discovering the gauge 0 boson Z can be significantly improved, even by one order of magnitude in gBL, due to additional production from the decay ' Z0Z0. The DUNE sensitivity is largely complementary to other long-lived Z0 searches ! at beam-dump facilities such as FASER and SHiP, as well as astrophysical and cosmological probes. On arXiv:2104.07681v2 [hep-ph] 27 Jul 2021 the other hand, the prospects of detecting ' itself at DUNE are to some extent weakened in presence of Z0, compared to the case without the gauge interaction. Contents 1 Introduction 1 2 The Model 3 3 Searches for Scalars and Gauge Bosons at DUNE5 3.1 Pure Gauge Boson Search7 3.1.1 Production of Gauge Bosons7 3.1.2 Sensitivity to Pure Gauge Boson Scenario9 3.2 Effects of Gauge Coupling on Searches for Scalar ' 11 3.2.1 Production of Scalar Boson 11 3.2.2 Effects on ' prospects at DUNE 12 3.3 Improving Z0 prospects at DUNE 14 4 Conclusion 16 A Details of ' Decay 18 B Additional Subdominant Contributions to the Gauge Boson Flux 18 C Additional Z0 Boson Constraints 19 1 Introduction The U(1)B−L gauge symmetry is a well-motivated extension [1,2] of the Standard Model (SM), which provides a natural framework to account for the tiny neutrino masses via the type-I seesaw mechanism [3{7]. It may also accommodate a light dark matter (DM) particle which interacts with the SM particles through the scalar or gauge portal of U(1)B−L [8]. In this paper, we focus on the class of B L extensions of SM, where − B L does not contribute to electric charge so that its gauge coupling gBL can be arbitrarily small making − the associated gauge boson Z0 very light with mass in the sub-GeV range [9{11]. This is especially true if the U(1)B−L-breaking scale is low, e.g., below the GeV-scale. In this case, we can expect the corresponding 0 U(1)B−L-breaking scalar (denoted here by ') to be also light. Both Z and ' are essential ingredients of the U(1)B−L extension, and play important role in connecting DM to the SM, in DM phenomenology [8, 12{17], and in explaining the observed light neutrino masses [18{24]. Since the seesaw mechanism does not depend directly on the gauge coupling value, such low gauge coupling models can still accommodate the seesaw mechanism. For phenomenological exploration of this class of B L extensions at a high mass scale and − larger gauge coupling range, see, e.g., Refs. [25{30]. If kinematically allowed, both ' and Z0 can be produced and detected in the high-intensity experiments such as the Deep Underground Neutrino Experiment (DUNE) [31]. One or both of these particles may be relatively long-lived and be able to travel from the DUNE target to its near detector complex where it decays in a striking fashion. It may then be possible to search for signatures of this class of beyond Standard Model (BSM) physics in such experiments. Our goal in this work is to determine how these gauge bosons, scalar { 1 { bosons, and their interplay can be searched for in the DUNE experiment at Fermilab. In particular, we will focus on the following three scenarios: (i) pure Z0 case with the scalar ' decoupled, (ii) the effect of ' Z0Z0 on the prospects of ' at DUNE, and (iii) improvement of the DUNE sensitivity of Z0 boson due ! to the scalar source ' Z0Z0. 0 ! The Z boson in the U(1)B−L model couples to all the SM quarks and leptons and thus can be produced from meson decays such as π γ + Z0 and η γ + Z0 as well as other hadronic decays where the π0 and ! ! η etc are final state particles in the pp collision [32]. The proton-proton bremsstrahlung process is also very important, in particular when the Z0 boson is heavier than the η meson [33, 34] (cf. Fig.3). After being produced, the Z0 boson may decay via Z0 e+e−; µ+µ−; νν¯ and hadrons such as πππ and KK [35{37], ! depending on its mass, and in the small gauge coupling limit can lead to displaced vertices with decays in the DUNE near detector hundreds of meters away. The observation of such displaced vertices may provide the 0 key signatures of the light Z boson. An analogous analysis of a leptonic gauge boson (e.g. one of U(1)Lµ−Lτ ) has been performed in Ref. [31]. Such gauge bosons can lead to anomalous neutrino-electron scattering and neutrino trident events, which have been explored in Refs. [38, 39]. We will perform a thorough study of the B LZ0 gauge boson and determine the DUNE near detector sensitivity. It turns out to be qualitatively − different from the leptonic Z0 boson, as presented in Fig.4. As for the light scalar ', if it mixes with the SM Higgs boson, it will obtain loop-level flavor-changing neutral current (FCNC) couplings to the SM quarks. As a result, it can be produced from the loop-level FCNC meson decays such as K π + ' at DUNE [40], and then decay into the light SM particles ' ! ! e+e−; µ+µ−; ππ; γγ, with the decay also induced by the mixing of ' with the SM Higgs. The sensitivity of a light scalar ' without the Z0 boson at DUNE has been studied in Ref. [31]. 0 0 In the U(1)B−L model, there is the gauge coupling 'Z Z , This will induce the extra decay channel ' Z0Z0, which could have multiple effects on the prospects of ' and Z0 at DUNE: ! • This new decay channel of ' will produce more Z0 bosons at DUNE, compared to the pure Z0 case, even by a factor of 105 (see Fig.6). As a result, the Z0 can be probed at DUNE with a smaller gauge 0 coupling gBL, with an improvement factor up to 45 (see Fig.7). This is only possible for a Z mass mZ0 200 MeV. This is because we require m' > 2mZ0 , and ' heavier than 400 MeV cannot be . ∼ produced from the meson decay K π + ' at DUNE. ! • The gauge portal scalar decay will not only change the branching fractions of ' (cf. Fig.2), but also shorten its lifetime. This will have some effects on the search for ' at DUNE, depending on the BR of ' decaying into SM particles, i.e. BR(' SM). As presented in Fig.5, the effect of ' Z0Z0 is most ! ! significant when ' is relatively heavy and the mixing angle sin # is relatively large. • The simultaneous existence of ' and Z0 will also induce the associated production of ' and Z0 at DUNE, for instance from the meson decay K π + Z0 + '. However, no matter whether the scalar ! ' is emitted from the Z0 boson line or from couplings to mesons, such decays will always be highly 4 2 2 suppressed by either gBL or sin #gBL, and can thus be neglected at DUNE. The rest of this paper is organized as follows. First, we provide a brief review of the model in Section2. Then, we begin the discussion of search strategies in Section3 with a brief discussion of the experimental setup and how proton-beam experiments (including the DUNE beamline) are well-suited for searches of these types of models. We divide the experimental search for this model by taking the following approach: first, 0 we discuss in Section 3.1 how the Z gauge boson of U(1)B−L can be searched for in DUNE making agnostic assumptions about the existence of the associated scalar '. Then, in Section 3.2, we will demonstrate that searches for ' in accelerator beam environments, including DUNE, are weakened in the presence of Z0, where { 2 { the produced ' can decay into Z0 instead of SM particles. We will also revisit the Z0 search strategy and discuss how additional fluxes sourced by ' (including a brief discussion of associated production of both ' and Z0) decays can be detected in Section 3.3. This improves the capability of discovering the gauge boson Z0.