Search

We propose an extension of the Standard Model (SM) with a $U_{A'}(1)$ gauge invariant dark dector connected to the SM via a new portal -- the Stueckelberg portal, arising in the framework of dark photon $A'$ mass generation via Stueckelberg mechanism. This portal opens through the effective dim=5 operators constructed from the covariant term of the auxiliary Stueckelberg scalar field $\sigma$ providing flavor non-diagonal renormalizable couplings of both $\sigma$ and $A'$ to the SM fermions $\psi$. The Stueckelberg scalar plays a role of Goldstone boson in the generation of mass of the Dark Photon. Contrary to the conventional kinetic mixing portal, in our scenario flavor diagonal $A'$-$\psi$ couplings are not proportional to the fermion charges and are, in general, flavor nondiagonal. These features drastically change the phenomenology of dark photon $A'$ relaxing or avoiding some previously established experimental constraints. We focus on the phenomenology of the described scenario of the Stueckelberg portal in the lepton sector and analyze the contribution of the dark sector fields $A'$ to the anomalous magnetic moment of muon $(g-2)_{\mu}$, lepton flavor violating decays $l_{i}\to l_{k}\gamma$ and $\mu-e$ conversion in nuclei. We obtain limits on the model parameters from the existing data on the corresponding observables., Comment: 15 pages, 8 figures (journal version)

We discuss new physics phenomenology of hidden scalar ($S$), pseudoscalar ($P$), vector ($V$) and axial-vector ($A$) particles coupled to nucleons and leptons, which could give contributions to proton charge radius, $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$, $^{8}\mathrm{Be}\text{\ensuremath{-}}^{4}\mathrm{He}$ anomaly and electric dipole moment (EDM) of Standard Model (SM) particles. In particular, we estimate sensitivity of $\mathrm{NA}64\ensuremath{\mu}$ experiment to observe muon missing energy events involving hidden scalar and vector particles. That analysis is based on geant4 Monte Carlo simulation of the signal process of muon scattering off target nuclei $\ensuremath{\mu}N\ensuremath{\rightarrow}\ensuremath{\mu}NS(V)$ followed by invisible boson decay into dark matter (DM) particles, $S(V)\ensuremath{\rightarrow}\ensuremath{\chi}\ensuremath{\chi}$. The existence of light sub-GeV bosons could possibly explain the muon ($g\ensuremath{-}2$) anomaly observed. We also summarize existing bounds on ATOMKI $X17({J}^{P}={0}^{\ensuremath{-}},{1}^{\ifmmode\pm\else\textpm\fi{}})$ boson coupling with neutron, proton, and electron. We implement these constraints to estimate the contribution of $P$, $V$. and $A$ particles to proton charge radius via direct 1-loop calculation of Sachs form factors. The analysis reveals the corresponding contribution is negligible. We also calculate bounds on dark axion portal couplings of dimension-five operators, which contribute to the EDMs of leptons and neutron.

We complete our derivation of upper limits on the $CP$ violating $\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi}$ couplings from an analysis of their two-loop contributions to the neutron electric dipole moment (nEDM). We use a phenomenological Lagrangian approach which is formulated in terms of hadronic degrees of freedom---nucleons and pseudoscalar mesons. The essential part of the Lagrangian contains the $CP$ violating couplings between $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})$ and pions. Previously, we included photons using minimal substitution in case of the proton and charged pions. Now we extend our Lagrangian by adding the nonminimal couplings, i.e., anomalous magnetic couplings of nucleons with the photon. The obtained numerical upper limits for the $\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi}$ couplings $|{f}_{\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}}({M}_{\ensuremath{\eta}}^{2})|l4.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $|{f}_{{\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi}}({M}_{{\ensuremath{\eta}}^{\ensuremath{'}}}^{2})|l3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ can be useful for the related, planned experiments at the JLab Eta Factory. Using present experimental limits on the nEDM, we derive upper limits on the $CP$ violating $\overline{\ensuremath{\theta}}$ parameter of $\overline{\ensuremath{\theta}}l4.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$.

We provide model-independent bounds on the rates of rare decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings, the nEDM arises at the two-loop level. The leading-order relativistic chiral perturbation theory calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counterterm-free result. This is an improvement upon previous estimates which used approximations in evaluating the two-loop contribution and were plagued by divergences. While constraints on the $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD $\ensuremath{\theta}$ term, our calculation means that whatever the origin of these couplings, the decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}2\ensuremath{\pi}$ will remain unobservable in the near future.

We study the lepton flavor violating (LFV) $e(\ensuremath{\mu})\ensuremath{-}\ensuremath{\tau}$ conversion in deep inelastic scattering (DIS) of electrons (muons) on fixed-target nuclei. Our model-independent analysis is based on the set of low-energy effective four-fermion LFV operators composed of leptons and quarks with the corresponding mass scales ${\mathrm{\ensuremath{\Lambda}}}_{k}$ for each operator. Using the estimated sensitivity of the search for this LFV process in events with large missing energy in the NA64 experiment at the CERN SPS, we derive lower limits for ${\mathrm{\ensuremath{\Lambda}}}_{k}$ and compared them with the corresponding limits existing in the literature. We show that the DIS $e(\ensuremath{\mu})\ensuremath{-}\ensuremath{\tau}$ conversion is able to provide a plenty of new limits as yet nonexisting in the literature. We also analyzed the energy spectrum of the final-state $\ensuremath{\tau}$ and discussed the viability of the observation of this process in the NA64 experiment and ones akin to it. The case of polarized beams and targets is also discussed.

The transition form factor of a gamma into three pions ${F}_{3\ensuremath{\pi}}$ is studied in a framework of nonlocal chiral quark model. In the local limit the result is in agreement with chiral perturbative theory and reproduce Wess-Zumino-Witten anomaly. Nonlocality does not change the value of transition form factor in chiral limit. On the physical threshold of reaction the form factor ${F}_{3\ensuremath{\pi}}$ obtained is in a good agreement with experimental data if the current quark mass is taken into account in the model.

Using the present upper bound on the neutron electric dipole moment, we give an estimate for the upper limit of the $CP$-violating couplings of the $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})$ to the nucleon. Using this result, we then derive constraints on the $CP$-violating $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings, which define the two-pion $CP$-violating decays of the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons. Our results are relevant for the running and planned measurements of rare decays of the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons by the GlueX Collaboration at JLab and the LHCb Collaboration at CERN.