Search

We consider a neutrinophilic $U(1)$ extension of the standard model (SM) which couples only to SM isosinglet neutral fermions, charged under the new group. The neutral fermions couple to the SM matter fields through Yukawa interactions. The neutrinos in the model get their masses from a standard inverse-seesaw mechanism while an added scalar sector is responsible for the breaking of the gauged $U(1)$ leading to a light neutral gauge boson ($Z'$) which has minimal interaction with the SM sector. We study the phenomenology of having such a light $Z'$ in the context of neutrinophilic interactions as well as the role of allowing kinetic mixing between the new $U(1)$ group with the SM hypercharge group. We show that current experimental searches allow for a very light $Z'$ if it does not couple to SM fields directly and highlight the search strategies at the LHC. We observe that multi-lepton final states in the form of $(4\ell + \mET)$ and $(3\ell + 2j + \mET)$ could be crucial in discovering such a neutrinophilic gauge boson lying in a mass range of $200$--$500$ GeV.

We discuss the naive lattice fermion without the issue of doublers. A local lattice massless fermion action with chiral symmetry and hermiticity cannot avoid the doubling problem from the Nielsen-Ninomiya theorem. Here we adopt the forward finite-difference deforming the $\gamma_5$-hermiticity but preserving the continuum chiral-symmetry. The lattice momentum is not hermitian without the continuum limit now. We demonstrate that there is no doubling issue from an exact solution. The propagator only has one pole in the first-order accuracy. Therefore, it is hard to know the avoiding due to the non-hermiticity. For the second-order, the lattice propagator has two poles as before. This case also does not suffer from the doubling problem. Hence separating the forward derivative from the backward one evades the doublers under the field theory limit. Simultaneously, it is equivalent to breaking the hermiticity. In the end, we discuss the topological charge and also demonstrate the numerical implementation of the Hybrid Monte Carlo., Comment: 18 pages, 4 figures, minor changes, reference changed

We study four-dimensional gauge theories coupled to fermions in the fundamental and meson-like scalars. All requisite beta functions are provided for general gauge group and fermion representation. In the regime where asymptotic freedom is absent, we determine all interacting fixed points using perturbation theory up to three loop in the gauge and two loop in the Yukawa and quartic couplings. We find that the conformal window of ultraviolet fixed points is narrowed-down by finite-$N$ corrections beyond the Veneziano limit. We also find a new infrared fixed point whose main features such as scaling exponents, UV-IR connecting trajectories, and phase diagram are provided. Both fixed points collide upon varying the number of fermion flavours $N_{\rm f}$, and conformality is lost through a saddle-node bifurcation. We further revisit the prospect for ultraviolet fixed points in the large $N_{\rm f}$ limit where matter field fluctuations dominate. Unlike at weak coupling, we do not find clear evidence for new scaling solutions even in the presence of scalar and Yukawa couplings., Comment: 20 pages, 10 figures

We present a major update on our investigations of SU(2) gauge theory with one Dirac flavor in the adjoint representation on the lattice. In particular we consider larger volumes, as well as four different values of the gauge coupling. We provide results for the spectrum including gluonic, fermionic, and hybrid observables, Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number. These data confirm that the theory is close to the lower boundary of the conformal window for adjoint fermions. Our investigations provide important insights regarding the realization of different infrared scenarios that have been conjectured for this theory., 19 pages, 10 figures. Version accepted for publication in PRD

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD), ${f}_{K}/{f}_{\ensuremath{\pi}}$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with ${N}_{f}=2+1+1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\ensuremath{\sim}0.068$ to $\ensuremath{\sim}0.092\text{ }\text{ }\mathrm{fm}$ with linear lattice size up to $L\ensuremath{\sim}5.5\text{ }\text{ }\mathrm{fm}$. The scale is set by the particle data group (PDG) value of the pion decay constant, ${f}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=130.4(2)\text{ }\text{ }\mathrm{MeV}$, at the ISOQCD pion point, ${M}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=135.0(2)\text{ }\text{ }\mathrm{MeV}$, obtaining for the gradient-flow scales the values ${w}_{0}=0.17383(63)\text{ }\text{ }\mathrm{fm}$, $\sqrt{{t}_{0}}=0.14436(61)\text{ }\text{ }\mathrm{fm}$ and ${t}_{0}/{w}_{0}=\phantom{\rule{0ex}{0ex}}0.11969(62)\text{ }\text{ }\mathrm{fm}$. The data are analyzed within the framework of SU(2) chiral perturbation theory without resorting to the use of renormalized quark masses. At the ISOQCD kaon point ${M}_{K}^{\text{ISO}\mathrm{QCD}}=494.2(4)\text{ }\text{ }\mathrm{MeV}$ we get $({f}_{K}/{f}_{\ensuremath{\pi}}{)}^{\text{ISO}\mathrm{QCD}}=1.1995(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{us}|$ and for the first-row Cabibbo-Kobayashi-Maskawa unitarity are discussed.

The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in the simulations of quantum many-body systems. In this method, the sign problem is alleviated by shifting the integration domain for the auxiliary fields, appearing, for example, in the conventional determinant quantum Monte Carlo method, from real space to an appropriate manifold in complex space. Here, we extend this method to quantum spin models with generic two-spin interactions, by using the Hubbard-Stratonovich transformation to decouple the exchange interactions and the Popov-Fedotov transformation to map the quantum spins to complex fermions. As a demonstration, we apply the method to the Kitaev model in a magnetic field whose ground state is predicted to deliver a topological quantum spin liquid with non-Abelian anyonic excitations. To illustrate how the sign problem is alleviated in this method, we visualize the asymptotic Lefschetz thimbles in complex space, together with the saddle points and the zeros of the fermion determinant. We benchmark our method in the low-temperature region in a magnetic field and show that the sign of the action is recovered considerably and unbiased numerical results are obtained with sufficient precision.

In a tour de force calculation, using new computational techniques, the authors compute the contribution of soft gluons, gluons with momenta smaller than the Debye screening mass, to the pressure of cold nuclear matter, a QCD medium at zero temperature but large chemical potential, at next-to-next-to-next-to-leading order.

In a topological description of elementary matter proposed by Bilson-Thompson, the leptons and quarks of a single generation, together with the electroweak gauge bosons, are represented as elements of the framed braid group of three ribbons. By identifying these braids with emergent topological excitations of ribbon networks, it has been possible to encode this braid model into the framework of quantum geometry provided by loop quantum gravity. One major hurdle in this promising approach to unifying matter and space-time has been the difficulty in implementing any dynamics that reflects observed particle interactions. In the case of trivalent networks, it has not been possible to generate particle interactions, because the braids correspond to noiseless subsystems, meaning they commute with the evolution algebra generated by the local Pachner moves. In the case of tetravalent networks, interactions are only possible when the model's original simplicity, in which interactions take place via the composition of braids, is sacrificed. The main result of the present paper is to demonstrate that it is possible to preserve both the original classification of fermions, as well as their interaction via the braid product, if we embed the braid in a trivalent scheme and supplement the local Pachner moves, with a nonlocal and graph-changing one-handle attachment. Moreover, we use Kauffman-Lins recoupling theory to obtain invariants of braided networks that distinguish topological configurations associated to particles in the Bilson-Thompson model.

The greybody factor of the massive Dirac field around the black hole in the dRGT massive gravity theory is investigated using the rigorous bound and the WKB approximation methods. In both methods, the greybody factor significantly depends on the shape of the potential. If the potential is smaller, there is more probability for the Dirac field to transmit through the black hole, therefore, the greybody factor is higher. Moreover, there exists a critical mass of the Dirac field such that the greybody factor is maximum. By comparing the results from these two methods, we argue that it is useful to use the rigorous bound method for the low potential cases, while using the WKB approximation method for the high potential cases.

We compute corrections to the hard thermal (or dense) loop photon polarization tensor associated to a small mass $m$ of the fermions of an electromagnetic plasma at high temperature $T$ (or chemical potential $��$). To this aim we use the on-shell effective field theory, amended with mass corrections. We also carry out the computation using transport theory, reaching to the same result. Interemediate steps in the computations reveal the presence of potential infrared divergencies. We use dimensional regularization, as it is respectful with the gauge symmetry, and then show that all infrared divergencies cancel in the final result. We compare the mass corrections with both the power and two-loop corrections, and claim that they are equally important if the mass is soft, that is, of order $e T$ (or $e ��$), where $e$ is the gauge coupling constant, but are dominat if the mass obeys $ e T < m \ll T $ (or $e ��< m \ll ��)$., 16 pages, 1 figure

We have performed a systematical analysis of lepton and quark mass models based on ${\mathrm{\ensuremath{\Gamma}}}_{4}\ensuremath{\cong}{S}_{4}$ modular symmetry with generalized $CP$ symmetry. We considered both cases; neutrinos are Majorana particles and Dirac particles. All possible nontrivial representation assignments of matter fields are considered, and the most general form of fermion mass matrices are given. The phenomenologically viable models with the lowest number of free parameters together with the results of fit are presented. We find out nine lepton models with seven real free parameters (including the real and imaginary parts of modulus for Majorana neutrinos) which can accommodate the lepton masses and neutrino oscillation data. The prediction for leptogenesis is studied in an example lepton model. The observed baryon asymmetry as well as lepton masses and mixing angles can be explained. For Dirac neutrinos, four lepton models with five real free couplings are compatible with the experimental data. Ten quark models containing seven couplings are found to be able to accommodate the hierarchical quark masses and mixing angles and the $CP$ violation phase. Furthermore, the ${S}_{4}$ modular symmetry can provide a unified description of lepton and quark flavor structure, and a benchmark model is presented.

We propose a $SU(5)\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}\ifmmode\times\else\texttimes\fi{}U(1{)}_{\mathrm{PQ}}$ model, where $U(1{)}_{X}$ is the generalization of the $B\ensuremath{-}L$ (baryon minus lepton number) gauge symmetry and $U(1{)}_{\mathrm{PQ}}$ is the global Peccei-Quinn (PQ) symmetry. There are four fermions families in $\overline{\mathbf{5}}+\mathbf{10}$ representations of $SU(5)$, a mirror family in $\mathbf{5}+\overline{\mathbf{10}}$ representations, and three $SU(5)$ singlet Majorana fermions. The $U(1{)}_{X}$ related anomalies all cancel in the presence of the Majorana neutrinos. The $SU(5)$ symmetry is broken at ${M}_{\mathrm{GUT}}\ensuremath{\simeq}(6--9)\ifmmode\times\else\texttimes\fi{}{10}^{15}\text{ }\text{ }\mathrm{GeV}$ and the proton lifetime ${\ensuremath{\tau}}_{p}$ is estimated to be well within the expected sensitivity of the future hyper-Kamiokande experiment, ${\ensuremath{\tau}}_{p}\ensuremath{\lesssim}1.3\ifmmode\times\else\texttimes\fi{}{10}^{35}\text{ }\text{ }\mathrm{years}$. The $SU(5)$ breaking also triggers the breaking of the PQ symmetry, resulting in axion dark matter (DM), with the axion decay constant ${f}_{a}$ of order ${M}_{\mathrm{GUT}}$ or somewhat larger. The CASPEr experiment can search for such an axion DM candidate. The Hubble parameter during inflation must be low, ${H}_{\mathrm{inf}}\ensuremath{\lesssim}{10}^{9}\text{ }\text{ }\mathrm{GeV}$, in order to successfully resolve the axion domain wall, axion DM isocurvature and $SU(5)$ monopole problems. With the identification of the $U(1{)}_{X}$ breaking Higgs field with the inflaton field, we implement inflection-point inflation, which is capable of realizing the desired value for ${H}_{\mathrm{inf}}$. The vectorlike fermions in the model are essential for achieving successful unification of the SM gauge couplings as well as the phenomenological viability of both axion DM and inflation scenario.

We computed the kinematics of Z-boson decay into a heavy-light neutrino pair when the Z-boson is produced at rest in electron-positron collisions, including the subsequent decay of the heavy neutrino into a visible final state containing a charged-lepton. We concentrated on heavy-neutrino masses of order dozens of GeV and the issue of addressing the nature of the neutrinos - Dirac fermions or Majorana fermions. We find that while it is not possible to tell the nature of the heavy and light neutrinos on an event-by-event basis, the nature of the neutrinos can nonetheless be inferred given a large-enough sample of heavy-light neutrino pairs. We identify two observables sensitive to the nature of neutrinos. One is the forward-backward asymmetry of the daughter-charged-leptons. This asymmetry is exactly zero if the neutrinos are Majorana fermions and is non-zero (and opposite) for positively- and negatively-charged daughter-leptons if the neutrinos are Dirac fermions. The other observable is the polarization of the heavy neutrino, imprinted in the laboratory-frame energy distribution of the daughter-charged-leptons. Dirac neutrinos and antineutrinos produced in electron-positron collisions at the Z-pole are strongly polarized while Majorana neutrinos are at most as polarized as the $Z$-bosons., 12 pages, 7 figures, references added in v2, results and conclusions unchanged

The recent measurement of the muon $g\ensuremath{-}2$ anomaly continues to defy a Standard Model explanation but can be accommodated within the framework of two-Higgs doublet models, although the pseudoscalar mass must be fairly light. If one further includes extra fermion content in the form of a generation of vectorlike leptons, the allowed parameter range that explains the anomaly is even further extended, and clashes with $B$-decay constraints may be avoided. We show how the muon magnetic moment anomaly can be fit within these models, under the assumption that the vectorlike leptons do not mix with the muon. We update previous analyses and include all theoretical and experimental constraints, including searches for extra scalars. It is shown that the inclusion of vectorlike fermions allows the lepton-specific and muon-specific models to perform much better in fitting the muon's $g\ensuremath{-}2$. However, these fits do require the Yukawa coupling between the Higgs and the vectorlike leptons to be large, causing potential problems with perturbativity and unitarity, and thus, models in which the vectorlike leptons mix with the muon may be preferred.

Motivated by the recent search for a Higgs portal scalar decaying inside the MicroBooNE detector, we demonstrate that the same search can be used to constrain heavy neutral leptons. These are gauge-singlet fermions that interact with the Standard Model by mixing with neutrinos only and could be related to the origin of neutrino masses. By recasting the results of the MicroBooNE Collaboration’s analysis, we show that, for a heavy neutral lepton that mixes predominantly with muon-flavored neutrinos, previously unexplored parameter space can be excluded for masses between 30 and 150 MeV. Additionally, we make our Monte Carlo tools publicly available.

We present a calculation of the pion and kaon Mellin moment $⟨{x}^{3}⟩$ extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark (${N}_{f}=2+1+1$) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass $\ensuremath{\sim}260\text{ }\text{ }\mathrm{MeV}$, and a kaon mass $\ensuremath{\sim}530\text{ }\text{ }\mathrm{MeV}$. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of 1.12--1.67 fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated nonperturbatively. Our results are converted to the $\overline{\mathrm{MS}}$ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are $⟨{x}^{3}{⟩}_{\ensuremath{\pi}}^{{u}^{+}}=0.024(18{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$, $⟨{x}^{3}{⟩}_{K}^{{u}^{+}}=0.035(6{)}_{\mathrm{stat}}(3{)}_{\mathrm{syst}}$, and $⟨{x}^{3}{⟩}_{K}^{{s}^{+}}=0.075(5{)}_{\mathrm{stat}}(1{)}_{\mathrm{syst}}$, where the systematic error is the uncertainty due to excited state contamination. We combine $⟨{x}^{3}⟩$ with the two lower moments, namely $⟨x⟩$ and $⟨{x}^{2}⟩$, to obtain the ratios $⟨{x}^{3}⟩/⟨x⟩$ and $⟨{x}^{3}⟩/⟨{x}^{2}⟩$, as well as $⟨{x}^{3}{⟩}_{K}^{{u}^{+}}/⟨{x}^{3}{⟩}_{\ensuremath{\pi}}^{{u}^{+}}$ and $⟨{x}^{3}{⟩}_{K}^{{u}^{+}}/⟨{x}^{3}{⟩}_{\ensuremath{\pi}}^{{u}^{+}}$. In addition, we reconstruct the $x$-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large $x$-dependence that falls as $(1\ensuremath{-}x{)}^{2}$ for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with $4\ensuremath{\le}n\ensuremath{\le}6$. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking.

Clockwork models can explain the flavor hierarchies in the Standard Model quark and lepton spectrum. We construct supersymmetric versions of such flavor clockwork models. The zero modes of the clockwork are identified with the fermions and sfermions of the minimal supersymmetric Standard Model. In addition to generating a hierarchical fermion spectrum, the clockwork also predicts a specific flavor structure for the soft SUSY breaking sfermion masses. We find sizeable flavor mixing among first and second generation squarks. Constraints from kaon oscillations require the masses of either squarks or gluinos to be above a scale of ∼3 PeV.

Many effective field theories describing gravity cannot arise from an underlying theory based on Riemann geometry or its extensions to include torsion and nonmetricity but may instead emerge from another geometry or may have a nongeometric basis. The Lagrange density for a broad class of such theories is investigated. The action for fermions coupled to gravity is linearized about a Minkowski background and is found to include terms describing small deviations from Lorentz invariance and gravitational gauge invariance. The corresponding nonrelativistic hamiltonian is derived at second order in the fermion momentum. The implications for laboratory experiments and astrophysical observations with fermions are studied, with primary focus on anomalous spin-gravity couplings. First constraints on some coefficients are extracted from existing data obtained via measurements at different potentials, comparisons of gravitational accelerations, interferometric methods, and investigations of gravitational bound states. Some prospects for future experimental studies are discussed., 24 pages two-column REVTeX, version accepted in Physical Review D

In a previous work [arXiv1905.01121] we have derived a quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical gravitational field. As standard matter is made of fermions, such an equation should be suitably extended to describe more relevant experimental situations. Here we derive a non relativistic model for the gravitational decoherence of spin 1/2 particles. We enrich the treatment by considering also a coupling with an external classical electromagnetic field. We comment on the differences with the scalar bosonic model and we describe the regimes in which they become negligible., Comment: 16 Pages. arXiv admin note: text overlap with arXiv:1905.01121

We examine the nonperturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantized approach to quantum field theory and analyze its gauge transformation properties induced by virtual photon exchange. This is then extended to the N-point functions where we derive an exact, generalized version of the fully nonperturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We discuss some general aspects of application in perturbation theory and investigate the structure of the LKF factor about D=2 dimensions.

We describe a proposal for constructing a lattice theory that we argue may be capable of yielding free Weyl fermions in the continuum limit. The model employs reduced staggered fermions and uses site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. The possibility for such symmetric mass generation is tied to the cancellation of certain discrete anomalies arising in the continuum limit. The latter place strong constraints on the number of lattice fermions -- constraints that are satisfied by this model. We present numerical results for the model in two dimensions which support this sc, 10 pages. 8 figures. Changes to text and figures added. Version to be published in PRD

A new dynamic is identified between dark matter and nuclei. Nuclei accelerated to MeV energies by the internal potential of composite dark matter can undergo nuclear fusion. This effect arises in simple models of composite dark matter made of heavy fermions bound by a light scalar field. Cosmologies and detection prospects are explored for composites that catalyze nuclear reactions in underground detectors and stars, including bremsstrahlung radiation from nuclei scattering against electrons in hot plasma formed in the composite interior. If discovered and collected, this kind of composite dark matter could in principle serve as a ready-made, compact nuclear fusion generator., Comment: 8 pages, 2 figures, PRD version

We study an extended 2 Higgs doublet model (2HDM) in which the Standard Model (SM) Yukawa interactions are forbidden due to a global $U(1)^\prime$ symmetry, but may arise via mixing with vector-like families. In this model, the hierarchical structure of Yukawa couplings of quarks and leptons in the SM arises from the heavy masses of the fourth and fifth vector-like families. Within this model, we consider various non-standard contributions to the electron and muon anomalous magnetic moments. We first consider the $W$ exchange at one-loop level, consistent with the $\mu \rightarrow e \gamma$ constraint, and show that it yields a negligible contribution to both electron and muon anomalous magnetic moments. We then consider Higgs scalar exchange, together with vector-like leptons, at one-loop level and show that it is possible to have non-standard contributions to the electron and muon anomalous magnetic moments within the $1\sigma$ constraint of certain experiments. We present some benchmark points for both the muon and the electron anomalies, together with some numerical scans around these points, which indicate the mass regions of the Higgs scalars of the 2HDM in this scenario., Comment: 41 pages, 12 figures. References added, discussions enlarged. Matches published version in PRD

We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In particular, classical Lagrangians are obtained for the operators $\hat{b}_{\mu}$ and $\hat{H}_{\mu\nu}$ as perturbative expansions in Lorentz violation. The functional dependence of the higher-order contributions in the background fields is found to be quite peculiar, which is probably attributed to particle spin playing an essential role for these cases. This paper closes one of the last gaps in understanding classical-particle propagation in the presence of Lorentz violation. Lagrangians of the kind presented will turn out to be valuable for describing particle propagation in curved backgrounds with diffeomorphism invariance and/or local Lorentz symmetry explicitly violated., Comment: 10 pages, prepared for submission to Phys. Lett. B

I present a numerical study of the crossover between the low temperature chirally broken phase and the high temperature chirally restored phase in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate fermion flavors. Fermion masses span a range of intermediate values (represented by the squared ratio of pseudoscalar to vector meson masses $(m_{PS}/m_V)^2\sim 0.25$ to 0.63). Observables include the temperature dependent chiral condensate and screening masses. At each fermion mass these quantities show nearly identical temperature dependence across $N_c$., published version, small changes from v.1, 24 pages, 9 figures

We investigate a model of dark sector based on non-Abelian $SU(2{)}_{D}$ gauge symmetry. This dark gauge symmetry is broken into discrete ${Z}_{2}$ via vacuum expectation values of two real triplet scalars, and an $SU(2{)}_{D}$ doublet Dirac fermion becomes ${Z}_{2}$---odd particles whose lighter component makes stable dark matter candidate. The standard model and dark sector can be connected via the scalar mixing and the gauge kinetic mixing generated by higher dimensional operators. We then discuss relic density of dark matter and implications to collider physics in the model. The most unique signatures of this model at the LHC would be the dark scalar (${\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}$) productions where it subsequently decays into: (1) a fermionic dark matter (${\ensuremath{\chi}}_{l}$) and a heavy dark fermion (${\ensuremath{\chi}}_{h}$) pair, ${\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\overline{\ensuremath{\chi}}}_{l}{\ensuremath{\chi}}_{h}({\overline{\ensuremath{\chi}}}_{h}{\ensuremath{\chi}}_{l})$, followed by ${\ensuremath{\chi}}_{h}$ decays into ${\ensuremath{\chi}}_{l}$ and non-Abelian dark gauge bosons (${X}_{i}$'s) which decays into SM fermion pair ${\overline{f}}_{\mathrm{SM}}{f}_{\mathrm{SM}}$ resulting in the reaction $pp\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\overline{\ensuremath{\chi}}}_{h}{\ensuremath{\chi}}_{l}({\overline{\ensuremath{\chi}}}_{l}{\ensuremath{\chi}}_{h})\ensuremath{\rightarrow}{f}_{\mathrm{SM}}{\overline{f}}_{\mathrm{SM}}{\ensuremath{\chi}}_{l}{\overline{\ensuremath{\chi}}}_{l}$, (2) a pair of ${X}_{i}$'s followed by ${X}_{i}$ decays into a DM pair or the SM fermions resulting in the reaction, $pp\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{X}_{i}{X}_{i}\ensuremath{\rightarrow}{\overline{\ensuremath{\chi}}}_{l}{\ensuremath{\chi}}_{l}{f}_{\mathrm{SM}}{\overline{f}}_{\mathrm{SM}}$ or even number of ${f}_{\mathrm{SM}}{\overline{f}}_{\mathrm{SM}}$ pairs.

We investigate the high temperature fate of four-dimensional gauge-Yukawa theories featuring short distance conformality of either interacting or noninteracting nature. The latter is known as complete asymptotic freedom and, as templates, we consider non-Abelian gauge theories featuring either two singlet scalars coupled to gauged fermions via Yukawa interactions or two gauged scalars with(out) fermions. For theories with interacting fixed points at short distance, known as asymptotically safe, we consider two calculable examples. Exploring the landscape of safe and free theories above we discover a class of complete asymptotically free theories for which symmetry breaks at arbitrary high temperatures. In its minimal form this class is constituted by a theory with two fundamental gauged scalars each gauged under an independent group., Facultad de Ciencias Exactas, Instituto de Física La Plata

We study symmetries and dynamics of chiral $SU(N)$ gauge theories with matter Weyl fermions in a two-index symmetric ($\ensuremath{\psi}$) or antisymmetric tensor ($\ensuremath{\chi}$) representation, together with $N\ifmmode\pm\else\textpm\fi{}4+p$ fermions in the antifundamental ($\ensuremath{\eta}$) and $p$ fermions in the fundamental ($\ensuremath{\xi}$) representations. They are known as the Bars-Yankielowicz (the former) and the generalized Georgi-Glashow models (the latter). The conventional 't Hooft anomaly matching algorithm is known to allow a confining, chirally symmetric vacuum in all these models, with a simple set of massless baryonlike composite fermions describing the infrared physics. We analyzed recently one of these models ($\ensuremath{\psi}\ensuremath{\eta}$ model), by applying the ideas of generalized symmetries and the consequent, stronger constraints involving certain mixed anomalies, finding that the confining, chirally symmetric, vacuum is actually inconsistent. In the present paper, this result is extended to a wider class of the Bars-Yankielowicz and the generalized Georgi-Glashow models. It is shown that for all these models with $N$ and $p$ both even, at least, the generalized anomaly matching requirement forbids the persistence of the full chiral symmetries in the infrared if the system confines. The most natural and consistent possibility is that some bifermion condensates form, breaking the color gauge symmetry dynamically, together with part of the global symmetry.

We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the 't~Hooft coupling proportional to $\exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced 't Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime., Comment: 14 pages, 7 figures

I make two comments about nuclear matter. First, I consider the effects of a coupling between the $O(4)$ chiral field, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}$, and the ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ meson, $\ensuremath{\sim}+{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{2}{\ensuremath{\omega}}_{\ensuremath{\mu}}^{2}$; for any net baryon density, a condensate for ${\ensuremath{\omega}}_{0}$ is unavoidably generated. I assume that with increasing density, a decrease of the chiral condensate and the effective ${\ensuremath{\omega}}_{0}$ mass gives a stiff equation of state (EOS). In order to match that onto a soft EOS for quarkyonic matter, I consider an $O(N)$ field at large $N$, where at nonzero temperature quantum fluctuations disorder, any putative pion ``condensates'' into a quantum pion liquid ($\mathrm{Q}\ensuremath{\pi}\mathrm{L}$) [R. D. Pisarski et al., Phys. Rev. D 102, 016015 (2020)]. In this paper, I show that the $\mathrm{Q}\ensuremath{\pi}\mathrm{L}$ persists at zero temperature. If valid qualitatively at $N=4$, the ${\ensuremath{\omega}}_{0}$ mass goes up sharply and suppresses the ${\ensuremath{\omega}}_{0}$ condensate. This could generate a spike in the speed of sound at high density, which is of relevance to neutron stars. Second, I propose a toy model of a $Z(3)$ gauge theory with three flavors of fermions, where $Z(3)$ vortices confine fermions into baryons. In $1+1$ dimensions, this model can be studied numerically with present techniques, using either classical or quantum computers.

We investigate the axial $U(1)$ anomaly of two-flavor QCD at temperatures 190--330 MeV. In order to preserve precise chiral symmetry on the lattice, we employ the M\"obius domain-wall fermion action as well as overlap fermion action implemented with a stochastic reweighting technique. Compared to our previous studies, we reduce the lattice spacing to 0.07 fm, simulate larger multiple volumes to estimate finite size effect, and take more than four quark mass points, including one below physical point to investigate the chiral limit. We measure the topological susceptibility, axial $U(1)$ susceptibility, and examine the degeneracy of $U(1)$ partners in meson/baryon correlators. All the data above the critical temperature indicate that the axial $U(1)$ violation is consistent with zero within statistical errors. The quark mass dependence suggests disappearance of the $U(1)$ anomaly at a rate comparable to that of the $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ symmetry breaking.

We build rigorously the attractive five-dimensional model where bulk fermions propagate along the ${\mathcal{S}}^{1}/{\mathbb{Z}}_{2}$ orbifold and interact with a Higgs boson localized at a fixed point of the extra dimension. The analytical calculation of the fermion mass spectrum and effective Yukawa couplings is shown to require the introduction of either essential boundary conditions (EBC) imposed by the model definition or certain bilinear brane terms (BBT) in the action, instead of the usual brane-Higgs regularizations. The obtained fermion profiles along the extra dimension turn out to undergo some discontinuities, in particular at the Higgs brane, which can be mathematically consistent if the action is well written with improper integrals. We also show that the ${\mathbb{Z}}_{2}$ parity transformations in the bulk do not affect the fermion chiralities, masses and couplings, in contrast with the EBC and the BBT, but when extended to the fixed points, they can generate the chiral nature of the theory and even select the Standard Model chirality setup while fixing as well the fermion masses and couplings. Thanks to the strict analysis developed, the duality with the interval model is scrutinized.

We study the conformal window of asymptotically free gauge theories containing $N_f$ flavors of fermion matter transforming to the vector and two-index representations of $SO(N),~SU(N)$ and $Sp(2N)$ gauge groups. For $SO(N)$ we also consider the spinorial representation. We determine the critical number of flavors $N_f^{\rm cr}$, corresponding to the lower end of the conformal window, by using the conjectured critical condition on the anomalous dimension of the fermion bilinear at an infrared fixed point, $\gamma_{\bar{\psi}\psi}=1$ or equivalently $\gamma_{\bar{\psi}\psi}(2-\gamma_{\bar{\psi}\psi})=1$. To compute the anomalous dimension we employ the Banks-Zaks conformal expansion up to the $4$th order in $\Delta_{N_f}=N_f^{\rm AF}-N_f$ with $N_f^{\rm AF}$ denoting the onset of the loss of asymptotic freedom, where we show that the latter critical condition provides a better performance along with this conformal expansion. To quantify the uncertainties in our analysis, which potentially originate from nonperturbative effects, we propose two distinct approaches by assuming the large order behavior of the conformal expansion separately, either convergent or divergent asymptotic. In the former case, we take the difference in the Pad\'e approximants to the two definitions of the critical condition, whereas in the latter case the truncation error associated with the singularity in the Borel plane is taken into account. Our results are further compared to other analytical methods as well as lattice results available in the literature. In particular, we find that $SU(2)$ with six and $SU(3)$ with ten fundamental flavors are likely on the lower edge of the conformal window, which are consistent with the recent lattice results. We also predict that $Sp(4)$ theories with fundamental and antisymmetric fermions have the critical numbers of flavors, approximately ten and five, respectively., Comment: 22 pages, 9 figures, 3 tables; Version accepted for publication in PRD

We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of ${N}_{f}=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is M\"obius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of ${t}_{\mathrm{gf}}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06\ensuremath{\lesssim}a\ensuremath{\lesssim}0.15\text{ }\text{ }\mathrm{fm}$, six pion masses in the range $130\ensuremath{\lesssim}{m}_{\ensuremath{\pi}}\ensuremath{\lesssim}400\text{ }\text{ }\mathrm{MeV}$ and multiple lattice volumes. On each ensemble, the gradient-flow scales ${t}_{0}/{a}^{2}$ and ${w}_{0}/a$ and the omega baryon mass $a{m}_{\mathrm{\ensuremath{\Omega}}}$ are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of $\sqrt{{t}_{0}}=0.1422(14)\text{ }\text{ }\mathrm{fm}$ and ${w}_{0}=0.1709(11)\text{ }\text{ }\mathrm{fm}$ with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for $\sqrt{{t}_{0}}$ there are comparable continuum extrapolation uncertainties. For ${w}_{0}$, there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.

This work continues our program of lattice-QCD baryon physics using staggered fermions for both the sea and valence quarks. We present a proof-of-concept study that demonstrates, for the first time, how to calculate baryon matrix elements using staggered quarks for the valence sector. We show how to relate the representations of the continuum staggered flavor-taste group $\text{SU}(8)_{FT}$ to those of the discrete lattice symmetry group. The resulting calculations yield the normalization factors relating staggered baryon matrix elements to their physical counterparts. We verify this methodology by calculating the isovector vector and axial-vector charges $g_V$ and $g_A$. We use a single ensemble from the MILC Collaboration with 2+1+1 flavors of sea quark, lattice spacing $a\approx 0.12$ fm, and a pion mass $M_\pi\approx305$ MeV. On this ensemble, we find results consistent with expectations from current conservation and neutron beta decay. Thus, this work demonstrates how highly-improved staggered quarks can be used for precision calculations of baryon properties, and, in particular, the isovector nucleon charges., Comment: 19 pages, 9 figures

The QCD axion remains experimentally viable in the mass range of $\mathcal{O}(10\text{ }\text{ }\mathrm{MeV})$ if (i) it couples predominantly to the first generation of SM fermions; (ii) it decays to ${e}^{+}{e}^{\ensuremath{-}}$ with a short lifetime ${\ensuremath{\tau}}_{a}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{s}$; and (iii) it has suppressed isovector couplings, i.e., if it is piophobic. Remarkably, these are precisely the properties required to explain recently observed anomalies in nuclear deexcitations, to wit: the ${e}^{+}{e}^{\ensuremath{-}}$ emission spectra of isoscalar magnetic transitions of $^{8}\mathrm{Be}$ and $^{4}\mathrm{He}$ nuclei showed a ``bumplike'' feature peaked at ${m}_{{e}^{+}{e}^{\ensuremath{-}}}\ensuremath{\sim}17\text{ }\text{ }\mathrm{MeV}$. In this paper, we argue that on-shell emission of the QCD axion (with the aforementioned properties) provides an extremely well-motivated, compatible explanation for the observed excesses in these nuclear deexcitations. The absence of anomalous features in other measured transitions is also naturally explained: piophobic axion emission is strongly suppressed in isovector magnetic transitions and forbidden in electric transitions. This QCD axion hypothesis is further corroborated by an independent observation: a $\ensuremath{\sim}2--3\ensuremath{\sigma}$ deviation in the measurement of $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})$ from the Standard Model theoretical expectation. This paper also includes detailed estimations of various axionic signatures in rare light meson decays, which take into account contributions from low-lying QCD resonance exchange, and, in the case of rare kaon decays, the possible effective implementations of $\mathrm{\ensuremath{\Delta}}S=1$ octet enhancement in chiral perturbation theory. These inherent uncertainties of the effective description of the strong interactions at low energies result in large variations in the predictions for hadronic signals of the QCD axion; in spite of this, the estimated ranges for rare meson decay rates obtained here can be probed in the near future in $\ensuremath{\eta}/{\ensuremath{\eta}}^{\ensuremath{'}}$ and kaon factories.

Conventional lore from Tremaine and Gunn excludes fermionic dark matter lighter than a few hundred eV, based on the Pauli exclusion principle. We highlight a simple way of evading this bound with a large number of species that leads to numerous non-trivial consequences. In this scenario there are many distinct species of fermions with quasi-degenerate masses and no couplings to the standard model. Nonetheless, gravitational interactions lead to constraints from measurements at the LHC, of cosmic rays, of supernovae, and of black hole spins and lifetimes. We find that the LHC constrains the number of distinct species, bosons or fermions lighter than $\sim 500$ GeV, to be $N \lesssim 10^{62}$. This, in particular, implies that roughly degenerate fermionic dark matter must be heavier than $\sim 10^{-14}$ eV, which thus relaxes the Tremaine-Gunn bound by $\sim 16$ orders of magnitude. Slightly weaker constraints applying to masses up to $\sim100$ TeV exist from cosmic ray measurements while various constraints on masses $\lesssim10^{-10}$ eV apply from black hole observations. We consider a variety of phenomenological bounds on the number of species of particles. Finally, we note that there exist theoretical considerations regarding quantum gravity which could impose more severe constraints that may limit the number of physical states to $N\lesssim 10^{32}$., Comment: 9 pages, 2 figures, comments welcome; v2: clarifying remarks, matches published version

Composite Higgs models can be extended to the Planck scale by means of the partially unified partial compositeness (PUPC) framework. We present in detail the Techni-Pati-Salam model, based on a renormalizable gauge theory SU(8)PS×SU(2)L×SU(2)R. We demonstrate that masses and mixings for all generations of standard model fermions can be obtained via partial compositeness at low energy, with four-fermion operators mediated by either heavy gauge bosons or scalars. The strong dynamics is predicted to be that of a confining Sp(4)HC gauge group, with hyperfermions in the fundamental and two-index antisymmetric representations, with fixed multiplicities. This is motivation for lattice studies of the infrared near-conformal walking phase, with results that may validate or rule out the model. This is the first complete and realistic attempt at providing an ultraviolet completion for composite Higgs models with top partial compositeness. In the baryon-number conserving vacuum, the theory also predicts a dark matter candidate, with a mass in the few TeV range, protected by semi-integer baryon number.

Models with gauge symmetry $SU(3{)}_{c}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{N}$ have different candidates for dark matter, for example, a heavy neutral fermion interacting with standard model particles through different mediators, scalar and vector portals. At the same time, these portals can produce signals in the anomalous magnetic moment of the muon that violate the present bounds on this quantity. Combining the requirement to have a dark matter candidate in the $SU(3{)}_{c}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{N}$ model with heavy neutral leptons and to explain the anomalous magnetic moment of the muon we set constraints on the highest symmetry breaking scale of the model. These bounds are competitive with the constraints from LHC and set a favored region that can also be tested in future direct detection experiments, such as the LUX-ZEPLIN (LZ) experiment.

We study the time evolution of the chirality imbalance $n_5$ and the chiral magnetic effect (CME) under the external parallel electromagnetic fields without assuming the artificial chiral asymmetric source. We adopt the time-dependent Sauter-type electric and constant magnetic field, and obtain analytical solutions of the Dirac equation for a massive fermion. We use the point-split regularization to calculate the vacuum contribution in the gauge invariant way. As a result, we find that $n_5$ and CME current increase substantially as the electric field increases, and stay finite after the electric field is switched off. The chirality imbalance and CME current are shown to consist of a dominant contribution, which is essentially proportional to relativistic velocity, and a small oscillating part. We find a simple analytical relation between $n_5$ and the fermion pair-production rate from the vacuum. We also discuss dynamical origin of the chirality imbalance in detail., 29 pages, 6 figures, revised version is accepted for publication in Phys.Rev.D

We present an exact computation of effective Hamiltonians for an elementary model obtained from the Yukawa theory by going to the limit of bare fermions being infinitely heavy and bare bosons being at rest with respect to the fermions that emit or absorb them. The coupling constant can be arbitrarily large. The Hamiltonians are computed by solving the differential equation of the renormalization group procedure for effective particles (RGPEP). Physical fermions, defined in the model as eigenstates of the effective Hamiltonians, are obtained in the form of an effective fermion dressed with a coherent state of effective bosons. The model computation illustrates the method that can be used in perturbative computations of effective Hamiltonians for realistic theories. It shows the mechanism by which the perturbative expansion and Tamm-Dancoff approximation increase in accuracy along the RGPEP evolution., 33 pages, 1 figure, plain latex

We describe the dynamical mass generation in pseudoquantum electrodynamics (PQED) coupled to the Gross-Neveu (GN) interaction, in (2+1) dimensions, at both zero and finite temperatures. We start with a gapless model and show that, under particular conditions, a dynamically generated mass emerges. In order to do so, we use a truncated Schwinger-Dyson equation, at the large-N approximation, in the imaginary-time formalism. In the instantaneous-exchange approximation (the static regime), we obtain two critical parameters, namely, the critical number of fermions Nc(T) and the critical coupling constant αc(T) as a function of temperature and of the finite cutoff Λ, which must be provided by experiments. In the dynamical regime, we find an analytical solution for the mass function Σ(p,T) as well as a zero-external momentum solution for p=0. In the continuum theory Λ=∞, where scale-invariance is respected, it is shown that the model has a dynamically generated mass for any value of the coupling constant α. Furthermore, after calculating the effective potential for PQED, we prove that the dynamically generated mass is an energetically favorable solution in comparison to the massless phase. We compare our analytical results with numerical tests and a good agreement is found.

We apply the gradient flow on a color-electric two-point function that encodes the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5\,T_c$. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations of this correlation function under Wilson flow are used to enhance the extrapolations of the non-perturbative lattice correlator. The final estimate for the continuum correlator at zero flow time largely agrees with one obtained from a previous study using the multi-level algorithm. We perform a spectral reconstruction based on perturbative model fits to estimate the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator and is also applicable for actions with dynamical fermions., Published version, 14 pages, 15 figures

Using a low-energy effective field theory approach, we study some properties of models with large extra dimensions, in which quarks and leptons have localized wave functions in the extra dimensions. We consider models with two types of gauge groups: (i) the Standard-Model gauge group, and (ii) the left-right symmetric (LRS) gauge group. Our main focus is on the lepton sector of models with $n=2$ extra dimensions, in particular, neutrino masses and mixing. We analyze the requisite conditions that the models must satisfy to be in accord with data and present a solution for lepton wave functions in the extra dimensions that fulfills these conditions. As part of our work, we also present a new solution for quark wave function centers. Issues with flavor-changing neutral current effects are assessed. Finally, we remark on baryogenesis and dark matter in these models., 38 pages, 1 figure

We present a calculation of the pion quark momentum fraction, $⟨x⟩$, and its third Mellin moment $⟨{x}^{2}⟩$. We also obtain directly, for the first time, $⟨x⟩$ and $⟨{x}^{2}⟩$ for the kaon using local operators. We use an ensemble of two degenerate light, a strange, and a charm quark (${N}_{f}=2+1+1$) of maximally twisted mass fermions with clover improvement. The quark masses are chosen so that they reproduce a pion mass of about 260 MeV and a kaon mass of 530 MeV. The lattice spacing of the ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze several values of the source-sink time separation within the range of 1.12--2.23 fm to study and eliminate excited-state contributions. The necessary renormalization functions are calculated nonperturbatively in the ${\mathrm{RI}}^{\ensuremath{'}}$ scheme and are converted to the modified minimal subtraction scheme at a scale of 2 GeV. The final values for the momentum fraction are $⟨x{⟩}_{{u}^{+}}^{\ensuremath{\pi}}=\phantom{\rule{0ex}{0ex}}0.261(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}$, $⟨x{⟩}_{{u}^{+}}^{K}=0.246(2{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$, and $⟨x{⟩}_{{s}^{+}}^{K}=0.317(2{)}_{\mathrm{stat}}(1{)}_{\mathrm{syst}}$. For the third Mellin moments, we find $⟨{x}^{2}{⟩}_{{u}^{+}}^{\ensuremath{\pi}}=0.082(21{)}_{\mathrm{stat}}(17{)}_{\mathrm{syst}}$, $⟨{x}^{2}{⟩}_{{u}^{+}}^{K}=0.093(5{)}_{\mathrm{stat}}(3{)}_{\mathrm{syst}}$, and $⟨{x}^{2}{⟩}_{{s}^{+}}^{K}=0.134(5{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio $⟨{x}^{2}⟩/⟨x⟩$ which is an indication of how quickly the parton distribution functions lose support at large $x$.

We argue that the search for dark vector boson through ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{Z}_{d}\ensuremath{\gamma}$ can determine the Lorentz structure of ${Z}_{d}{l}^{+}{l}^{\ensuremath{-}}$ couplings with the detection of leptonic decays ${Z}_{d}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}$. We assume a general framework that the dark vector boson interacts with ordinary fermions through vector and axial-vector couplings. As a consequence of Ward-Takahashi identity, ${Z}_{d}$ is transversely polarized in the limit ${m}_{{Z}_{d}}\ensuremath{\ll}\sqrt{s}$. On the other hand, the fraction of longitudinal ${Z}_{d}$ is non-negligible for ${m}_{{Z}_{d}}$ comparable to $\sqrt{s}$. Such polarization effects can be analyzed through angular distributions of final-state particles in ${Z}_{d}$ decays. Taking ${l}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\equiv}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}$, we study the correlation between ${Z}_{d}$ angle relative to ${e}^{\ensuremath{-}}$ beam direction in ${e}^{+}{e}^{\ensuremath{-}}$ center of momentum frame and ${\ensuremath{\mu}}^{\ensuremath{-}}$ angle relative to the boost direction of ${Z}_{d}$ in ${Z}_{d}$ rest frame. This correlation is shown to be useful for probing the Lorentz structure of ${Z}_{d}{l}^{+}{l}^{\ensuremath{-}}$ couplings. We discuss the measurement of such correlation in Belle II detector, taking into account the detector acceptance and energy resolution.

Two-neutrino double-beta decay of certain nuclear isotopes is one of the rarest Standard Model processes observed in nature. Its neutrinoless counterpart is an exotic lepton-number nonconserving process that is widely searched for to determine if the neutrinos are Majorana fermions. In order to connect the rate of these processes to the Standard Model and beyond the Standard Model interactions, it is essential that the corresponding nuclear matrix elements are constrained reliably from theory. Lattice quantum chromodynamics (LQCD) and low-energy effective field theories (EFTs) are expected to play an essential role in constraining the matrix element of the two-nucleon subprocess, which could in turn provide the input into ab initio nuclear-structure calculations in larger isotopes. Focusing on the two-neutrino process $nn \to pp \, (ee \bar{\nu}_e\bar{\nu}_e)$, the amplitude is constructed in this work in pionless EFT at next-to-leading order, demonstrating the emergence of a renormalization-scale independent amplitude and the absence of any new low-energy constant at this order beyond those present in the single-weak process. Most importantly, it is shown how a LQCD four-point correlation function in Euclidean and finite-volume spacetime can be used to constrain the Minkowski infinite-volume amplitude in the EFT. The same formalism is provided for the related single-weak process, which is an input to the double-$\beta$ decay formalism. The LQCD-EFT matching procedure outlined for the double-weak amplitude paves the road toward constraining the two-nucleon matrix element entering the neutrinoless double-beta decay amplitude with a light Majorana neutrino., Comment: 32 pages, 7 figures. v2 matches the published version in which typos are corrected, a reference and a clarifying footnote are added

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\ensuremath{\pi}$ scattering amplitudes as a function of the center-of-mass energy using L\"uscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\ensuremath{\pi}}{L}$; this includes irreducible representations (irreps) that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\ensuremath{\kappa}$ resonance in the $S$-wave and the narrow ${K}^{*}(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of 317.2(2.2) and 175.9(1.8) MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave, we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $\ensuremath{\kappa}$-resonance pole positions are found to be $[0.86(12)\ensuremath{-}0.309(50)i]\text{ }\text{ }\mathrm{GeV}$ at the heavier pion mass and $[0.499(55)\ensuremath{-}0.379(66)i]\text{ }\text{ }\mathrm{GeV}$ at the lighter pion mass. The $P$-wave ${K}^{*}$-resonance pole positions are found to be $[0.8951(64)\ensuremath{-}0.00250(21)i]\text{ }\text{ }\mathrm{GeV}$ at the heavier pion mass and $[0.8718(82)\ensuremath{-}0.0130(11)i]\text{ }\text{ }\mathrm{GeV}$ at the lighter pion mass, which corresponds to couplings of ${g}_{{K}^{*}K\ensuremath{\pi}}=5.02(26)$ and ${g}_{{K}^{*}K\ensuremath{\pi}}=4.99(22)$, respectively.

The Universe is awash with tens-of-MeV neutrinos of all species coming from all past core-collapse supernovae. These have never been observed, but this state of affairs will change in the near future. In the less than ten years, the Super-Kamiokande experiment, loaded with gadolinium, is expected to collect dozens of events induced by the scattering of neutrinos from the diffuse supernova neutrino background (DSNB). Next-generation projects, including Hyper-Kamiokande and Theia, are expected to collect data samples with hundreds of DSNB events after a decade of running. Here, we study quantitatively how well the DSNB, including its energy spectrum, will be measured by different current or upcoming large neutrino detectors. We analyze the simulated data in order to estimate how well measurements of the DSNB can be used to inform research topics in cosmology -- including measurements of the Hubble parameter -- astrophysics -- including the star-formation-rate -- and particle physics -- including the neutrino lifetime and the possibility that neutrinos are pseudo-Dirac fermions., 21 pages, 11 figures, new channel to measure H0 with neutrinos; references included, small corrections, matches version published in PRD