The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration has recently reported strong evidence for a stochastic process affecting the 12.5 yr dataset of pulsar timing residuals. We show that the signal can be interpreted in terms of a stochastic gravitational wave background emitted from a network of axionic strings in the early Universe. The spontaneous breaking of the Peccei-Quinn symmetry originate the axionic string network and the QCD axion, the dark matter particle in the model. We explore a nonstandard cosmological model driven by an exotic scalar field $\varphi$ which evolves under the influence of a self-interacting potential; the axion field starts to oscillate during the modified cosmology, and provides the dark matter observed. For an equation of state $w_{\varphi }<1/3$, the QCD axion mass is smaller than expected in the standard cosmology and the GW spectrum from axionic strings is larger. We assess the parameter space of the model which is consistent with the NANOGrav-12.5 yr detection, which can be explained within 95% limit by a QCD axion field evolving in a dust-like scenario, as well as within 68% limit in a cosmology with $w_{\varphi }<0$.

In this paper we introduce a novel filtering method for the search of continuous gravitational wave signals in the data of interferometric detectors, based on the estimation of the harmonic content of the detector sidereal pattern. Thanks to the very specific properties of the sidereal modulation, the method is powerful in discriminating among continuous wave signals of astrophysical origin and detector artefacts or noise outliers. We describe here the statistical properties of the filter by using both software and hardware simulated signals injected in the data of the LIGO second science run O2 and we give an estimate of the method sensitivity. A study of the method robustness with respect to a nonoptimal correction of the signal frequency variation, referring in particular to the spin-down, is also presented. This novel filtering procedure is well suited for directed searches of sources with known—or loosely known—position and largely unknown frequency and spin-down, and for the follow-up of all-sky candidates. Used as an initial processing step it has, moreover, the potential to improve the sensitivity of wide-band hierarchical searches.

The excess of $\gamma$ rays in the data measured by the Fermi Large Area Telescope from the galactic center region is one of the most intriguing mysteries in astroparticle physics. This “galactic center excess” (GCE) has been measured with respect to different interstellar emission models (IEMs), source catalogs, data selections, and techniques. Although several proposed interpretations have appeared in the literature, there are no firm conclusions as to its origin. The main difficulty in solving this puzzle lies in modeling a region of such complexity and thus, precisely measuring the characteristics of the GCE. In this paper, we use 11 years of Fermi-LAT data, state of the art IEMs, and the newest 4FGL source catalog to provide precise measurements of the energy spectrum, spatial morphology, position, and sphericity of the GCE. We find that the GCE has a spectrum that is peaked at a few GeV and is well fit with a log parabola. The normalization of the spectrum changes by roughly 60% when using different IEMs, data selections, and analysis techniques. The spatial distribution of the GCE is compatible with a dark matter (DM) template produced with a generalized Navarro-Frenk-White density profile with slope $\gamma =1.2–1.3$. No energy evolution is measured for the GCE morphology between 0.6–30 GeV at a level larger than 10% of the $\gamma$ average value, which is 1.25. The analysis of the GCE modeled with a DM template divided into quadrants shows that the spectrum and spatial morphology of the GCE is similar in different regions around the galactic center. Finally, the GCE centroid is compatible with the galactic center, with a best-fit position between $l=[-0.3°,0.0°],b=[-0.1°,0.0°]$, and it is compatible with a spherical symmetric morphology. In particular, fitting the DM spatial profile with an ellipsoid gives a major-to-minor axis ratio (aligned along the galactic plane) between 0.8–1.2.

We use a simple model consisting of energy-momentum tensor conservation and a Maxwell-Cattaneo equation for its viscous part to study nonlinear phenomena in a real relativistic fluid. We focus on new types of behavior without nonrelativistic equivalents, such as an entropy cascade driven by fluctuations in the tensor degrees of freedom of the theory. We write down the von Kármán–Howarth equations for this kind of turbulence and consider the correlations corresponding to fully developed turbulence.

We present the study of radiative tau decay (${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }\gamma$), computing the structure dependent contribution using light cone sum rules. This decay includes the same form factors as the radiative pion decay with the crucial difference that the momentum transfer squared, $t$, between the pion-photon system is positive, which makes these form factors timelike and also as $t$ can now take values up to $m_{\tau }^2$, it can produce real hadronic resonances. The analytical form for these form factors has been calculated using the light cone sum rules method and the invariant mass spectrum in the $\pi -\gamma$ system and the decay width are presented. The structure dependent parameter, $\gamma$, the ratio of the axial vector to vector form factor is found to be in good agreement with the experimental determination.

We consider a flavor model based on the $A_4$ modular group to account for both lepton and quark parameters (masses and mixing). The inverse seesaw mechanism is considered to produce the light neutrino masses. Lepton masses and mixing are obtained in terms of Yukawa coupling ratios and values of the modulus $\tau$ nearby some fixed points for inverted neutrino mass hierarchy. The quark masses and mixing are arisen at the same $\tau$ values used in inverted neutrino mass hierarchy and are in agreement with the recent data.

We investigate the renormalization group flow of the field-dependent Yukawa coupling in the framework of the three flavor quark-meson model. In a conventional perturbative calculation, given that the field rescaling is trivial, the Yukawa coupling does not get renormalized at the one-loop level if it is coupled to an equal number of scalar and pseudoscalar fields. Its field-dependent version, however, does flow with respect to the scale. Using the functional renormalization group technique, we show that it is highly nontrivial how to extract the actual flow of the Yukawa coupling as there are several new chirally invariant operators that get generated by quantum fluctuations in the effective action, which need to be distinguished from that of the Yukawa interaction.

We perform a comprehensive analysis of the homogeneous finite modular group ${\mathrm{\Gamma }}_4^{\prime }\equiv S_4^{\prime }$, which is the double covering of $S_4$ group. The weight 1 modular forms of level 4 are constructed in terms of the Dedekind eta function, and they transform as a triplet ${\widehat{\mathbf{3}}}^{\prime }$ of $S_4^{\prime }$. The integral weight modular forms until weight 6 are built from the tensor products of weight 1 modular forms. We perform a systematical classification of $S_4^{\prime }$ modular models for lepton masses and mixing with and without generalized $CP$, where the left-handed leptons are assigned to a triplet of $S_4^{\prime }$ and right-handed charged leptons transform as singlets under $S_4^{\prime }$, and we consider both scenarios where the neutrino masses arise from a Weinberg operator or type-I seesaw mechanism. The phenomenological implications of the minimal models for lepton masses, mixing angles, $CP$ violation phases, and neutrinoless double decay are discussed. The $S_4^{\prime }$ modular symmetry is extended to the quark sector, and we present several predictive models which use nine or ten free parameters including real and imaginary parts of $\tau$ to describe quark masses and the Cabibbo-Kobayashi-Maskawa mixing matrix. We give a quark-lepton unified model which can explain the flavor structure of quarks and leptons simultaneously for a common value of $\tau$.

We have studied the correlations among the three absolute neutrino mass observables—the effective Majorana mass ($m_{ee}$) which can be obtained from neutrinoless double beta decay, the electron neutrino mass ($m_{\beta }$) which is measured in single beta decay experiments, and the sum of the light neutrino masses ($\mathrm{\Sigma }$) which is constrained from cosmological observations, in the context of minimal left-right symmetric model. Two phenomenologically interesting cases of type-I seesaw dominance as well as type-II seesaw dominance have been considered. We have taken into account the independent constraints coming from lepton flavor violation, single $\beta$ decay, cosmology, and neutrinoless double beta decay and have determined the combined allowed parameter space that can be probed in the future experiments. We have also analyzed the correlations and tensions between the different mass variables. In addition, the constraints on the masses of the heavy particles coming from lepton flavor violation and the bounds on three absolute neutrino mass observables are also determined. We show that these constraints can rule out some of the parameter space which are not probed by the collider experiments.

Motivated in part by the pseudo-Nambu Goldstone boson mechanism of electroweak symmetry breaking in composite Higgs models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-$N$ extrapolation, we perform lattice studies of the Yang-Mills theories with $Sp(2N)$ gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate two-point correlation functions of operators organized as irreducible representations of the octahedral symmetry group. We perform the continuum extrapolation and study the magnitude of finite-size effects, showing that they are negligible in our calculation. We present new numerical results for $N=1$, 2, 3, 4, combine them with data previously obtained for $N=2$, and extrapolate toward $N\to \infty$. We confirm explicitly the expectation that, as already known for $N=1$, 2 also for $N=3$, 4 a confining potential rising linearly with the distance binds a static quark to its antiquark. We compare our results to the existing literature on other gauge groups, with particular attention devoted to the large-$N$ limit. We find agreement with the known values of the mass of the $0^{++}$, $0^{++*}$, and $2^{++}$ glueballs obtained taking the large-$N$ limit in the $SU(N)$ groups. In addition, we determine for the first time the mass of some heavier glueball states at finite $N$ in $Sp(2N)$ and extrapolate the results toward $N\to +\infty$ taking the limit in the latter groups. Since the large-$N$ limit of $Sp(2N)$ is the same as in $SU(N)$, our results are relevant also for the study of QCD-like theories.

We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot be uniquely determined solely based on discrete experimental measurements because of a mathematical property of mimicry of PDF parametrizations that we prove using a representation based on Bézier curves. Predictions of nonperturbative QCD approaches for the $x$ dependence of PDFs instead should be cast in a form that enables decisive comparisons against experimental measurements. Predictions for effective power laws of ($1-x$) dependence of PDFs may play this role. Expectations for PDFs in a proton based on quark counting rules are compared against the effective power laws of ($1-x$) dependence satisfied by CT18 next-to-next-to-leading-order parton distributions. We comment on implications for studies of PDFs in a pion, in particular on the comparison of nonperturbative approaches with phenomenological PDFs.

We propose a mass-dependent momentum subtraction (MOM) scheme to renormalize UV divergence of unpolarized PDFs at one-loop order. This approach, which is based on a once subtracted dispersion relation, does not need a regulator. The overall counterterms are obtained from the imaginary part of the large transverse momentum region in loop integrals. The mass-dependent characteristic of the scheme yields to mass-dependent splitting functions for the DGLAP evolution equations. While the flavor number is fixed at any renormalization scale, the decoupling theorem is automatically imposed by the mass-dependent splitting functions. The required symmetries are also automatically respected by our prescription.

Motivated by the successful interpretation of these observed $P_c$ and $P_{cs}$ states under the meson-baryon molecular picture, we systematically investigate the possible hidden-charm molecular pentaquark states with triple strangeness which is due to the ${\mathrm{\Omega }}_c^{(*)}{\overline{D}}_s^{(*)}$ interactions. We perform a dynamical calculation of the possible hidden-charm molecular pentaquarks with triple strangeness by the one-boson-exchange model, where the $S\text{−}D$ wave mixing effect and the coupled channel effect are taken into account in our calculation. Our results suggest that the ${\mathrm{\Omega }}_c{\overline{D}}_s^{*}$ state with $J^P=3/2^{-}$ and the ${\mathrm{\Omega }}_c^{*}{\overline{D}}_s^{*}$ state with $J^P=5/2^{-}$ can be recommended as the candidates of the hidden-charm molecular pentaquark with triple strangeness. Furthermore, we discuss the two-body hidden-charm strong decay behaviors of these possible hidden-charm molecular pentaquarks with triple strangeness by adopting the quark-interchange model. These predictions are expected to be tested at the LHCb, which can be a potential research issue with more accumulated experimental data in near future.

We examine the thermalization of an ensemble of the octet of pseudoscalar mesons, in the isospin symmetric limit, whose interactions are constrained through chiral symmetry, unitarity, and measurements. We use unitarized reaction amplitudes from next-to-leading-order chiral perturbation theory which generate all resonances up to masses of about 2 GeV, with 12 input parameters, namely, $f_{\pi }$, three masses, and eight low-energy constants of chiral perturbation theory. In linear response theory, we find that the relaxation time is around 100 fm at a temperature of 150 MeV and increases rapidly with temperature. The long relaxation times are directly related to the fact that these mesons are pseudo-Goldstone bosons of chiral symmetry breaking.

We search for the process $e^{+}{e}^{-}\to {\chi }_{cJ}{\pi }^{+}{\pi }^{-}$ ($J=0$, 1, 2) and for a charged charmoniumlike state in the ${\chi }_{cJ}{\pi }^{\pm }$ subsystem. The search uses datasets collected with the BESIII detector at the BEPCII storage ring at center-of-mass energies between 4.18 GeV and 4.60 GeV. No significant ${\chi }_{cJ}{\pi }^{+}{\pi }^{-}$ signals are observed at any center-of-mass energy, and thus upper limits are provided which also serve as limits for a possible charmoniumlike structure in the invariant ${\chi }_{cJ}{\pi }^{\pm }$ mass.

We present a measurement of the transverse single-spin asymmetry for ${\pi }^0$ and $\eta$ mesons in $p^{\uparrow }+p$ collisions in the pseudorapidity range $|\eta |<0.35$ and at a center-of-mass energy of 200 GeV with the PHENIX detector at the Relativistic Heavy Ion Collider. In comparison with previous measurements in this kinematic region, these results have factor-of-3-smaller uncertainties. As hadrons, ${\pi }^0$ and $\eta$ mesons are sensitive to both initial- and final-state nonperturbative effects for a mix of parton flavors. Comparisons of the differences in their transverse single-spin asymmetries have the potential to disentangle the possible effects of strangeness, isospin, or mass. These results can constrain the twist-3 trigluon collinear correlation function as well as the gluon Sivers function.

We point out that a nonrelativistic approximately 2 GeV dark matter (DM) which interacts with visible matter through higher-dimensional Rayleigh operators could explain the excess of “electron recoil” events recently observed by the XENON1T Collaboration. A DM scattering event results in a few keV photon that on average carries most of the deposited energy, while the nuclear recoil energy is only a subleading correction. Since the XENON1T detector does not discriminate between electrons and photons, such events would be interpreted as excess of the keV electrons. Indirect constraints from dark matter annihilation are avoided for light mediators of $\mathcal{O}(10\mathrm{MeV})$ that have sizable couplings to neutrinos. One-loop induced spin-independent scattering in dark matter may soon lead to a confirmation signal or already excludes regions of viable parameter space for the Rayleigh DM model, depending on what the exact values of the unknown nonperturbative nuclear matrix elements are.

Gauge theories with confining phases at low temperatures tend to deconfine at high temperatures. In some cases, for example in supersymmetric theories, confinement can persist for all temperatures provided the partition function includes a grading by $(-1{)}^F$. When it is possible to define partition functions that smoothly interpolate between no grading and $(-1{)}^F$ grading, it is natural to ask if there are other choices of grading that have the same effect as $(-1{)}^F$ on confinement. We explore how this works for $\mathcal{N}=4$ SYM on $S^1\times S^3$ in the large $N$ limit at both small and large coupling. We find evidence for a continuous range of grading parameters that preserve confinement for all temperatures at large coupling, while at small coupling only a discrete set of gradings preserves confinement.