We calculate the two-loop beta functions of the right-handed neutrino mass matrix in the Standard Model extended with right-handed neutrinos. We show that two-loop quantum effects induced by the heavier right-handed neutrinos can induce sizable contributions (sometimes dominant) to the physical masses of the lighter right-handed neutrinos. These effects can significantly affect the masses of the active neutrinos in the seesaw mechanism and the low-energy phenomenology.

We propose to utilize the polarization information of the $Z$ bosons in $ZZ$ production, via the gluon-gluon fusion process $gg\to ZZ$, to probe the $Zt\overline{t}$ gauge coupling. The contribution of longitudinally polarized $Z$ bosons is sensitive to the axial-vector component ($a_t$) of the $Zt\overline{t}$ coupling. We demonstrate that the angular distribution of the charged lepton from $Z$ boson decays serves well for measuring the polarization of $Z$ bosons and the determination of $a_t$. We show that $ZZ$ production via the $gg\to ZZ$ process complement to $Zt\overline{t}$ and $tZj$ productions in measuring the $Zt\overline{t}$ coupling at hadron colliders.

We extract the pion valence quark distribution $q_{\mathrm{v}}^{\pi }(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q_{\mathrm{v}}^{\pi }(x)$ and that obtained from experimental data across the entire $x$ range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{\mathrm{v}}^{\pi }(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD-calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.

We calculate the scattering cross section between two $0^{++}$ glueballs in $SU(2)$ Yang-Mills theory on a lattice at $\beta =2.1$, 2.2, 2.3, 2.4, and 2.5 using the indirect (HAL QCD) method. We employ the cluster-decomposition error reduction technique and use all space-time symmetries to improve the signal. In the use of the HAL QCD method, the centrifugal force was subtracted to remove the systematic effect due to the nonzero angular momenta of lattice discretization. From the extracted interglueball potential, we determine the low energy glueball effective theory by matching with the one-glueball exchange process. We then calculate the scattering phase shift and derive the relation between the interglueball cross section and the scale parameter $\mathrm{\Lambda }$ as ${\sigma }_{\varphi \varphi }=(2–51){\mathrm{\Lambda }}^{-2}$ ($\text{stat}+\text{sys}$). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter as $\mathrm{\Lambda }>60\mathrm{MeV}$. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.

The three-photon decay rate of $J/\psi$ is studied using two $N_f=2$ twisted-mass gauge ensembles with lattice spacings $a\simeq 0.085$ and 0.067 fm. Using a new method, only the correlation functions directly related to the physical decay width are computed with all polarizations of the initial and final states summed over. The final result can be obtained after a naive extrapolation to the continuum limit. To be specific, the result for such rare decay is given as $\mathcal{B}(J/\psi \to 3\gamma )=(2.13\pm 0.14\pm 0.29)\times {10}^{-5}$, where the first error is statistical and the second is an estimate of the systematics. We also propose a method to analyze the Dalitz plot of the corresponding process based on the lattice data which can provide direct information for the relevant experiments.

In the last years it became possible to measure in HADES the dilepton decays of several baryons. The baryon dilepton decays provide information about the electromagnetic structure of the baryons in the timelike region. In the present work, we study the $B^{\prime }\to e^{+}{e}^{-}B$ decays, where $B^{\prime }$ is a baryon decuplet member and $B$ is a baryon octet member. Our calculations are based on the covariant spectator quark model, where the contribution of the quark core is complemented with an $SU(3)$ contribution from the pion cloud. The pion cloud contribution prove to be relevant in the range of study. We present predictions for the ${\mathrm{\Sigma }}^0(1385)\to e^{+}{e}^{-}\mathrm{\Lambda }(1116)$ and ${\mathrm{\Sigma }}^{+}(1385)\to e^{+}{e}^{-}{\mathrm{\Sigma }}^{+}(1193)$ decays, which may be tested at HADES in a near future. Predictions for the remaining decuplet baryon Dalitz decays are also presented. We conclude that different orders of magnitudes are expected for the baryon decuplet Dalitz decay widths, according to the quark content of the baryons. We also conclude that the dependence of the transition form factors on the square momentum transfer ($q^2$) is important for some transitions.

We present in this work a study of tree-dominated charmless three-body decays of $B$ mesons, $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$, within the factorization approach. The main results are: (i) There are two distinct sources of nonresonant contributions: one arises from the $b\to u$ tree transition and the other from the nonresonant matrix element of scalar densities $⟨M_1{M}_2|{\overline{q}}_1{q}_2|0{⟩}^{\mathrm{NR}}$. It turns out that even for tree-dominated three-body decays, dominant nonresonant contributions originate from the penguin diagram rather than from the $b\to u$ tree process, as implied by the large nonresonant component observed recently in the ${\pi }^{-}{K}^{+}$ system which accounts for one third of the $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ rate. (ii) The calculated branching fraction of $B^{-}\to f_2(1270){\pi }^{-}\to K^{+}{K}^{-}{\pi }^{-}$ is smaller than the LHCb by a factor of $\sim 7$ in its central value, but the predicted $\mathcal{B}(B^{-}\to f_2(1270){\pi }^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-})$ is consistent with the data. Branching fractions of $B^{-}\to f_2(1270){\pi }^{-}$ extracted from the LHCb measurements of these two processes also differ by a factor of seven! Therefore, it is likely that the $f_2(1270)$ contribution to $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ is largely overestimated experimentally. Including $1/m_b$ power corrections from penguin annihilation inferred from QCD factorization (QCDF), a sizable $CP$ asymmetry of 25% in the $f_2(1270)$ component agrees with experiment. (iii) A fraction of 5% for the $\rho (1450)$ component in $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ is in accordance with the theoretical expectation. However, a large fraction of 30% in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ is entirely unexpected. This issue needs to be clarified in the future. (iv) We study final-state $\pi \pi \leftrightarrow K\overline{K}$ rescattering and find that the rescattering contributions to both $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ seem to be overestimated experimentally by a factor 4. (v) Using the QCDF expression for the $B^{-}\to \sigma /f_0(500){\pi }^{-}$ amplitude to study the decay $B^{-}\to \sigma {\pi }^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$, the resultant branching fraction and $CP$ violation of 15% agree with experiment. (vi) $CP$ asymmetry for the dominant quasi-two-body decay mode $B^{-}\to {\rho }^0{\pi }^{-}$ was found by the LHCb to be consistent with zero in all three $S$-wave models. In the QCDF approach, $1/m_b$ power corrections, namely, penguin annihilation and hard spectator interactions contribute destructively to ${\mathcal{A}}_{CP}(B^{-}\to {\rho }^0{\pi }^{-})$ to render it consistent with zero. (vii) A significant $CP$ asymmetry has been seen in the ${\rho }^0(770)$ region for positive- and negative-helicity angle cosines. Considering the low ${\pi }^{+}{\pi }^{-}$ invariant mass region of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ Dalitz plot of $CP$ asymmetries divided into four zones, the pattern of $CP$ violation in each zone is well described by the interference between $\rho (770)$ and $\sigma (500)$ as well as the nonresonant background.

We study the problem of interacting theories with partially-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends the well-known class of purely massless theories. More generally, it is proved that the complete theory has to have a form of the flatness condition for a connection of a Lie algebra, which, provided there is a nondegenerate invariant bilinear form, can be derived from the Chern-Simons action. We also point out the existence of higher spin theories without the dynamical graviton in the spectrum. As an application of a more general statement that the framelike formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent formulation approach, we also obtain an explicit uplift of any given metriclike vertex to its framelike counterpart. This procedure is valid for general gauge theories while in the case of higher spin fields in d-dimensional Minkowski space one can even use as a starting point metriclike vertices in the transverse-traceless gauge. In particular, this gives the fully off-shell lift for transverse-traceless vertices.

Black hole photon spheres or light rings are closely linked to astronomical phenomena, such as gravitational waves and the shadow in spherically symmetric or axisymmetric spacetime. In Cunha and Herdeiro [Phys. Rev. Lett. 124, 181101 (2020)], a topological argument was applied for the four-dimensional stationary, axisymmetric, asymptotically flat black hole, and the result indicates that at least, there exists one standard light ring outside the black hole horizon for each rotation sense. Inspired by it, in this paper, we would like to consider a similar issue for a nonrotating, static, spherically symmetric black hole not only with asymptotically flat behavior, but also with AdS and dS behaviors. Following Duan’s topological current $\varphi$-mapping theory, the topological current and charge for the photon spheres are introduced. The topological current is nonzero only at the zero point of the vector field determining the location of the photon sphere. So each photon sphere can be assigned a topological charge. Considering the full exterior region, we find the total topological charge always equals $-1$. This result confirms that there exists at least one standard photon sphere outside of the black hole not only in asymptotically flat spacetime, but also in asymptotically AdS and dS spacetime. Then we apply the study to the dyonic black holes. We observe that even when more photon spheres are included, the total topological charge stays unchanged. Moreover, for a naked singularity, it has a vanishing topological charge, indicating that the black hole and naked singularity are in different topological classes. It is expected that this novel topological argument could provide an insightful idea on the study of the black hole photon spheres or light rings, and further cast new light on the black hole astronomical phenomena.

Fermion-boson stars are solutions of the gravitationally coupled Einstein-Klein-Gordon-hydrodynamic equations system. By means of methods developed in previous works, we perform a stability analysis of fermion-boson stars that include a quartic self-interaction in their bosonic part. Additionally, we describe the complete structure of the stability and instability regions of the space of free parameters, which we argue is qualitatively the same for any value of the quartic self-interaction. The relationship between the total mass of mixed stars and their general stability is also discussed in terms of the structure identified within the stability region.

Degenerate scalar-tensor theories of gravity extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order. In some cases, this is a mere consequence of a disformal field redefinition carried out in a nondegenerate theory. More generally, this is made possible by the existence of an additional constraint that removes the would-be ghost. It has been noted that this constraint can be thwarted when the coupling to matter involves time derivatives of the metric, which results in a modification of the canonical momenta of the gravitational sector. In this paper we expand on this issue by analyzing the precise ways in which the extra degree of freedom may reappear upon minimal coupling to matter. Specifically, we study examples of matter sectors that lead either to a direct loss of the special constraint or to a failure to generate a pair of secondary constraints. We also discuss the recurrence of the extra degree of freedom using the language of disformal transformations in particular for what concerns “veiled” gravity. On the positive side, we show that the minimal coupling of spinor fields is healthy and does not spoil the additional constraint. We argue that this virtue of spinor fields to preserve the number of degrees of freedom in the presence of higher derivatives is actually very general and can be seen from the level decomposition of Grassmann-valued classical variables.

We classify the asymptotic charges of a class of polyhomogeneous asymptotically flat spacetimes with finite shear, generalizing recent results on smooth asymptotically flat spacetimes. Polyhomogeneous spacetimes are a formally consistent class of spacetimes that do not satisfy the well-known peeling property. As such, they constitute a more physical class of asymptotically flat spacetimes compared to the smooth class. In particular, we establish that the generalized conserved nonlinear Newman-Penrose charges that are known to exist for such spacetimes are a subset of asymptotic BMS charges.

Bondi-like (single-null) characteristic formulations of general relativity are used for numerical work in both asymptotically flat and anti–de Sitter spacetimes. The well posedness of the resulting systems of partial differential equations, however, remains an open question. The answer to this question affects accuracy and, potentially, the reliability of conclusions drawn from numerical studies based on such formulations. A numerical approximation can converge to the continuum limit only for well-posed systems; for the initial value problem in the $L^2$ norm, this is characterized by strong hyperbolicity. We find that, due to a shared pathological structure, the systems arising from the aforementioned formulations are, however, only weakly hyperbolic. We present numerical tests for toy models that demonstrate the consequence of this shortcoming in practice for the characteristic initial boundary value problem. Working with alternative norms in which our model problems may be well posed, we show that convergence may be recovered. Finally, we examine the well posedness of a model for Cauchy-characteristic matching in which model symmetric and weakly hyperbolic systems communicate through an interface, with the latter playing the role of general relativity in the Bondi gauge on characteristic slices. We find that, due to the incompatibility of the norms associated with the two systems, the composite problem does not naturally admit energy estimates.

Using a Hamiltonian approach, we introduce black hole entropy for Kerr-AdS spacetimes with torsion as the canonical charge on horizon. In spite of a completely different geometric setting with respect to GR, the resulting thermodynamic variables, energy, angular momentum and entropy, are shown to be proportional to the corresponding GR expressions. The validity of the first law is confirmed.

We study if the discrepancy between the local and cosmological measurements of the Hubble constant $H_0$ can be affected by the choice of the cosmic microwave background (CMB) monopole temperature $T_0$. The latter is customarily fixed to the Far-Infrared Absolute Spectrophotometer (FIRAS) best-fit value in CMB data analyses. Although this value was confirmed by several independent experiments, it is interesting to see how much parameter constraints depend on this prior. We first provide a detailed pedagogical description of the $T_0$ effects on cosmological observables. We show that the recombination history and transfer functions do not depend on $T_0$, provided they are parametrized by the energy scale rather than redshift and at fixed dark matter and baryon densities per CMB photon. Thus, $T_0$ is only a property of the observer, quantifying the amount of expansion between key cosmological events and today. As a consequence, the sole effect of $T_0$ on small-scale primary CMB anisotropies is through the angular diameter distance to the epoch of last scattering, resulting in a near-perfect degeneracy between $T_0$ and $H_0$. This geometric degeneracy is partially lifted by the late-time integrated Sachs-Wolfe effect and CMB lensing. Still, Planck data alone are consistent with a broad region in the $H_0-T_0$ plane, implying that removing the FIRAS prior on $T_0$ can make Planck and SH0ES less discrepant, without introducing new physics beyond $\mathrm{\Lambda }\mathrm{CDM}$. One may break the degeneracy by combining Planck with SH0ES, yielding an independent measurement of $T_0$, but the latter happens to be in $3\sigma$ tension with FIRAS. The agreement with FIRAS is restored anyway when combining Planck with the baryon acoustic oscillation data instead of SH0ES. Thus, the tension between SH0ES and cosmological measurements of $H_0$ persists even if we discard the FIRAS $T_0$ prior.

In recent work, two of us proposed a nonsingular ekpyrotic cosmology making use of an S-brane which forms at the end of the phase of ekpyrotic contraction. This S-Brane mediates a transition between contraction and expansion. Gravitational waves passing through the S-brane acquire a roughly scale-invariant spectrum, and if the S-brane has zero shear, then a roughly scale-invariant spectrum of cosmological perturbatiions results. Here, we study the production of gauge field fluctuations driven by the decay of the S-brane, and we show that the reheating process via gauge field production will be efficient, leading to a radiation-dominated expanding phase.

The cosmic distance duality relation (CDDR), $D_{\mathrm{L}}(1+z{)}^{-2}/D_{\mathrm{A}}=\eta =1$, with $D_{\mathrm{L}}$ and $D_{\mathrm{A}}$, being the luminosity and angular diameter distances, respectively, is a crucial premise in cosmological scenarios. Many investigations try to test CDDR through observational approaches, even some of these ones also consider a deformed CDDR, i.e., $\eta =\eta (z)$. In this paper, we use type Ia supernovae luminosity distances and galaxy cluster measurements (their angular diameter distances and gas mass fractions) in order to perform a Bayesian model comparison between $\eta (z)$ functions. We show that the data here used are unable to pinpoint, with a high degree of Bayesian evidence, which $\eta (z)$ function best captures the evolution of CDDR.

As two neutron stars merge, they emit gravitational waves that can potentially be detected by Earth-bound detectors. Matched-filtering-based algorithms have traditionally been used to extract quiet signals embedded in noise. We introduce a novel neural-network-based machine learning algorithm that uses time series strain data from gravitational-wave detectors to detect signals from nonspinning binary neutron star mergers. For the Advanced LIGO design sensitivity, our network has an average sensitive distance of 130 Mpc at a false-alarm rate of ten per month. Compared to other state-of-the-art machine learning algorithms, we find an improvement by a factor of 4 in sensitivity to signals with a signal-to-noise ratio between 8 and 15. However, this approach is not yet competitive with traditional matched-filtering-based methods. A conservative estimate indicates that our algorithm introduces on average 10.2 s of latency between signal arrival and generating an alert. We give an exact description of our testing procedure, which can be applied not only to machine-learning-based algorithms but all other search algorithms as well. We thereby improve the ability to compare machine learning and classical searches.

Dark matter could potentially manifest itself in the form of asymmetric dark stars. In this paper we entertain the possibility of probing such asymmetric bosonic dark matter stars by the use of atomic clocks. If the dark sector connects to the standard model sector via a Higgs or photon portal, the interiors of boson stars that are in a Bose-Einstein condensate state can change the values of physical constants that control the timing of atomic clock devices. Dilute asymmetric dark matter boson stars passing through the Earth can induce frequency shifts that can be observed in separated Earth-based atomic clocks. This gives the opportunity to probe a class of dark matter candidates that for the moment cannot be detected with any different conventional method.

We study the role of the pasta phases on the properties of rotating and magnetized neutron stars. In order to investigate such systems, we make use of two different relativistic mean-field unified inner-crust–core equations of state, with a different density dependence of the symmetry energy, and an inner crust computed within a Thomas-Fermi calculation. Special attention is given to the crust-core transition density, and the pasta phases effects on the global properties of stars. The effects of strong magnetic fields and fast rotation are computed by solving the Einstein-Maxwell equations self-consistently, taking into account anisotropies induced by the centrifugal and the Lorentz force. The location of the magnetic field neutral line and the maximum of the Lorentz force on the equatorial plane are calculated. The conditions under which they fall inside the inner crust region are discussed. We verified that models with a larger symmetry energy slope show more sensitivity to the variation of the magnetic field. One of the maxima of the Lorentz force, as well as the neutral line, and for a certain range of frequencies, fall inside the inner crust region. This may have consequences in the fracture of the crust, and may help explain phenomena associated with star quakes.