The nature of neutrinos, whether Dirac or Majorana, is hitherto not known. Assuming that the neutrinos are Dirac, which needs $B-L$ to be an exact symmetry, we make an attempt to explain the observed proportionality between the relic densities of dark matter (DM) and baryonic matter in the present Universe i.e., ${\mathrm{\Omega }}_{\mathrm{DM}}\approx 5{\mathrm{\Omega }}_{\mathrm{B}}$. We extend the Standard Model (SM) by introducing heavy scalar doublets $X_i,i=1$, 2 and $\eta$, two singlet scalars $\mathrm{\Phi }$ and ${\mathrm{\Phi }}^{\prime }$, a vectorlike Dirac fermion $\chi$ representing the DM and three right-handed neutrinos ${\nu }_{R_i},i=1$, 2, 3. Assuming $B-L$ is an exact symmetry of the early Universe, the $CP$-violating out-of-equilibrium decay of heavy scalar doublets; $X_i,i=1$, 2 to the SM lepton doublet $L$ and the right-handed neutrino ${\nu }_R$, generate equal and opposite $B-L$ asymmetry among left (${\nu }_L$) and right (${\nu }_R$)-handed neutrinos. We ensure that ${\nu }_L-{\nu }_R$ equilibration does not occur until below the electroweak (EW) phase transition during which a part of the lepton asymmetry gets converted to dark matter asymmetry through a dimension eight operator, which conserves $B-L$ symmetry and remains in thermal equilibrium above sphaleron decoupling temperature. A part of the remaining $B-L$ asymmetry then gets converted to a net $B$ asymmetry through EW-sphalerons which are active at a temperature above 100 GeV. To alleviate the small-scale anomalies of $\mathrm{\Lambda }\mathrm{CDM}$, we assume the DM ($\chi$) to be self-interacting via a light mediator $\mathrm{\Phi }$, which not only depletes the symmetric component of the DM, but also paves a way to detect the DM at terrestrial laboratories through $\mathrm{\Phi }-H$ mixing, where $H$ is the SM Higgs doublet.

In this work, we consider the simple $Z_2$ symmetric extension to the Standard Model (SM) and proceed to study the nature of electroweak phase transition (EWPT) in the early Universe. We show that the nature of the phase transition changes from a smooth crossover in the SM to a strong first order with this addition of the real scalar. Furthermore, we show that the entropy release in this scenario is higher than that of the SM. This can lead to a strong dilution of the energy density of gravitational waves, as we show in the latter part of the paper.

We study Yang-Mills lattice theories with $Sp(N_c)$ gauge group, with $N_c=2N$, for $N=1,\dots ,4$. We show that if we divide the renormalized couplings appearing in the Wilson flow by the quadratic Casimir $C_2(F)$ of the $Sp(N_c)$ group, then the resulting quantities display a good agreement among all values of $N_c$ considered, over a finite interval in flow time. We use this scaled version of the Wilson flow as a scale-setting procedure, compute the topological susceptibility of the $Sp(N_c)$ theories, and extrapolate the results to the continuum limit for each $N_c$.

We study the decay behaviors of the fully bottom tetraquark states within the diquark-antidiquark picture and calculate their relative branching ratios through the Fierz rearrangement. Our results suggest that the $C=+$ states can be searched for in the ${\mu }^{+}{\mu }^{-}\mathrm{\Upsilon }(1S)$ and ${\mu }^{+}{\mu }^{-}\mathrm{\Upsilon }(2S)$ channels with the relative branching ratio $\mathcal{B}(X\to \mu \mu \mathrm{\Upsilon }(2S))/\mathcal{B}(X\to \mu \mu \mathrm{\Upsilon }(1S))\approx 0.4$. Our results also suggest that the $C=-$ states can be searched for in the ${\mu }^{+}{\mu }^{-}{\eta }_b(1S)$ and ${\mu }^{+}{\mu }^{-}{\eta }_b(2S)$ channels with the similar relative branching ratio $\mathcal{B}(X\to \mu \mu {\eta }_b(2S))/\mathcal{B}(X\to \mu \mu {\eta }_b(1S))\approx 0.4$. We also reanalyze the fully charm tetraquark states and study the $X(6900)$ decay into the $J/\psi \psi (2S)$ channel to obtain the relative branching ratio $\mathcal{B}(X\to J/\psi \psi (2S))/\mathcal{B}(X\to J/\psi J/\psi )\approx 0.1$.

A measurement of the $CP$-even fraction of the decay $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is performed with a quantum-correlated $\psi (3770)\to D\overline{D}$ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of $2.93{\mathrm{fb}}^{-1}$. Using a combination of $CP$ eigenstates, $D\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $D\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ as tagging modes, the $CP$-even fraction is measured to be $F_{+}^{4\pi }=0.735\pm 0.015\pm 0.005$, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa matrix with $B^{\pm }\to D{K}^{\pm }$ decays, and for time-dependent studies of $CP$ violation and mixing in the $D^0\text{−}{\overline{D}}^0$ system.

We search for stochastic gravitational wave background emitted from cosmic strings using the Parkes Pulsar Timing Array data over 15 years. While the common power-law excess revealed by several pulsar timing array experiments might be accounted for by the gravitational wave background from cosmic strings, the lack of the characteristic Hellings-Downs correlation cannot establish its physical origin yet. The constraints on the cosmic string model parameters are thus derived with the conservative assumption that the common power-law excess is due to unknown background. Two representative cosmic string models with different loop distribution functions are considered. We obtain constraints on the dimensionless string tension parameter $G\mu <{10}^{-11}–{10}^{-10}$, which is more stringent by two orders of magnitude than that obtained by the high-frequency LIGO-Virgo experiment for one model, and less stringent for the other. The results provide the chance to test the grand unified theories, with the spontaneous symmetry breaking scale of $U(1)$ being two-to-three orders of magnitude below ${10}^{16}\mathrm{GeV}$. The pulsar timing array experiments are thus entirely complementary to the LIGO-Virgo experiment in probing the cosmic strings and the underlying beyond standard model physics in the early Universe.

We derive relativistic dissipative spin hydrodynamics from kinetic theory featuring a nonlocal collision term using the method of moments. In this framework, the components of the spin tensor are dynamical variables which obey relaxation-type equations. We find that the corresponding relaxation times are determined by the local part of the collision term, while the nonlocal part contributes to the Navier-Stokes terms in these equations of motion. The spin relaxation timescales are comparable to those of the usual dissipative currents. Finally, the Navier-Stokes limit of the Pauli-Lubanski vector receives contributions proportional to the shear tensor of the fluid, which implies that the polarization of hadrons observed in heavy-ion collisions is influenced by dissipative effects.

In the paper by de Oliveira, Mosna, Pitelli, and Richartz [Phys. Rev. D 104, 024036 (2021)], exact (not only conformally related) analog models for the Schwarzschild and Reissner-Nordström spacetimes were found. The background nonrelativistic fluid flow was sustained by an external body force which is not affected by the linearized fluctuations. Following a different route, by modeling the external force as the gradient of an external pressure, it was shown by Bilić [Phys. Rev. D 105, 064052 (2022)] that the speed of sound is significantly modified. This effective speed of sound turns out to be inconsistent with the continuity equation. In this Comment we analyze these two contradictory conclusions. We first show that the heuristic justification for the introduction of the external force via a variational principle given by Bilić is conceptually incorrect. Then, by adding the external force appropriately, we show that the conclusions by de Oliveira, Mosna, Pitelli, and Richartz remain valid.

We examine the structure of higher-derivative string corrections under a cosmological reduction and make connection to generalized geometry and $T$ duality. We observe that the natural $T$ duality quantities are a linear combination of the $B$ field and graviton, which readily appears in the torsionful connection, ${\mathrm{\Omega }}_{\pm }=\mathrm{\Omega }\pm \frac{1}{2}H$. We revisit the tree-level ${\alpha }^{\prime }{R}^2$ corrections to the bosonic and heterotic string using the ${\mathrm{\Omega }}_{\pm }$ framework. We then turn to the structure of the $T$ duality completion of tree-level ${\alpha }^{\prime 3}{R}^4$ in the type II string and validate results in literature obtained for the tree-level five-point contact terms of the form $H^2{R}^3$.

We present the Becchi-Rouet-Stora-Tyupin (BRST) formalism of a Weyl conformal gravity in Weyl geometry. Choosing the extended de Donder gauge-fixing condition (or harmonic gauge condition) for the general coordinate invariance and the new scalar gauge fixing for the Weyl invariance, we find that there is a Poincaré-like $IOSp(10|10)$ supersymmetry as in a Weyl invariant scalar-tensor gravity in Riemann geometry. We also point out that there is a gravitational conformal symmetry in quantum gravity although there is a massive Weyl gauge field as a result of spontaneous symmetry breakdown of Weyl gauge symmetry, and we account for how the gravitational conformal symmetry is spontaneously broken to the Poincaré symmetry. The corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also show the unitarity of the physical $S$-matrix on the basis of the BRST quartet mechanism in the case of an absence of anomalies.

We work perturbatively with an interacting quantum field theory comprised of two distinct scalar fields. In this theory, we introduce a sudden quench of the mass of one of the scalars at time $t_0$. Also, the quartic interaction between the two scalars is turned on at time $t_{\mathrm{in}}$. These break time-translation invariance. In this setup we examine the effects of the relative ordering of $t_0$ and $t_{\mathrm{in}}$ on composite operator mixing. We study how such operator mixing affects features of the scalar potential. We find that the late time effective potential can be sensitive enough to the quenches to trigger phase transitions.

For renormalizable theories with a single coupling constant regularized by higher derivatives we investigate the coefficients at powers of logarithms present in the renormalization constants assuming that divergences are removed by minimal subtractions of logarithms. According to this higher-derivatives and minimal-subtractions-of-logarithms ($\mathrm{HD}+\mathrm{MSL}$) renormalization prescription, the renormalization constants include only powers of $\ln \mathrm{\Lambda }/\mu$, where $\mathrm{\Lambda }$ and $\mu$ are the dimensionful regularization parameter and the renormalization point, respectively. We construct general explicit expressions for arbitrary coefficients at powers of this logarithm present in the coupling constant renormalization and in the field renormalization constant which relate them to the $\beta$-function and (in the latter case) to the corresponding anomalous dimension. To check the correctness, we compare the results with the explicit four-loop calculation made earlier for $\mathcal{N}=1$ supersymmetric quantum electrodynamics and (for the supersymmetric case) rederive a relation between the renormalization constants following from the Novikov, Shifman, Vainshtein, and Zakharov equation.

The relativistic spin-0 matter field is quantized in the background of a straight cosmic string with nonvanishing transverse size. The most general boundary condition ensuring the impenetrability of the matter field into the interior of the cosmic string is shown to be the Robin condition with a boundary parameter varying arbitrarily from point to point of the boundary. The role of the bound states in the spectrum of solutions to the Fock-Klein-Gordon equation is elucidated. We derive, in the general case, an analytic expression for the total magnetic flux, which is induced in the vacuum in the cosmic string background. Further numerical analysis and the requirement of physical plausibility are shown to restrict ambiguity, which is due to the boundary condition. The dependence of the induced vacuum magnetic flux on the string flux and tension, as well as on the transverse size of the string, is analyzed.

Discrete spacetime symmetries of parity $P$ or reflection $R$, and time reversal $T$, act naively as ${\mathbb{Z}}_2$ involutions in the passive transformation on the spacetime coordinates; but together with a charge conjugation $C$, the total $C\text{−}P\text{−}R\text{−}T$ symmetries have enriched active transformations on fields in representations of the spacetime-internal symmetry groups of quantum field theories (QFTs). In this work, we derive that these symmetries can be further fractionalized, especially in the presence of the fermion parity $(-1{)}^{\mathrm{F}}$. We elaborate on examples including relativistic Lorentz invariant QFTs (e.g., spin-$1/2$ Dirac or Majorana spinor fermion theories) and nonrelativistic quantum many-body systems (involving Majorana zero modes), and comment on applications to spin-1 Maxwell electromagnetism (QED) or interacting Yang-Mills (QCD) gauge theories. We discover various $C\text{−}P\text{−}R\text{−}T\text{−}(-1{)}^{\mathrm{F}}$ group structures, e.g., Dirac spinor is in a projective representation of ${\mathbb{Z}}_2^C\times {\mathbb{Z}}_2^P\times {\mathbb{Z}}_2^T$ but in an (anti)linear representation of an order-16 non-Abelian finite group, as the central product between an order-8 dihedral (generated by $C$ and $P$) or quaternion group and an order-4 group generated by $T$ with $T^2=(-1{)}^{\mathrm{F}}$. The general theme may be coined as $C\text{−}P\text{−}T$ or $C\text{−}R\text{−}T$ fractionalization.

Using self-force methods, we consider the hyperbolic-type scattering of a pointlike particle carrying a scalar charge $Q$ off a Schwarzschild black hole. For given initial velocity and impact parameter, backreaction from the scalar field modifies the scattering angle by an amount $\propto Q^2$, which we calculate numerically for a large sample of orbits (neglecting the gravitational self-force). Our results probe both strong-field and field-weak scenarios, and in the latter case we find a good agreement with post-Minkowskian expressions. The scalar-field self-force has a component tangent to the four-velocity that exchanges particle’s mass with scalar-field energy, and we also compute this mass exchange as a function along the orbit. The expressions we derive for the scattering angle (in terms of certain integrals of the self-force along the orbit) can be used to obtain the gravitational self-force correction to the angle in the physical problem of a binary black hole with a large mass ratio. We discuss the remaining steps necessary to achieve this goal.

We investigate the Hamilton-Jacobi equation of a probe particle moving on $d$-dimensional generalized Lense-Thirring metric. This spacetime is different from the slowly rotating Myers-Perry black hole at second order in rotation parameters. We show that the dynamics of the probe particle along the timelike geodesic of the generalized Lense-Thirring spacetime is superintegrable and has more constants of motion with respect to the same dynamics on Myers-Perry black hole. We also discuss the second rank Killing tensors associated with the generalized Lense-Thirring metric.

As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BHs). The coupling function that defines the theory is the main character in the process and nature of scalarization. With the right choice, the theory becomes an extension of general relativity (GR) in the sense any solution to the GR field equations remains a solution in the EsGB theory, but it can destabilize if a certain threshold value of the spacetime curvature is exceeded. Thus BHs can spontaneously scalarize. The most studied driving mechanism to this phenomenon is a tachyonic instability due to an effective negative squared mass for the scalar field. However, even when the coupling is chosen such that this mass is zero, higher order terms with respect to the scalar field can lead to what is coined nonlinear scalarization. In this paper we investigate how Kerr BHs spontaneously scalarize by evolving the scalar field on a fixed background via solving the nonlinear Klein-Gordon equation. We consider two different coupling functions with higher order terms, one that yields a nonzero effective mass and another that does not. We sweep through the Kerr parameter space in its mass and spin and obtain the scalar charge by the end of the evolution when the field settles in an equilibrium stationary state. When there is no tachyonic instability present, there is no probe limit in which the BH scalarizes with zero charge, i.e., there is a gap between bald and hairy BHs and they only connect when the mass goes to zero together with the charge.

The mode stability of the Kerr black hole in four dimensions was demonstrated by Whiting in 1989, by separating the Teukolsky equation that describes gravitational perturbations and then transforming the radial and angular equations in such a way that the problem can be reformulated as a wave equation in an auxiliary spacetime in which the proof of stability is greatly simplified, owing to the absence of an ergoregion. As a preliminary step towards extending these ideas to higher-dimensional black holes, we study the mode stability of the massless scalar wave equation in the five-dimensional black hole solutions of Einstein gravity and supergravity. We show how the wave equation can again be mapped into one in an auxiliary spacetime in which there is no ergoregion, allowing us to give a proof of the mode stability of the solutions of the scalar wave equation.

We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $\mathrm{\Lambda }\mathrm{CDM}$ model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=\lambda =0.1$) can be achieved in the case of D-term inflation on the brane.