We study the mesonic nonlinear (NL) interaction equation of state (EOS) employing the relativistic mean-field model and investigate the effect of the $\sigma$-cut potential (NL-$\sigma$ cut) and dark matter (NL DM) on the nonradial and radial oscillation modes of neutron stars. For the NL-$\sigma$ cut, we include the $\sigma$-cut potential $U_{\mathrm{cut}}(\sigma )$ to study its effect. For dark matter, we use the neutron decay anomaly model. For each model, we investigate two extreme EOSs, stiff and soft, that cover the entire allowed parameter range from the given model, consistent with the current astrophysical constraints. The EOS and the stellar properties, such as mass and radius, are calculated, and the effect of the $\sigma$ cut and DM is discussed. Both nonradial and radial oscillation modes are computed in the general relativistic framework. We study the nonradial $f$ and $p_1$ mode frequency, damping time, and some quasiuniversal relations connecting the frequencies of the $f$ mode to the average density and compactness. The analysis shows that the $f$ and $p_1$ mode frequencies at both $1.4M_{\odot }$ and the maximum mass configuration are higher in the NL-DM model compared to the NL and NL-$\sigma$ models. The consistent alignment between our prior parametrizations and current calculations strongly supports the existence of quasiuniversal relations that hold true irrespective of the particular matter components involved. For the radial oscillations, we compute 10 lowest-order modes ($f$, $p$) and study the radial perturbations as well as the large frequency separation with the NL-$\sigma$ cut and NL-DM EOS, showing that the microphysics involved in the NS EOS is imprinted on the frequency separation between different nodes.

The neutron star starts to cool down shortly after its birth by emitting neutrinos. As it becomes cold enough, the Cooper pairs of neutrons are formed, triggering a superfluid transition. Previous studies on neutron superfluidity focused on finite-temperature transitions, with little attention paid to the potentially important quantum critical phenomena associated with superfluidity. Here, we provide the first theoretical analysis of superfluid quantum criticality, concentrating on its impact on neutron star cooling. Extensive calculations found that superfluidity occurs within a finite range of neutron star density $\rho$. The density serves as a nonthermal parameter for a superfluid quantum phase transition. In a broad quantum critical region, gapless neutrons are strongly coupled to the quantum critical fluctuations of the superfluid order parameter. We handle this coupling using both perturbation theory and renormalization group methods and find that it leads to non-Fermi liquid behavior, which yields a logarithmic $T\ln (1/T)$ correction to the neutron specific heat $c_{\mathrm{n}}\propto T$ and also dramatically alters the neutrino emissivity. Quantum critical phenomena emerge much earlier than the onset of superfluidity and persist throughout almost the entire lifetime of a neutron star. At low temperatures, these phenomena coexist with superfluidity in the neutron star interior but occupy different layers. We incorporate superfluid quantum criticality into the theoretical description of neutron star cooling and show that it substantially prolongs the thermal relaxation time. By varying the strength of superfluid fluctuations and other quantities, we obtain an excellent fit to the observed cooling data of a number of neutron stars. Our results indicate an intriguing correlation between superfluid quantum criticality and the thermal evolution of neutron stars.

Short-period Galactic double white dwarf (DWD) systems will be observable both in visible light through photometric monitoring and in mHz-range gravitational waves (GWs) with forthcoming space-based laser interferometry such as the Laser Interferometer Space Antenna. When only photometric variability is used to measure DWD intrinsic properties, there is a degeneracy between the chirp mass and binary tidal interaction, as the orbital frequency time derivative is set by both GW radiation and tides. Without expensive radial velocity data from spectroscopic monitoring, this degeneracy may be lifted in principle by directly measuring the second time derivative of the orbital frequency through photometric monitoring over an ultralong time baseline. Alternatively, the degeneracy can be removed by exploiting information in both photometric variability and the coherent GW waveform. Investigating both approaches, we find that direct measurement of the second time derivative is likely infeasible for most DWDs, while the multimessenger method will disentangle measurements of the chirp mass and the binary moments of inertia for a large sample of tidally locked systems. The latter information will enable empirical tests of white dwarf structure models with finite temperature effects.

Motivated by two new states $h_1(1911)$ and $X(2300)$ observed by BESIII, we have investigated the mass spectrum and the strong decay properties of the strangeonium mesons within the modified Godfrey-Isgur model by considering the screening effects. We have determined the free parameters using the masses and widths of the well-established $s\overline{s}$ states $\varphi (1020)$, $\varphi (1680)$, $h_1(1415)$, $f_2^{\prime }(1525)$, and ${\varphi }_3(1850)$. According to our results, $h_1(1911)$ and $X(2300)$ could be well explained as $h_1(2^1{P}_1)$ and $h_1(3^1{P}_1)$ $s\overline{s}$ states, respectively. Meanwhile, the possible assignments of $X(2000)$, ${\eta }_2(1870)$, and $\varphi (2170)$ as $3^3{S}_1$, $1^1{D}_2$, and $2^3{D}_1$ are also discussed. Furthermore, the masses and widths of the $2S$, $3S$, $1P$, $2P$, $3P$, $1D$, and $2D$ $s\overline{s}$ states are also given and compared with various theoretical predictions, which will be helpful for the observations and confirmations of these states in the future.

We investigate the sensitivity of future high-energy muon colliders to heavy Majorana neutrinos, considering both opposite-sign (${\mu }^{+}{\mu }^{-}$) and same-sign (${\mu }^{+}{\mu }^{+}$) collision modes. We focus on ${\mu }^{+}{\mu }^{-}$ colliders operating at center-of-mass energies of 1, 3, and 10 TeV, as well as the proposed $\mu \mathrm{TRISTAN}$ facility at 2 TeV, and we analyze the production of heavy neutrinos via vector boson fusion in the $t$-channel, a mechanism that becomes dominant in the multi-TeV regime. We evaluate its exclusion potential in terms of the heavy neutrino mass and the mixing of the heavy neutrino with its Standard Model counterparts, using both cut-based selections and boosted decision trees trained to exploit the distinct kinematic signatures of heavy Majorana neutrino exchanges. Our results demonstrate the complementarity between collider configurations and show that active-sterile mixing angles as small as 0.001 could be probed for neutrino masses up to 100 TeV, an experimentally inaccessible region of the parameter space at current facilities. Altogether, this work establishes the discovery potential of muon colliders for testing super-heavy Majorana neutrinos, complementary to conventional probes, and provides compelling motivation for the next generation of high-energy lepton colliders.

Axionlike particles (ALPs) are hypothetical particles that serve as promising candidates for cold dark matter. Portals like inelastic axion scattering and axion propagated force have been employed to search for the upper limit of the ALPs’ coupling with standard model particles. Other methods, like the axion-fermion interaction in the CASPEr experiment, integrate the dark matter motion into the measurement. We suggest a new method for detecting dark matter axions based on axion-electron elastic scattering. In the pseudoscalar axion model, this interaction can be seen as an effective magnetic field, so high-sensitivity atomic magnetometers can be utilized to measure this interaction. The scattering cross section of this process is significantly amplified by the high number density and occupation number of axion dark matter. The upper limit of the electron-axion coupling coefficient obtained from this process can reach two orders of magnitude higher than previous results at low axion mass, and will exceed the astrophysics limits by using a developing magnetometer. This scattering process also provides an efficient way to detect local structures of dark matter.

The radiative seesaw model with gauged ${\mathrm{U}(1)}_{B-L}\times {\mathbb{Z}}_2$ extension is a well-motivated scenario that gives consistent predictions of active neutrino masses and the abundance of dark matter. Majorana masses of right-handed neutrinos, the lightest of which can be identified as dark matter, are given by the spontaneous breaking of the ${\mathrm{U}(1)}_{B-L}$ gauge symmetry. We revisit this model with the latest constraints from dark-matter searches, neutrino oscillations, flavor experiments, and collider experiments. We examine several benchmark scenarios and identify the valid parameter space of this model, finding that there are still allowed regions under the latest experimental constraints. We present new viable benchmark scenarios for this model, i.e., the right-handed neutrino dark-matter scenario and the scalar dark-matter scenario. We also mention the testability of these benchmark scenarios in future experiments.

The singlet-doublet model is an economical model of weakly interacting dark matter. We revisit it in light of improved dark matter direct detection limits. We characterize the now well-defined regions of remaining parameter space with suppressed direct detection cross sections and discuss features of the spectrum accessible at the Large Hadron Collider. We discuss when and how parameters in these special regions might be realized as the result of renormalization group evolution when starting with generic ultraviolet initial conditions.

We present a lattice QCD calculation of the pion scalar form factor and associated radii with fully controlled systematics. Lattice results are computed on a large set of 17 gauge ensembles with $N_f=2+1$ Wilson Clover-improved sea quarks. These ensembles cover four values of the lattice spacing between $a=0.049\mathrm{fm}$ and $a=0.086\mathrm{fm}$, a pion mass range of 130–350 MeV, and various physical volumes. A precise determination of the notorious quark-disconnected contributions facilitates an unprecedented momentum resolution for the form factor, particularly on large and fine ensembles in the vicinity of physical quark mass. A large range of source-sink separations $1.0\mathrm{fm}\lesssim t_{\mathrm{sep}}\lesssim 3.25\mathrm{fm}$ is used to reliably extract the relevant ground state matrix elements at vanishing and nonvanishing momentum transfer. This allows us for the first time to obtain the scalar radii from a $z$-expansion parametrization of the $Q^2$ dependence of the resulting form factors rather than a simple, linear approximation at small momentum transfer. The physical extrapolation for the radii is carried out using three-flavor NLO chiral perturbation theory to parametrize the quark mass dependence in terms of three low-energy constants, including the first lattice determination of $L_4^r$. Systematic uncertainties on the final results related to the ground state extraction, form factor parametrization as well as the physical extrapolation are accounted for via model averages based on the Akaike information criterion. Our physical results for the pion singlet and octet scalar radii are $⟨r_S^2{⟩}_{\pi }^0=0.550(32{)}_{\mathrm{stat}}(39{)}_{\mathrm{sys}}[50{]}_{\text{total}}{\mathrm{fm}}^2$ and $⟨r_S^2{⟩}_{\pi }^8=0.443(16{)}_{\mathrm{stat}}(45{)}_{\mathrm{sys}}[47{]}_{\text{total}}{\mathrm{fm}}^2$, respectively. The values of the relevant low energy constants are given by $f_0=116.5(5.5{)}_{\mathrm{stat}}(13.7{)}_{\mathrm{sys}}[14.8{]}_{\text{total}}\mathrm{MeV}$, $L_4^r(\mu =770\mathrm{MeV})=+0.38(09{)}_{\mathrm{stat}}(15{)}_{\mathrm{sys}}[18{]}_{\text{total}}\times {10}^{-3}$ and $L_5^r(\mu =770\mathrm{MeV})=+0.58(0.38{)}_{\mathrm{stat}}(1.08{)}_{\mathrm{sys}}[1.14{]}_{\text{total}}\times {10}^{-3}$. For the light quark contribution to the pion scalar radius, we obtain $⟨r_S^2{⟩}_{\pi }^l=0.515(28{)}_{\mathrm{stat}}(32{)}_{\mathrm{sys}}[43{]}_{\text{total}}{\mathrm{fm}}^2$, resulting in a value of ${\overline{\ell }}_4=3.99(15{)}_{\mathrm{stat}}(17{)}_{\mathrm{sys}}[23{]}_{\text{total}}$ for the pertinent low-energy constant in two-flavor chiral perturbation theory.

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these nonperturbative functions are generated through fits to global data. A problem that several PDF fitting groups encounter is the presence of tension in datasets that appear to pull the fits in different directions. In other words, the best fit depends on the choice of dataset. Several methods to capture the uncertainty in PDFs in presence of seemingly inconsistent fits have been proposed and are currently in use. These methods are important to ensure that uncertainty in PDFs are not underestimated. Here we propose a novel method for estimating the uncertainty by introducing a generalized statistical model based on Bayesian hierarchical models, which is implemented via the Gaussian Mixture Model (GMM). The methodology is inspired by unsupervised machine learning techniques and is closely related to the statistical methods of ensemble learning and Bayesian model averaging. Using a toy model of PDFs, we demonstrate how the GMM can be used to faithfully reconstruct the likelihood associated with PDF fits, which can in turn be used to accurately determine the uncertainty on PDFs, especially in the presence of tension in the fitted datasets. We further show how this statistical model reduces to the usual ${\chi }^2$ likelihood function for a consistent dataset and provide measures to optimize the number of Gaussians in the GMM.

In this work, we systematically study the interactions of the $S$-wave $D^{(*)}{\overline{B}}^{(*)}$ systems within the framework of chiral effective field theory in heavy hadron formalism. We calculate the $D^{(*)}{\overline{B}}^{(*)}$ effective potentials up to next-to-leading order, explore the bound state formations, and investigate the $D^{(*)}{\overline{B}}^{(*)}$ scattering properties, such as scattering rate, scattering length, and effective range. Our results show that all $I=1$ $D^{(*)}{\overline{B}}^{(*)}$ potentials are repulsive, preventing the formation of bound states, while the $I=0$ potentials are generally attractive. Specifically, we get two important observations: first, the shallow bound state is more likely to exist in the $D\overline{B}[I(J^P)=0(0^{+})]$ system than in the $D{\overline{B}}^{*}[I(J^P)=0(1^{+})]$ system; second, $D^{*}{\overline{B}}^{*}[I(J^P)=0(0^{+})]$ and $D^{*}{\overline{B}}^{*}[I(J^P)=0(1^{+})]$ systems possess relatively large binding energies and positive scattering lengths, which suggests strong bound state formations in these channels. So, the attractions in the $D^{*}{\overline{B}}^{*}[I=0]$ systems are deeper than those in the $D{\overline{B}}^{(*)}[I=0]$ systems, thus we strongly recommend the future experiment to search for the $D^{*}{\overline{B}}^{*}[I=0]$ tetraquark systems. We also investigate the coupled-channel effects on the $J=0,1$ systems and conclude that the inclusion of the coupled channels introduces small but visible influences. In addition, we also investigate the dependencies of the $D{\overline{B}}^{(*)}$ binding energies on the contact low-energy coupling constants.

In this work we compute the branching fraction of $B\to D^{(*)}\tau {\nu }_{\tau }$ and $B_s\to D_s^{(*)}\tau {\nu }_{\tau }$ within the relativistic independent quark model, emphasizing the harmonic potential model-dependent analysis of these decay channels in the precision flavor physics era. Considering the experimental observation of longitudinal $\tau$-polarization and fraction of longitudinal polarization at LHCb and Belle, we have also investigated these observables within our model framework which are aligning well with the standard model expectations. We perform a comprehensive analysis of the form factors across the whole accessible kinematic range of $q^2$. Our results are consistent and compatible with other theoretical approaches as well as with the experimental measurements. Furthermore, we evaluated the clean ratios of $B_s$ to $B_0$ in the semimuonic mode that are in accordance with the LHCb measurements, and support the validity of the SU(3) flavor symmetry. Although the concept of new physics is facing a significant challenge at the current TeV scale, semileptonic $B$ decays, nevertheless, always serve as a valuable probe to study the decay dynamics.

The black hole information paradox has been an important problem in quantum gravity. In the study of evaporating black hole, it has been proposed that the holographic map between the semiclassical effective description in bulk and the fundamental description in boundary cannot be isometric. In this work, we would like to study the reflected entropy in an evaporating black hole model through a nonisometric holographic map. We assume that the evaporating is slow enough that it makes sense to ascribe a slowly varying temperature to the Hawking radiation. We then introduce a two-sided black hole model to canonically purify the semiclassical state. The holographic map to the fundamental description is nonisometric and defined by a Haar random unitary matrix. We show that the entropy of radiation in the model computed in the fundamental description matches the result read from the quantum extremal surface formula and agrees with the Page curve. Furthermore, through a nonisometric holographic map, we study the reflected entropies between different regions, including the one between the black holes on different sides, the one between the radiations distributed symmetrically but disconnectedly, and the one between the black hole and the radiation on a single side. Our results are consistent with the existing ones based on the effective descriptions.

Starobinsky gravity, as one of the simplest and best-behaved higher-curvature gravity theories, has been extensively studied in the context of neutron stars over the past few decades. In this work, we investigate the adiabatic radial oscillation stability of neutron stars within the framework of Starobinsky gravity. We find that gravitational modifications can significantly impact stellar stability. Specifically, the higher-derivative nature of the theory causes the exterior spacetime to dynamically respond to fluid oscillations, in contrast to general relativity where Birkhoff’s theorem ensures a static exterior. For stellar models with low central densities, the fundamental frequency becomes nearly independent of the central density when the coupling constant is large. For stellar models with high central densities, the transition from stability to instability still approximately occurs near the maximum-mass configuration, similar to the case in general relativity. Our main analysis is conducted in the Jordan frame of the scalar-tensor gravity equivalent to Starobinsky gravity, and we explicitly verify consistency with results obtained in the Einstein frame. We further extend our study to a class of Gauss-Bonnet extensions of Starobinsky gravity.

We investigate the spectral behavior of scalar fluctuations generated by gravity during inflation and the subsequent reheating phase. We consider a nonperturbative Bogoliubov treatment within the context of pure gravitational reheating. We compute both long- and short-wavelength spectra, first for a massless scalar field, revealing that the spectral index in part of the infrared (IR) regime varies between $-6$ and $-3$, depending on the postinflationary equation of state (EoS), $0\le w_{\varphi }\le 1$. Furthermore, we study the mass-breaking effect of the IR spectrum by including the finite mass, $m_{\chi }$, of the daughter scalar field. We show that for $m_{\chi }/H_{\mathrm{e}}\gtrsim 3/2$, where $H_{\mathrm{e}}$ is the Hubble parameter during inflation, the IR spectrum of scalar fluctuations experiences exponential mass suppression, while for smaller masses, $m_{\chi }/H_{\mathrm{e}}<3/2$, the spectrum remains flat in the IR regime regardless of the postinflationary EoS. For any general EoS, we also compute a specific IR scale, $k_m$, of fluctuations below which the IR spectrum will suffer from this finite mass effect. In the UV regime, oscillations of the inflaton background lead to interference terms that explain the high-frequency oscillations in the spectrum. Interestingly, we find that for any EoS, $1/9\lesssim w_{\varphi }\lesssim 1$, the spectral behavior turns out to be independent of the EoS, with a spectral index $-6$. We have compared this Bogoliubov treatment for the UV regime to perturbative computations with solutions to the Boltzmann equation and found an agreement between the two approaches for any EoS, $0\lesssim w_{\varphi }\lesssim 1$. We also explore the relationship between the gravitational reheating temperature and the reheating EoS employing the nonperturbative analytic approach, finding that reheating can occur for $w_{\varphi }\gtrsim 0.6$.

$R$-modes are oscillations in rotating stars, primarily restored by the Coriolis force. Among stellar oscillations, they are the most susceptible to the Chandrasekhar-Friedman-Schutz (CFS) instability driven by gravitational wave emission, making them promising targets for current and future gravitational wave searches. The development of this instability, however, requires it to overcome dissipative processes within the star. As a result, $r$-modes become unstable only for certain combinations of stellar angular velocity $\mathrm{\Omega }$ and (redshifted) temperature $T^{\infty }$, defining the so-called instability window on the $(\mathrm{\Omega },T^{\infty })$ plane. At high temperatures, bulk viscosity $\zeta$, arising from out-of-equilibrium chemical reactions, is the dominant dissipative mechanism suppressing the CFS instability. Dissipation due to $\zeta$ can be greatly enhanced by two independent mechanisms: (1) the presence of hyperons, which significantly increases the bulk viscosity, and (2) the distinctive properties of relativistic $r$-modes in nonbarotropic matter, which further amplify dissipation beyond Newtonian predictions. In this work, we present the first investigation of the combined impact of these two mechanisms on $r$-mode instability windows. Our calculations also account for the fact that chemical reactions modify the adiabatic index, in addition to producing bulk viscosity. We further estimate the influence of nucleon superconductivity and superfluidity on the instability windows. By comparing our predictions with recent observations of neutron stars in low-mass x-ray binaries, we find that bulk viscosity in hyperonic matter may provide the necessary dissipation to stabilize $r$-modes in the fastest-spinning and moderately hot stars, even when nucleon superfluidity and superconductivity are taken into account. These results have important implications for the interpretation of observations and for the broader understanding of relativistic $r$-mode physics.

This work investigates the discovery potential for singly produced vectorlike quarks (VLQs) $T$ ($Q=+2/3e$) and $Y$ ($Q=-4/3e$) decaying to $Wb$ at future $\mu p$ colliders with $\sqrt{s}=5.29$, 6.48, and 9.16 TeV, analyzing both leptonic and hadronic $W$ decay channels through detailed detector simulations. The hadronic channel demonstrates superior sensitivity, enabling $5\sigma$ discovery up to $m_T=3750\mathrm{GeV}$ ($m_Y=4100\mathrm{GeV}$) at 9.16 TeV with $100{\mathrm{fb}}^{-1}$, while exclusion limits reach $m_T=4500\mathrm{GeV}$ ($g^{*}\ge 0.06$) and $m_Y=4800\mathrm{GeV}$ (${\kappa }_Y\ge 0.04$)—significantly beyond LHC capabilities. At 5.29 TeV, discovery regions cover $g^{*}\in [0.15,0.5]$ for $m_T\in [1500,2520]\mathrm{GeV}$ and ${\kappa }_Y\in [0.12,0.5]$ for $m_Y\in [1700,2700]\mathrm{GeV}$, with exclusions extending to $m_T=2750\mathrm{GeV}$ and $m_Y=3020\mathrm{GeV}$. These results, obtained within a simplified two-parameter framework ($m_{T/Y}$ and electroweak couplings $g^{*}$), establish $\mu p$ colliders as uniquely powerful tools for probing high-mass VLQ states, particularly in the boosted jet regime.

Left-right symmetric models which employ a generalized seesaw mechanism to generate quark and charged lepton masses are known to solve the strong $CP$ problem via parity symmetry, without the need for the axion. These models lead to naturally light Dirac neutrinos with their masses arising through radiative corrections. In this work, we show how baryogenesis via Dirac leptogenesis can be implemented in this framework. A pair of left-right symmetric scalar doublets ${\varphi }_{L,R}$ carrying ($B-L$) charge of 3 is introduced for this purpose, which preserves the parity solution to the strong $CP$ problem. Small neutrino masses are generated through one-loop diagrams mediated by these scalars. The decay of vectorlike leptons ($E_i$) involved in the seesaw mechanism to generate charged lepton masses, $E_i\to {\overline{\nu }}_{jR}{\varphi }_R^{-}$, creates a right-handed neutrino (${\nu }_R$) asymmetry, while preserving total lepton number. The compensating lepton asymmetry is converted to baryon asymmetry via electroweak sphalerons. We show that for a large range of model parameters successful baryogenesis can be realized, with the $W_R^{\pm }$ gauge boson mass of order ${10}^{11}\mathrm{GeV}$.

The IceCube Upgrade will provide unprecedented sensitivity to dark matter particles annihilating in the core of the Sun. For dark matter candidates with spin-dependent couplings to nuclei and that annihilate significantly to tau leptons or neutrinos, we find that the IceCube Upgrade will be capable of testing parameter space that is beyond the reach of existing direct detection experiments. After calculating the sensitivity of the IceCube Upgrade to dark matter annihilation in the Sun, we explore dark matter models that could be tested by this experiment, identifying two classes of scenarios as promising targets for such searches.

All charmless $B\to PV{\ell }^{+}{\nu }_{\ell }$ ($P$ denotes the light pseudoscalar meson and $V$ denotes the vector meson) decays have not been experimentally observed to date, but some of them might be measured in the near future. The charmless $B\to PV{\ell }^{+}{\nu }_{\ell }$ decays with the axial-vector ($A$) resonance states, the tensor ($T$) resonance states, and the excited vector ($V_{E,D}$) resonance states are studied based on flavor SU(3) analysis in this work, where $V_E$ contains $\{\rho (1450),K^{*}(1410),\omega (1420),\varphi (1680)\}$ with quantum numbers $n^{2S+1}{L}_J=2^3{S}_1$ and $V_D$ contains $\{\rho (1700),K^{*}(1680),\omega (1650),\varphi (2170)\}$ with quantum numbers $n^{2S+1}{L}_J=1^3{D}_1$. The hadronic amplitudes of the $B\to A/T{\ell }^{+}{\nu }_{\ell }$ decays are related by the nonperturbative parameters, and the branching ratio predictions of $B\to A/T/V_{E,D}{\ell }^{+}{\nu }_{\ell }$ are obtained, and then the branching ratios of the $B\to A(A\to PV){\ell }^{+}{\nu }_{\ell }$, $B\to T(T\to PV){\ell }^{+}{\nu }_{\ell }$, $B\to V_E(V_E\to PV){\ell }^{+}{\nu }_{\ell }$, and $B\to V_D(V_D\to PV){\ell }^{+}{\nu }_{\ell }$ are obtained by the narrow width approximation or further considering the width effects. We find that most branching ratios of the $B\to A{\ell }^{+}{\nu }_{\ell }$ decays and many branching ratios of the $B\to A(A\to PV){\ell }^{+}{\nu }_{\ell }$ decays are on the order of $\mathcal{O}({10}^{-4}–{10}^{-3})$, and all branching ratios with the tensor resonance states and the excited vector resonance states are small. Our results could be tested in the future Belle II and LHCb experiments.