Stimulated by the $D_2^{*}(3000)$ recently observed by LHCb, we study the decay behaviors of the $3P$ and $2F$ charmed mesons. Comparing the masses and decay properties of the $3{{}^{3}P}_2$ and $2{{}^{3}F}_2$ with the observed $D_2^{*}(3000)$, we conclude that the most probable assignment is the $3{{}^{3}P}_2$, while the assignment of the $2{{}^{3}F}_2$ may not be fully excluded. The results of the unobserved $3P$ and $2F$ charmed mesons in this work may provide some fundamental information when further searching for these charmed mesons in the experiments by LHCb and the forthcoming Belle II.

We calculate the rho meson mass in a weak magnetic field using effective $\rho \pi \pi$ interaction. It is seen that both ${\rho }^0$ and ${\rho }^{\pm }$ masses decrease with the magnetic field in vacuum. The $\rho$ meson dispersion relation has been calculated and shown to be different for ${\rho }^0$ and ${\rho }^{\pm }$. We also calculate the $\rho \pi \pi$ decay width and spectral functions of ${\rho }^0$ and ${\rho }^{\pm }$. The width is seen to decrease with $eB$ and the spectral functions become narrower.

We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: we propose an Ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity $\sigma$ and the second-order transport coefficient ${\tau }_J$.

We study the masses of open charm and bottom tetraquark states within the diquark-antidiquark scenario in the relativized quark model proposed by Godfrey and Isgur. The diquark and antidiquark masses are first solved by relativized quark potential, and then treated as the usual antiquark and quark, respectively. The masses of tetraquark states are obtained by solving the Schrödinger-type equation between the new diquark and antidiquark. We find the masses of $sq\overline{b}\overline{q}$ tetraquark configuration are much higher than that of $X(5568)$. This conclusion disfavors the possibility of $X(5568)$ as a tetraquark state within the diquark-antidiquark scenario. Further experimental searches are needed to clarify the nature of the signal observed by the D0 Collaboration.

We study the semiclassical interpretation of the $x^3$ and $x^4$ moments of twist-3 parton distribution functions (PDFs). While no semiclassical interpretation for the higher moments of $g_T(x)$ and $e(x)$ was found, the $x^3$ moment of the chirally odd spin-dependent twist-3 PDF $h_L^3(x)$ can be related to the longitudinal gradient of the transverse force on transversely polarized quarks in longitudinally polarized nucleons in a deep-inelastic scattering experiment. We discuss how this result relates to the torque acting on a quark in the same experiment. This has further implications for comparisons between the Jaffe-Manohar and the Ji decompositions of the nucleon spin.

In this work, we study the hadronic loop contribution to the $\mathrm{\Upsilon }(5S)\to \mathrm{\Upsilon }(1^3{D}_J)\eta$ ($J=1$, 2, 3) transitions. We predict that the branching ratios of $\mathrm{\Upsilon }(5S)\to \mathrm{\Upsilon }(1^3{D}_1)\eta$, $\mathrm{\Upsilon }(5S)\to \mathrm{\Upsilon }(1^3{D}_2)\eta$, and $\mathrm{\Upsilon }(5S)\to \mathrm{\Upsilon }(1^3{D}_3)\eta$ can reach up to $(0.5–5.1)\times {10}^{-3}$, $(0.7–7.5)\times {10}^{-3}$ and $(0.9–9.6)\times {10}^{-4}$, respectively. Since these predicted hadronic transitions of $\mathrm{\Upsilon }(5S)$ are comparable with these observed $\mathrm{\Upsilon }(5S)\to \mathrm{\Upsilon }(nS){\pi }^{+}{\pi }^{-}$ ($n=1$, 2, 3), we suggest for future experiments like Belle and BelleII to carry out the search for these anomalous $\mathrm{\Upsilon }(5S)\to \mathrm{\Upsilon }(1^3{D}_J)\eta$ transitions.

Models beyond the standard model with extra scalars have been highly motivated by the recent discovery of the Higgs boson. The two Higgs doublet model type III considers the most general case for the scalar potential, allowing mixing between neutral $CP$-even and $CP$-odd scalar fields. This work presents the results of the study on the $t\to c\gamma$ decay at one loop level if neutral flavor changing is generated by top-charm-Higgs coupling given by the Yukawa matrix. For instance, a value for the branching ratio $\mathrm{Br}(t\to c\gamma )\sim {10}^{-6}$ for $\tan \beta =2.5$ and general neutral Higgs mixing parameters, $1.16\le {\alpha }_1\le 1.5$, $-0.48\le {\alpha }_2\le -0.1$. The number of events for the $t\to c\gamma$ decay with an integrated luminosity of $300{\mathrm{fb}}^{-1}$ is estimated as $10\lesssim N_{\mathrm{Eff}}\lesssim 100$ for the parameters of the model constrained by experimental data.

We investigate the numerical values of the low-energy constants in the chiral effective Lagrangian for the interactions between the charmed mesons and the lightest pseudoscalar mesons, the Goldstone bosons of the spontaneous breaking of chiral symmetry for QCD. This problem is tackled from two sides: estimates using the resonance-exchange model and positivity constraints from the general properties of the $S$-matrix including analyticity, crossing symmetry, and unitarity. These estimates and constraints are compared with the values determined from fits to lattice data of the scattering lengths. Tensions are found, and possible reasons are discussed. We conclude that more data from lattice calculations and experiments are necessary to fix these constants better. As a byproduct, we also estimate the coupling constant $g_{DD{a}_2}$, with $a_2$ the light tensor meson, via the QCD sum rule approach.

We study the phase-space distributions of gluons inside a nucleon/nucleus in the small-$x$ regime including the gluon saturation effect. This can be done by using the relation between the gluon Wigner distribution and the dipole S matrix at small $x$, which latter satisfies the Balitsky-Kovchegov (BK) equation. By efficiently solving the BK equation with impact parameter dependence, we compute the Wigner, Husimi and generalized transverse momentum dependent distributions in the saturation regime. We also investigate the elliptic angular dependence of these distributions which has been recently shown to be measurable in DIS experiments.

Motivated by recent measurements of the radiative decay rates of the $P$-wave spin singlet charmonium $h_c$ to the light meson $\eta$ or ${\eta }^{\prime }$ by the BESIII Collaboration, we investigate the decay rates of these channels at order $\alpha {\alpha }_s^4$. The photon is radiated mainly from charm quark pairs in the lowest-order Feynman diagrams, because the diagrams where a photon radiated from light quarks are suppressed by ${\alpha }_s$ or the relative charm quark velocity $v$, due to charge-parity conservation. The form factors of two gluons to $\eta$ or ${\eta }^{\prime }$, which are the major mechanism for $\eta$ and ${\eta }^{\prime }$ production, are employed. $\eta ({\eta }^{\prime })$ is treated as a light-cone object when we consider that the parent charmonium mass is much heavier than that of the final light meson. We obtain the branching ratio $\mathcal{B}(h_c\to \gamma {\eta }^{\prime })=(1.94_{-0.51}^{+0.70})\times {10}^{-3}$ in the nonrelativistic QCD approach, which is in agreement with the BESIII measurement. The prediction of the branching ratio of $h_c\to \gamma \eta$ is also within the range of experimental error after including the larger uncertainty of the total decay width ${\mathrm{\Gamma }}_{h_c}$. The applications of these formulas to the radiative decays to $\eta ({\eta }^{\prime })$ of the $P$-wave spin singlet bottomonium $h_b(nP)$ are presented. These studies will shed some light on the $\eta -{\eta }^{\prime }$ mixing effects, the flavor SU(3) symmetry breaking, and the nonperturbative dynamics of charmonium and bottomonium.

We study ground states and excitations of light octet and decuplet baryons within the framework of Dyson-Schwinger and Faddeev equations. We improve upon similar approaches by explicitly taking into account the momentum-dependent dynamics of the quark-gluon interaction that leads to dynamical chiral symmetry breaking. We perform calculations in both the three-body Faddeev framework and the quark-diquark approximation in order to assess the impact of the latter on the spectrum. Our results indicate that both approaches agree well with each other. The resulting spectra furthermore agree one-to-one with experiment, provided well-known deficiencies of the rainbow-ladder approximation are compensated for. We also discuss the mass evolution of the Roper and the excited $\mathrm{\Delta }$ with varying pion mass and analyze the internal structure in terms of their partial wave decompositions.

A two-loop induced radiative neutrino model is proposed as an extension of our previous work in which the first- and second-generation standard model fermion masses are generated at the one-loop level in both quark and lepton sectors. Then we discuss the current neutrino oscillation data, lepton flavor violations, muon anomalous magnetic moment, and a bosonic dark matter candidate, for both the normal and inverted neutrino mass hierarchy. Our numerical analysis shows that fewer hierarchical Yukawa coupling constants can fit the experimental data with TeV-scale dark matter.

We consider a low-scale seesaw scenario where the masses of its heavy Majorana neutrinos are arranged in a pattern of three quasidegenerate pairs, in the range of $\mathcal{O}(1–6\mathrm{GeV})$. Since they can violate lepton number by two units, they contribute to rare decays of $D_s$ and $B_c$ mesons, providing the conditions for maximal $CP$ violation. We find that new phenomenology is possible depending on how many of on-shell pairs mediate these decays. In particular, we present new constraints on muon-heavy neutrino mixing parameters.

The strong coupling dynamics of a $2+1$ dimensional U(1) gauge theory coupled to charged matter is holographically modeled via a top-down construction with intersecting D3- and D5-branes. We explore the resulting phase diagram at finite temperature and charge density using correlation functions of monopole operators, dual to magnetically charged particles in the higher-dimensional bulk theory, as a diagnostic.

Microseconds after the Big Bang quarks and gluons formed a strongly coupled nonconformal liquid driven out of equilibrium by the expansion of the Universe. We use holography to determine the nonequilibrium behavior of this liquid in a Friedmann-Lemaître-Robertson-Walker universe and develop an expansion for the corresponding entropy production in terms of the derivatives of the cosmological scale factor. We show that the resulting series has zero radius of convergence and we discuss its resurgent properties. Finally, we compute the resummed entropy production rate in a de Sitter universe at late times and show that the leading order approximation given by bulk viscosity effects can strongly overestimate/underestimate the rate depending on the microscopic parameters.

Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized $\mathfrak{osp}(1|2)$ superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.

Starting from the quaternionic quantization scheme proposed by Emch and Jadczyk for describing the motion of a quantum particle in the magnetic monopole field, we derive an algorithm for finding the differential representation of the star product generated by the quaternionic Weyl correspondence on phase-space functions. This procedure is illustrated by the explicit calculation of the star product up to the second order in the Planck constant $\hslash$. Our main tools are an operator analog of the twisted convolution and the Zassenhaus formula for the products of exponentials of noncommuting operators.

We explore the mathematical relation between stochastic quantization (SQ) and the holographic Wilsonian renormalization group (HWRG) of a massive scalar field defined in asymptotically anti–de Sitter space. We compute the stochastic two-point correlation function by quantizing the boundary on-shell action (it is identified with the Euclidean action in our stochastic frame) of the scalar field, requiring the initial value of the stochastic field Dirichlet boundary condition, and study its relationship with the double-trace deformation in HWRG computation. It turns out that the stochastic two-point function precisely corresponds to the double-trace deformation through the relation proposed in [J. High Energy Phys. 11 (2012) 144] even in the case that the scalar field mass is arbitrary. In our stochastic framework, the Euclidean action constituting the Langevin equation is not the same as that in the original stochastic theory; in fact, it contains the stochastic time “$t$-dependent” kernel in it. A justification for the exotic Euclidean action is provided by proving that it transforms to the usual form of the Euclidean action in a new stochastic frame by an appropriate rescaling of both the stochastic fields and time. We also apply the Neumann boundary condition to the stochastic fields to study the relation between SQ and the HWRG when alternative quantization is allowed. It turns out that the application of the Neumann boundary condition to the stochastic fields generates the radial evolution of the single-trace operator as well as the double-trace term.

The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, a choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.

We investigate the invariant canonical transformation of a spatially covariant scalar-tensor theory of gravity, called the XG theory. Under the invariant canonical transformation, the forms of the action or the Hamiltonian and the primary constraints are preserved, but the action or the Hamiltonian is not invariant. We derive the Hamiltonian in a nonperturbative manner and perform the Hamiltonian analysis for full theory. We confirm that the theory has at most 3 degrees of freedom as long as the theory has the spatial diffeormorphism symmetry. Then, we derive the invariant canonical transformation by using the infinitesimal transformation. The invariant metric transformation of the XG theory contains a vector product as well as the disformal transformation. The vector product and the disformal factor can depend on the higher order derivatives of the scalar field and the metric. Furthermore, we discover additional canonical transformation which leaves the theory invariant. Using the invariant transformation, we study the relation between the Horndeski theory and a beyond Horndeski theory, called the GLPV theory, and find that we cannot obtain general GLPV theory from the Horndeski theory through the invariant canonical transformation we found.