The Bethe-Salpeter amplitude $\mathrm{\Phi }(k,p)$ is expressed, by means of the Nakanishi integral representation, via a smooth function $g(\gamma ,z)$. This function satisfies a canonical equation $g=Ng$. However, calculations of the kernel $N$ in this equation, presented previously, were restricted to one-boson exchange and, depending on method, dealt with complex multivalued functions. Although these difficulties are surmountable, in practice, they complicate finding the unambiguous result. In the present work, an unambiguous expression for the kernel $N$ in terms of real functions is derived. For the one-boson scalar exchange, the explicit formula for $N$ is found. With this equation and kernel, the binding energies, calculated previously, are reproduced. Their finding, as well as calculation of the Bethe-Salpeter amplitude in the Minkowski space, become no more difficult than in the Euclidean one. The method can be generalized to any kernel given by irreducible Feynman graph. This generalization is illustrated by example of the cross-ladder kernel.

The lepton pair production in ultraperipheral collisions is studied in the classical field approximation. We derive a general form of the cross section in terms of photon distributions that depend on the transverse momentum and coordinate based on the wave packet form of nuclear wave functions. Such a general form of the cross section in the classical field approximation contains the results of the generalized equivalent photon approximation (EPA) as well as the corrections beyond EPA in the Born approximation. By rewriting the general form of the cross section in light-cone coordinates, we find a good connection with the transverse momentum dependent distribution factorization formalism in the Born approximation. Our numerical results are consistent with current experimental data.

In the framework of singlet vectorlike lepton (VLL) model, we study a search for VLL in the semileptonic channel at high energy $e^{+}{e}^{-}$ colliders. According to the different decay modes of the electroweak gauge bosons, we divide the signal into two modes, that is mode A and mode B. We performed a detailed detector simulation and displayed the excluding and discovering capability of VLL at different colliders. Compared to the mode B, we find that it is more promising to exclude and discover the VLL in mode A.

Electroweak symmetry nonrestoration up to high temperatures well above the electroweak scale offers new alternatives for baryogenesis. We propose a new approach for electroweak symmetry nonrestoration via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. We implement renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures. We present examples of benchmark scenarios that allow for electroweak symmetry nonrestoration all the way up to hundreds of TeV temperatures and also feature suppressed sphaleron washout factors down to the electroweak scale. Our method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector has several intriguing implications for (electroweak) baryogenesis and early universe thermal histories and can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

Solutions to the $\mu$ problem in supersymmetry based on the Kim-Nilles mechanism naturally feature a Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion with a decay constant of the order of the geometric mean of the Planck and TeV scales, consistent with astrophysical limits. We investigate minimal models of this type with two gauge-singlet fields that break a Peccei-Quinn symmetry and extensions with an extra vectorlike quark and lepton supermultiplets consistent with gauge coupling unification. We show that there are many anomaly-free discrete symmetries, depending on the vectorlike matter content, that protect the Peccei-Quinn symmetry to sufficiently high order to solve the strong $CP$ problem. We study the axion couplings in this class of models. Models of this type that are automatically free of the domain wall problem require at least one pair of strongly interacting vectorlike multiplets with mass at the intermediate scale and predict axion couplings that are greatly enhanced compared to the minimal supersymmetric DFSZ models, putting them within reach of proposed axion searches.

We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an “invisible” axion arises from a single low scale breaking of the gauge and global symmetries.

In this work, we self-consistently explore the possibility of charged pion superfluidity and cosmic trajectories in the early Universe under the framework of Polyakov-Nambu–Jona-Lasinio model. By taking the badly constrained lepton flavor asymmetries $l_{\mathrm{e}}$ and $l_{\mu }$ as free parameters, the upper boundaries of pion superfluidity phase are consistently found to be around the pseudocritical temperature at zero chemical potentials. So the results greatly support the choice of $T=0.16\mathrm{GeV}$ as the upper boundary of pion superfluidity in the previous lattice QCD study. Take $l_{\mathrm{e}}+l_{\mu }=-0.2$ as an example, where we demonstrate the features of pion condensation and the associated cosmic trajectories with the evolution of the early Universe. While the trajectory of electric chemical potential reacts strongly at both the lower and upper boundaries of reentrant pion superfluidity, the trajectories of other chemical potentials only respond strongly at the upper boundary.

Nambu quantum mechanics, proposed in [Phys. Lett. B 536, 305 (2002)], is a deformation of canonical quantum mechanics in which only the time-evolution of the “phases” of energy eigenstates is modified. We discuss the effect this theory will have on oscillation phenomena, and place a bound on the deformation parameters utilizing the data on the atmospheric neutrino mixing angle ${\theta }_{23}$.

Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order ${\alpha }^{\prime 3}$. In this paper we use the cosmological reduction on the couplings and show that, up to one-dimensional field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.

We show the existence of self-dual (topological) solitons in a gauged version of the baby Skyrme model in which the Born-Infeld term governs the gauge field dynamics. The successful implementation of the Bogomol’nyi-Prasad-Sommerfield formalism provides a lower bound for the energy and the respective self-dual equations whose solutions are the solitons saturating such a limit. The energy lower bound (Bogomol’nyi bound) is proportional to the topological charge of the Skyrme field and therefore quantized. In contrast, the total magnetic flux is a nonquantized quantity. Furthermore, the model supports three types of self-dual solitons profiles: the first describes compacton solitons, the second follows a Gaussian decay law, and the third portrays a power-law decay. Finally, we perform numerical solutions of the self-dual equations and depict the soliton profiles for different values of the parameters controlling the nonlinearity of the model.

It is pointed out that MOND defines a fiducial specific angular momentum (SAM) for a galaxy of total (baryonic) mass $\mathcal{M}$: $j_M(\mathcal{M})\equiv {\mathcal{M}}^{3/4}(G^3/a_0{)}^{1/4}\approx 383(\mathcal{M}/{10}^{10}{M}_{\odot }{)}^{3/4}\mathrm{kpc}\mathrm{km}{\mathrm{s}}^{-1}$. It plays important roles in disc-galaxy dynamics and evolution: It underlies scaling relations in virialized galaxies that involve their angular-momentum. I show that the disc SAM should be $j_D\approx [⟨r⟩/r_M(\mathcal{M})]j_M(\mathcal{M})=[{\mathrm{\Sigma }}_M/⟨\mathrm{\Sigma }⟩{]}^{1/2}{j}_M(\mathcal{M})$, with $⟨r⟩$ the mean radius of the disc, $⟨\mathrm{\Sigma }⟩=\mathcal{M}/2\pi ⟨r{⟩}^2$ some mean surface density of the galaxy, $r_M=(\mathcal{M}G/a_0{)}^{1/2}$ is the MOND radius of the galaxy, and ${\mathrm{\Sigma }}_M=a_0/2\pi G$ is the (universal) MOND surface density. So, e.g., for a fixed $⟨\mathrm{\Sigma }⟩$, $j_D\propto {\mathcal{M}}^{3/4}$, while for a fixed $⟨r⟩$, $j_D\propto {\mathcal{M}}^{1/4}$. Furthermore, $j_M(\mathcal{M})$ is a reference predictor of the type of galaxy a protogalaxy will settle into, if it evolves in isolation: A protogalaxy of mass $\mathcal{M}$, and SAM $j\gg j_M(\mathcal{M})$ should settle into a low-surface-density disc—with mean acceleration $⟨a⟩/a_0\approx j_M/j\ll 1$. While a protogalaxy with $j\lesssim j_M(\mathcal{M})$ should end up with a disc of mass ${\mathcal{M}}_D\approx j\mathcal{M}/j_M(\mathcal{M})$, having a SAM $j_D\approx j_M(\mathcal{M})$, which is tantamount to $⟨a⟩\approx a_0$ (i.e., at the “Freeman limit”); it should also develop a low-SAM component (e.g., a bulge or a halo), taking up the rest of the mass ${\mathcal{M}}_B\approx \mathcal{M}-{\mathcal{M}}_D$.

We analyze the field equations for the perfect fluid solutions admitting a group ${\mathrm{G}}_3$ of isometries acting on orbits ${\mathrm{S}}_2$ whose curvature has a gradient that is tangent to the fluid flow ($T$-models). We propose several methods to integrate the field equations and we present the general solution without the need to calculate any integral.

We demonstrate how pulsar timing arrays (PTAs) yield a purely gravitational wave (GW) measurement of the luminosity distance and comoving distance to a supermassive black hole binary source, hence providing an estimate of the source redshift and the Hubble constant. The luminosity distance is derived through standard measurement of the chirp mass, which for the slowly evolving binary sources in the PTA band can be found by comparing the frequency of GW-timing residuals at the Earth compared to those at distant pulsars in the array. The comoving distance can be measured from GW-timing parallax caused by the curvature of the GW wave fronts. This can be detected for single sources at the high-frequency end of the PTA band at distances up to 10 Gpcs with a future PTA containing well-timed pulsars out to $\mathcal{O}(10)\mathrm{kpc}$, when the pulsar distance is constrained to less than a GW wavelength. While, for the farthest pulsars, achieving this precision in pulsar distance measurements poses a great challenge, it may be met by future spaced-based very long baseline interferometry (VLBI) pulsar distance measurements coupled with GW-based pulsar distance measurements. Such a future PTA, with $\gtrsim 30$ pulsars with precise distance measurements between 1 and 20 kpc, could measure the Hubble constant to better than 30% for a single source at $0.1\lesssim z\lesssim 1.5$. At $z\lesssim 0.1$, the luminosity and comoving distances are too similar to disentangle, unless the fractional error in the luminosity distance measurement is decreased below 10%. At $z\gtrsim 1.5$, this measurement will likely be restricted by a signal-to-noise ratio threshold. Generally, clarification of the different types of cosmological distances that can be probed by PTAs, and their relation to pulsar distance measurements is important for ongoing PTA experiments aimed at detecting and characterizing GWs.

Within SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a classical spinor field, we study the dependence of the mass gap on the coupling constant between the gauge and nonlinear spinor fields. It is shown that the total dimensionless energy of the monopole interacting with the nonlinear spinor fields depends only on the dimensionless coupling constant.

The Randall Sundrum models receive significant constraints from the neutral kaon system. The $CP$ violating observable ${\epsilon }_K$, in the Randall Sundrum scenario, requires the lightest $KK$ gluon to be heavier than $\sim 24\mathrm{TeV}$. The constraint is even stronger in the little Randall Sundrum (LRS) models, $\gtrsim 32\mathrm{TeV}$. The LRS models are motivated for their possible visibility at the LHC. We show that the stringent constraints from $K$ physics can be relaxed in the LRS models, in the presence of the brane localized kinetic terms (BLKT). In particular, for a range of values, a UV BLKT could significantly modify the lightest $KK$ gluon wave function such that the limit can reduces to 5 TeV. We also show that such a relaxation of the constraints can also be achieved by imposing flavor symmetries à la minimal flavor protection.

We present a calculation of the pion and kaon Mellin moment $⟨x^3⟩$ extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass $\sim 260\mathrm{MeV}$, and a kaon mass $\sim 530\mathrm{MeV}$. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of 1.12–1.67 fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated nonperturbatively. Our results are converted to the $\overline{\mathrm{MS}}$ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are $⟨x^3{⟩}_{\pi }^{u^{+}}=0.024(18{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$, $⟨x^3{⟩}_K^{u^{+}}=0.035(6{)}_{\mathrm{stat}}(3{)}_{\mathrm{syst}}$, and $⟨x^3{⟩}_K^{s^{+}}=0.075(5{)}_{\mathrm{stat}}(1{)}_{\mathrm{syst}}$, where the systematic error is the uncertainty due to excited state contamination. We combine $⟨x^3⟩$ with the two lower moments, namely $⟨x⟩$ and $⟨x^2⟩$, to obtain the ratios $⟨x^3⟩/⟨x⟩$ and $⟨x^3⟩/⟨x^2⟩$, as well as $⟨x^3{⟩}_K^{u^{+}}/⟨x^3{⟩}_{\pi }^{u^{+}}$ and $⟨x^3{⟩}_K^{u^{+}}/⟨x^3{⟩}_{\pi }^{u^{+}}$. In addition, we reconstruct the $x$-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large $x$-dependence that falls as $(1-x{)}^2$ for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with $4\le n\le 6$. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking.

Confinement remains one the most interesting and challenging nonperturbative phenomenon in non-Abelian gauge theories. Recent semiclassical [for $SU(2)$] and lattice (for QCD) studies have suggested that confinement arises from interactions of statistical ensembles of instanton dyons with the Polyakov loop. We extend studies of a semiclassical ensemble of dyons to the $SU(3)$ Yang-Mills theory. We find that such interactions do generate the expected first-order deconfinement phase transition. The properties of the ensemble, including correlations and topological susceptibility, are studied over a range of temperatures above and below $T_c$. Additionally, the dyon ensemble is studied in the Yang-Mills theory containing an extra trace-deformation term. It is shown that such a term can cause the theory to remain confined and even retain the same topological observables at high temperatures.

In this work we have studied the QCD phase structure and critical dynamics related to the $3\text{−}d$ $O(4)$ and $Z(2)$ symmetry universality classes in the two-flavor quark-meson low energy effective theory within the functional renormalization group approach. We have employed the expansion of Chebyshev polynomials to solve the flow equation for the order-parameter potential. The chiral phase transition line of $O(4)$ symmetry in the chiral limit and the $Z(2)$ line of critical end points related to the explicit chiral symmetry breaking are depicted in the phase diagram. Various critical exponents related to the order parameter, chiral susceptibilities, and correlation lengths have been calculated for the $3\text{−}d$ $O(4)$ and $Z(2)$ universality classes in the phase diagram, respectively. We find that the critical exponents obtained in the computation, where a field-dependent mesonic nontrivial dispersion relation is taken into account, are in quantitative agreement with results from other approaches, e.g., the conformal bootstrap, the Monte Carlo simulations, and the $d=3$ perturbation expansion. Moreover, the size of the critical regime in the QCD phase diagram is found to be very small.

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for the decay cascade $D\to K_1(1270,1400){\ell }^{+}{\nu }_{\ell }\to (K\pi \pi ){\ell }^{+}{\nu }_{\ell }(\ell =e,\mu )$, in which the electron and muon mass is explicitly included. Using a set of phenomenological results for $D\to K_1$ form factors, we calculate partial decay widths and branching fractions for $D^0\to K_1^{-}{\ell }^{+}{\nu }_{\ell }$ and $D^{+}\to K_1^0{\ell }^{+}{\nu }_{\ell }$, but find that results for $\mathcal{B}(D\to K_1(1270)e^{+}{\nu }_e)$ are about a factor 1.5 larger than recent BESIII measurements. We further demonstrate that the measurement of up-down asymmetry in $D\to K_1{e}^{+}{\nu }_e\to (K\pi \pi )e^{+}{\nu }_e$ and angular distributions in $D\to K_1{\ell }^{+}{\nu }_{\ell }\to (K\pi \pi ){\ell }^{+}{\nu }_{\ell }$ can help to determine the hadronic amplitude requested in $B\to K_1(\to K\pi \pi )\gamma$.

Using a data sample of $980{\mathrm{fb}}^{-1}$ collected with the Belle detector operating at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider, we present evidence for the $\mathrm{\Omega }(2012{)}^{-}$ in the resonant substructure of ${\mathrm{\Omega }}_c^0\to {\pi }^{+}(\overline{K}\mathrm{\Xi }{)}^{-}$ ($(\overline{K}\mathrm{\Xi }{)}^{-}=K^{-}{\mathrm{\Xi }}^0+{\overline{K}}^0{\mathrm{\Xi }}^{-}$) decays. The significance of the $\mathrm{\Omega }(2012{)}^{-}$ signal is $4.2\sigma$ after considering the systematic uncertainties. The ratio of the branching fraction of ${\mathrm{\Omega }}_c^0\to {\pi }^{+}\mathrm{\Omega }(2012{)}^{-}\to {\pi }^{+}(\overline{K}\mathrm{\Xi }{)}^{-}$ relative to that of ${\mathrm{\Omega }}_c^0\to {\pi }^{+}{\mathrm{\Omega }}^{-}$ is calculated to be $0.220\pm 0.059(\mathrm{stat}.)\pm 0.035(\mathrm{syst}.)$. The individual ratios of the branching fractions of the two isospin modes are also determined and found to be $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\pi }^{+}\mathrm{\Omega }(2012{)}^{-})\times \mathcal{B}(\mathrm{\Omega }(2012{)}^{-}\to K^{-}{\mathrm{\Xi }}^0)/\mathcal{B}({\mathrm{\Omega }}_c^0\to {\pi }^{+}{K}^{-}{\mathrm{\Xi }}^0)=(9.6\pm 3.2(\mathrm{stat}.)\pm 1.8(\mathrm{syst}.))\%$ and $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\pi }^{+}\mathrm{\Omega }(2012{)}^{-})\times \mathcal{B}(\mathrm{\Omega }(2012{)}^{-}\to {\overline{K}}^0{\mathrm{\Xi }}^{-})/\mathcal{B}({\mathrm{\Omega }}_c^0\to {\pi }^{+}{\overline{K}}^0{\mathrm{\Xi }}^{-})=(5.5\pm 2.8(\mathrm{stat}.)\pm 0.7(\mathrm{syst}.))\%$.