International Journal of Modern Physics A

Parton distribution functions are key quantities for us to understand the hadronic structures in high-energy scattering, but they are difficult to calculate from lattice QCD. Recent years have seen fast development of the large-momentum effective theory which allows extraction of the x-dependence of parton distribution functions from a quasi-parton distribution function that can be directly calculated on lattice. The extraction is based on a factorization formula for the quasi-parton distribution function that has been derived rigorously in perturbation theory. A systematic procedure that includes renormalization, perturbative matching, and power corrections has been established to calculate parton distribution functions. Latest progress from lattice QCD has shown promising signs that it will become an effective tool for calculating parton physics.

A descriptive summary is given of the results to-date from the framed standard model (FSM) which:

• Assigns geometric meaning to the Higgs field and to fermion generations, hence offering an explanation for the observed mass and mixing patterns of quarks and leptons, reproducing near-quantitatively 17 of SM parameters with only 7.
• Predicts a new vector boson $G$ which mixes with $\gamma$ and $Z$, leading to deviations from the SM mixing scheme. For $m_G>1$ TeV, these deviations are within present experimental errors but should soon be detectable at LHC when experimental accuracy is further improved.
• Suggests the existence of a hidden sector of particles as yet unknown to experiment which interact but little with the known particles. The lowest members of the hidden sector of mass around 17 MeV, being electrically neutral and stable, may figure as dark matter constituents.

The idea is to retrace the steps leading to the above results unencumbered by details already worked out and reported elsewhere. This has helped to clarify the logic, tighten some arguments and dispense with one major assumption previously thought necessary, thus strengthening earlier results in opening up possibly a new and exciting vista for further exploration.

We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external magnetic field: since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum-dependent terms. We find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of “successive approximations,” which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).

It is analyzed the influence of a fixed background that breaks the Lorentz symmetry on the scalar field in the nonrelativistic regime. It is considered a medium with a nonuniform magnetization and the presence of an induced electric field. Then, due to the effects of the Lorentz symmetry violation, it is shown that the interaction of the scalar field with the magnetic field (produced by the nonuniform magnetization) and the induced electric field yields an effective potential analogous to the double anharmonic oscillator. Thereby, a discrete spectrum of energy can stem from the effects of the violation of the Lorentz symmetry on the scalar field.

The strong coupling constant is an important parameter that can help us understand the strong decay behaviors of baryons. In our previous work, we have analyzed the strong vertices ${\mathrm{\Sigma }}_c^{\ast }ND$, ${\mathrm{\Sigma }}_b^{\ast }NB$, ${\mathrm{\Sigma }}_{c}ND$ and ${\mathrm{\Sigma }}_{b}NB$ in QCD sum rules. Following these works, we further analyze the strong vertices ${\mathrm{\Sigma }}_{c}N{D}^{\ast }$ and ${\mathrm{\Sigma }}_{b}N{B}^{\ast }$ using the three-point QCD sum rules under Dirac structures $q/p/{\gamma }_{\alpha }$ and $q/p/p_{\alpha }$. In this work, we first calculate strong form-factors considering contributions of the perturbative part and the condensate terms $〈\bar{q}q〉$, $〈\frac{{\alpha }_s}{\pi }GG〉$ and $〈\bar{q}{g}_s\sigma Gq〉$. Then, these form-factors are used to fit into analytical functions. According to these functions, we finally determine the values of the strong coupling constants for these two vertices ${\mathrm{\Sigma }}_{c}N{D}^{\ast }$ and ${\mathrm{\Sigma }}_{b}N{B}^{\ast }$.

In this study, we investigate the influences of fermionic q-deformation on the Einstein equations by taking into account of Verlinde’s entropic gravity approach and Strominger’s proposal on quantum black holes. According to Verlinde’s proposal, gravity is interpreted as an entropic force. Moreover, Strominger’s suggestion claims that extremal black holes obey deformed statistics instead of the standard Bose or Fermi statistics. Inspired by Verlinde’s and Strominger’s suggestions, we represent some thermostatistical functions of VPJC-type q-deformed fermion gas model for the high-temperature limit. Applying the Verlinde’s entropic gravity approach to the q-deformed entropy function, q-deformed Einstein equations with the effective cosmological constant are derived. The results obtained in this work are compared with the related works in the literature.

In this paper, we propose a UV complete, quantum improved picture of a black hole geometry that conforms to the IR gravity of effective field theory. Our work builds on identifying an effective space-distributed notion of black hole fluid in quantum improved regular Einstein gravity and its theoretical correspondence with a cosmology inspired power law fluctuation of matter. Hence, we make use of phenomenological asymptotic scales of matter fluctuation in static space to consequently derive a UV complete line-element of black hole space–time. In this appraisal, it gets explicit how principle of causality is preserved even while there is an effective spread of black hole fluid across horizon(s). Gravity changes from its conventional classical geometry-state to a quantum masked profile across a hypersurface of characteristic radius $r_{\ast }\sim {(\hslash G{r}_S/c^3)}^{1/3}$. We make analyses that probe the newly proposed quantum improved gravity in the contexts of regularity of Einstein fields, complete predictability of Hawking radiation process, and first law of black hole thermodynamics. It emerges that quantum black hole geometry self-regulates a regular timelike core that is abide by every quantum theoretical constraint while being flat around its center.

To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the connection representation. Then we perform functional integration over connection. The module of the result of this integration arises in the leading order of the expansion over a scale of the discrete lapse-shift functions and has maxima at finite (Planck scale) areas/lengths and rapidly decreases at large areas/lengths, as we have mainly considered previously; the phase arises in the leading order (Regge action) of the stationary phase expansion.

Now we consider the possibility of confining ourselves to these leading terms in a certain region of the parameters of the theory; consider background edge lengths as an optimal starting point for the perturbative expansion of the theory; estimate the background length scale and consider the form of the graviton propagator. In parallel with the general simplicial structure, we consider the simplest periodic simplicial structure with a part of the variables frozen (“hypercubic”), for which also the propagator in the leading approximation over metric variations can be written in a closed form.

We consider recently developed Cohomological Field Theory (CohFT) soliton counting diagram technique for Khovanov (Kh) and Khovanov–Rozansky (KhR) invariants.${}^{1,2}$ Although, the expectation to obtain a new way for computing the invariants has not yet come true, we demonstrate that soliton counting technique can be totally formalized at an intermediate stage, at least in particular cases. We present the corresponding algorithm, based on the approach involving deformed ${ℛ}$-matrix and minimal positive division, developed previously in Ref. 3. We start from a detailed review of the minimal positive division approach, comparing it with other methods, including the rigorous mathematical treatment.⁴ Pieces of data obtained within our approach are presented in the Appendices.

In this paper, the fractional singular Lagrangian system is studied. The Hamilton–Jacobi treatment is developed to be applicable for fractional singular Lagrangian system. The equations of motion are obtained for the fractional singular systems and the Hamilton–Jacobi partial differential equations are obtained and solved to determine the action integral. Then the wave function for fractional singular system is obtained. Besides, to demonstrate this theory, the fractional Christ-Lee model is discussed and quantized using the WKB approximation.

By using a projective connection over the space of two-dimensional affine connections, we are able to show that the metric interaction of Polyakov two-dimensional gravity with a coadjoint element arises naturally through the projective Ricci tensor. Through the curvature invariants of Thomas and Whitehead, we are able to define an action that could describe dynamics to the projective connection. We discuss implications of the projective connection in higher dimensions as related to gravitation.

This article summarizes a brief development of exotic mesons with vector–vector (VV) final states starting from the $J/\psi \varphi$ mass spectrum, as well as extensions to other final states for strong-interaction physics and physics beyond standard model. These VV final states are very suitable to be studied at the CEPC through associate production and two-photon production, as well as a visionary low energy photon collider.

We study the rare semileptonic $B\to \pi {\mu }^{+}{\mu }^{-}$ and $B\to \rho {\mu }^{+}{\mu }^{-}$ decay modes mediated by the quark level $b\to d{\mu }^{+}{\mu }^{-}$ transition in this paper. We analyze observables such as the differential branching ratio, lepton polarization asymmetry and forward–backward asymmetry within the standard model in the large hadronic recoil region. We then analyze these observables within the 331 or $S{U}_C(3)\times S{U}_L(3)\times U_X(1)$ model in which a new heavy $Z^{\prime }$ boson contributes. The effects of the $Z^{\prime }$-mediated flavor changing neutral current (FCNC) transitions on these modes are examined by varying the mass $M_{Z^{\prime }}$ and the model parameter $\beta$. The new $Z^{\prime }$ couplings are constrained by flavor observables of $B_d-{\bar{B}}_d$ mixing. For the obtained parameter space, we observe $Z^{\prime }$ sensitivities of our observables of interest and deviations from standard model can range from moderate to large depending on the $\beta$ value.

We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincaré AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T\bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the $T\bar{T}$ deformation. Under the boost and $T\bar{T}$ deformation, the $c$-function of the entanglement entropy exactly shows the features expected by the Zamolodchikov’s $c$-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincaré cutoff AdS space can reproduce the exact same result of the $T\bar{T}$ deformed theory on a two-dimensional sphere.