International Journal of Modern Physics A

In this paper, I review recent progress in lattice-QCD calculations of hadron structure with an emphasis on nucleon structure. A wide range of nucleon observables are being studied in modern lattice calculations, and important progress has been made at physical pion mass, including the spin decomposition of the nucleon and the Bjorken-$x$ dependence of hadron structure. Challenges and perspectives for future lattice hadron-structure calculations will be discussed.

By computing the operator product expansions between the first two ${𝒩}=4$ higher spin multiplets in the unitary coset model, the (anti-)commutators of higher spin currents are obtained under the large $(N,k)$ ’t Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti-)commutators for generic spins $s_1$ and $s_2$ with manifest $SO(4)$ symmetry at vanishing ’t Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the ${𝒩}=2$ ${{𝒲}}_{\infty }$ algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two $SO(4)$ invariant tensors. We also describe the ${𝒩}=4$ higher spin generators, by using the above coset construction results, for general superspin $s$ in terms of oscillators in the matrix generalization of ${\mathrm{\text{AdS}}}_3$ Vasiliev higher spin theory at nonzero ’t Hooft-like coupling constant. We obtain the ${𝒩}=4$ higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins $s_1$ and $s_2$.

A Schwarzschild-type solution in Regge calculus is considered. Earlier, we considered a mechanism of loose fixing of edge lengths due to the functional integral measure arising from integration over connection in the functional integral for the connection representation of the Regge action. The length scale depends on a free dimensionless parameter that determines the final functional measure. For this parameter and the length scale large in Planck units, the resulting effective action is close to the Regge action.

Earlier, we considered the Regge action in terms of affine connection matrices as functions of the metric inside the 4-simplices and found that it is a finite-difference form of the Hilbert–Einstein action in the leading order over metric variations between the 4-simplices.

Now we take the (continuum) Schwarzschild problem in the form where spherical symmetry is not set a priori and arises just in the solution, take the finite-difference form of the corresponding equations and get the metric (in fact, in the Lemaitre or Painlevé–Gullstrand like frame), which is nonsingular at the origin, just as the Newtonian gravitational potential, obeying the difference Poisson equation with a point source, is cutoff at the elementary length and is finite at the source.

In a version of the PA-2HDM where only mixing between third and second fermion generations is allowed, we propose a mechanism to generate the second Yukawa matrix through a Unitary V-spin flavor transformation on the mass matrix for quarks and leptons. This flavor structure is constrained to be universal, that is, we use the same parameters to generate Yukawa matrix elements in the quark and leptonic sectors, reducing drastically the number of free parameters of the PA-2HDM.

As a consequence of this restrictive condition, we obtain relations between the Yukawa matrix elements, that we call the Universal Texture Constraint (UTC). We obtained an interval of values for the second Yukawa matrix elements, expressed in terms of the Cheng and Sher ansatz, for $\tau \to \mu {\mu }^{+}{\mu }^{-}$ and $\tau \to \gamma \mu$ coming from the UTC and experimental bounds for light scalar masses. Finally, we find the allowed parameter region when the experimental bounds and values for $B_s\to \mu \mu$ decays, $B_s^0-{\bar{B}}_s^0$ mixing, $\tau \to \mu {\mu }^{+}{\mu }^{-}$ and $\tau \to \gamma \mu$ are considered.

Angular distribution of the final particles in the decay ${\mathrm{\Lambda }}_c^{+}\to K^{-}\mathrm{\Delta }{(1232)}^{++}\to K^{-}p{\pi }^{+}$ of the polarized charmed baryon is discussed. Asymmetries are proposed that allow for determination of the components of the ${\mathrm{\Lambda }}_c^{+}$ polarization vector. The precession angle of the polarization in the process of baryon channeling in a bent crystal is directly related to these asymmetries. The decay rate and asymmetry parameter for the ${\mathrm{\Lambda }}_c^{+}\to K^{-}\mathrm{\Delta }{(1232)}^{++}$ decay are calculated in the pole model and compared with experiment.

It is generally assumed in the literature that a Lorentz transformation on a neutral current loop results in a moving current loop with a nonvanishing charge distribution and an electric dipole moment. We show in this paper that this is not, in fact, correct. The derivation that leads to the charge distribution was based on an incomplete Lorentz transformation, which transforms the charge-current four-vector $j^{\mu }=[\rho (r,t),j(r,t)]$, but not the space–time four-vector $x^{\mu }=(t,r)$. We show that completing the Lorentz transformation by using the variable $t^{\prime }$ in the moving frame, rather than keeping the rest frame time variable $t$, results in there being no induced charge density and no resulting electric dipole moment.