Next-to-leading-order QCD corrections to heavy quark fragmentation into $${}^1S^{(1,8)}_0$$ quarkonia

Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the $${}^1S_0^{(1,8)}$$ 1 S 0 ( 1 , 8 ) components of a heavy quarkonium. Starting from the Collins and Soper’s operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.

ON THE NEW EXPLICIT SOLUTIONS OF THE FRACTIONAL NONLINEAR SPACE-TIME NUCLEAR MODEL

In this research, the analytical and numerical solutions of the fractional nonlinear space-time Phi-four model are investigated by employing two systematic schemes and the B-spline schemes. A new fractional operator definition is applied to this model to convert the model from its fractional formula to an integer-order nonlinear ordinary differential equation. The considered model is of major interest for studying the nuclear interaction, elementary particles in a condensed medium, and propagation of dislocations in crystals. Explicit wave solutions are obtained.

Entropy Generation in a Mass-Spring-Damper System Using a Conformable Model

This article studies the entropy generation of a mass-spring-damper mechanical system, under the conformable fractional operator definition. We perform several simulations by varying the fractional order γ and the damping ratio ζ , including the usual dynamic response when γ = 1.0 and the typical damping cases. We analyze the entropy production for this system and its strong dependency on both γ and ζ parameters. Therefore, we determine their optimal values to obtain the highest efficiency of the MSD response, as well as other impressive features.

Parity-odd fragmentation functions

Quantum chromodynamics is a non-Abelian gauge theory of strong interactions, in which the parity symmetry can be violated by the nontrivial [Formula: see text]-vacuum tunneling effects. The [Formula: see text]-vacuum induces the local parity-odd domains. Those reactions that occur in these domains can be affected by the tunneling effects and quantities become parity-odd. In this paper we consider the fragmentation process where parity-odd fragmentation functions are introduced. We present the fragmentation functions by decomposing the quark–quark correlator. Among the total 16 fragmentation functions, eight of them are parity conserved, and the others are parity violated. They have a one-to-one correspondence. Positivity bounds of these one-dimensional fragmentation functions are shown. To be explicit, we also introduce an operator definition of the parity-odd correlator. According to the definition, we give a proof that the parity-odd fragmentation functions are local quantities and vanish when sum over all the hadrons [Formula: see text].

TRANSVERSE-MOMENTUM-DEPENDENT PARTON DISTRIBUTIONS AT THE EDGE OF THE LIGHTCONE

We present a completely gauge-invariant operator definition of transverse-momentum-dependent parton densities (TMD), supplied with longitudinal lightlike gauge links as well as transverse gauge links at lightcone infinity. Within this framework, we consider the consistent treatment of specific divergences, emerging in the "unsubtracted" TMD beyond the tree approximation, and construct the soft factors to cancel unphysical singularities. We confront this approach with factorization schemes, which make use of covariant gauges with off-the-lightcone gauge links, and discuss their mutual connection.

Video digitizer analysis of birefringence along the lengths of single chromosomal spindle fibres. I. Description of the system and general results

A new system, based on a video digitizer interfaced to a microcomputer, has been developed to quantify birefringence of individual chromosomal spindle fibres from videotaped images of spindles. (The system also can be used for any other purpose that requires the analysis of video intensities.) Retardations along the lengths of single chromosomal spindle fibres have been studied throughout metaphase and anaphase in cells kept at constant temperatures. The instrumental readings are accurate to within less than 0.06 nm retardation, but operationally the retardation values along a single chromosomal spindle fibre can vary by up to 0.15 nm, primarily because of variation in operator definition of the spindle fibre. Retardations vary with position along the fibre. During anaphase the retardations along a given chromosomal spindle fibre do not move poleward, but rather change as if the oriented material is disorganized at the kinetochore. The retardation at the kinetochore of a chromosomal spindle fibre does not change during anaphase, except for nonpredictable jumps of 20–30% that sometimes occur. Thus there is no ‘decay of birefringence’ during anaphase, such as has been described in other species. In this regard our data, that pertain only to single chromosomal spindle fibres, differ from those previously published; we argue that this is because the published data deal with mixtures of chromosomal and continuous spindle fibres, and because changes in birefringence can appear to occur, artefactually, when measurements of birefringence are made at a single spot in a spindle.