Evolution Of Fragmentation Functions Research Articles

Predicting the sinϕS single-spin asymmetry of Λ production off a transversely polarized nucleon in SIDIS

We investigate the transverse target spin asymmetry $A^{\sin\phi_{S}}_{UT}$ for the unpolarized $\Lambda$ production in semi-inclusive deep inelastic scattering with the transverse momentum of the final-state lambda hyperon being integrated out. The asymmetry is contributed by the product of the transversity distribution function $h_1(x)$ of the nucleon and the collinear twist-3 fragmentation function $\tilde{H}(z)$ of the $\Lambda$ hyperon. The later one originates from the quark-gluon-quark correlation and is a naive time-reversal-odd function. We calculate $\tilde{H}$ of the $\Lambda$ hyperon by adopt a diquark spectator model. Using the numerical result of $\tilde{H}(z)$ and the available parametrization of $h_1(x)$ from SIDIS data, we predict the $\sin\phi_{S}$ asymmetry in the electroproduction of the $\Lambda$ hyperon in the kinematical region of EIC, EicC and COMPASS. In the phenomenological analysis we include the evolution effect of the distribution functions and the fragmentation functions. The results show that the asymmetries for the $\Lambda$ production SIDIS process is around 0.1 and may be accessible at EIC, EicC and COMPASS. We also find that the evolution of fragmentation function can affect the size of asymmetry.

Altarelli-parisi equation in non-equilibrium QCD

The Q 2 evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions f q (\(\vec p\)) and f g (\(\vec p\)), we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in α s . We make a comparison of these splitting functions with that obtained by Altarelli and Parisi in vacuum.

Injection spectrum of ultrahigh energy cosmic rays in the top-down scenario

We analyze the uncertainties involved in obtaining the injection spectra of UHECR particles in the top-down scenario of their origin. We show that the DGLAP $Q^2$ evolution of fragmentation functions (FF) to $Q=M_X$ (mass of the X particle) from their initial values at low $Q$ is subject to considerable uncertainties. We therefore argue that, for $x\lsim 0.1$ (the $x$ region of interest for most large $M_X$ values of interest, $x\equiv 2E/M_X$ being the scaled energy variable), the FF obtained from DGLAP evolution is no more reliable than that provided, for example, by a simple Gaussian form (in the variable $\ln(1/x)$) obtained under the Modified Leading Log Approximation (MLLA). Additionally, we find that for $x\gsim0.1$, the evolution in $Q^2$ of the singlet FF, which determines the injection spectrum, is ``minimal'' -- the singlet FF changes by barely a factor of 2 after evolving it over $\sim$ 14 orders of magnitude in $Q\sim M_X$. We, therefore, argue that as long as the measurement of the UHECR spectrum above $\sim10^{20}\ev$ is going to remain uncertain by a factor of 2 or larger, it is good enough for most practical purposes to directly use any one of the available initial parametrisations of the FFs in the $x$ region $x\gsim0.1$ based on low energy data even without evolving them to the requisite $Q^2$ value.

Fragmentation functions in supersymmetric QCD and ultrahigh energy cosmic ray spectra produced in top-down models

We present results from two different methods for the calculation of hadron spectra in QCD and supersymmetric QCD with large primary energies $\sqrt{s}$ up to ${10}^{16}\mathrm{GeV}.$ The two methods considered are a Monte Carlo (MC) simulation and the evolution of fragmentation functions described by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. We find that the pion, nucleon, and all-hadron spectra calculated with the two methods agree well. The MC simulation is performed with new hadronization functions (in comparison with our previous work), motivated by low energy $(\sqrt{s}<{M}_{Z})$ data and the DGLAP equation. The hadron spectra calculated with both sets of hadronization functions agree well, which indicates that our method for calculating the hadronization function works successfully. The small difference in the calculated hadron spectra characterizes the uncertainties of this method. We calculate also the spectra of photons, neutrinos, and nucleons and compare them with other published results. The agreement is good for all x from $\ensuremath{\sim}{10}^{\ensuremath{-}5}$ up to $x<~0.3.$ The consistency of the spectra calculated by different methods allows us to consider the spectral shape as a signature of models with decays or annihilations of superheavy particles, such as topological defects or superheavy dark matter. The ultrahigh energy cosmic ray spectra from these sources are calculated.

Next-to-leading order QCD evolution of transversity fragmentation functions

We derive the next-to-leading order splitting kernels for the scale evolution of fragmentation functions for transversely polarized quarks into transversely polarized hadrons.