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Register a new userThe behavior of the heavy-quarks structure functions at small-$x$
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The behavior of the charm and bottom structure functions ($F_{k}^{i}(x,Q^{2})$, i=c,b; k=2,L) at small-$x$ is considered with respect to the hard-Pomeron and saturation models. Having checked that this behavior predicate the heavy flavor reduced cross sections concerning the unshadowed and shadowed corrections. We will show that the effective exponents for the unshadowed and saturation corrections are independent of $x$ and $Q^{2}$, and also the effective coefficients are dependent to $ln{Q^{2}}$ compared to Donnachie-Landshoff (DL) and color dipole (CD) models.
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In the paper, we derive the next-to-leading order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium $J/Psi$ or $Upsilon$. The ultra-violet divergences in the real corrections are removed through the operator renormalization, which is performed under the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g. $mu_{F}=3 m_c$ for $cto J/Psi$ and $mu_{F}=3m_b$ for $bto Upsilon$, which can be evolved to any scale via the use of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial application of those fragmentation functions, we study the $J/Psi$ ($Upsilon$) production at a high luminosity $e^+e^-$ collider which runs at the energy around the $Z$ pole and could be a suitable platform for testing the fragmentation function.
The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world-line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In particular, in a shockwave approximation valid in this limit, we show how one recovers the well-known dipole model for unpolarized structure functions. In a follow-up work, we will discuss the world-line computation of polarized structure functions at small x.
Recent data on the structure function F_2(x,Q^2) at small values of x are analysed and compared with theoretical expectations. It is shown that the observed rise at small x is consistent with a logarithmic increase, growing logarithmically also with Q^2. A stronger increase, which may be incompatible with unitarity when extrapolated to asymptotically small values of x, cannot be inferred from present data.
We discuss the longitudinal structure function in nuclear DIS at small $x$. We work within the framework of universal parton densities obtained in DGLAP analyses at NLO. We show that the nuclear effects on the longitudinal structure function closely follow those on the gluon distribution. The error analyses available from newest sets of nuclear PDFs also allow to propagate the uncertainties from present data. In this way, we evaluate the minimal sensitivity required in future experiments for this observable to improve the knowledge of the nuclear glue. We further discuss the uncertainties on the extraction of $F_2$ off nuclear targets, introduced by the usual assumption that the ratio $F_L/F_2$ is independent of the nuclear size. We focus on the kinematical regions relevant for future lepton-ion colliders.
Lattice quantum chromodynamics provides first principles calculations for hadrons containing heavy quarks -- charm and bottom quarks. Their mass spectra, decay rates, and some hadronic matrix elements can be calculated on the lattice in a model independent manner. In this review, we introduce the effective theories that treat heavy quarks on the lattice. We summarize results on the heavy quarkonium spectrum, which verify the validity of the effective theory approach. We then discuss applications to $B$ physics, which is the main target of the lattice theory of heavy quarks. We review progress in lattice calculations of the $B$ meson decay constant, the $B$ parameter, semi-leptonic decay form factors, and other important quantities.)
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