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Register a new userWhat are the low-$Q$ and large-$x$ boundaries of collinear QCD factorization theorems?
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Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, $Q sim$ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable $x_{bj}$ is large, $x_{bj} gtrsim 0.5$, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. We use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-$Q$ and large-$x_{bj}$ physics.
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We calculate large mass diphoton exclusive photoproduction in the framework of collinear QCD factorization at next to leading order in {alpha}s and at leading twist. Collinear divergences of the coefficient function are absorbed by the evolution of the generalized parton distributions (GPDs). This result enlarges the existing factorization proofs to 2 -> 3 processes, opening new reactions to a trustable extraction of GPDs.
We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers $lesssim$ few GeV$^2$. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrino-nucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic (CCQE) cross section differs by 3-5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, $[r_M^p, r_M^n] = [ 0.739(41)(23), 0.776(53)(28)]$ fm and $[r_Z^p, r_Z^n] = [ 1.0227(94)(51), -0.0445(14)(3)]$ fm; the Friar radius of nucleons, $[(r^p_F)^3, (r^n_F)^3] = [2.246(58)(2), 0.0093(6)(1)]$ fm$^3$; the electric curvatures, $[langle r^4 rangle^p_E, langle r^4 rangle^n_E ] = [1.08(28)(5), -0.33(24)(3)]$ fm$^4$; and bounds on the magnetic curvatures, $[ langle r^4 rangle^p_M, langle r^4 rangle^n_M ] = [ -2.0(1.7)(0.8), -2.3(2.1)(1.1)]$ fm$^4$. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.
We perform a Taylor series expansion of Tsallis distribution by assuming the Tsallis parameter $q$ close to 1. The $q$ value shows the deviation of a system from a thermalised Boltzmann distribution. By taking up to first order in $(q-1)$, we derive an analytical result for Tsallis distribution including radial flow. Further, in the present work, we also study the speed of sound ($c_s$) as a function of temperature using the non-extensive Tsallis statistics for different $q$ values and for different mass cut-offs.
We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard $W+Y$ prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and $Q$-dependence of the cross sections at lower $Q$ are largely governed by the matching to the $Y$-term.
It is unusual to find QCD factorization explained in the language of quantum information science. However, we will discuss how the issue of factorization and its breaking in high-energy QCD processes relates to phenomena like decoherence and entanglement. We will elaborate with several examples and explain them in terms familiar from basic quantum mechanics and quantum information science.
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