Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering

Abstract

The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-)weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

Operator analysis of pT -widths of TMDs

“…It is not directly observable. In this article we will not focus on this aspect and just view such transverse moments as idealized quantities, that are limits of well-defined Bessel moments for example [31,32]. Such Bessel moments are less sensitive to the large p T behavior of the TMDs, but they are still scale dependent and under changes in scale they will involve operator mixing between quark and gluon operators, and even between operator combinations describing unpolarized and polarized gluons.…”

“…For the purpose of regularizing this kind of divergence, a generalization of the weighting with powers of transverse momentum was suggested in [31], the so-called Bessel weighting. Bessel moments can be given as derivatives of Fourier transformed TMDsf (x, b 2 T ) in impact parameter space,…”

“…Although it is not expected that the ratios are scale-independent, some of the scale dependence (of both µ and ζ) may cancel in the ratio [31]. But even information about them at some fixed scales would already be very interesting.…”

Average Transverse Momentum Quantities Approaching the Lightfront

“…The n = 1 moment of the Sivers function appears in the Sivers shift, which is the average transverse momentum shift orthogonal to a given transverse polarization [34]:…”

“…An additional advantage is that nonzero b T ≡ |b T | (and finite ζ ) allows for calculation of TMDs on the lattice. The Bessel-weighted analogue of the Sivers shift is [34]:…”