Chiral-odd parton distributions and polarized Drell-Yan process

Abstract

We study the chiral-odd spin structure functions of the nucleon, h~(x) and h2(x), their physical significance, sum rules, and model estimates. We show that they can be measured in the Drell-Yan process with polarized beams at order g and g ', respectively.

I – Experimental investigation of transverse spin asymmetries in μ-p SIDIS processes: Collins asymmetries

“…In those data no size-able Collins asymmetry was observed within the accuracy of the measurements [10][11][12], a fact that was understood in terms of a cancellation between the u-and d-quark contributions [11]. The COMPASS data are still today the only SIDIS data ever taken on a transversely polarised deuteron target and provide constraints on the d-quark contribution 1 . Together with the HERMES and Belle data they allowed for the first global analyses and first extractions [14,15] of the transversity distributions for u-and d-quarks and of favoured and unfavoured Collins FFs.…”

“…Since the 90's [1] it is well known that in order to fully specify the quark structure of the nucleon at twisttwo level in quantum chromodynamics (QCD), the transversity distributions ∆ T q(x) (or h q 1 (x)) have to be introduced in addition to the momentum distributions q(x) and the helicity distributions ∆q(x). For a given quark flavour q, ∆ T q(x) is the analog of the helicity distribution in the case of a transversely polarised nucleon.…”

On the QCD evolution of the transversity distribution

“…We assume h q 1 and ∆q to be equal at a small scale Q 2 0 and let the two distributions evolve differently, according to their own evolution equation. The assumption h q 1 (x, Q 2 0 ) = ∆q(x, Q 2 0 ) is suggested by quark model calculations [2,10] of h q 1 and ∆q, which show that these two distributions are almost equal at a scale Q 2 0 ∼ < 0.5 GeV 2 . For ∆q(x, Q 2 0 ) we use the leading order GRV parametrization [17] whose input scale is Q 2 0 = 0.23 GeV 2 .…”

“…However, h q 1 is chirally odd [2] and decouples from inclusive deep inelastic scattering. This makes it a rather elusive observable.…”

“…The transversity distribution, originally introduced by Ralston and Soper [1] (see also [2,3,4]), and now customarily called h 1 , measures the polarization asymmetry of quarks (or antiquarks) in a transversely polarized hadron. More explicitly, h 1 (x) is the number density of quarks polarized in a transverse direction +n with a given longitudinal momentum fraction x minus the number density of quarks polarized in the opposite direction −n, when the hadron's spin points in the direction +n, i.e.…”