Phenomenological constraints on A in p↑p→πX from Lorentz invariance relations

Abstract

We present a new analysis of A N in p ↑ p → π X within the collinear twist-3 factorization formalism. We incorporate recently derived Lorentz invariance relations into our calculation and focus on input from the kinematical twist-3 functions, which are weighted integrals of transverse momentum dependent (TMD) functions. In particular, we use the latest extractions of the Sivers and Collins functions with TMD evolution to compute certain terms in A N . Consequently, we are able to constrain the remaining contributions from the lesser known dynamical twist-3 correlators. (Daniel Pitonyak), prokudin@jlab.org (Alexei Prokudin) 1 One could also have C transversely polarized instead of A.2 Studies of the contribution to A N from the convolution of the transversity and Collins TMD functions in the framework of the so-called Generalized Parton Model are presented in Ref. [58]. 3 The dynamical FFs are complex, and we indicate their real and imaginary parts by and superscripts, respectively. 4 Of course there are still uncertainties in these TMD inputs because they are not well-constrained in the forward x F region where A N is large. 5 Note from our discussion before that we can never write the entire cross section only in terms of kinematical functions.

Nuclear Dependence of the Transverse Single-Spin Asymmetry in the Production of Charged Hadrons at Forward Rapidity in Polarized p+p , p+Al , and Aidala1, Akiba2, Alfred3 et al. 2019Phys. Rev. Lett.

“…The twist-3 functions describe quark-gluon-quark correlations and trigluon correlations in the polarized proton and have been studied in detail [19][20][21][22][23][24][25][26][27]. Recently, calculations of the twist-3 contribution from parton fragmentation have been carried out and have shown this to be an important mechanism for understanding TSSA measurements [28][29][30].…”

“…The recent efforts to calculate A N in p ↑ +p and p ↑ +A collisions, accounting for gluon saturation effects [30,[49][50][51] suggested that A N could be A-independent or A −1/3dependent for the different contributions to A N in the region where p T < Q s . However, p T ∼ 2.9 GeV/c in our results is much larger than the saturation scale in the Au nucleus (Q Au s ∼ 0.9 GeV) for the kinematics of this measurement and would lead to no strong A dependence of TSSAs under these models, as calculated in Ref.…”

Introduction to the Transverse-Momentum-Weighted Technique in the Twist-3 Collinear Factorization Approach

“…A series of important work have been done in the past a few decades and the SSAs for the hadron production was completed at leading-order (LO) with respect to the QCD strong coupling constant α s [8][9][10][11][12][13][14] . Recent numerical simulations based on the complete LO result confirmed that the twist-3 approach gives a reasonable description of the SSA data provided by RHIC [19,20].…”

Connections between TMDs and collinear twist-3 functions within the context of single-spin asymmetries

“…However, several works in the literature showed later that this cannot be the case [62,63,64]. What is currently understood as the cause of SSAs in pion production is the third term in (2.1) involving twist-3 fragmentation effects [65,66]. The functions we are sensitive to from this mechanism areH(z) and H ⊥(1) 1 (z) [41,67].…”

“…4 how to approximately recover this relation in the CSS formalism. Both (z) couple to transversity h 1 (x) at larger x values, where the function is currently unconstrained, we can extract h 1 (x) in this region through SSAs in pion production [65,66].…”