Global fitting of single spin asymmetry: an attempt

TL;DR

This work attempts a first global analysis of single spin asymmetries by simultaneously fitting SIDIS data, sensitive to the Sivers function $f_{1T}^{\perp q}$ via TMD factorization, and proton-proton data, described by collinear twist-3 ETQS functions $T_{q,F}(x,x)$. By parameterizing the Sivers function with a flexible x- and k_⊥-dependent form and linking it to $T_{q,F}(x,x)$, the authors perform a nine-parameter fit to SIDIS and STAR/BRAHMS data to probe if a node in $x$ or $k_⊥$ can solve the observed sign-mismatch between SIDIS and pp extractions. The results show that while SIDIS and STAR π^0 data can be described, BRAHMS $π^{±}$ data cannot within this framework, and neither a node in $x$ nor a node in $k_⊥$ satisfactorily resolves the sign puzzle, implying a sizable contribution from twist-3 fragmentation functions and highlighting the need for additional experimental constraints. Overall, the work emphasizes limitations of current formalisms in unifying SIDIS and pp spin asymmetries and points to future measurements and theoretical developments to accurately separate Sivers and fragmentation contributions.

Abstract

We present an attempt of global analysis of Semi-Inclusive Deep Inelastic Scattering (SIDIS) $\ell p^\uparrow \to \ell' πX$ data on single spin asymmetries and data on left-right asymmetry $A_N$ in $p^\uparrow p \to πX$ in order to simultaneously extract information on Sivers function and twist-three quark-gluon Efremov-Teryaev-Qiu-Sterman (ETQS) function. We explore different possibilities such as node of Sivers function in $x$ or $k_\perp$ in order to explain "sign mismatch" between these functions. We show that $π^\pm$ SIDIS data and $π^0$ STAR data can be well described in a combined TMD and twist-3 fit, however $π^\pm$ BRAHMS data are not described in a satisfactory way. This leaves open a question to the solution of the "sign mismatch". Possible explanations are then discussed.

Figures (7)

• Figure 1: First moment of (a) $u$ quark Sivers function and (b) $d$ quark Sivers function as found using parameters of Table \ref{['table:I']}, here $f_{1T}^{\perp q(1)}(x)\equiv -T_{q,F}(x,x)/2M$.
• Figure 2: Description of (a) HERMES :2009ti and (b) COMPASS :2008dn data on $\pi^+$ production as a function of $x_B$.
• Figure 3: Description of STAR $\pi^0$ data :2008qb at rapidity (a) $y=3.3$ and (b) $y=3.7$ at $\sqrt{S}=200$ GeV. Solid curves correspond to the scale $\mu=P_{h\perp}$, while dashed and dotted ones correspond to $\mu=P_{h\perp}/2$ and $\mu=2 P_{h\perp}$, respectively.
• Figure 4: Description of BRAHMS $\pi^+$ (a) and $\pi^-$ (b) data Lee:2007zzh at forward angle $\theta=4^\circ$ at $\sqrt{S}=200$ GeV. Solid curves correspond to the scale $\mu=P_{h\perp}$, and dashed and dotted ones correspond to $\mu=P_{h\perp}/2$ and $\mu=2 P_{h\perp}$, respectively.
• Figure 5: Prediction of Drell-Yan asymmetry for RHIC kinematics $p^\uparrow p \to \ell^+\ell^-X$, $0<y<3$. Solid line corresponds to Sivers function with a node from this work and dashed line to Sivers function without node from Ref. Anselmino:2008sga. The same convention for the hadronic frame and asymmetry is used as in Ref. Anselmino:2009st.