Azimuthal asymmetry in electro-production of neutral pions in SIDIS

TL;DR

The paper links azimuthal asymmetries in SIDIS to the proton transversity distribution $h_1^a(x)$ and the Collins fragmentation function $H_1^{\perp a}(z_h)$. Using the chiral quark-soliton model to predict $h_1^a(x)$ and DELPHI data for $H_1^{\perp}$, the authors perform a parameter-free analysis of HERMES $A_{UL}^{\sin\phi}$ for $\pi^0$, $\pi^+$, and $\pi^-$. They find $H_1^{\perp}(z_h)$ consistent with $H_1^{\perp}(z_h)\propto z_h D_1(z_h)$ and extract $\langle H_1^{\perp}\rangle/\langle D_1\rangle$ around 6% across channels, with results from SMC and DELPHI supporting weak scale dependence. This work strengthens the flavor structure of transversity and Collins effects and provides a parameter-free, QCD-consistent determination of the Collins function from SIDIS data.

Abstract

Recently HERMES has observed an azimuthal asymmetry in electro-production of neutral pions in semi-inclusive deep-inelastic scattering of unpolarized positrons off longitudinally polarized protons. This asymmetry (like those observed in the production of charged pions) is well reproduced theoretically by using the non-perturbative calculation of the proton transversity distribution in the effective chiral quark-soliton model combined with experimental DELPHI-data on the new T-odd Collins fragmentation function. There are no free, adjustable parameters in the analysis. Using the $z$-dependence of the HERMES azimuthal asymmetry and the calculated transversity distributions the z-dependence of the Collins fragmentation function is obtained. The value obtained from HERMES data is consistent with the DELPHI result, even though these results refer to different scales.

Figures (5)

• Figure 1: The chiral quark-soliton model prediction for the proton $x h_1^a(x)$ vs. $x$ at the scale $Q^2=4\,{\rm GeV}^2$. The $u$-quark dominates the proton transversity distribution.
• Figure 2: Kinematics of the process $lp\rightarrow l'\pi X$ in the lab frame. In the HERMES experiment the lepton $l$ is a positron.
• Figure 3: a.The prefactors $B_L(x)$ (dashed) and $B_T(x)$ (dotted line) -- as defined in Eq.(\ref{['A-prefactors-def']}) -- vs. $x$. Clearly $B_L(x)\gg B_T(x)$ for HERMES kinematics. Figure 3: b.$x^3\!\int_x^1\! {\rm d} \xi h_1^u(\xi)/\xi^2$ (dashed) and $xh_1^u(x)$ (dotted line) at $Q^2=4\,{\rm GeV}^2$ vs. $x$. One observes that $xh_1^u(x)\gg x^3\!\int_x^1\! {\rm d} \xi h_1^u(\xi)/\xi^2$. The situation is similar for other flavours. Figure 3: c.The contribution of longitudinal (L, dashed) and transverse (T, dotted) spin part to the total (tot, solid line) azimuthal $\pi^0$ asymmetry $A^{\sin\phi}_{UL}(x)$ and data from hermes-pi0 vs. $x$.
• Figure 4: Azimuthal asymmetries $A_{UL}^{W(\phi)}(x,\pi)$ weighted by $W(\phi)=\sin\phi$ and $\sin 2\phi$, respectively, for $\pi^0$ (a), $\pi^+$ (b) and $\pi^-$ (c) as function of $x$. The rhombuses denote data on $A_{UL}^{\sin\phi}(x,\pi)$, the squares data on $A_{UL}^{\sin 2\phi}(x,\pi)$ from Ref. hermes-pi0hermes. The enclosed areas correspond to the azimuthal asymmetries evaluated using the prediction of the chiral quark-soliton model for $h_1^a(x)$ and the DELPHI result for the analyzing power $\langle H_1^\perp\rangle/\langle D_1\rangle=(6.3\pm 2.0)\%$todd, and take into account the statistical error of the analyzing power.
• Figure 5: a.$H_1^\perp(z_h)/D_1^\perp(z_h)$ vs. $z_h$, as extracted from HERMES data hermes-pi0hermes on the azimuthal asymmetries $A_{UL}^{\sin\phi}(z_h)$ for $\pi^+$ and $\pi^0$ production using the prediction of the chiral quark-soliton model for $h_1^a(x)$h1-model. The error-bars are due to the statistical error of the data. Figure 5: b.The same as Fig. 5a with data points from $\pi^+$ and $\pi^0$ combined. The line plotted in both figures is the best fit to the form $H_1^\perp(z_h)/D_1^\perp(z_h)= a\,z_h$ with $a=0.15$.