Threshold resummation for polarized high-$p_T$ hadron production at COMPASS

We study the cross section for the photoproduction process $\gamma N\to hX$ where the incident photon and nucleon are longitudinally polarized and a hadron $h$ is observed at high transverse momentum. Specifically, we address the “direct” part of the cross section, for which the photon interacts in a pointlike way. For this contribution we perform an all-order resummation of logarithmic threshold corrections generated by soft or collinear gluon emission to next-to-leading logarithmic accuracy. We present phenomenological results relevant for the COMPASS experiment and compare to recent COMPASS data.

Figure 1

High-$p_T$ hadron production in muon-nucleon scattering via direct photon-parton interaction.

Figure 2

High-$p_T$ hadron production in muon-nucleon scattering via a resolved photon.

Figure 3

Our choices for the contours of the inverse Mellin transform: ${\mathcal{C}}_1$ for $x^2<1$ and ${\mathcal{C}}_2$ for $x^2\ge 1$.

Figure 4

Direct parts of the spin averaged and spin dependent LO, NLO and matched resummed differential cross sections for $\mu d\to {\mu }^{\prime }{h}^{\pm }X$. We also show the NLO expansions of the resummed results (symbols), as well as the NLO resolved contributions.

Figure 5

Scale dependence of the spin-dependent cross section at LO, NLO, and for the resummed case. For the resummed cross section we include the resolved contributions at NLO. We vary the scale $\mu ={\mu }_r={\mu }_{fi}={\mu }_{ff}$ in the range $p_T/2\le \mu \le 2p_T$. The upper ends of the bands correspond to $\mu =p_T/2$, the lower ones to $\mu =2p_T$. We show results only when the scale $\mu$ exceeds 1 GeV.

Figure 6

Double-longitudinal spin asymmetries $A_{LL}$ for (a) a deuteron and (b) a proton target for COMPASS kinematics with the full rapidity range $-0.1\le \eta \le 2.38$. In both cases, we show the NLO and matched resummed results for two different sets of parton distributions (see text). The asymmetries include the resolved contributions at NLO; for illustration we also show in (a) the resummed asymmetry without the resolved contributions. The theoretical results are compared to the recent COMPASS data [2].