Phenomenology of single spin asymmetries in p(transv. polarized)-p -> pion + X

Abstract

A phenomenological description of single transverse spin effects in hadron-hadron inclusive processes is proposed, assuming a generalized factorization scheme and pQCD hard interactions. The transverse momentum, k_T, of the quarks inside the hadrons and of the hadrons relatively to the fragmenting quark, is taken into account in distribution and fragmentation functions, and leads to possible non zero single spin asymmetries. The role of k_T and spin dependent quark fragmentations -- the so-called Collins effect -- is investigated in details in p(transv. polarized)-p -> pion + X processes: it is shown how the experimental data could be described, obtaining an explicit expression for the spin asymmetry of a polarized fragmenting quark, on which some comments are made. Predictions for other processes, possible further applications and experimental tests are discussed.

Figures (6)

• Figure 1: The pion intrinsic average transverse momentum $k_{\perp}^0$ in a jet as a function of $z$. The diamonds are the data from Abreu et al. [19], the continuous line is our fit, as given by equation (17).
• Figure 2: Single spin asymmetry for pion production, $p^\uparrow \, p \to \, \pi \, X$. The data points are the E704 experimental single spin asymmetry for $\pi ^+$ (diamonds), $\pi ^0$ (squares) and $\pi ^-$ (triangles) [3]. The solid line is our best fit for $\pi ^+$, the dashed line for $\pi^0$ and the dotted line for $\pi^-$, obtained under the assumption of Collins effect only.
• Figure 3: The ratio between $|\Delta ^N D _{val}|$ and twice the valence unpolarized fragmentation function $D$, Eq. (28), as a function of $z$. Notice that $|\Delta ^N D| /2D = 1$ for $z \geq 0.97742$.
• Figure 4: The ratio between $|\Delta ^N f _{val}|$ and twice the valence unpolarized distribution function $f$, Eq. (29), as a function of $x$. The solid line refers to $u$ quarks and the dashed line to $d$ quarks. Notice that in both cases $|\Delta ^N f| /2f \to 0$ for $x \to 1$.
• Figure 5: Single spin asymmetry for pion production in $\overline p ^{\uparrow} \, p \, \to \, \pi \, X$. The data points are the E704 experimental single spin asymmetries [22] for $\pi ^+$ (diamonds), $\pi ^0$ (squares) and $\pi ^-$ (triangles). The solid line is the result of our model (with Collins effect only) for $\pi ^+$, the dashed line for $\pi^0$ and the dotted line for $\pi^-$.