Transverse momentum dependence of semi-inclusive pion production

Abstract

Cross sections for semi-inclusive electroproduction of charged pions ($π^{\pm}$) from both proton and deuteron targets were measured for $0.2<x<0.5$, $2<Q^2<4$ GeV$^2$, $0.3<z<1$, and $P_t^2<0.2$ GeV$^2$. For $P_t<0.1$ GeV, we find the azimuthal dependence to be small, as expected theoretically. For both $π^+$ and $π^-$, the $P_t$ dependence from the deuteron is found to be slightly weaker than from the proton. In the context of a simple model, this implies that the initial transverse momenta width of $d$ quarks is larger than for $u$ quarks and, contrary to expectations, the transverse momentum width of the favored fragmentation function is larger than the unfavored one.

Figures (5)

• Figure 1: Schematic diagram of semi-inclusive pion electroproduction within a factorized QCD parton model at lowest order in $\alpha_s$. Final transverse momenta of the detected pion $\vec{P}_t$ arises from convolving the struck quark transverse momenta $\vec{k}_t$ with the transverse momentum generated during fragmentation process $\vec{p}_t$.
• Figure 2: $P_t$ distribution of data from this experiment as a function of $\phi$.
• Figure 3: The parameters $A$ and $B$ [the relative coefficients of the $\cos{\phi}$ ($\sigma_{LT}$) and $\cos{2\phi}$ ($\sigma_{TT}$) terms] averaged over $\pi^+$ and $\pi^-$ detected from proton and deuteron targets, as a function of $x$ at $\langle z\rangle$=0.55 (left), and as a function of $z$ at $\langle x\rangle$=0.32 (right). The average value of transverse momentum ($\langle \vert P_t\vert \rangle$) is $\sim$0.05 GeV. The dashed lines indicate the weighted averages for $z<0.7$, which are also enumerated in each panel. Errors indicated include only statistical contributions. Systematic errors are highly correlated from point to point, and are estimated at 0.03 on both $A$ and $B$. The open symbols are from exclusive pion production (see text). The solid lines are theoretical predictions Cahn.
• Figure 4: The $P^2_t$ dependence of differential cross-sections per nucleus for $\pi^\pm$ production on hydrogen (H) and deuterium (D) targets at $\langle z\rangle$=0.55 and $\langle x\rangle$=0.32. The solid lines show the result of the seven-parameter fit described in the text. The error bars are statistical only. Systematic errors are typically 4% (relative, see text for details). The average value of $\cos(\phi)$ varies with $P_t^2$ (see Table 1.
• Figure 5: Fit parameters (crosses) and two-standard-deviation contours from the seven-parameter fit to the data shown in Fig. 3: a) $u$ quark width squared $\mu_u^2$ versus favored fragmentation width squared $\mu_+^2$; b) $\mu_d^2$ versus $\mu_-^2$; c) $\mu_u^2$ versus $\mu_d^2$; d) $\mu_-^2$ vs $\mu_+^2$. The large dot near the bottom of panel c is from a di-quark model Jakob. The dashed line in panels c and d indicate $\mu_u^2=\mu_d^2$ and $\mu_-^2=\mu_+^2$, respectively.