Measurement of Collins asymmetries in inclusive production of charged pion pairs in e^+e^- annihilation at BABAR

TL;DR

<3-5 sentence high-level summary>Measurement of Collins asymmetries in inclusive $e^+e^-\to \pi\pi X$ at $\sqrt{s} \simeq 10.6$ GeV is performed with the BABAR dataset of ${\cal L}\approx 468\,\mathrm{fb}^{-1}$. The analysis employs two reference frames (RF12 and RF0) and a double-ratio technique to suppress detector and radiative uncertainties, enabling access to the Collins fragmentation function and, by universality, transversity. The results show clear, nonzero asymmetries that grow with pion fractional energies $z$ and transverse momenta $p_t$, with a notable difference between unlike- and like-sign pion pairs consistent with favored and disfavored fragmentation contributions. These measurements provide essential input for global extractions of the Collins function and transversity, and offer valuable constraints on the $Q^2$ evolution of spin-dependent fragmentation at $e^+e^-$ energies.

Abstract

We present measurements of Collins asymmetries in the inclusive process e+e- -->pi pi X, where pi stands for charged pions, at a center-of-mass energy of 10.6 GeV. We use a data sample of 468 fb-1 collected by the BABAR experiment at the PEP-II B factory at SLAC, and consider pairs of charged pions produced in opposite hemispheres of hadronic events. We observe clear asymmetries in the distributions of the azimuthal angles in two distinct reference frames. We study the dependence of the asymmetry on several kinematic variables, finding that it increases with increasing pion momentum and momentum transverse to the analysis axis, and with increasing angle between the thrust and beam axis.

Figures (18)

• Figure 1: (color online). Definition of the azimuthal angle $\phi$ for a quark with transverse spin $\hbox{$\mathbf{S}_q$}\xspace$ which fragments into a spinless hadron of momentum P$_\mathrm{h}$ with a component $\mathbf{P}^\perp_h$ transverse to the quark momentum $\mathbf{k}$.
• Figure 2: (color online). Thrust reference frame (RF12). The azimuthal angles $\phi_1$ and $\phi_2$ are the angles between the scattering plane and the transverse pion momenta $\mathbf{p}_{ti}$ around the thrust axis. The polar angle $\theta_{th}$ is defined as the angle between the beam axis and the thrust axis $\bf{\hat{n}}$. The pion transverse momenta $\mathbf{p}_{ti}$ used in the analysis differ from the corresponding $\hbox{$\mathbf{P}^\perp_h$}\xspace$, which refer to the true $q\overline q$ direction.
• Figure 3: (color online). Second-pion reference frame (RF0). The azimuthal angle $\phi_0$ is defined as the angle between the plane spanned by the beam axis and the second pion momentum $\mathbf{P}_{2}$, and the transverse momentum $\mathbf{p}_{t0}$ of the first pion around the second-pion direction. The polar angle $\theta_2$ is defined as the angle between the beam axis and the momentum $\mathbf{P}_{2}$ of the second pion.
• Figure 4: (color online). Thrust distributions for simulated events under the $焇{(4S)}$ resonance for multi-hadronic events with at least one pair of good quality tracks: $e^+e^- \rightarrow B\overline{ B}{}\xspace\xspace$ (horizontal lines), $e^+e^- \rightarrow c\overline c\xspace$ (asterisks), $e^+e^- \rightarrow q\overline q\xspace, \,q=uds$ (white histogram) and $e^+e^- \rightarrow \tau\tau$ (vertical lines). The samples are normalized to an arbitrary luminosity.
• Figure 5: (color online). Total visible energy of the event in the laboratory frame vs. the thrust value for the on-resonance data sample. The events at high thrust value and low total energy are due to the $e^+e^-\xspace\to\tau^+\xspace\tau^-\xspace$ process. The black line is the cut applied in the analysis in order to remove this background. The peak at $E_{vis} \sim 12$$\mathrm{\,Ge V}$ and high thrust values, is due to radiative BhaBha and $\mu^+\mu^-\xspace(\gamma)$ events.