Abstract
We investigate the theoretical framework of the cos 2phi azimuthal asymmetry contributed by the coupling of two Boer-Mulders functions in the dilepton production unpolarized pi p Drell–Yan process by applying the transverse momentum dependent factorization at leading order. We adopt the model calculation results of the unpolarized distribution function f_1 and Boer-Mulders function h_1^perp of pion meson from the light-cone wave functions. We take into account the transverse momentum dependent evolution effects for both the distribution functions of pion and proton by adopting the existed extraction of the nonperturbative Sudakov form factor for the pion and proton distribution functions. An approximate kernel is included to deal with the energy dependence of the Boer-Mulders function related twist-3 correlation function T_{q,F}^{(sigma )}(x,x) needed in the calculation. We numerically estimate the Boer-Mulders asymmetry nu _{BM} as the functions of x_p, x_pi , x_F and q_T considering the kinematics at COMPASS Collaboration.
Highlights
As a chiral-odd distribution, the Boer-Mulders function has to be coupled with another chiral-odd distribution/fragmentation function to survive in a high energy scattering process
By applying the transverse momentum dependent (TMD) factorization with evolution effect, we set up the necessary framework of the cos 2φ azimuthal angular asymmetry contributed by the Boer-Mulders functions in the pion induced unpolarized Drell–Yan process
We find from the plots that, in the TMD formalism, the cos 2φ azimuthal asymmetry in the unpolarized π − p Drell–Yan process contributed by the Boer-Mulders functions is around several percent
Summary
As a chiral-odd distribution, the Boer-Mulders function has to be coupled with another chiral-odd distribution/fragmentation function to survive in a high energy scattering process. Two promising processes for accessing the Boer-Mulders function are the Drell–Yan and the semiinclusive deep inelastic scattering (SIDIS) processes In the former case, the corresponding observables are the cos 2φ azimuthal angular dependence of the final-state dilepton, which is originated by the convolution of two Boer-Mulders functions from each hadron. [34], the authors applied a Gaussian ansatz to estimate the kT -evolution effect of the Boer-Mulders function and the cos 2φ asymmetry in π p Drell–Yan process, following the effective description on the energy-dependent broadening of transverse momentum in Ref. The purpose of this work is to apply the TMD factorization to estimate the cos 2φ azimuthal asymmetry in the pion induced Drell–Yan process contributed by the Boer-Mulders effect. 3, we present the theoretical framework of the cos 2φ azimuthal asymmetry νBM contributed by the coupling of two Boer-Mulders functions in the pion induced unpolarized Drell–Yan process under the TMD factorization framework.
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