Abstract
We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution (jT) for the single hadron production with the thrust axis in an electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit jT « Q, and joint transverse momentum and threshold limit jT « Q(1 − zh) « Q, where Q and zh are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms ln(Q/jT) and ln(1 − zh) to all orders. In the end, we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.
Highlights
The TMD factorization formalism for the non-global hemisphere event shape has been studied by one of the authors in [54], where they find that the rapidity logarithms evolution does not constitute an essential complicated structure, since it is tied with a universal transverse momentum dependent jet function which appears in the global observables
For kinematic regions distinguished by zh bins, adopting TMD resummation in intermediate zh regions while making use of joint resummation for large zh bins can lead to excellent agreement with measurement for e+e− → πX process, suggesting our factorization and resummation formula results in a reasonable approach for describing single inclusive hadron production at the electron-positron colliders
We develop a TMD factorization formalism for such an observable, which resums logarithms ln(Q/jT )
Summary
E+ + e− → h (zh, jT ) + X, in e+e− annihilation. The center-ofmass (CM) energy of the e+e− collisions is given by s = Q2 = (pe+ + pe−), and the hadron momentum fraction zh = 2ph · q/Q2 = 2Eh/Q is measured. The hadron’s transverse momentum jT is measured with respect to the so-called thrust axis n, which maximizes the event-shape variable thrust T [55]:. It is important to emphasize that even though we measure the hadron transverse momentum jT with respect to the thrust axis, our cross section is not differential in the thrust variable T. The kinematics in the left hemisphere are unconstrained, our observable in eq (2.2) is a non-global observable [57]. Such observables will involve non-global structures which can not be captured by the traditional exponential formula [52]. Since the full factorization structure is quite complicated which we save for the section, we will for the moment ignore the NGLs that arise from the non-global structure, and write down a factorized formalism to resum the global logarithms and build our intuition
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
