Semi-inclusive production of two back-to-back hadron pairs in e+e− annihilation revisited

Abstract

The cross section for back-to-back hadron pair production in e þ e − annihilation provides access to the dihadron fragmentation functions (DiFF) needed to extract nucleon parton distribution functions from the semi-inclusive deep inelastic scattering (SIDIS) experiments with two detected final state hadrons. Particular attention is given to the so-called interference DiFF (IFF), which makes it possible to extract the transversity parton distribution of the nucleon in the collinear framework. However, previously unnoticed discrepancies were recently highlighted between the definitions of the IFFs appearing in the collinear kinematics when reconstructed from DiFFs entering the unintegrated fully differential cross sections of SIDIS and e þ e − annihilation processes. In this work, to clarify this problem we re-derive the fully differential cross section for e þ e − annihilation at the leading-twist approximation. We find a mistake in the definition of the kinematics in the original expression that systematically affects a subset of terms and that leads to two significant consequences. First, the discrepancy between the IFF definitions in the cross sections for SIDIS and e þ e − annihilation is resolved. Second, the previously derived azimuthal asymmetry for accessing the helicity dependent DiFF G ⊥ 1 in e þ e − annihilation vanishes, which explains the nonobservation of this asymmetry in the recent experimental searches by the BELLE collaboration. We discuss the recently proposed alternative option to extract G ⊥ 1 .

Semi-inclusive back-to-back production of a hadron pair and a single hadron in e+e− annihilation

“…3. Here we have eight TMD FFs for the baryon convoluted with four DiFFs for the unpolarized hadron pair, whereas in the case of two back-to-back dihadron pairs there are only the four DiFFs involved from each side [23]. Nonetheless, further developing the weighted asymmetry method we used in accessing the helicity-dependent DiFFs in Ref.…”

“…We restrict our consideration to the case where the center-of-mass energy of the electronpositron pair is far below the mass of the Z boson. We use the conventional framework for the inclusive hadron production in e + e − annihilation [22][23][24][25]. In the next subsection we first describe the kinematics of the process and then detail the calculation of the cross section in the following subsection.…”

“…The chiral-even nature of G ⊥ 1 entails that in SIDIS it couples to the well-determined quark unpolarized and helicity PDFs [21]. In e + e − annihilation though, the G ⊥ 1 from one pair couples to that for the second pair on the other side [22,23], making it not possible (or at least very hard) to determine the sign of this function. Thus, such measurements allow one to test only for the agreement between the magnitudes of G ⊥ 1 extracted from the two measurements.…”

Accessing Quark Helicity through Dihadron Studies

“…The model calculations of the specific form of the integrated G ⊥ 1 entering this asymmetry was recently performed in [9], producing a result that is smaller than that for IFF calculated within the same model, but still non-negligible. Recently, motivated by the findings in [10], we rederived the cross section expressions for dihadron production in e + e − annihilation [11], and found a number of disagreements with the previous calculations. The two most important conclusions were the resolution of the apparent inconsistencies between the definitions of IFF entering the two mentioned processes and the realization that the originally proposed azimuthal asymmetry for determining G ⊥ 1 in e + e − annihilation should vanish.…”

First extraction of transversity from data on lepton-hadron scattering and hadronic collisions

“…The coefficient of this modulation is the simple product h 1 H 1 where H 1 is a chiral-odd di-hadron fragmentation function (DiFF) quantifying the above correlation [3,4,5]. The function H 1 can be independently determined by looking at correlations between the azimuthal orientations of two hadron pairs in back-to-back jets in e + e − annihilation [6,7,8]. The advantage of this method is that collinear factorization makes it possible to isolate the same combination h 1 H 1 also in proton-proton collisions [9], giving rise to an azimuthally asymmetric distribution of the final hadron pair when one of the two initial protons is transversely polarized [10].…”