Accessing Quark Helicity through Dihadron Studies

We present a new proposal to study the helicity-dependent dihadron fragmentation functions (DiFF), which describe the correlations of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair. Recent experimental searches for this DiFF via azimuthal asymmetries in back-to-back hadron pair production in $e^{+}{e}^{-}$ annihilation by the BELLE Collaboration did not yield a signal. Here we propose a new way to access this DiFF in $e^{+}{e}^{-}$ annihilation, motivated by the recently recalculated cross section of this reaction, which explains why there was in fact no signal for the BELLE Collaboration to see. In this new approach the azimuthal asymmetry is weighted by the virtual photon’s transverse momentum square multiplying sine and cosine functions of difference of azimuthal angles of relative and total momentum for each pair. The integration over the virtual photon’s transverse momentum has the effect of separating the convolution between the helicity-dependent DiFFs in the quark and antiquark jets and results in a nonzero collinear expression containing Fourier moments of helicity-dependent DiFFs. A second new measurement is also proposed for two-hadron production in semi-inclusive deep inelastic scattering, where the asymmetry is weighted in a similar way for a single pair. This results in a collinear factorized form of the asymmetry, which includes the quark helicity parton distribution function and the same helicity-dependent DiFF, as in $e^{+}{e}^{-}$ production and will allow us to check the universality of this DiFF.

Figure 1

The kinematics of two back-to-back dihadron pair creation in $e^{+}{e}^{-}$ annihilation.