Abstract
The back-to-back $$J/\psi $$ and $$\pi $$ associated production at $$e^+ e^-$$ colliders is proposed to detect the gluon transverse momentum dependent (TMD) fragmentation functions. TMD factorization is assumed for this process. With a spinless pion, unpolarized and linearly polarized gluon TMD fragmentation functions can be defined. It is found that at parton level the hadronic tensor can be described by three independent structure functions. As a result, there are three independent angular distributions, of which the $$\cos {2\phi }$$ azimuthal asymmetry is sensitive to the linearly polarized gluon fragmentation function.
Highlights
1 Introduction and final states and all soft divergences can be absorbed into the fragmentation function and nonrelativistic QCD (NRQCD) matrix elements and a proper soft factor
A potential problem is whether the fragmentation function is general, or is the same as that derived from semi-inclusive deep inelastic scattering (SIDIS)
Since our knowledge about gluon transverse momentum dependent fragmentation function (TMDFF) and the four involved NRQCD matrix elements is very limited, here we refrain from giving a numerical estimate of the cross section
Summary
Where l , l, P1, P2 are the momenta for each particle, respectively For this process, it is convenient to work in the hadron frame [5]. It is convenient to work in the hadron frame [5] This is a frame in the center of mass system (CMS) of the leptons and with +z-axis along the three momentum of the pion P2. The +x-axis can be an arbitrary fixed direction denoted by n, which is perpendicular to P2 It is convenient to define the transverse direction through two light-like vectors: P2 and q ≡ q −.
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