Next-to-leading-order QCD corrections to heavy quark fragmentation into $${}^1S^{(1,8)}_0$$ quarkonia

Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the $${}^1S_0^{(1,8)}$$ 1 S 0 ( 1 , 8 ) components of a heavy quarkonium. Starting from the Collins and Soper’s operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.

Fragmentation function of g → $$ Q\overline{Q} $$(3$$ {S}_1^{\left[8\right]} $$) in soft gluon factorization and threshold resummation

We study the fragmentation function of the gluon to color-octet 3S1 heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet 3S1 soft gluon distribution (SGD). The short distance hard part is calculated to the next-to-leading order in αs and all orders in velocity expansion. By deriving and solving the renormalization group equation of the SGD, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study.

The transverse polarization of $$\Lambda $$ hyperons in $$e^+e^-\rightarrow \Lambda ^\uparrow h X$$ processes within TMD factorization

We investigate the transverse polarization of the $$\Lambda $$ Λ hyperon in the processes $$e^+e^-\rightarrow \Lambda ^\uparrow \pi ^\pm X$$ e + e - → Λ ↑ π ± X and $$e^+e^-\rightarrow \Lambda ^\uparrow K^\pm X$$ e + e - → Λ ↑ K ± X within the framework of the transverse momentum dependent (TMD) factorization. The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function (PFF) $$D_{1T}^\perp $$ D 1 T ⊥ of the lambda hyperon and the unpolarized fragmentation function $$D_1$$ D 1 of pion/kaon. We adopt the spectator diquark model result for $$D_{1T}^{\perp }$$ D 1 T ⊥ to numerically estimate the transverse polarization in $$e^+e^-\rightarrow \Lambda ^\uparrow h X$$ e + e - → Λ ↑ h X process at the kinematical region of Belle Collaboration. To implement the TMD evolution formalism of the fragmentation functions, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the fragmentation functions of the $$\Lambda $$ Λ , pion and kaon. It is found that our prediction on the polarization in the $$\Lambda \pi ^+$$ Λ π + production and $${\bar{\Lambda }} \pi ^-$$ Λ ¯ π - is consistent with the recent Belle measurement in size and sign, while the model predictions on the polarizations in $$\Lambda \pi ^-$$ Λ π - and $$\Lambda K^\pm $$ Λ K ± productions show strong disagreement with the Belle data. The reason for the discrepancies is discussed and possible approaches to improve the calculation in the future are also discussed.

The fragmentation spectrum from space-time reciprocity

Analyzing the single inclusive annihilation spectrum of charged hadrons in e+e− collisions, I confront the hadronization hypothesis of local parton-hadron duality with a systematic resummation of the dependence on the small energy fraction. This resummation is based on the reciprocity between time-like and space-like splitting processes in 4 − 2ϵ-dimensions, which I extend to resum all the soft terms of the cross-section for inclusive jet production. Under the local-parton-hadron duality hypothesis, the resulting distribution of jets essentially determines the spectrum of hadrons as the jet radius goes to zero. Thus I take the resummed perturbative jet function as the non-perturbative fragmentation function with an effective infra-red coupling. I find excellent agreement with data, and comment on the mixed leading log approximation previously used to justify local parton-hadron duality.