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Register a new userFragmentation functions for a quark into a spin-singlet quarkonium: Different flavor case
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In the paper, we calculate the fragmentation functions for a quark to fragment into a spin-singlet quarkonium, where the flavor of the initial quark is different from that of the constituent quark in the quarkonium. The ultraviolet divergences in the phase space integral are removed through the operator renormalization under the modified minimal subtraction scheme. The fragmentation function $D_{q to eta_Q}(z,mu_F)$ is expressed as a two-dimensional integral. Numerical results for the fragmentation functions of a light quark or a bottom quark to fragment into the $eta_c$ are presented. As an application of those fragmentation functions, we study the processes $Z to eta_c+qbar{q}g(q=u,d,s)$ and $Z to eta_c+bbar{b}g$ under the fragmentation and the direct nonrelativistic QCD approaches.
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In the paper, we calculate the fragmentation functions for $c to eta_c$ and $b to eta_b$ up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{c to eta_c}(z,mu_F)$ and $D_{b to eta_b}(z,mu_F)$ up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly.
Fragmentation is the dominant mechanism for hadron production with high transverse momentum. For spin-triplet S-wave heavy quarkonium production, contribution of gluon fragmenting to color-singlet channel has been numerically calculated since 1993. However, there is still no analytic expression available up to now because of its complexity. In this paper, we calculate both polarization-summed and polarized fragmentation functions of gluon fragmenting to a heavy quark-antiquark pair with quantum number $^3S_1^{[1]}$. Our calculations are performed in two different frameworks. One is the widely used nonrelativistic QCD factorization, and the other is the newly proposed soft gluon factorization. In either case, we calculate at both leading order and next-to-leading order in velocity expansion. All of our final results are presented in terms of compact analytic expressions.
We study the transverse-momentum spectrum of quarkonium production from single light-parton fragmentation mechanism. In the case of semi-inclusive deep inelastic scattering, we observe that there are two possible initiating processes, namely photon-gluon fusion and light-quark fragmentation. For the second case we derive the factorization theorem, which involves a new hadronic quantity: the quarkonium transverse-momentum-dependent fragmentation functions in NRQCD. We calculate their matching onto the non-perturbative long distance matrix elements at the lowest order in the strong-coupling constant (${mathcal O}(alpha_s^2)$). Focusing on the case of the electron-ion collider, we make a comparative phenomenological study of the two production mechanisms and find the regions of the phase space where one is dominant over the other.
We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calculation is greatly simplified and we are able to obtain the next-to-next-to-leading order results up to $mathcal{O}(epsilon^2)$ in dimensional regularization. These terms are necessary for a higher order calculation which is made possible with the simplification brought by the new regulator. As a by-product, we have obtained the two-loop quark jet function for the Energy-Energy Correlator in the back-to-back limit, which is the last missing ingredient for its N$^3$LL resummation.
We present the first calculation at next-to-leading order (NLO) in $alpha_s$ of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of $z$, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction terms in $4-2epsilon$ dimensions. We also extract the divergences in the virtual NLO corrections analytically, and detail the cancellation of all divergences after renormalization. The NLO corrections have a dramatic effect on the shape of the fragmentation function, and they significantly increase the fragmentation probability.
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