Following the operator definition of the fragmentation function developed by Collins and Soper, we compute the gluon-to-$h_c$ fragmentation function at the lowest order in the velocity expansion in NRQCD factorization approach. Utilizing some modern technique developed in the area of multi-loop calculation, we are able to analytically deduce the infrared-finite color-singlet short-distance coefficient associated with the fragmentation function. The fragmentation probability for gluon into $h_c$ is estimated to be order $10^{-6}$.
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 $D_{q \to η_Q}(z,μ_F)$ 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 $η_c$ are presented. As an appli…
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 cons…
We present the calculation at next-to-leading order (NLO) in alpha_s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual …
Inspired by the recent measurements of the $η_c$ meson production at LHC, we investigate the relativistic correction effect for the fragmentation function of the gluon into $η_c$, which constitutes the crucial nonperturbative elements to understand $η_c$ production at high $p_T$. Employing three distinct methods, we calculate the leading relativistic correction to the $g\toη_c$ fragmentation function in the NRQCD factorization framework, as well as verify the existing NLO result for the $c\to η_c$ fragmentation function. We also study the evolution behavior of these fragmentation functions wit…
In the paper, we calculate the fragmentation functions for $c \to η_c$ and $b \to η_b$ 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 $D_{c \to η_c}(z,μ_F)$ and $D_{b \to η_b}(z,μ_F)$ 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 th…
Heavy Quark Fragmentation Functions for D-wave Quarkonium and Charmed Beauty Mesons
在大横动量区，高能$e^+e^-$和强子碰撞中，部分子碎裂控制了重-重束缚态如粲偶素、底偶素和$\bar bc$介子的产生.在强耦合常数和非相对论展开下，我们计算了重夸克碎裂成D波夸克偶素和$\bar bc$介子的前序函数。在$\bar b c$介子的情况下，它的一组D波状态预计将低于开放味阈值。$\bar b$反夸克分裂为D波$\bar b c$介子的总碎裂几率约为$2 \times 10^{-5}$，这意味着总赝标基态$B_c$中只有2%来自这些轨道激发态的级联.
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 …
Based on the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), we calculate the production cross section for the charmonium and the bottomonium produced by the hard photoproduction processes and fragmentation processes in relativistic heavy ion collisions. It is shown that the existing experimental data on heavy quarkonium production at the Large Hadron Collider (LHC) can be described in the framework of the NRQCD formalism, and the phenomenological values of matrix elements for color-singlet and color-octet components give the main contribution. The numerical results …
Next-to-next-to-leading-order QCD corrections to ${}^3S_1^{(8)}$ gluon fragmentation function for quarkonium
China University of Mining and Technology（中国矿业大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；South China Normal University（华南师范大学）；Southwest University（西南大学）
Recently we have proved factorization of infrared divergences in NRQCD S-wave heavy quarkonium production at high energy colliders at all orders in coupling constant. One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of non-canceling infrared divergences due to real soft gluons exchange, although no such infrared divergences are present in the color singlet S-wave heavy quarkonium. In this paper we find that since the non-perturbative matrix element of the color singlet P-wave heavy quar…
The non-singlet kaon fragmentation function from e^+e^- kaon production
我们进行了适合的$e^++e^-\to K+X$，$K=K^\pm and K^0_S$中可用的带电和中性K介子生产数据，并确定非单态组合的K介子碎裂函数$D_u^{K^\pm}-D_d^{K^\pm}$在一个模型独立的方式，没有任何相关性的其他碎裂功能。只假定核的同位旋不变性。使用非单重态使我们能够包括在非常低的动量分数下的数据，到目前为止，这些数据在全局拟合中被排除在外，并首次对碎裂函数进行NNLO拟合。我们发现，在大$z$的K介子非单重碎裂函数是大于其他合作从全球拟合分析，并在低$z$显着不同。
