We calculate the fragmentation functions for a gluon into $P$-wave $B_c$ mesons within the nonrelativistic QCD factorization framework, incorporating color-singlet and color-octet contributions. Ultraviolet divergences arising from phase-space integrals are removed via operator renormalization in the modified minimal subtraction scheme. The resulting fragmentation functions are presented in both graphical form and as fitted analytic expressions.
We study the fragmentation function of the gluon to color-octet $^3S_1$ 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 $^3S_1$ soft gluon distribution (SGD). The short distance hard part is calculated to next-to-leading order in $α_s$ and a renormalization group equation for the SGD is derived. By solving the renormalization group equation, threshold logarithms are resummed to all orders in perturbation theory. The comparison w…
In the paper, we calculate the fragmentation functions for $g \to B_c$ and $g \to B_c^*$. The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{g \to B_c}(z,μ_F)$ and $D_{g \to B_c^*}(z,μ_F)$, which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for $\bar{b}\to B_c(B_c^*)$ and $c\to B…
A novel method of formulating the twist-3 gluon fragmentation function contribution to hyperon polarization in the proton-proton collision is presented. The method employs a covariant gauge and takes full advantage of the Ward-Takahashi identities before performing the collinear expansion. It provides a robust way of constructing the general cross section formula, and also a clear understanding for the absence of the ghost-like terms in the twist-3 cross section in the leading order with respect to the QCD coupling constant.
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${\cal O}(ε^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized compo…
We perform a systematic study on the twist-3 gluon distribution and fragmentation functions which appear in the collinear twist-3 factorization for hard inclusive processes. Three types of twist-3 distribution and fragmentation functions, i.e., intrinsic, kinematical and dynamical ones, which are necessary to describe all kinds of twist-3 cross sections, are related to each other by the operator identities based on the QCD equation of motion and the Lorentz invariance properties of the correlation functions. We derive the exact relations for all twist-3 gluonic distribution and fragmentation f…
The universal fragmentation functions of gluon into the flavored quarkonia $B_c$ and (polarized) $B_c^*$ are computed within NRQCD factorization framework, at the lowest order in velocity expansion and strong coupling constant. It is mandatory to invoke the DGLAP renormalization program to render the NRQCD short-distance coefficients UV finite in a point-wise manner. The calculation is facilitated with the sector decomposition method, with the final results presented with high numerical accuracy. This knowledge is useful to enrich our understanding toward the large-$p_T$ behavior of $B_c^{(*)}…
Hadronic Production of S-wave and P-wave Charmed Beauty Mesons via Heavy Quark Fragmentation
在强子对撞机上，具有大横向动量的$(\bar bc)$介子的主要产生机制是部分子碎裂。计算了Tevatron中通过底反夸克直接碎裂和Altarelli-Parisi诱导胶子碎裂产生S波和P波$(\bar b c)$介子的速率和横动量谱.由于所有的径向和轨道激发的$(\bar b c)$介子低于$BD$味阈值将级联到赝标基态$B_c$通过电磁和/或强子跃迁，他们都有助于包括生产$B_c$。激发S波和P波态对$B_c$的贡献分别为58%和23%，因此是显著的.
