scholarly journals NEXT-TO-LEADING ORDER CALCULATION OF THE COLOR-OCTET 3S1 GLUON FRAGMENTATION FUNCTION FOR HEAVY QUARKONIUM

2001 ◽  
Vol 16 (supp01a) ◽  
pp. 229-231
Author(s):  
JUNGIL LEE
Keyword(s):  
Fragmentation Function ◽  
Short Distance ◽  
Feynman Diagrams ◽  
Heavy Quarkonium ◽  
Leading Order ◽  
Light Cone Gauge ◽  
Color Octet ◽  
Feynman Gauge ◽  
Fragmentation Functions ◽  
Gluon Fragmentation

Next-to-leading order corrections to fragmentation functions in a light-cone gauge are discussed. This gauge simplifies the calculation by eliminating many Feynman diagrams at the expense of introducing spurious poles in loop integrals. As an application, the short-distance coefficients for the color-octet 3S1 term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are re-calculated to order [Formula: see text]. We show that the ill-defined spurious poles cancel and the appropriate prescriptions for the remaining spurious poles can be determined by calculating a subset of the diagrams in the Feynman gauge. Our answer agrees with the recent calculation of Braaten and Lee in the Feynman gauge, but disagrees with another previous calculation.

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

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Feng Feng ◽  
Yu Jia ◽  
Wen-Long Sang
Keyword(s):  
Heavy Quark ◽  
Fragmentation Function ◽  
Short Distance ◽  
Decomposition Method ◽  
Heavy Quarkonium ◽  
Leading Order ◽  
Quark Fragmentation ◽  
Definition Of ◽  
Perturbative Corrections ◽  
Operator Definition

AbstractWithin 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.

scholarly journals Gluon fragmentation into 3$$ {P}_J^{\left[1,8\right]} $$ quark pair and test of NRQCD factorization at two-loop level

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Peng Zhang ◽  
Ce Meng ◽  
Yan-Qing Ma ◽  
Kuang-Ta Chao
Keyword(s):  
Short Distance ◽  
Distance Matrix ◽  
Matrix Elements ◽  
Leading Order ◽  
Long Distance ◽  
Loop Level ◽  
Matching Procedure ◽  
Fragmentation Functions ◽  
Infrared Divergences ◽  
Gluon Fragmentation

Abstract The next-to-leading order (NLO) ($$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in 3$$ {P}_J^{\left[1,8\right]} $$ P J 1 8 states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) perturbative NRQCD matrix elements ⟨$$ {\mathcal{O}}^3{P}_J^{\left[1,8\right]} $$ O 3 P J 1 8 (3$$ {S}_1^{\left[8\right]} $$ S 1 8 )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

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

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
An-Ping Chen ◽  
Xiao-Bo Jin ◽  
Yan-Qing Ma ◽  
Ce Meng
Keyword(s):  
Fragmentation Function ◽  
Short Distance ◽  
Phenomenological Study ◽  
Renormalization Group Equation ◽  
Soft Gluon ◽  
Group Equation ◽  
Hard Part ◽  
Threshold Resummation ◽  
Color Octet ◽  
Gluon Fragmentation

Abstract 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.

scholarly journals SUSY-like relation of the splitting functions in evolution of gluon and quark jet multiplicities

2018 ◽  
Vol 191 ◽  
pp. 04006
Author(s):  
Anatoly Kotikov
Keyword(s):  
Evolution Equations ◽  
Dglap Evolution ◽  
Leading Order ◽  
Logarithmic Order ◽  
World Data ◽  
Charged Hadrons ◽  
Anomalous Dimensions ◽  
The World ◽  
Fragmentation Functions ◽  
Gluon Fragmentation

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. So far, such relationships have only been known from supersymmetric (SUSY) QCD. Exploiting available next-to-nextto- next-to-leading-order (NNNLO) information on the ratio D+g (μ2)=D+q (μ2) of the dominant plus components, the fit of the world data of Dq,g(μ2) for charged hadrons measured in e+e- annihilation leads to α(5)s (MZ) = 0:1205 +0:0016 -0:0020.

scholarly journals Fragmentation of ω and ϕ mesons in e+e− and pp collisions at NLO

2017 ◽  
Vol 32 (33) ◽  
pp. 1750199
Author(s):  
H. Saveetha ◽  
D. Indumathi
Keyword(s):  
Transverse Momentum ◽  
Differential Cross Section ◽  
Cross Section ◽  
Leading Order ◽  
Text Data ◽  
Quark Fragmentation ◽  
Fragmentation Functions ◽  
Error Bars ◽  
First Time ◽  
Gluon Fragmentation

A combined analysis of both [Formula: see text] (LEP, SLD) and [Formula: see text] (RHIC-PHENIX and LHC-ALICE) hadroproduction processes are done for the first time for the vector meson nonet at the next-to-leading order (NLO) using a model with broken SU(3) symmetry. The transverse momentum ([Formula: see text]) and rapidity ([Formula: see text]) dependence of the differential cross-section for [Formula: see text] and [Formula: see text] mesons of the [Formula: see text] data are also discussed. The input universal quark (valence and singlet) fragmentation functions at a starting scale of [Formula: see text], after evolution, have values that are consistent with the earlier analysis for [Formula: see text] at NLO. However, the universal gluon fragmentation function is now well determined from this study with significantly smaller error bars, as the [Formula: see text] hadroproduction cross-section is particularly sensitive to the gluon fragmentation since it occurs at the same order as the quark fragmentation, in contrast to the [Formula: see text] hadroproduction process. Additional parameters involved in describing the strangeness and sea suppression and octet–singlet mixing are found to be close to the earlier analysis; in addition, a new relation between the gluon and sea suppression in [Formula: see text] and [Formula: see text] hadroproduction has been observed.

scholarly journals Power expansion for heavy quarkonium production at next-to-leading order in e+e− annihilation

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Kyle Lee ◽  
George Sterman
Keyword(s):  
Heavy Quark ◽  
Dimensional Regularization ◽  
Heavy Quarkonium ◽  
Group Equation ◽  
Leading Order ◽  
Energy Fraction ◽  
Analytical Results ◽  
Quarkonium Production ◽  
Fragmentation Functions ◽  
Heavy Quark Pair

Abstract We study heavy quarkonium production associated with gluons in e+e− annihilation as an illustration of the perturbative QCD (pQCD) factorization approach, which incorporates the first nonleading power in the energy of the produced heavy quark pair. We show how the renormalization of the four-quark operators that define the heavy quark pair fragmentation functions using dimensional regularization induces “evanescent” operators that are absent in four dimensions. We derive closed forms for short-distance coefficients for quark pair production to next-to-leading order ($$ {\alpha}_s^2 $$ α s 2 ) in the relevant color singlet and octet channels. Using non-relativistic QCD (NRQCD) to calculate the heavy quark pair fragmentation functions up to v4 in the velocity expansion, we derive analytical results for the differential energy fraction distribution of the heavy quarkonium. Calculations for $$ {}^3{S}_1^{\left[1\right]} $$ 3 S 1 1 and $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 channels agree with analogous NRQCD analytical results available in the literature, while several color-octet calculations of energy fraction distributions are new. We show that the remaining corrections due to the heavy quark mass fall off rapidly in the energy of the produced state. To explore the importance of evolution at energies much larger than the mass of the heavy quark, we solve the renormalization group equation perturbatively to two-loop order for the $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 case.

scholarly journals ηQ Meson Photoproduction in Ultrarelativistic Heavy Ion Collisions

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Gong-Ming Yu ◽  
Gao-Gao Zhao ◽  
Zhen Bai ◽  
Yan-Bing Cai ◽  
Hai-Tao Yang ◽  
...  
Keyword(s):  
Heavy Ion Collisions ◽  
Hadron Collider ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Heavy Quarkonium ◽  
Color Singlet ◽  
Initial State ◽  
Color Octet ◽  
Ion Collisions ◽  
The Matrix

The transverse momentum distributions for inclusive ηc,b meson described by gluon-gluon interactions from photoproduction processes in relativistic heavy ion collisions are calculated. We considered the color-singlet (CS) and color-octet (CO) components within the framework of Nonrelativistic Quantum Chromodynamics (NRQCD) in the production of heavy quarkonium. The phenomenological values of the matrix elements for the color-singlet and color-octet components give the main contribution to the production of heavy quarkonium from the gluon-gluon interaction caused by the emission of additional gluon in the initial state. The numerical results indicate that the contribution of photoproduction processes cannot be negligible for midrapidity in p-p and Pb-Pb collisions at the Large Hadron Collider (LHC) energies.

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