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.

Bc → J/ψ tensor form factors at large momentum recoil

2021 ◽  
pp. 2150135
Author(s):  
Dandan Shen ◽  
Huimin Ren ◽  
Fan Wu ◽  
Ruilin Zhu
Keyword(s):  
Form Factors ◽  
Distance Matrix ◽  
Relativistic Correction ◽  
Large Momentum ◽  
Matrix Elements ◽  
Leading Order ◽  
Lattice Data ◽  
Tensor Form ◽  
Long Distance ◽  
Current Form

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

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 Prompt $${J/\psi }$$-pair production at the LHC: impact of loop-induced contributions and of the colour-octet mechanism

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Jean-Philippe Lansberg ◽  
Hua-Sheng Shao ◽  
Nodoka Yamanaka ◽  
Yu-Jie Zhang
Keyword(s):  
Pair Production ◽  
Good Control ◽  
Distance Matrix ◽  
High Energy ◽  
Matrix Elements ◽  
Hadron Colliders ◽  
Long Distance ◽  
Gauge Invariant ◽  
Energy Hadron ◽  
Colour Octet

AbstractPrompt double-$$J/\psi $$J/ψ production at high-energy hadron colliders can be considered as a golden channel to probe double parton scatterings (DPS)—in particular to study gluon–gluon correlations inside the proton—and, at the same time, to measure the distribution of linearly-polarised gluons inside the proton. Such studies, however, require a good control of both single parton scatterings (SPS) and DPS in the respective regions where they are carried out. In this context, we have critically examined two mechanisms of SPS that may be kinematically enhanced where DPS are thought to be dominant, even though they are either at higher orders in the strong-coupling or velocity expansion. First, we have considered a gauge-invariant and infrared-safe subset of the loop-induced contribution via colour-singlet (CS) transitions. We have found it to become the leading CS SPS contributions at large rapidity separation, yet too small to account for the data without invoking the presence of DPS yields. Second, we have surveyed the possible colour-octet (CO) contributions using both old and up-to-date non-perturbative long-distance matrix elements (LDMEs). We have found that the pure CO yields crucially depend on the LDMEs. Among all the LDMEs we used, only two result into a visible modification of the NRQCD (CS+CO) yield, but only in two kinematical distributions measured by ATLAS, those of the rapidity separation and of the pair invariant mass. These modifications, however, do not impact the control region used for their DPS study.

scholarly journals Quarkonium Production: Velocity-Scaling Rules and Long-Distance Matrix Elements

1997 ◽  
Vol 12 (22) ◽  
pp. 3951-3963 ◽  
Author(s):  
Gerhard A. Schuler
Keyword(s):  
Heavy Quark ◽  
Bound States ◽  
Potential Model ◽  
Distance Matrix ◽  
Bound State ◽  
Matrix Elements ◽  
Long Distance ◽  
Quarkonium Production ◽  
Quark Potential ◽  
Colour Octet

The hierarchy of long-distance matrix elements (MEs) for quarkonium production depends on their scaling with the velocity v of the heavy quark in the bound state. Ranges for the velocities in various bound states and uncertainties of colour-singlet MEs are estimated in a quark-potential model. Different possibilities for the scaling with v of the MEs are discussed; they depend on the actual values of v and the QCD scale. As an application, J/ψ polarization in e+e- annihilation is discussed. The first non-perturbative estimates of colour-octet MEs are presented and compared with phenomenological determinations. Finally, various predictions of prompt quarkonium production at LEP are compared.

scholarly journals Inclusive production of heavy quarkonia in pNRQCD

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Nora Brambilla ◽  
Hee Sok Chung ◽  
Antonio Vairo
Keyword(s):  
Cross Sections ◽  
Production Cross ◽  
Distance Matrix ◽  
Effective Field ◽  
Heavy Quarkonia ◽  
Inclusive Production ◽  
Theory Approach ◽  
Matrix Elements ◽  
Long Distance ◽  
Nonrelativistic Qcd

Abstract We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order $$ 1/{N}_c^2 $$ 1 / N c 2 . These expressions enhance the predictive power of the nonrelativistic effective field theory approach to inclusive production processes by reducing the number of nonperturbative unknowns, and make possible first-principle determinations of long-distance matrix elements once the gluonic correlators are known. Based on this formalism, we compute the production cross sections of P-wave charmonia and bottomonia at the LHC, and find good agreement with measurements.

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 Study on branching ratios and direct CP asymmetries of D → PV decays

2014 ◽  
Vol 29 ◽  
pp. 1460209 ◽  
Author(s):  
Qin Qin ◽  
Hsiang-Nan Li ◽  
Cai-Dian Lü ◽  
Fu-Sheng Yu
Keyword(s):  
Experimental Data ◽  
Pseudoscalar Meson ◽  
Short Distance ◽  
D Mesons ◽  
Branching Ratios ◽  
Matrix Elements ◽  
Long Distance ◽  
Global Fit ◽  
Belle Ii ◽  
Cp Asymmetries

We study the non-leptonic two-body decays of D mesons decaying into one pseudoscalar meson (P) and one vector meson (V) in the factorization-asisted topological-amplitude approach. In this approach, the decay amplitudes are factorized into two parts, the short-distance contribution (Wilson coefficients) and the long-distance contribution (hadronic matrix elements). We predict the branching ratios of D → PV decays using a global fit with the non-perturbative parameters. Our results agree well with the experimental data. We also predict the direct CP asymmetries by combining short-distance dynamics associated with penguin operators and long-distance hadronic matrix elements determined by branching ratios. The large asymmetries in D+ → π+ρ0 and [Formula: see text] may be measurable in the LHCb and future Belle II experiments.

scholarly journals Prompt $$J/\psi $$ photoproduction within the non-relativistic QCD framework at the CEPC

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Xi-Jie Zhan ◽  
Jian-Xiong Wang
Keyword(s):  
Transverse Momentum ◽  
Total Cross Section ◽  
Cross Section ◽  
Hadron Collider ◽  
Distance Matrix ◽  
Matrix Elements ◽  
Long Distance ◽  
Color Octet ◽  
Electron Positron ◽  
The Future

Abstract The prompt $$J/\psi $$J/ψ photoproduction within the non-relativistic QCD (NRQCD) framework at the future Circular Electron Positron Collider (CEPC) is studied, including the contributions from both direct and resolved photons. Employing different sets of long distance matrix elements, the total cross section is dominated by the color-octet channel. We present different kinematic distributions of $$J/\psi $$J/ψ production and the results show there will be about 50 $$J/\psi $$J/ψ events when the transverse momentum of $$J/\psi $$J/ψ is up to 20 GeV. It renders that the $$J/\psi $$J/ψ photoprodution at the CEPC is a well laboratory to test the NRQCD and further clarify the universality problem in NRQCD between electron positron collider and hadron collider.

scholarly journals Short-distance matrix elements for D0 -meson mixing from Nf=2+1 lattice QCD

2018 ◽  
Vol 97 (3) ◽  
Author(s):  
A. Bazavov ◽  
C. Bernard ◽  
C. M. Bouchard ◽  
C. C. Chang ◽  
C. DeTar ◽  
...  
Keyword(s):  
Lattice Qcd ◽  
Short Distance ◽  
Distance Matrix ◽  
Matrix Elements ◽  
Meson Mixing
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