scholarly journals $$\chi _{c1}$$ and $$\chi _{c2}$$ polarization as a probe of color octet channel

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
S. P. Baranov ◽  
A. V. Lipatov
Keyword(s):  
Bound States ◽  
Distance Matrix ◽  
Wave Functions ◽  
Color Singlet ◽  
Matrix Elements ◽  
Polarization Data ◽  
Long Distance ◽  
Factorization Approach ◽  
Color Octet ◽  
Polar Anisotropy

AbstractWe analyze joint LHC data on the production of $$\chi _{c1}$$ χ c 1 and $$\chi _{c2}$$ χ c 2 mesons together with the polarization data obtained very recently by the CMS Collaboration at $$\sqrt{s} = 8$$ s = 8  TeV. Our consideration is based on the $$k_T$$ k T -factorization approach and nonrelativistic QCD formalism for the formation of bound states. The observed polar anisotropy of $$\chi _{c1}$$ χ c 1 and $$\chi _{c2}$$ χ c 2 decays can be described as a combined effect of the color-singlet and color-octet contributions. We extract the corresponding long-distance matrix elements from the fits. Our fits point to unequal color singlet wave functions for $$\chi _{c1}$$ χ c 1 and $$\chi _{c2}$$ χ c 2 states.

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 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.

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 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 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 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 NEXT-TO-LEADING ORDER TESTS OF NON-RELATIVISTIC-QCD FACTORIZATION WITH J/ψ YIELD AND POLARIZATION

2013 ◽  
Vol 28 (09) ◽  
pp. 1350027 ◽  
Author(s):  
MATHIAS BUTENSCHOEN ◽  
BERND A. KNIEHL
Keyword(s):  
Relativistic Quantum ◽  
Distance Matrix ◽  
Data Sets ◽  
Leading Order ◽  
Fixed Target ◽  
Polarization Data ◽  
Long Distance ◽  
Qcd Factorization ◽  
Global Fit ◽  
Photo Production

We report on recent progress in testing the factorization formalism of non-relativistic quantum chromodynamics (NRQCD) at next-to-leading order (NLO) for J/ψ yield and polarization. We demonstrate that it is possible to unambiguously determine the leading color-octet (CO) long-distance matrix elements (LDMEs) in compliance with the velocity scaling rules through a global fit to experimental data of unpolarized J/ψ production in pp, [Formula: see text], ep, γγ, and e+e-collisions. Three data sets not included in the fit, from hadro-production and from photo-production in the fixed-target and colliding-beam modes, are nicely reproduced. The polarization observables measured in different frames at DESY HERA and CERN LHC reasonably agree with NLO NRQCD predictions obtained using the LDMEs extracted from the global fit, while measurements at the FNAL Tevatron exhibit severe disagreement. We demonstrate that the alternative LDME sets recently obtained, with different philosophies, in two other NLO NRQCD analyses of J/ψ yield and polarization also fail to reconcile the Tevatron polarization data with the other available world data.

scholarly journals ϒ(3S) and χb(3P) production and polarization in the NRQCD with kT–factorization

2019 ◽  
Vol 222 ◽  
pp. 03013
Author(s):  
Nizami Abdulov ◽  
Artem Lipatov
Keyword(s):  
Transverse Momentum ◽  
Bound States ◽  
Matrix Elements ◽  
Unintegrated Gluon ◽  
Factorization Approach ◽  
Transverse Momentum Dependent ◽  
High Energies ◽  
Radiation Theory ◽  
Shell Production ◽  
Good Agreement

The ϒ(3S) production and polarization at high energies is studied in the framework of kT–factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The transverse momentum dependent (TMD, or unintegrated) gluon densities in a proton were derived from the CiafaloniCatani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the nonperturbative color octet transitions in terms of the mulitpole radiation theory and taking into account feed-down contributions from radiative χb(3P) decays, we extract the corresponding non-perturbative matrix elements for ϒ(3S) and χb(3P) mesons from a combined fit to ϒ(3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies √s = 7 and 13 TeV and central rapidities. Then we apply the extracted values to investigate the polarization parameters λθ, λφ and λθφ, which determine the ϒ(3S) spindensity matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

scholarly journals Inclusive Hadroproduction of P-wave Heavy Quarkonia in pNRQCD

2022 ◽  
Vol 258 ◽  
pp. 04005
Author(s):  
Hee Sok Chung
Keyword(s):  
Cross Sections ◽  
Production Cross ◽  
Distance Matrix ◽  
Heavy Quarkonia ◽  
P Wave ◽  
Inclusive Production ◽  
Matrix Elements ◽  
Long Distance ◽  
Strongly Coupled ◽  
Section Data

We compute NRQCD long-distance matrix elements that appear in the inclusive production cross sections of P-wave heavy quarkonia in the framework of potential NRQCD. The formalism developed in this work applies to strongly coupled charmonia and bottomonia. This makes possible the determination of color-octet NRQCD long-distance matrix elements without relying on measured cross section data, which has not been possible so far. We obtain results for inclusive production cross sections of χcJ and χbJ at the LHC, which are in good agreement with measurements.

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