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 $${J/\psi }$$-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 $$\chi _{c1}$$ 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.

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 TOWARDS A THREE-DIMENSIONAL SOLUTION FOR 3N BOUND STATES WITH 3NFs

2009 ◽  
Vol 24 (11n13) ◽  
pp. 816-822 ◽  
Author(s):  
M. R. HADIZADEH ◽  
S. BAYEGAN
Keyword(s):  
Partial Wave ◽  
Integral Equations ◽  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Matrix Elements ◽  
Dimensional Solution ◽  
Dimensional Integral

After a brief discussion about the necessity of using the 3D approach, we present the non partial wave (PW) formalism for 3N bound state with the inclusion of 3N force (3NF). As an example the evaluation of 3NF matrix elements, which appear in the obtained coupled three-dimensional integral equations, for 2π-exchange Tucson–Melbourne 3NF show how would be this formalism efficient and less cumbersome in comparison with the PW formalism.

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 Long and short distance behavior of the imaginary part of the heavy-quark potential

2022 ◽  
Vol 258 ◽  
pp. 04008
Author(s):  
Kirill Boguslavski ◽  
Babak Kasmaei ◽  
Michael Strickland
Keyword(s):  
Heavy Quark ◽  
Imaginary Part ◽  
Short Distance ◽  
Bound States ◽  
Yang Mills ◽  
Temporal Decay ◽  
Wide Range ◽  
Quark Potential ◽  
Heavy Quark Potential ◽  
Distance Behavior

The imaginary part of the effective heavy-quark potential can be related to the total in-medium decay width of of heavy quark-antiquark bound states. We extract the static limit of this quantity using classical-statistical simulations of the real-time Yang-Mills dynamics by measuring the temporal decay of Wilson loops. By performing the simulations on finer and larger lattices we are able to show that the nonperturbative results follow the same form as the perturbative ones. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. We also extract approximations for the short-distance behavior of the classical potential.

scholarly journals Relativistic Friedrichs–Lee model and quark-pair creation model

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Zhi-Yong Zhou ◽  
Zhiguang Xiao
Keyword(s):  
Potential Model ◽  
Scattering Amplitude ◽  
Bound State ◽  
Pair Creation ◽  
The Other ◽  
Hadron Spectrum ◽  
Lee Model ◽  
Continuum States ◽  
Quark Potential ◽  
The Continuum

AbstractIn this paper, we present how the Friedrichs–Lee model could be extended to the relativistic scenario and be combined with the relativistic quark pair creation model in a consistent way. This scheme could be applied to study the “unquenched” effect of the meson spectra. As an example, if the lowest $$J^{PC}=0^{++}$$ J PC = 0 + + $$(u\bar{u}+d\bar{d})/\sqrt{2}$$ ( u u ¯ + d d ¯ ) / 2 bound state in the potential model is coupled to the $$\pi \pi $$ π π continuum, two resonance poles could be found from the scattering amplitude for the continuum states. One of them could correspond to the $$f_0(500)/\sigma $$ f 0 ( 500 ) / σ and the other probably $$f_0(1370)$$ f 0 ( 1370 ) . This scheme might shed more light on why extra states could appear in the hadron spectrum other than the prediction of the quark potential model.

scholarly journals Energy levels in muonic helium

2019 ◽  
Vol 222 ◽  
pp. 03009
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Hyperfine Structure ◽  
Bound States ◽  
Energy Levels ◽  
Computer Code ◽  
Bound State ◽  
Relativistic Correction ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.

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