scholarly journals Bottomonium production and polarization in the NRQCD with $$k_T$$-factorization. III: $$\Upsilon (1S)$$ and $$\chi _b(1P)$$ mesons

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
N. A. Abdulov ◽  
A. V. Lipatov
Keyword(s):  
Bound States ◽  
Meson Production ◽  
Spin Density Matrix ◽  
Factorization Approach ◽  
Direct Production ◽  
Transverse Momentum Dependent ◽  
Radiation Theory ◽  
Multipole Radiation ◽  
Shell Production ◽  
Upsilon 1S

AbstractThe $$\Upsilon (1S)$$ Υ ( 1 S ) meson production and polarization at high energies is studied in the framework of the $$k_T$$ k T -factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative $$\chi _b(mP)$$ χ b ( m P ) decays and contributions from $$\Upsilon (3S)$$ Υ ( 3 S ) and $$\Upsilon (2S)$$ Υ ( 2 S ) decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and the Kimber-Martin–Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for $$\Upsilon (1S)$$ Υ ( 1 S ) and $$\chi _b(1P)$$ χ b ( 1 P ) mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters $$\lambda _\theta $$ λ θ , $$\lambda _\phi $$ λ ϕ and $$\lambda _{\theta \phi }$$ λ θ ϕ , which determine the $$\Upsilon (1S)$$ Υ ( 1 S ) spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

scholarly journals Bottomonia production and polarization in the NRQCD with $$k_T$$-factorization. I: $$\Upsilon (3S)$$ and $$\chi _b(3P)$$ mesons

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
N. A. Abdulov ◽  
A. V. Lipatov
Keyword(s):  
Bound States ◽  
Spin Density Matrix ◽  
Unintegrated Gluon ◽  
Factorization Approach ◽  
Transverse Momentum Dependent ◽  
High Energies ◽  
Radiation Theory ◽  
Multipole Radiation ◽  
Shell Production ◽  
Good Agreement

Abstract The $$\Upsilon (3S)$$Υ(3S) production and polarization at high energies is studied in the framework of $$k_T$$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 Ciafaloni-Catani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the non-perturbative color octet transitions in terms of the multipole radiation theory and taking into account feed-down contributions from radiative $$\chi _b(3P)$$χb(3P) decays, we extract the corresponding non-perturbative matrix elements for $$\Upsilon (3S)$$Υ(3S) and $$\chi _b(3P)$$χb(3P) mesons from a combined fit to $$\Upsilon (3S)$$Υ(3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies $$\sqrt{s} = 7$$s=7 and 13 TeV and central rapidities. Then we apply the extracted values to describe the CDF and LHCb data on $$\Upsilon (3S)$$Υ(3S) production and to investigate the polarization parameters $$\lambda _\theta $$λθ, $$\lambda _\phi $$λϕ and $$\lambda _{\theta \phi }$$λθϕ, which determine the $$\Upsilon (3S)$$Υ(3S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

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 Spin Density Matrix Elements from diffractive φ meson production at HERMES

2008 ◽  
Author(s):  
Witold Augustyniak ◽  
A Borissov ◽  
S Manayenkov
Keyword(s):  
Density Matrix ◽  
Spin Density ◽  
Meson Production ◽  
Spin Density Matrix ◽  
Matrix Elements

scholarly journals J/ψ meson production in SIDIS: matching high and low transverse momentum

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Daniël Boer ◽  
Umberto D’Alesio ◽  
Francesco Murgia ◽  
Cristian Pisano ◽  
Pieter Taels
Keyword(s):  
Transverse Momentum ◽  
Meson Production ◽  
Distance Matrix ◽  
Inelastic Electron ◽  
High Transverse Momentum ◽  
Shape Functions ◽  
Long Distance ◽  
Collinear Factorization ◽  
Transverse Momentum Dependent ◽  
Gluon Distributions

Abstract We consider the transverse momentum spectrum and the cos 2ϕ azimuthal distribution of J/ψ mesons produced in semi-inclusive, deep-inelastic electron-proton scattering, where the electron and the proton are unpolarized. At low transverse momentum, we propose factorized expressions in terms of transverse momentum dependent gluon distributions and shape functions. We show that our formulae, at the order αs, correctly match with the collinear factorization results at high transverse momentum. The latter are computed at the order $$ {\alpha}_s^2 $$ α s 2 in the framework of nonrelativistic QCD (NRQCD), with the inclusion of the intermediate $$ {}^3{S}_1^{\left[1\right]} $$ 3 S 1 1 color-singlet Fock state, as well as the subleading color-octet ones that are relatively suppressed by a factor v4 in the NRQCD velocity parameter v. We show that the $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 and $$ {}^3{P}_J^{\left[8\right]} $$ 3 P J 8 (J = 0, 1, 2) contributions diverge in the small transverse momentum region and allow us to determine the perturbative tails of the shape functions, which carry the same quantum numbers. These turn out to be identical, except for the overall magnitude given by the appropriate NRQCD long distance matrix element.

SHAPE OF PION DISTRIBUTION AMPLITUDE AND TRANSVERSE MOMENTUM IN HARD EXCLUSIVE PROCESSES

2011 ◽  
Vol 04 ◽  
pp. 200-215
Author(s):  
A. V. RADYUSHKIN
Keyword(s):  
Transverse Momentum ◽  
Real Photon ◽  
Third Way ◽  
Factorization Approach ◽  
Transverse Momentum Dependent ◽  
Local Duality ◽  
Duality Approach ◽  
Exclusive Processes ◽  
Inclusive Processes ◽  
Low K

Inclusion of transverse momentum effects into the description of the pion-photon transition form factor is discussed. At low k⊥, a consistent description may be obtained within the light-front formalism. On the other hand, the large-k⊥ limit is most conveniently treated within the Sudakov parameterization framework. The third way of introducing k⊥ is based on the "local duality" approach motivated by QCD sum rules. It is shown that, while the local duality gives a correct (coinciding with the axial anomaly based prediction) result for the real photon point, a straightforward extension of the formulas of the modified factorization approach into the small virtualities domain produces a divergent result. It is pointed out that such lessons should be taken into account while constructing transverse-momentum-dependent schemes for inclusive processes.

scholarly journals Forward trijet production in p-p and p-Pb collisions at LHC

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Marcin Bury ◽  
Andreas van Hameren ◽  
Piotr Kotko ◽  
Krzysztof Kutak
Keyword(s):  
Center Of Mass ◽  
Azimuthal Angle ◽  
Final States ◽  
Forward Rapidity ◽  
Factorization Approach ◽  
Proton Proton ◽  
Transverse Momentum Dependent ◽  
Center Of Mass Energy ◽  
Gluon Distributions ◽  
Saturation Effects

Abstract We calculate various azimuthal angle distributions for three jets produced in the forward rapidity region with transverse momenta pT> 20 GeV in proton-proton (p-p) and proton-lead (p-Pb) collisions at center of mass energy 5.02 TeV. We use the multiparton extension of the so-called small-x Improved Transverse Momentum Dependent factorization (ITMD). We study effects related to change from the standard kT -factorization to ITMD factorization as well as changes as one goes from p-p collision to p-Pb. We observe rather large differences in the distribution when we change the factorization approach, which allows to both improve the small-x TMD gluon distributions as well as validate and improve the factorization approach. We also see significant depletion of the nuclear modification ratio, indicating a possibility of searches for saturation effects using trijet final states in a more exclusive way than for dijets.

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