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 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 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 Intrinsic charm in the nucleon and charm production at large rapidities in collinear, hybrid and kT-factorization approaches

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Rafał Maciuła ◽  
Antoni Szczurek
Keyword(s):  
Transverse Momentum ◽  
High Energy ◽  
Charm Production ◽  
Leading Order ◽  
Collinear Factorization ◽  
Factorization Approach ◽  
High Energies ◽  
Neutrino Production ◽  
Intrinsic Charm ◽  
Gluon Distributions

Abstract We discuss the role of intrinsic charm (IC) in the nucleon for forward production of c-quark (or $$ \overline{c} $$ c ¯ -antiquark) in proton-proton collisions for low and high energies. The calculations are performed in collinear-factorization approach with on-shell partons, kT-factorization approach with off-shell partons as well as in a hybrid approach using collinear charm distributions and unintegrated (transverse momentum dependent) gluon distributions. For the collinear-factorization approach we use matrix elements for both massless and massive charm quarks/antiquarks. The distributions in rapidity and transverse momentum of charm quark/antiquark are shown for a few different models of IC. Forward charm production is dominated by gc-fusion processes. The IC contribution dominates over the standard pQCD (extrinsic) gg-fusion mechanism of $$ c\overline{c} $$ c c ¯ -pair production at large rapidities or Feynman-xF. We perform similar calculations within leading-order and next-to-leading order kT-factorization approach. The kT-factorization approach leads to much larger cross sections than the LO collinear approach. At high energies and large rapidities of c-quark or $$ \overline{c} $$ c ¯ -antiquark one tests gluon distributions at extremely small x. The IC contribution has important consequences for high-energy neutrino production in the Ice-Cube experiment and can be, to some extent, tested at the LHC by the SHIP and FASER experiments by studies of the ντ neutrino production.

scholarly journals The Boer-Mulders Transverse Momentum Distribution in the Pion and its Evolution in Lattice QCD

2015 ◽  
Vol 37 ◽  
pp. 1560034 ◽  
Author(s):  
M. Engelhardt ◽  
B. Musch ◽  
P. Hägler ◽  
A. Schäfer ◽  
J. Negele
Keyword(s):  
Transverse Momentum ◽  
Lattice Qcd ◽  
Momentum Distribution ◽  
Transverse Momentum Distribution ◽  
Matrix Elements ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Gauge Link ◽  
Definition Of ◽  
Type Parameter

Starting from a definition of transverse momentum-dependent parton distributions (TMDs) in terms of hadronic matrix elements of a quark bilocal operator containing a staple-shaped gauge link, selected TMD observables can be evaluated within Lattice QCD. A TMD ratio describing the Boer-Mulders effect in the pion is investigated, with a particular emphasis on its evolution as a function of a Collins-Soper-type parameter which quantifies the proximity of the staple-shaped gauge links to the light cone.

TRANSVERSE MOMENTUM-DEPENDENT PARTON DISTRIBUTIONS FROM LATTICE QCD

2012 ◽  
Vol 20 ◽  
pp. 153-161
Author(s):  
M. ENGELHARDT ◽  
B. MUSCH ◽  
P. HÄGLER ◽  
J. NEGELE ◽  
A. SCHÄFER
Keyword(s):  
Transverse Momentum ◽  
Inelastic Scattering ◽  
Lattice Qcd ◽  
Lorentz Frame ◽  
Matrix Elements ◽  
Lattice Calculation ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Calculation Results ◽  
Definition Of

Starting from a definition of transverse momentum-dependent parton distributions for semi-inclusive deep inelastic scattering and the Drell-Yan process, given in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection, a scheme to determine such observables in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are presented, focusing in particular on their dependence on the staple extent and the Collins-Soper evolution parameter.

Mass and energy dependence of the transverse momentum densities in covariant parton model

2015 ◽  
Vol 30 (27) ◽  
pp. 1550133 ◽  
Author(s):  
M. M. Yazdanpanah ◽  
A. Mirjalili ◽  
A. Behjat Ramezani
Keyword(s):  
Binding Energy ◽  
Transverse Momentum ◽  
Quark Model ◽  
Energy Dependence ◽  
Parton Model ◽  
Longitudinal Momentum ◽  
Transverse Momentum Dependent ◽  
Unpolarized Case ◽  
Covariant Quark Model ◽  
Good Agreement

The parton densities which are dependent on transverse momentum, open a way to understand better the structure of quarks and gluons in a more complete way. We are investigating a method based on the covariant quark model which enables us to extract the transverse momentum dependent (TMD) densities from the usual parton densities which are just dependent on the longitudinal momentum. In continuation, we obtain the dependence of the TMDs on binding energy and the mass of quarks. We do some calculations to obtain the TMDs in the unpolarized case while the mass and binding energy of partons are varying. Considering these effects, the results for TMDs are in good agreement with the results of the recent related models.

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 Determination of the Collins-Soper Kernel from Lattice QCD

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Maximilian Schlemmer ◽  
Alexey Vladimirov ◽  
Christian Zimmermann ◽  
Michael Engelhardt ◽  
Andreas Schäfer
Keyword(s):  
Transverse Momentum ◽  
Lattice Qcd ◽  
Energy Dependence ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Good Agreement

Abstract We present lattice results for the non-perturbative Collins-Soper (CS) kernel, which describes the energy-dependence of transverse momentum-dependent parton distributions (TMDs). The CS kernel is extracted from the ratios of first Mellin moments of quasi-TMDs evaluated at different nucleon momenta. The analysis is done with dynamical Nf = 2 + 1 clover fermions for the CLS ensemble H101 (a = 0.0854 fm, mπ = mK = 422 MeV). The computed CS kernel is in good agreement with experimental extractions and previous lattice studies.

scholarly journals UNIVERSALITY OF QUARK AND GLUON TMD CORRELATORS

2014 ◽  
Vol 25 ◽  
pp. 1460003 ◽  
Author(s):  
M. G. A. BUFFING ◽  
P. J. MULDERS ◽  
A. MUKHERJEE
Keyword(s):  
Transverse Momentum ◽  
Finite Number ◽  
Operator Product Expansion ◽  
Distribution Functions ◽  
Operator Product ◽  
Matrix Elements ◽  
Universal Functions ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Gauge Link

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs), in short referred to as TMDs, also take into account the transverse momentum (pT) of the partons. Just as the pT-integrated analogues we want to link them to quark and gluon matrix elements using Operator Product Expansion methods in QCD, involving operators of definite twist. The TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Using the expression for TMDs involving nonlocal matrix elements of quark and gluon fields there is a gauge link dependence, which also introduces an inherent process dependence. Using transverse moments, which are specific pT-weightings, we can establish the link with quark and gluon fields including the higher twist ones. We introduce (a finite number of) universal TMDs of definite rank and show how the process dependent TMDs can be written as combinations of these universal functions.

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