scholarly journals Quarkonium TMD fragmentation functions in NRQCD

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Miguel G. Echevarria ◽  
Yiannis Makris ◽  
Ignazio Scimemi
Keyword(s):  
Transverse Momentum ◽  
Phenomenological Study ◽  
Light Quark ◽  
Distance Matrix ◽  
Gluon Fusion ◽  
Coupling Constant ◽  
Long Distance ◽  
Transverse Momentum Dependent ◽  
Quarkonium Production ◽  
Fragmentation Functions

Abstract We study the transverse-momentum spectrum of quarkonium production from single light-parton fragmentation mechanism. In the case of semi-inclusive deep inelastic scattering, we observe that there are two possible initiating processes, namely photon-gluon fusion and light-quark fragmentation. For the second case we derive the factorization theorem, which involves a new hadronic quantity: the quarkonium transverse-momentum-dependent fragmentation functions in NRQCD. We calculate their matching onto the non-perturbative long distance matrix elements at the lowest order in the strong-coupling constant, $$ \mathcal{O}\left({\alpha}_s^2\right) $$ O α s 2 . Focusing on the case of the electron-ion collider, we make a comparative phenomenological study of the two production mechanisms and find the regions of the phase space where one is dominant over the other.

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.

BESSEL-WEIGHTED ASYMMETRIES AND TRANSVERSE SPIN EFFECTS

2012 ◽  
Vol 20 ◽  
pp. 168-176
Author(s):  
LEONARD GAMBERG
Keyword(s):  
Transverse Momentum ◽  
Cross Section ◽  
Parton Distribution ◽  
Evolution Equations ◽  
Distribution Functions ◽  
Transverse Spin ◽  
High Transverse Momentum ◽  
Transverse Momentum Dependent ◽  
Fragmentation Functions ◽  
The Cross

We consider the cross section for semi-inclusive deep inelastic scattering in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

scholarly journals General helicity formalism for two-hadron production in e+e− annihilation within a TMD approach

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Umberto D’Alesio ◽  
Francesco Murgia ◽  
Marco Zaccheddu
Keyword(s):  
Transverse Momentum ◽  
Hadron Production ◽  
Probabilistic Interpretation ◽  
Leading Order ◽  
Transverse Momentum Dependent ◽  
Factorization Scheme ◽  
Helicity Formalism ◽  
Double Polarization ◽  
Fragmentation Functions ◽  
Polarization Observables

Abstract We present the complete leading-order results for the azimuthal dependences and polarization observables in e+e−→ h1h2 + X processes, where the two hadrons are produced almost back-to-back, within a transverse momentum dependent (TMD) factorization scheme. We consider spinless (or unpolarized) and spin-1/2 hadron production and give the full set of the corresponding quark and gluon TMD fragmentation functions (TMD-FFs). By adopting the helicity formalism, which allows for a more direct probabilistic interpretation, single- and double-polarization cases are discussed in detail. Simplified expressions, useful for phenomenological analyses, are obtained by assuming a factorized Gaussian-like dependence on intrinsic transverse momenta for the TMD-FFs.

scholarly journals Back-to-Back Isolated Photon-Quarkonium Production at the LHC and the Transverse-Momentum-Dependent Distributions of the Gluons in the Proton

2016 ◽  
Vol 40 ◽  
pp. 1660015 ◽  
Author(s):  
J. P. Lansberg
Keyword(s):  
Transverse Momentum ◽  
Experimental Determination ◽  
Heavy Quarkonia ◽  
Proton Proton ◽  
Transverse Momentum Dependent ◽  
Proton Collisions ◽  
Quarkonium Production ◽  
Linearly Polarized ◽  
Proton Proton Collisions

The study of isolated heavy quarkonia, such as [Formula: see text] and [Formula: see text], produced in association with a photon in proton-proton collisions at the LHC, is probably the optimal way to get right away a first experimental determination of two gluon transverse-momentum-dependent distribution (TMDs) in an unpolarized proton, [Formula: see text] and [Formula: see text], the latter giving the distribution of linearly polarized gluons. To substantiante this, we calculate the transverse-momentum-dependent effects that arise in the process under study and discuss the feasibility of their measurements.

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.

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