84 research outputs found
On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions
Transverse-momentum dependent parton distributions (TMDs) are studied in the
framework of quark models. In particular, quark-model relations among TMDs are
reviewed, elucidating their physical origin in terms of the quark-spin
structure in the nucleon. The formal aspects of the derivation of these
relations are complemented with explicit examples, emphasizing how and to which
extent the conditions which lead to relations among TMDs are implemented in
different classes of quark models.Comment: 38 pages, 3 figures, 3 table
The angular momentum controversy: What's it all about and does it matter?
The general question, crucial to an understanding of the internal structure
of the nucleon, of how to split the total angular momentum of a photon or gluon
into spin and orbital contributions is one of the most important and
interesting challenges faced by gauge theories like Quantum Electrodynamics and
Quantum Chromodynamics. This is particularly challenging since all QED
textbooks state that such an splitting cannot be done for a photon (and a
fortiori for a gluon) in a gauge-invariant way, yet experimentalists around the
world are engaged in measuring what they believe is the gluon spin! This
question has been a subject of intense debate and controversy, ever since, in
2008, it was claimed that such a gauge-invariant split was, in fact, possible.
We explain in what sense this claim is true and how it turns out that one of
the main problems is that such a decomposition is not unique and therefore
raises the question of what is the most natural or physical choice. The
essential requirement of measurability does not solve the ambiguities and leads
us to the conclusion that the choice of a particular decomposition is
essentially a matter of taste and convenience. In this review, we provide a
pedagogical introduction to the question of angular momentum decomposition in a
gauge theory, present the main relevant decompositions and discuss in detail
several aspects of the controversies regarding the question of gauge
invariance, frame dependence, uniqueness and measurability. We stress the
physical implications of the recent developments and collect into a separate
section all the sum rules and relations which we think experimentally relevant.
We hope that such a review will make the matter amenable to a broader community
and will help to clarify the present situation.Comment: 96 pages, 11 figures, 5 tables, review prepared for Physics Report
Modeling the transverse momentum dependent parton distributions
We review quark model calculations of the transverse momentum dependent
parton distributions (TMDs). For the T-even TMDs, we discuss the physical
origin of model relations which hold in a large class of quark models. For the
T-odd TMDs we review results in a light-cone constituent quark model (CQM) with
the final state interaction effects generated via single-gluon exchange
mechanism. As phenomenological application, we show the good agreement between
results in the light-cone CQM and available experimental data for the Collins
asymmetry.Comment: 8 pages, 2 figures, 2 tables; invited talk at "The 4th Workshop on
Exclusive Reactions at High Momentum Transfer", Jefferson Lab., May 18-21,
201
Quark Wigner Distributions and Orbital Angular Momentum
We study the Wigner functions of the nucleon which provide multidimensional
images of the quark distributions in phase space. These functions can be
obtained through a Fourier transform in the transverse space of the generalized
transverse-momentum dependent parton distributions. They depend on both the
transverse position and the three-momentum of the quark relative to the
nucleon, and therefore combine in a single picture all the information
contained in the generalized parton distributions and the transverse-momentum
dependent parton distributions. We focus the discussion on the distributions of
unpolarized/longitudinally polarized quark in an unpolarized/longitudinally
polarized nucleon. In this way, we can study the role of the orbital angular
momentum of the quark in shaping the nucleon and its correlations with the
quark and nucleon polarizations. The quark orbital angular momentum is also
calculated from its phase-space average weighted with the Wigner distribution
of unpolarized quarks in a longitudinally polarized nucleon. The corresponding
results obtained within different light-cone quark models are compared with
alternative definitions of the quark orbital angular momentum, as given in
terms of generalized parton distributions and transverse-momentum dependent
parton distributions.Comment: 29 pages, 10 figures, 3 table
Models for TMDs and numerical methods
We study the connection between the quark orbital angular momentum and the
pretzelosity transverse-momentum dependent parton distribution function. We
discuss the origin of this relation in quark models, identifying as key
ingredient for its validity the assumption of spherical symmetry for the
nucleon in its rest frame. Finally we show that the individual quark
contributions to the orbital angular momentum obtained from this relation can
not be interpreted as the intrinsic contributions, but include the contribution
from the transverse centre of momentum which cancels out only in the total
orbital angular momentum.Comment: 43 pages, 8 figures; proceedings of International School of Physics
"Enrico Fermi", Course CLXXX - "Three-dimensional Partonic Structure of the
Nucleon", 28 June - 8 July 2011, Varenna (Italy
The Parton Orbital Angular Momentum: Status and Prospects
Theoretical progress on the formulation and classification of the quark and
gluon orbital angular momenta (OAM) is reviewed. Their relation to parton
distributions and open questions and puzzles are discussed. We give a status
report on the lattice calculation of the parton kinetic and canonical OAM and
point out several strategies to calculate the quark and gluon canonical OAM on
the lattice.Comment: 16 pages, contribution to the EPJA speical issue on "3D Structure of
the Nucleon
Pretzelosity TMD and Quark Orbital Angular Momentum
We study the connection between the quark orbital angular momentum and the
pretzelosity transverse-momentum dependent parton distribution function. We
discuss the origin of this relation in quark models, identifying as key
ingredient for its validity the assumption of spherical symmetry for the
nucleon in its rest frame. Finally we show that the individual quark
contributions to the orbital angular momentum obtained from this relation can
not be interpreted as the intrinsic contributions, but include the contribution
from the transverse centre of momentum which cancels out only in the total
orbital angular momentum.Comment: 8 pages; references added, version to appear in Phys. Lett.
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