28,081 research outputs found
Spin and angular momentum in the nucleon
Using the covariant spectator theory (CST), we present the results of a
valence quark-diquark model calculation of the nucleon structure function f(x)
measured in unpolarized deep inelastic scattering (DIS), and the structure
functions g1(x) and g2(x) measured in DIS using polarized beams and targets.
Parameters of the wave functions are adjusted to fit all the data. The fit
fixes both the shape of the wave functions and the relative strength of each
component. Two solutions are found that fit f(x) and g1(x), but only one of
these gives a good description of g2(x). This fit requires the nucleon CST wave
functions contain a large D-wave component (about 35%) and a small P-wave
component (about 0.6%). The significance of these results is discussed.Comment: 27 pages; 13 figure
Fixed-axis polarization states: covariance and comparisons
Addressing the recent criticisms of Kvinikhidze and Miller, we prove that the
spectator wave functions and currents based on ``fixed-axis'' polarization
states (previously introduced by us) are Lorentz covariant, and find an
explicit connection between them and conventional direction-dependent
polarization states. The discussion shows explicitly how it is possible to
construct pure -wave models of the nucleon.Comment: Changed title and introductory material to match accepted pape
Emergent bipartiteness in a society of knights and knaves
We propose a simple model of a social network based on so-called
knights-and-knaves puzzles. The model describes the formation of networks
between two classes of agents where links are formed by agents introducing
their neighbours to others of their own class. We show that if the proportion
of knights and knaves is within a certain range, the network self-organizes to
a perfectly bipartite state. However, if the excess of one of the two classes
is greater than a threshold value, bipartiteness is not observed. We offer a
detailed theoretical analysis for the behaviour of the model, investigate its
behaviou r in the thermodynamic limit, and argue that it provides a simple
example of a topology-driven model whose behaviour is strongly reminiscent of a
first-order phase transitions far from equilibrium.Comment: 12 pages, 5 figure
Covariant nucleon wave function with S, D, and P-state components
Expressions for the nucleon wave functions in the covariant spectator theory
(CST) are derived. The nucleon is described as a system with a off-mass-shell
constituent quark, free to interact with an external probe, and two spectator
constituent quarks on their mass shell. Integrating over the internal momentum
of the on-mass-shell quark pair allows us to derive an effective nucleon wave
function that can be written only in terms of the quark and diquark
(quark-pair) variables. The derived nucleon wave function includes
contributions from S, P and D-waves.Comment: 13 pages and 1 figur
Scalable reconstruction of density matrices
Recent contributions in the field of quantum state tomography have shown
that, despite the exponential growth of Hilbert space with the number of
subsystems, tomography of one-dimensional quantum systems may still be
performed efficiently by tailored reconstruction schemes. Here, we discuss a
scalable method to reconstruct mixed states that are well approximated by
matrix product operators. The reconstruction scheme only requires local
information about the state, giving rise to a reconstruction technique that is
scalable in the system size. It is based on a constructive proof that generic
matrix product operators are fully determined by their local reductions. We
discuss applications of this scheme for simulated data and experimental data
obtained in an ion trap experiment.Comment: 9 pages, 5 figures, replaced with published versio
Matrix string states in pure 2d Yang Mills theories
We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field
strength is diagonal. Because of the topological obstructions to a global
smooth diagonalization, we find string-like states in the spectrum similar to
the ones introduced by various authors in Matrix string theory. We write
explicitly the partition function, which generalizes the one already known in
the literature, and we discuss the role of these states in preserving modular
invariance. Some speculations are presented about the interpretation of 2d
Yang-Mills theory as a Matrix string theory.Comment: Latex file of 38 pages plus 6 eps figures. A note and few references
added, figures improve
Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space
We formulate the covariant equations for quark-antiquark bound states in
Minkowski space in the framework of the Covariant Spectator Theory. The quark
propagators are dressed with the same kernel that describes the interaction
between different quarks. We show that these equations are charge-conjugation
invariant, and that in the chiral limit of vanishing bare quark mass, a
massless pseudoscalar bound state is produced in a Nambu-Jona-Lasinio (NJL)
mechanism, which is associated with the Goldstone boson of spontaneous chiral
symmetry breaking. In this introductory paper, we test the formalism by using a
simplified kernel consisting of a momentum-space delta-function with a vector
Lorentz structure, to which one adds a mixed scalar and vector confining
interaction. The scalar part of the confining interaction is not chirally
invariant by itself, but decouples from the equations in the chiral limit and
therefore allows the NJL mechanism to work. With this model we calculate the
quark mass function, and we compare our Minkowski-space results to lattice QCD
data obtained in Euclidean space. In a companion paper, we apply this formalism
to a calculation of the pion form factor.Comment: 17 pages, 12 figures, version published in Phys. Rev.
Pion electromagnetic form factor in the Covariant Spectator Theory
The pion electromagnetic form factor at spacelike momentum transfer is
calculated in relativistic impulse approximation using the Covariant Spectator
Theory. The same dressed quark mass function and the equation for the pion
bound-state vertex function as discussed in the companion paper are used for
the calculation, together with a dressed quark current that satisfies the
Ward-Takahashi identity. The results obtained for the pion form factor are in
agreement with experimental data, they exhibit the typical monopole behavior at
high-momentum transfer, and they satisfy some remarkable scaling relations.Comment: 11 pages, 8 figures, version published in Phys. Rev.
Two-pion exchange potential and the amplitude
We discuss the two-pion exchange potential which emerges from a box diagram
with one nucleon (the spectator) restricted to its mass shell, and the other
nucleon line replaced by a subtracted, covariant scattering amplitude
which includes , Roper, and isobars, as well as contact terms
and off-shell (non-pole) dressed nucleon terms. The amplitude satisfies
chiral symmetry constraints and fits data below 700 MeV pion
energy. We find that this TPE potential can be well approximated by the
exchange of an effective sigma and delta meson, with parameters close to the
ones used in one-boson-exchange models that fit data below the pion
production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped
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