229 research outputs found
The rainbow modified-ladder approximation and degenerate pion
Correlation functions can be described by the corresponding equations,
, gap equation for quark propagator and the inhomogeneous Bethe-Salpeter
equation for vector dressed-fermion-Abelian-gauge-boson vertex in which
specific truncations have to be implemented. The general vector and
axial-vector Ward-Green-Takahashi identities require these correlation
functions to be interconnected, in consequence of this, truncations made must
be controlled consistently. It turns out that if the rainbow approximation is
assumed in gap equation, the scattering kernel in Bethe-Salpeter equation can
adopt the ladder approximation, which is one of the most basic attempts to
truncate the scattering kernel. Additionally, a modified-ladder approximation
is also found to be a possible symmetry-preserving truncation scheme. As an
illustration of this approximation for application a treatment of pion is
included. Pion mass and decay constant are found to be degenerate in ladder and
modified-ladder approximations, even though the Bethe-Salpeter amplitude are
with apparent distinction. The justification for the modified-ladder
approximation is examined with the help of the Gell-Mann-Oakes-Renner (GMOR)
relation.Comment: 9 pages, 4 figure
Thermal properties of and meson
We computed the pole masses and decay constants of and meson at
finite temperature in the framework of Dyson-Schwinger equations and
Bethe-Salpeter equations approach. Below transition temperature, pion pole mass
increases monotonously, while meson seems to be temperature independent.
Above transition temperature, pion mass approaches the free field limit,
whereas meson is about twice as large as that limit. Pion and the
longitudinal projection of meson decay constants have similar behaviour
as the order parameter of chiral symmetry, whereas the transverse projection of
meson decay constant rises monotonously as temperature increases. The
inflection point of decay constant and the chiral susceptibility get the same
phase transition temperature. Though there is no access to the thermal width of
mesons within this scheme, it is discussed by analyzing the
Gell-Mann-Oakes-Renner (GMOR) relation in medium. These thermal properties of
hadron observables will help us understand the QCD phases at finite temperature
and can be employed to improve the experimental data analysis and heavy ion
collision simulations.Comment: 8 pages, 4 figures, matched the published versio
Two Photon Transition Form Factor of Quarkonia
The two photon transition of quarkonia are studied within a
covariant approach based on the consistent truncation scheme of the quantum
chromodynamics Dyson-Schwinger equation for the quark propagator and the
Bethe--Salpeter equation for the mesons. We find the decay widths of
and in good
agreement with experimental data. The obtained transition form factor of
for a wide range of space-like photon
momentum transfer squared is also in agreement with the experimental findings
of the BABAR experiment. As a by-product, the decay widths of
and the transition form factor of
are predicted, which
await for experimental test
Leading-twist parton distribution amplitudes of S-wave heavy-quarkonia
The leading-twist parton distribution amplitudes (PDAs) of ground-state
and - and -quarkonia are calculated using a
symmetry-preserving continuum treatment of the meson bound-state problem which
unifies the properties of these heavy-quark systems with those of light-quark
bound-states, including QCD's Goldstone modes. Analysing the evolution of
and PDAs with current-quark mass, , increasing away
from the chiral limit, it is found that in all cases there is a value of for which the PDA matches the asymptotic form appropriate to QCD's
conformal limit and hence is insensitive to changes in renormalisation scale,
. This mass lies just above that associated with the -quark. At
current-quark masses associated with heavy-quarkonia, on the other hand, the
PDAs are piecewise convex-concave-convex. They are much narrower than the
asymptotic distribution on a large domain of ; but nonetheless deviate
noticeably from , which is the result in
the static-quark limit. There are also material differences between and
PDAs, and between the PDAs for different vector-meson polarisations,
which vanish slowly with increasing . An analysis of moments of the
root-mean-square relative-velocity, , in and
systems reveals that -contributions may be needed
in order to obtain a reliable estimate of matrix elements using such an
expansion, especially for processes involving heavy pseudoscalar quarkonia.Comment: 6 pages, 2 figures, 3 table
Sieving parton distribution function moments via the moment problem
Reconstructing parton distribution function (PDF) from the corresponding
Mellin moments belongs to a classical mathematical problem: the moment problem,
which has been overlooked for years in the contemporary hadron community. We
propose the strategy to sieve the moments leveraging PDF properties such as
continuity, unimodality, and symmetry. Through an error-inclusive sifting
process, we refine three sets of lattice QCD PDF moments. This refinement
significantly reduces the errors, particularly for higher order moments, and
locates the peak of PDF simultaneously. As our method is universally applicable
to PDF moments from any methodology, we strongly advocate its integration into
all PDF moment calculations.Comment: 6 pages, 2 figure
Symmetry, symmetry breaking, and pion parton distributions
Pion valence, glue and sea distributions are calculated using a continuum
approach to the two valence-body bound-state problem. Since the framework is
symmetry preserving, physical features of the distributions are properly
expressed. The analysis reveals that the emergent phenomenon of dynamical
chiral symmetry breaking causes a hardening of the valence-quark distribution
function, . Nevertheless, this distribution exhibits the behaviour predicted by quantum chromodynamics (QCD). At the scale
GeV, the following momentum fractions are predicted: , ,
. Evolving to GeV, the
result for agrees with that computed using lattice QCD. These
outcomes should both spur improved analyses of existing experiments and
stimulate efforts to obtain new data on the pion distribution functions using
available and envisioned facilities.Comment: 13 pages, 7 figures, 2 table
transition form factors
Using a continuum approach to the hadron bound-state problem, we calculate
transition form factors on the
entire domain of spacelike momenta, for comparison with existing experiments
and in anticipation of new precision data from next-generation
colliders. One novel feature is a model for the contribution to the
Bethe-Salpeter kernel deriving from the non-Abelian anomaly, an element which
is crucial for any computation of properties. The study
also delivers predictions for the amplitudes that describe the light- and
strange-quark distributions within the . Our results compare
favourably with available data. Important to this at large- is a sound
understanding of QCD evolution, which has a visible impact on the
in particular. Our analysis also provides some insights into the properties of
mesons and associated observable manifestations of the
non-Abelian anomaly.Comment: 16 pages, 7 figures, 3 table
A fresh look at the generalized parton distributions of light pseudoscalar mesons
We present a symmetry-preserving scheme to derive the pion and kaon
generalized parton distributions (GPDs) in Euclidean space. The key to
maintaining crucial symmetries under this approach is the treatment of the
scattering amplitude, such that it contains both the traditional leading-order
contributions and the scalar/vector pole contribution automatically, the latter
being necessary to ensure the soft-pion theorem. The GPD is extracted
analytically via the uniqueness and definition of the Mellin moments and we
find that it naturally matches the double distribution; consequently, the
polynomiality condition and sum rules are satisfied. The present scheme thus
paves the way for the extraction of the GPD in Euclidean space using the
Dyson-Schwinger equation framework or similar continuum approaches.Comment: 5 pages, 2 figures, references adde
Deformation and fracture characteristics of ferrite/bainite dual-phase steels
The deformation and fracture characteristics of a low carbon Si–Mn steel with ferrite/bainite dual–phase structure were investigated by thermo–mechanical controlled process (TMCP). The results showed that the curves of the instantaneous work–hardening factor n* value versus true strain ε are made up with three stages during uniform plastic deformation: n* value is relatively higher at stage I, decreases slowly with ε in stage II, and then decreases quickly with ε in stage III. Compared tothe equiaxed ferrite/bainite dual–phase steel, the quasi–polygonal ferrite/bainite dual–phase steel shows higher tensile strength and n*value in the low strain region. The voids or micro–cracks formed not only at ferrite–bainite interfaces but also within ferrite grains in the necked region, which can improve the property of resistance to crack propagation by reducing local stress concentration of the crack tips.<br /
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