585 research outputs found

### QCD topological susceptibility from the nonlocal chiral quark model

We investigate the QCD topological susceptibility $\chi_t$ by using the
nonlocal chiral quark model (NL$\chi$QM). This model is based on the liquid
instanton QCD-vacuum configuration in which $\mathrm{SU}(3)$ flavor symmetry is
explicitly broken by the current quark mass $(m_{u,d},m_s)\approx(5,135)$ MeV.
To compute $\chi_t$, the local topological charge density operator $Q_t(x)$ is
derived from the effective partition function of NL$\chi$QM. We take into
account the contributions from the leading-order (LO) ones
$\sim\mathcal{O}(N_c)$ in the $1/N_c$ expansion. We also verify that the
analytical expression of $\chi_t$ in NL$\chi$QM satisfy the Witten-Veneziano
(WV) and the Leutwyler-Smilga (LS) formulae. Once the average instanton size
and inter-instanton distance are fixed with $\bar{\rho}=1/3$ fm and $\bar{R}=1$
fm, respectively, all the associated model parameters are all determined
self-consistently within the model, including the $\eta$ and $\eta'$ weak decay
constants. We obtain the results such as $F_{\eta}=96.77$ MeV and
$F_{\eta'}=102.53$ MeV for instance. Numerically we observe that
$\chi_{t}=(165.57\,\mathrm{MeV})^4$ in our full calculation. This value is
comparable with its empirical one $\chi_t=(175\pm5\,\mathrm{MeV})^4$. We also
find that our $\chi^\mathrm{WV}_t=\chi^\mathrm{QL}_t=(194.30,\mathrm{MeV})^4$
in the quenched limit and $\chi^\mathrm{LS}_t=(162.54\,\mathrm{MeV})^4$ in the
chiral limit. Consequently, we conclude that $\chi_{t}<\chi^\mathrm{QL}_t$. Our
result also implies that the $(10\sim20)\,\%$ decrease with the dynamical quark
contributions.Comment: 10 pages, 1 figur

### The third Zemach moment and the size of the proton

To resolve the puzzle of the proton size raised from the recent result of
muonic hydrogen Lamb shift, De R\'{u}jula has proposed that a large value of
the third Zemach moment ${(2)}$ of the proton to be the solution. His
suggestion has been criticized by many groups based on the $ep$ scattering data
at low $Q^2$ regime. However, if there is a "thorn" or "lump" in the electric
form factor of the proton $G_{E}(Q^2)$ at extremely low $Q^2$ regime, then the
third Zemach moment ${(2)}$ would be as large as De R\'{u}jula
suggested. In this article, we show that the existence of such a "thorn" or
"lump" has not been completely excluded, although tightly restricted, by the
current data of $ep$ elastic scattering. We also suggest a more sophisticated
global fitting procedure of $G_{E}(Q^2)$ for the future fitting.Comment: 10 pages. 2 table, 2 figur

### Chiral restoration at finite T under the magnetic field with the meson-loop corrections

We investigate the (partial) chiral restoration at finite temperature (T)
under the strong external magnetic field B_0 of the SU(2) light-flavor QCD
matter. To this end, we employ the instanton-liquid QCD vacuum configuration
accompanied with the linear Schwinger method for inducing the magnetic field.
The Harrington-Shepard caloron solution is used to modify the instanton
parameters, i.e. the average instanton size (rho) and inter-instanton distance
(R), as functions of T. In addition, we include the meson-loop corrections
(MLC) as the large-N_c corrections because they are critical for reproducing
the universal chiral restoration pattern. We present the numerical results for
the constituent-quark mass as well as chiral condensate which signal the
spontaneous breakdown of chiral-symmetry SBCS, as functions of T and B_0. From
our results we observe that the strengths of those chiral order parameters are
enhanced with respect to B_0 due to the magnetic catalysis effect. We also find
that there appears a region where the u and d-quark constituent masses coincide
with each other at eB_0 = (7 ~ 9) m^2_pi, even in the presence of the explicit
isospin breaking. The critical T for the chiral restoration T_c tends to shift
to the higher temperature in the presence of the B_0 for the chiral limit but
keeps almost stationary for the physical quark mass case. We also compute the
pion weak-decay constant F_pi and pion mass m_pi below T_c, varying the
strength of the magnetic field, showing correct partial chiral restoration
behaviors. Besides we find that the changes for the F_pi and m_pi due to the
magnetic field is relatively small, in comparison to those caused by the finite
T effect.Comment: 15 pages, 14 figures, accepted for publication in Phys.Rev.

### Shear viscosity of quark matter at finite temperature in magnetic fields

We have applied the Green-Kubo formula to investigate the shear viscosity in
the SU(2) light-flavor quark matter at finite temperature under the external
strong magnetic field e|B| ~ m^2_pi. For this purpose, we employ the
temperature-modified instanton model and the Schwinger method to induce the
magnetic field. The quark spectral function with the finite width motivated by
the instanton model is adopted to compute the shear viscosity. We find that
shear viscosity increases as temperature increases even beyond the transition
temperature T_0=170 MeV if temperature-dependent (TDP) model parameters is
used. On the other hand, with temperature-independent ones the shear viscosity
starts to drop when temperature goes beyond T_0. Although the magnetic field
reduces the shear viscosity in terms of the magnetic catalysis, its effects are
almost negligible in the chiral-restored phase even for very strong magnetic
field, e|B| ~ 10^20 gauss. We also compute the ratio of the shear viscosity and
entropy density eta/s. Our numerical results are well compatible with other
theoretical results for a wide temperature regions. We obtain the
parameterization of the temperature-dependent ratio from our numerical result
as eta/s=0.27-0.87/t+1.19/t^2-0.28/t^3 with t = T/T_0 for T=(100 ~ 350) MeV and
e|B|=0.Comment: 11 pages, 6 figure

### Kaon quark distribution functions in the chiral constituent quark model

We investigate the valence $u$ and $\bar{s}$ quark distribution functions of
the $K^+$ meson, $v^{K(u)}(x,Q^2)$ and $v^{K(\bar{s})}(x,Q^2)$, in the
framework of the chiral constituent quark model. We judiciously choose the bare
distributions at the initial scale to generate the dressed distributions at the
higher scale, considering the meson cloud effects and the QCD evolution, which
agree with the phenomenologically satisfactory valence quark distribution of
the pion and the experimental data of the ratio $v^{K(u)}(x,Q^2)/v^{\pi
(u)}(x,Q^2)$. We show how the meson cloud effects affect the bare distribution
functions in detail. We find that a smaller $SU(3)$ flavor symmetry breaking
effect is observed, compared with results of the preceding studies based on
other approaches.Comment: 13 pages, 8 figure

### Meson cloud effects on kaon quark distribution functions and the SU(3) flavor symmetry

We present our analysis on the valence quark distribution functions of the
$K^{+}$ meson, $v^{K (u)} (x, Q^2)$ and $v^{K (\bar{s})} (x, Q^2)$, taking into
account the meson cloud effects in the framework of the chiral constituent
quark model. Assuming appropriate bare quark distribution functions at the
initial scale, evaluating the Goldstone boson dressing corrections with the
model, and performing the QCD evolution, one can obtain the realistic dressed
distributions at a certain scale. The phenomenologically satisfactory valence
quark distribution of the pion was obtained in the previous study and there are
available experimental data of the valence $u$ quark distribution ratio
$v^{K(u)} (x, Q^2) / v^{\pi (u)} (x, Q^2)$, which enable us to obtain the kaon
quark distribution functions. Besides presenting the resulting dressed
distributions, we also show how the meson cloud effects affect the bare
distributions in detail. A striking result is that the observed size of the
SU(3) flavor symmetry breaking is considerably smaller than those seen in the
preceding works based on other approaches.Comment: 5 pages, 6 figures, prepared for the proceedings of the 21st
International Conference in Quantum Chromodynamics (QCD 18), 2 - 6 July 2018,
Montpellier, Franc

### The Pion Electroproduction in the $\Delta$(1232) region region

The amplitudes of the pion electroproduction from the nucleon are derived up
to third order in the chiral effective theory including explicit $\Delta$(1232)
>. The Q^2 evolutions of weighted integrals of amplitudes are presented.Comment: 15 pages, no figure

### Partonic calculation of $\gamma Z$ Exchange Corrections to Parity-Violating Elastic Electron-Proton Scattering

We calculate $\gamma Z$ exchange corrections to the parity-violating
asymmetry of the elastic electron-proton scattering in a parton model using the
formalism of generalized parton distributions(GPDs). We also examine the
validity of the zero-momentum-transfer approximation adopted in the literatures
and find that it overestimates the $\gamma Z$ exchange effect significantly at
the forward scattering angles.Comment: 4pages, 5 fig

### Fragmentation and quark distribution functions for the pion and kaon with explicit flavor-SU(3)-symmetry breaking

We investigate the unpolarized pion and kaon fragmentation functions,
employing the nonlocal chiral-quark model, which manifests the nonlocal
interactions between the quarks and pseudoscalar mesons, considering the
explicit flavor-SU(3)-symmetry breaking in terms of the current-quark masses.
Moreover, we study the quark-distribution functions, derived from the
fragmentation ones with the Drell-Yan-Levi relation. Numerical results are
evaluated to higher Q^2 by the DGLAP evolution and compared with the empirical
data. The ratios between the relevant valance quark-distribution functions are
also discussed. It turns out that the present results are in relatively good
agreement with available data and other theoretical estimations.Comment: 13 pages, 16 figure

### Extraction of the charged pion polarizabilities from radiative charged pion photoproduction in Heavy Baryon Chiral Perturbation Theory

We analyze the amplitude of radiative charged pion photoproduction within the
framework of heavy baryon chiral perturbation theory (HBChPT) and discuss the
best experimental setup for the extraction of the charged pion polarizabilities
from the differential cross section. We find that the contributions from two
unknown low energy constants(LECs) in the $\pi N$ chiral Lagrangian at order
$p^{3}$ are comparable with the contributions of the charged pion
polarizabilities. As a result, it is necessary to take these two LECs' effects
into account. Furthermore, we discuss the applicability of the extrapolation
method and conclude that this method is applicable only if the polarization
vector of the incoming photon is perpendicular to the scattering plane in the
center of mass frame of the final $\gamma-\pi$ system.Comment: 14pages, 11 figure

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