585 research outputs found

    QCD topological susceptibility from the nonlocal chiral quark model

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    We investigate the QCD topological susceptibility χt\chi_t by using the nonlocal chiral quark model (NLχ\chiQM). This model is based on the liquid instanton QCD-vacuum configuration in which SU(3)\mathrm{SU}(3) flavor symmetry is explicitly broken by the current quark mass (mu,d,ms)(5,135)(m_{u,d},m_s)\approx(5,135) MeV. To compute χt\chi_t, the local topological charge density operator Qt(x)Q_t(x) is derived from the effective partition function of NLχ\chiQM. We take into account the contributions from the leading-order (LO) ones O(Nc)\sim\mathcal{O}(N_c) in the 1/Nc1/N_c expansion. We also verify that the analytical expression of χt\chi_t in NLχ\chiQM satisfy the Witten-Veneziano (WV) and the Leutwyler-Smilga (LS) formulae. Once the average instanton size and inter-instanton distance are fixed with ρˉ=1/3\bar{\rho}=1/3 fm and Rˉ=1\bar{R}=1 fm, respectively, all the associated model parameters are all determined self-consistently within the model, including the η\eta and η\eta' weak decay constants. We obtain the results such as Fη=96.77F_{\eta}=96.77 MeV and Fη=102.53F_{\eta'}=102.53 MeV for instance. Numerically we observe that χt=(165.57MeV)4\chi_{t}=(165.57\,\mathrm{MeV})^4 in our full calculation. This value is comparable with its empirical one χt=(175±5MeV)4\chi_t=(175\pm5\,\mathrm{MeV})^4. We also find that our χtWV=χtQL=(194.30,MeV)4\chi^\mathrm{WV}_t=\chi^\mathrm{QL}_t=(194.30,\mathrm{MeV})^4 in the quenched limit and χtLS=(162.54MeV)4\chi^\mathrm{LS}_t=(162.54\,\mathrm{MeV})^4 in the chiral limit. Consequently, we conclude that χt<χtQL\chi_{t}<\chi^\mathrm{QL}_t. Our result also implies that the (1020)%(10\sim20)\,\% decrease with the dynamical quark contributions.Comment: 10 pages, 1 figur

    The third Zemach moment and the size of the proton

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    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){(2)} of the proton to be the solution. His suggestion has been criticized by many groups based on the epep scattering data at low Q2Q^2 regime. However, if there is a "thorn" or "lump" in the electric form factor of the proton GE(Q2)G_{E}(Q^2) at extremely low Q2Q^2 regime, then the third Zemach moment (2){(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 epep elastic scattering. We also suggest a more sophisticated global fitting procedure of GE(Q2)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

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    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

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    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

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    We investigate the valence uu and sˉ\bar{s} quark distribution functions of the K+K^+ meson, vK(u)(x,Q2)v^{K(u)}(x,Q^2) and vK(sˉ)(x,Q2)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 vK(u)(x,Q2)/vπ(u)(x,Q2)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)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

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    We present our analysis on the valence quark distribution functions of the K+K^{+} meson, vK(u)(x,Q2)v^{K (u)} (x, Q^2) and vK(sˉ)(x,Q2)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 uu quark distribution ratio vK(u)(x,Q2)/vπ(u)(x,Q2)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 Δ\Delta(1232) region region

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

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

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    We calculate γZ\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 γZ\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

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    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

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    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 πN\pi N chiral Lagrangian at order p3p^{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 γπ\gamma-\pi system.Comment: 14pages, 11 figure
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