On a modification method of Lefschetz thimbles

The QCD at finite density is not well understood yet, where standard Monte Carlo simulation suffers from the sign problem. In order to overcome the sign problem, the method of Lefschetz thimble has been explored. Basically, the original sign problem can be less severe in a complexified theory due to the constancy of the imaginary part of an action on each thimble. However, global phase factors assigned on each thimble still remain. Their interference is not negligible in a situation where a large number of thimbles contribute to the partition function, and this could also lead to a sign problem.In this study, we propose a method to resolve this problem by modifying the structure of Lefschetz thimbles such that only a single thimble is relevant to the partition function. It can be shown that observables measured in the original and modified theories are connected by a simple identity. We exemplify that our method works well in a toy model.Comment: 7 pages, 4 figures, talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism

We calculate the tensor charge of the quark in the QCD-like theory in the Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed tensor charge of the quark is significantly suppressed against the bare quark contribution, and the result agrees qualitatively with the analyses in the collinear factorization approach and lattice QCD. We also analyze the quark confinement effect with the phenomenological strong coupling given by Richardson, and find that this contribution is small. We show that the suppression of the quark tensor charge is due to the superposition of the spin flip of the quark arising from the successive emission of gluons which dress the tensor vertex. We also consider the relation between the quark and the nucleon electric dipole moments by combining with the simple constituent quark model.Comment: 16 pages, 11 figures. arXiv admin note: text overlap with arXiv:1401.285

Quark scalar, axial, and pseudoscalar charges in the Schwinger-Dyson formalism

We calculate the scalar, axial, and pseudoscalar charges of the quark in the Schwinger-Dyson formalism of Landau gauge QCD. It is found that the dressed quark scalar density of the valence quark is significantly enhanced against the bare quark contribution, and the result explains qualitatively the phenomenologically known value of the pion-nucleon sigma term and also that given by lattice QCD. Moreover, we show that the Richardson's interquark potential suppresses the quark scalar density in the Higashjima-Miransky approximation. This fact suggests that the quark scalar density is an observable that is sensitive to quark confinement. For the quark axial charge, we find that it is suppressed due to the gluon dynamics. The result of the quenched analysis agrees qualitatively with the experimental data of the isovector axial coupling constant $g_A$. We show that the suppression of the quenched axial charge is due to a mechanism similar to that of the quark tensor charge. In the Schwinger-Dyson equation with the leading unquenching quark-loop contribution the quark axial charge is more suppressed, due to the anomaly effect. The quark pseudoscalar density is found to be large, and is divergent as the bare quark becomes massless. This result is in agreement with the phenomenological current algebraic analysis, and explains well the dominance of the pion-pole contribution.Comment: 28 pages, 22 figure