Real-time thermal Schwinger-Dyson equation for quark self-energy in Landau gauge

By means of a formal expression of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by $A(p^2)\not{p}-B(p^2)$, we argue that, when temperature $T$ is less than the given infrared momentum cutoff $p_c$, $A(p^2)=1$ is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.Comment: 8 pages, Latex, no figur

Quark-Antiquark and Diquark Condensates in Vacuum in a 3D Two-Flavor Gross-Neveu Model

The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on less or bigger than the critical value 2/3 of $G_S/H_P$, where $G_S$ and $H_P$ are respectively the coupling constants of scalar quark-antiquark channel and pseudoscalar diquark channel, the system will have the ground state with pure diquark condensates or with pure quark-antiquark condensates, but no the one with coexistence of the two forms of condensates. The similarities and differences in the interplay between the quark-antiquark and the diquark condensates in vacuum in the 2D, 3D and 4D two-flavor four-fermion interaction models are summarized.Comment: 5 pages, revtex4, no figure, minor typos correcte

Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

Pairing Mechanism of the Heavily Electron Doped FeSe Systems: Dynamical Tuning of the Pairing Cutoff Energy

We studied pairing mechanism of the heavily electron doped FeSe (HEDIS) systems, which commonly have one incipient hole band -- a band top below the Fermi level by a finite energy distance $\epsilon_b$ -- at $\Gamma$ point and ordinary electron bands at $M$ points in Brillouin zone (BZ). We found that the system allows two degenerate superconducting solutions with the exactly same $T_c$ in clean limit: the incipient $s^{\pm}_{he}$-gap ($\Delta_h^{-} \neq 0$, $\Delta_e^{+} \neq 0$) and $s_{ee}^{++}$-gap ($\Delta_h =0$, $\Delta_e^{+} \neq 0$) solutions with different pairing cutoffs, $\Lambda_{sf}$ (spin fluctuation energy) and $\epsilon_b$, respectively. The $s_{ee}^{++}$-gap solution, in which the system dynamically renormalizes the original pairing cutoff $\Lambda_{sf}$ to $\Lambda_{phys}=\epsilon_b$ ($< \Lambda_{sf}$), therefore actively eliminates the incipient hole band from forming Cooper pairs, but without loss of $T_c$, becomes immune to the impurity pair-breaking. As a result, the HEDIS systems, by dynamically tuning the pairing cutoff and selecting the $s_{ee}^{++}$-pairing state, can always achieve the maximum $T_c$ -- the $T_c$ of the degenerate $s^{\pm}_{he}$ solution in the ideal clean limit -- latent in the original pairing interactions, even in dirty limit.Comment: 12 pages, 11 figures; Appendix A is adde

Random Guess and Wishful Thinking are the Best Blinding Scenarios.

Blinding is a methodologic safeguard of treatment evaluation, yet severely understudied empirically. Mathieu et al.'s theoretical analysis (2014) provided an important message that blinding cannot eliminate potential for bias associated with belief about allocation in randomized controlled trial; just like the intent-to-treat principle does not guarantee unbiased estimation under noncompliance, the blinded randomized trial as a golden standard may produce bias. They showed possible biases but did not assess how large the bias could be in different scenarios. In this paper, we examined their findings, and numerically assessed and compared the bias in treatment effect parameters by simulation under frequently encountered blinding scenarios, aiming to identify the most ideal blinding scenarios in practice. We conclude that Random Guess and Wishful Thinking (e.g., participants tend to believe they received treatment) are the most ideal blinding scenarios, incurring minimal bias. We also find some evidence that imperfect or partial blinding can be better than no blinding