A general noncommutative quantum mechanical system in a central potential $V=V\left(r\right)\mathrm{}$ in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter $\theta ,$ we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction $V\left(r\right)\mathrm{}$ is replaced by $V=V(H_{\mathrm{HO}},L_z),$ where $H_{\mathrm{HO}}$ is the Hamiltonian of the two-dimensional harmonic oscillator and $L_z$ is the z component of the angular momentum. For other finite values of $\theta$ the model can be solved by using perturbation theory.

We compute the vacuum one-loop quark–gluon vertex correction at zero temperature in the presence of a magnetic field. From the vertex function we extract the effective quark–gluon coupling and show that it grows with increasing magnetic field strength. The effect is due to a subtle competition between the color charge associated to gluons and the color charge associated to quarks, the former being larger than the latter. In contrast, at high temperature the effective thermo-magnetic coupling results exclusively from the contribution of the color charge associated to quarks. This produces a decrease of the coupling with increasing field strength. We interpret the results in terms of a geometrical effect whereby the magnetic field induces, on average, a closer distance between the (electrically charged) quarks and antiquarks. At high temperature, since the effective coupling is proportional only to the color charge associated to quarks, such proximity with increasing field strength makes the effective coupling decrease due to asymptotic freedom. In turn, this leads to a decreasing quark condensate. In contrast, at zero temperature both the effective strong coupling and the quark condensate increase with increasing magnetic field. This is due to the color charge associated to gluons dominating over that associated to quarks, with both having the opposite sign. Thus, the gluons induce a kind of screening of the quark color charge, in spite of the quark–antiquark proximity. We discuss the implications for the inverse magnetic catalysis phenomenon

We discuss the charged pion condensation phenomenon in the linear sigma model, in the presence of an external uniform magnetic field. The critical temperature is obtained as a function of the external magnetic field, assuming the transition is of second order, by considering a dilute gas at low temperature. As a result we found magnetic catalysis for high values of the external magnetic field. This behavior confirms previous results with a single charged scalar field.DOI: http://dx.doi.org/10.1103/PhysRevD.89.016004Published 6 January 2014Received 30 October 2013© 2014 American Physical Society

The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard ``contour-improved'' method based on a derivative expansion of the Adler function. The new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the renormalization scheme dependence remains approximately equal. The extracted QCD coupling at the tau mass scale is by 2% lower than the contour-improved value. We find $\alpha${}s(MZ2)=0.1211\ifmmode\pm\else\textpm\fi{}0.0010.

We calculate light-quark mass differences in the framework of the Laplace-transform QCD sum rules using an improved parametrization of the hadronic spectral functions. Our results are (m${¯}_s$-m${¯}_u$)${\Vert }_1$ GeV=185±15 MeV and (m${¯}_d$-m${¯}_u$)${\Vert }_1$ GeV=4±1 MeV. Using an earlier determination of the quark-mass sums based on similar techniques, these results lead to: m${¯}_u$(1 GeV)=6±1 MeV, m${¯}_d$(1 GeV)=10±1 MeV, and m${¯}_s$(1 GeV)=192±15 MeV. Next, we estimate the difference of the light-quark vacuum condensates in the framework of the Laplace-transform QCD sum rules. Our results are ψ${\mathrm{}\left(0\right)\mathrm{}}_u^s$=-(0–3.5)×${10}^{\mathrm{-}4}$ ${\mathrm{GeV}}^4$ and ψ${\mathrm{}\left(0\right)\mathrm{}}_u^d$=-(0–2.4)×${10}^{\mathrm{-}7}$ ${\mathrm{GeV}}^4$, where ψ${\mathrm{}\left(0\right)\mathrm{}}_i^j$ are the renormalization-group-invariant quantities ψ${\mathrm{}\left(0\right)\mathrm{}}_i^j$=-(m${¯}_j$-m${¯}_i$) 〈ψ${¯}_j$ ${\psi }_j$-ψ${¯}_i$ ${\psi }_i$〉. These values imply a small flavor symmetry breaking in the QCD nonperturbative vacuum, i.e., 〈s¯s〉/〈ūu〉=0.9±0.1 and 1-〈d¯d〉/〈ūu〉=(0–6)×${10}^{\mathrm{-}3}$. .AE

The light-quark correlator in the axial-vector channel is used, in conjunction with finite energy QCD sum rules at finite temperature, in order to (a) establish a relation between chiral-symmetry restoration and deconfinement, and (b) determine the temperature behavior of the $a_1(1260)$ width and coupling. Results indicate that deconfinement takes place at a slightly lower temperature than chiral-symmetry restoration, although this difference is not significant given the accuracy of the method. The behavior of the $a_1(1260)$ parameters is consistent with quark-gluon deconfinement, as the width grows and the coupling decreases with increasing temperature. DOI: http://dx.doi.org/10.1103/PhysRevD.86.034030 © 2012 American Physical Society