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Register a new userThermal effects on $rho$ meson properties in an external magnetic field
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A detailed study of the analytic structure of 1-loop self energy graphs for neutral and charged $rho$ mesons is presented at finite temperature and arbitrary magnetic field using the real time formalism of thermal field theory. The imaginary part of the self energy is obtained from the discontinuities of these graphs across the Unitary and Landau cuts, which is seen to be different for $rho^0$ and $rho^pm$. The magnetic field dependent vacuum contribution to the real part of the self energy, which is usually ignored, is found to be appreciable. A significant effect of temperature and magnetic field is seen in the self energy, spectral function, effective mass and dispersion relation of $rho^0$ as well as of $rho^pm$ relative to its trivial Landau shift. However, for charged $rho$ mesons, on account of the dominance of the Landau term, the effective mass appears to be independent of temperature. The trivial coupling of magnetic moment of $rho^pm$ with external magnetic field, when incorporated in the calculation, makes the $rho^pm$ to condense at high magnetic field.
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Properties of $rho$-meson in symmetric nuclear matter are investigated in a light-front constituent quark model (LFCQM), using the in-medium inputs calculated by the quark-meson coupling (QMC) model. The LFCQM used in this study was already applied for the studies of the electromagnetic properties of $rho$-meson in vacuum, namely, the charge~$G_0$, magnetic~$G_1$, and quadrupole~$G_2$ form factors, electromagnetic charge radius, and electromagnetic decay constant. We predict that the electromagnetic decay constant, charge radius, and quadrupole moment are enhanced as increasing the nuclear matter density, while the magnetic moment is slightly quenched. Furthermore, we predict that the value $Q^2_{rm zero}$, which crosses zero of the charge form factor, $G_0(Q^2_{rm zero})=0$ ($Q^2 = -q^2 > 0$ with $q$ being the four-momentum transfer), decreases as increasing the nuclear matter density.
We study the behavior of neutral meson properties in the presence of a static uniform external magnetic field in the context of nonlocal chiral quark models. The formalism is worked out introducing Ritus transforms of Dirac fields, which allow to obtain closed analytical expressions for $pi^0$ and $sigma$ meson masses and for the $pi^0$ decay constant. Numerical results for these observables are quoted for various parameterizations. In particular, the behavior of the $pi^0$ meson mass with the magnetic field is found to be in good agreement with lattice QCD results. It is also seen that the Goldberger-Treiman and Gell-Mann-Oakes-Renner chiral relations remain valid within these models in the presence of the external magnetic field.
We find a general expression for the one-loop self-energy function of neutral $rho$-meson due to $pi^+pi^-$ intermediate state in a background magnetic field, valid for arbitrary magnitudes of the field. The pion propagator used in this expression is given by Schwinger, which depends on a proper-time parameter. Restricting to weak fields, we calculate the decay rate $Gamma(rho^0 rightarrow pi^+ +pi^-)$, which changes negligibly from the vacuum value.
It is simply anticipated that in a strong magnetic configuration, the Landau quantization ceases the neutral rho meson to decay to the charged pion pair, so the neutral rho meson will be long-lived. To closely access this naive observation, we explicitly compute the charged pion-loop in the magnetic field at the one-loop level, to evaluate the magnetic dependence of the lifetime for the neutral rho meson as well as its mass.Due to the dimensional reduction induced by the magnetic field (violation of the Lorentz invariance), the polarization (spin $s_z=-1,0,+1$) modes of the rho meson, as well as the corresponding pole mass and width, are decomposed in a nontrivial manner compared to the vacuum case. To see the significance of the reduction effect, we simply take the lowest-Landau level approximation to analyze the spin-dependent rho masses and widths. We find that the fate of the rho meson may be more complicated because of the magnetic-dimensional reduction: as the magnetic field increases, the rho width for the spin $s_z=0$ starts to develop, reach a peak, to be vanishing at the critical magnetic field to which the folklore refers. On the other side, the decay rates of the other rhos for $s_z=-1,+1$ monotonically increase as the magnetic field develops. The correlation between the polarization dependence and the Landau-level truncation is also addressed.
We calculate the rho meson mass in a weak magnetic field using effective $rhopipi$ interaction. It is seen that both $rho^0$ and $rho^pm$ masses decrease with the magnetic field in vacuum. $rho$ meson dispersion relation has been calculated and shown to be different for $rho^0$ and $rho^pm$. We also calculate the $rhopipi$ decay width and spectral functions of $rho^0$ and $rho^pm$. The width is seen to decrease with $eB$ and the spectral functions become narrower.
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