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Register a new userRho meson decay in presence of magnetic field
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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.
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We calculate the momentum dependence of the $rho^0-omega$ mixing amplitude in vacuum with vector nucleon-nucleon interaction in presence of a constant homogeneous weak magnetic field background. The mixing amplitude is generated by the nucleon-nucleon ($NN$) interaction and thus driven by the neutron-proton mass difference along with a constant magnetic field. We find a significant effect of magnetic field on the mixing amplitude. We also calculate the Charge symmetry violating (CSV) $NN$ potential induced by the magnetic field dependent mixing amplitude. The presence of the magnetic field influences the $NN$ potential substantially which can have important consequences in highly magnetized astrophysical compact objects, such as magnetars. The most important observation of this work is that the mixing amplitude is non-zero, leading to positive contribute to the CSV potential if the proton and neutron masses are taken to be equal.
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.
We present preliminary results on the $rho$ meson decay width estimated from the scattering phase shift of the I=1 two-pion system. The phase shift is calculated by the finite size formula for non-zero total momentum frame (the moving frame) derived by Rummukainen and Gottlieb, using the $N_f=2$ improved Wilson fermion action at $m_pi/m_rho=0.41$ and $L=2.53 {rm fm}$.
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.
We perform a lattice QCD study of the $rho$ meson decay from the $N_f=2+1$ full QCD configurations generated with a renormalization group improved gauge action and a non-perturbatively $O(a)$-improved Wilson fermion action. The resonance parameters, the effective $rhotopipi$ coupling constant and the resonance mass, are estimated from the $P$-wave scattering phase shift for the isospin I=1 two-pion system. The finite size formulas are employed to calculate the phase shift from the energy on the lattice. Our calculations are carried out at two quark masses, $m_pi=410,{rm MeV}$ ($m_pi/m_rho=0.46$) and $m_pi=300,{rm MeV}$ ($m_pi/m_rho=0.35$), on a $32^3times 64$ ($La=2.9,{rm fm}$) lattice at the lattice spacing $a=0.091,{rm fm}$. We compare our results at these two quark masses with those given in the previous works using $N_f=2$ full QCD configurations and the experiment.
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