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Register a new userDetermination of the magnetic dipole moment of the rho meson using 4 pion electroproduction data
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We determine the magnetic dipole moment of the rho meson using preliminary data from the BaBar Collaboration for the $e^+ e^- to pi^+ pi^- 2 pi^0$ process, in the center of mass energy range from 0.9 to 2.2 GeV. We describe the $gamma^* to 4pi$ vertex using a vector meson dominance model, including the intermediate resonance contributions relevant at these energies. We find that $mu_rho = 2.1 pm 0.5$ in $e/2 m_rho$ units.
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The invariant amplitudes for pion electroproduction on the nucleon are evaluated by dispersion relations at constant t with MAID as input for the imaginary parts of these amplitudes. In the threshold region these amplitudes are confronted with the predictions of several low-energy theorems derived in the soft-pion limit. In general agreement with Chiral Perturbation Theory, the dispersive approach yields large corrections to these theorems because of the finite pion mass.
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.
Using the soft pion theorem, crossing, and the dispersion relations for the two pion distribution amplitude ($2pi$DA) we argue that the second Gegenbauer moment the $rho$-meson DA ($a_2^{(rho)}$) most probably is negative. This result is at variance with the majority of the model calculations for $a_2^{(rho)}$. Using the instanton theory of the QCD vacuum, we computed $a_2^{(rho)}$ at a low normalisation point and obtain for the ratio $ a_2^{(rho)}/M_3^{(pi)}$ {it definitely negative value} in the range of $a_2^{(rho)}/M_3^{(pi)}in [-2, -1]$. The range of values corresponds to a generous variation of the parameters of the instanton vacuum. The value of the second Gegenbauer moment of pion DA is positive in the whole range and is compatible with its the most advanced lattice measurement. It seems that the topologically non-trivial field configurations in the QCD vacuum (instantons) lead to qualitatively different shapes of the pion and the $rho$-meson DAs.
We present a calculation of the electromagnetic form factors of the $rho^+$ meson. Our formalism is based on the point-form of relativistic quantum mechanics. Electron-$rho$-meson scattering is formulated as a coupled-channel problem for a Bakamjian-Thomas mass operator, such that the dynamics of the exchanged photon is taken explicitly into account. The $rho$-meson current is extracted from on-shell matrix elements of the optical potential of the scattering process. As a consequence of the violation of cluster separability in the Bakamjian-Thomas framework, our current includes additional, unphysical contributions, which can be separated from the physical ones uniquely. Our results for the form factors are in good agreement with other approaches.
The effective photon-quark-antiquark ($gamma q overline{q}$) vertex function is evaluated at finite temperature in the presence of an arbitrary external magnetic field using the two-flavor gauged Nambu--Jona-Lasinio (NJL) model in the mean field approximation. The lowest order diagram contributing to the magnetic form factor and the anomalous magnetic moment (AMM) of the quarks is calculated at finite temperature and external magnetic field using the imaginary time formalism of finite temperature field theory and the Schwinger proper time formalism. The Schwinger propagator including all the Landau levels with non-zero AMM of the dressed quarks is considered while calculating the loop diagram. Using sharp as well as smooth three momentum cutoff, we regularize the UV divergences arising from the vertex function and the parameters of our model are chosen to reproduce the well known phenomenological quantities at zero temperature and zero magnetic field, such as pion-decay constant ($f_pi$), vacuum quark condensate, vacuum pion mass ($m_pi$) as well as the magnetic moments of proton and neutron. We then study the temperature and magnetic field dependence of the AMM and constituent mass of the quark. We found that, the AMM as well as the constituent quark mass are large at the chiral symmetry broken phase in the low temperature region. Around the pseudo-chiral phase transition they decrease rapidly and at high temperatures both of them approach vanishingly small values in the symmetry restored phase.
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