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Register a new userProblems with Extraction of the Nucleon to Delta(1232) Photonic Amplitudes
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We investigate the model dependence and the importance of choice of database in extracting the {it physical} nucleon-Delta(1232) electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.
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We calculate the electromagnetic moments and radii of the Delta(1232) in the nonrelativistic quark model, including two-body exchange currents. We show that two-body exchange currents lead to nonvanishing Delta and N-->Delta transition quadrupole moments even if the wave functions have no D-state admixture. The usual explanation based on the single-quark transition model involves D-state admixtures but no exchange currents. We derive a parameter- free relation between the N-->Delta transition quadrupole moment and the neutron charge radius: Q(N-->Delta) = r^2(neutron)/sqrt(2). Furthermore, we calculate the M1 and E2 amplitudes for the process photon + N -->Delta. We find that the E2 amplitude receives sizeable contributions from exchange currents. These are more important than the ones which result from D-state admixtures due to tensor forces between quarks if a reasonable quark core radius of about 0.6 fm is used. We obtain a ratio of E2/M1=-3.5%.
The E2/M1 ratio (EMR) of the $Delta$(1232) is extracted from the world data in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the $Delta$(1232) resonance. The textit{bare} s-channel $Delta$(1232) contribution is well isolated and Final State Interactions (FSI) are effectively taken into account fulfilling Watsons theorem. The obtained EMR value, EMR$=(-1.30pm0.52)$%, is in good agreement with the latest lattice QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with results of current quark model calculations.
We discuss the pole mass and the width of the $Delta(1232)$ resonance to third order in chiral effective field theory. In our calculation we choose the complex-mass renormalization scheme (CMS) and show that the CMS provides a consistent power-counting scheme. In terms of the pion-mass dependence, we compare the convergence behavior of the CMS with the small-scale expansion (SSE).
We construct the Lorentz-invariant chiral Lagrangians up to the order $mathcal{O}(p^4)$ by including $Delta(1232)$ as an explicit degree of freedom. A full one-loop investigation on processes involving $Delta(1232)$ can be performed with them. For the $piDeltaDelta$ Lagrangian, one obtains 38 independent terms at the order $mathcal{O}(p^3)$ and 318 independent terms at the order $mathcal{O}(p^4)$. For the $pi NDelta$ Lagrangian, we get 33 independent terms at the order $mathcal{O}(p^3)$ and 218 independent terms at the order $mathcal{O}(p^4)$. The heavy baryon projection is also briefly discussed.
We determine the $Delta(1232)$ resonance parameters using lattice QCD and the Luscher method. The resonance occurs in elastic pion-nucleon scattering with $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is performed with $N_f=2+1$ flavors of clover fermions on a lattice with $Lapprox 2.8$ fm. The pion and nucleon masses are $m_pi =255.4(1.6)$ MeV and $m_N=1073(5)$ MeV, and the strong decay channel $Delta rightarrow pi N$ is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $vec{P}=frac{2pi}{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass $m_Delta=1378(7)(9)$ MeV and the coupling $g_{Deltatext{-}pi N}=23.8(2.7)(0.9)$.
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