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Isoscalar M1 and E2 Amplitudes in n+p -> d+gamma  [PDF]
Jiunn-Wei Chen,Gautam Rupak,Martin J. Savage
Physics , 1999, DOI: 10.1016/S0370-2693(99)01007-2
Abstract: The low energy radiative capture process n+p -> d+gamma provides a sensitive probe of the two-nucleon system. The cross section for this process is dominated by the isovector M1 amplitude for capture from the 1S0 channel via the isovector magnetic moment of the nucleon. In this work we use effective field theory to compute the isoscalar M1 and isoscalar E2 amplitudes that are strongly suppressed for cold neutron capture. The actual value of the isoscalar E2 amplitude is expected to be within 15% of the value computed in this work. In contrast, due to the vanishing contribution of the one-body operator at leading order and next-to-leading order, the isoscalar M1 amplitude is estimated to have a large uncertainty. We discuss in detail the deuteron quadrupole form factor and SD mixing.
E2/M1 ratio from the Mainz $p(\vec γ, p)π^0$ data  [PDF]
R. L. Workman
Physics , 1997, DOI: 10.1103/PhysRevLett.79.4511
Abstract: We suggest that the error quoted in the Mainz determination of the E2/M1 ratio (at the resonance energy) should be enlarged. A term dropped in expressions used by this group could be significant.
E2/M1 ratio from the Mainz $p(\vecγ, p)π^0$  [PDF]
R. Beck,H. P. Krahn
Physics , 1997,
Abstract: We reply to the Comment of R.L. Workman on the E2/M1 ratio from the Mainz photoproduction data, nucl-th/9702052. We support our published result for the E2/M1 ratio of REM = -(2.5 +- 0.2 +- 0.2)%.
How to extract the P_{33}(1232) resonance contributions from the amplitudes M_{1+}^{3/2},E_{1+}^{3/2},S_{1+}^{3/2} of pion electroproduction on nucleons  [PDF]
I. G. Aznauryan
Physics , 1997, DOI: 10.1103/PhysRevD.57.2727
Abstract: Within the dispersion relation approach, solutions of integral equations for the multipoles M_{1+}^{3/2},E_{1+}^{3/2},S_{1+}^{3/2} are found at 0 < Q^2 < 3 GeV^2. These solutions should be used as input for the resonance and nonresonance contributions in the analyses of pion electroproduction data in the P_{33}(1232) resonance region. It is shown that the traditional identification of the amplitude M_{1+}^{3/2} (as well of the amplitudes E_{1+}^{3/2},S_{1+}^{3/2}) with the P_{33}(1232) resonance contribution is not right; there is a contribution in these amplitudes which has a nonresonance nature and is produced by rescattering effects in the diagrams corresponding to the nucleon and pion poles. This contribution is reproduced by the dispersion relations. Taking into account nonresonance contributions in the amplitudes M_{1+}^{3/2},E_{1+}^{3/2}, the helicity amplitudes A_p^{1/2},~A_p^{3/2} and the ratio E2/M1 for the gamma N -> P_{33}(1232) transition are extracted from experiment at Q^2=0. They are in good agreement with quark model predictions.
$E2/M1$ Ratio for the $γN\rightarrow Δ$ Transition in the Chiral Quark Soliton Model  [PDF]
T. Watabe,Chr. V. Christov,K. Goeke
Physics , 1995, DOI: 10.1016/0370-2693(95)00227-C
Abstract: We calculate the electric quadrupole to magnetic dipole transition ratio $E2/M1$ for the reaction $\gamma N \ra \Delta(1232)$ in the chiral quark soliton model. The calculated $E2/M1$ ratio is in a good agreement with the very new experimental data. We obtain non-zero negative value for the electric quadrupole $N-\Delta$ transition moment, which suggests an oblate deformed charge structure of the nucleon or/and the delta isobar. Other observables related to this quantity, namely the $N-\Delta$ mass splitting, the isovector charge radius, and isovector magnetic moment, are properly reproduced as well.
The P_33(1232) resonance contribution into the amplitudes M_{1+}^{3/2},E_{1+}^{3/2},S_{1+}^{3/2} from an analysis of the p(e,e'p)π^0 data at Q^2 = 2.8, 3.2, and 4 (GeV/c)^2 within dispersion relation approach  [PDF]
I. G. Aznauryan,S. G. Stepanyan
Physics , 1998, DOI: 10.1103/PhysRevD.59.054009
Abstract: Within the fixed-t dispersion relation approach we have analysed the TJNAF and DESY data on the exclusive p(e,e'p)\pi^0 reaction in order to find the P_{33}(1232) resonance contribution into the multipole amplitudes M_{1+}^{3/2},E_{1+}^{3/2},S_{1+}^{3/2}. As an input for the resonance and nonresonance contributions into these amplitudes the earlier obtained solutions of the integral equations which follow from dispersion relations are used. The obtained values of the ratio E2/M1 for the \gamma^* N \to P_{33}(1232) transition are: 0.039\pm 0.029, 0.121\pm 0.032, 0.04\pm 0.031 for Q^2= 2.8, 3.2, and 4 (GeV/c)^2, respectively. The comparison with the data at low Q^2 shows that there is no evidence for the presence of the visible pQCD contribution into the transition \gamma N \to P_{33}(1232) at Q^2=3-4 GeV^2. The ratio S_{1+}^{3/2}/M_{1+}^{3/2} for the resonance parts of multipoles is: -0.049\pm 0.029, -0.099\pm 0.041, -0.085\pm 0.021 for Q^2= 2.8, 3.2, and 4 (GeV/c)^2, respectively. Our results for the transverse form factor G_T(Q^2) of the \gamma^* N \to P_{33}(1232) transition are lower than the values obtained from the inclusive data. With increasing Q^2, Q^4G_T(Q^2) decreases, so there is no evidence for the presence of the pQCD contribution here too.
The E2/M1 and C2/M1 ratios and form factors in N -> Delta transitions  [PDF]
L. Tiator,D. Drechsel,O. Hanstein,S. S. Kamalov,S. N. Yang
Physics , 2000, DOI: 10.1016/S0375-9474(01)00835-1
Abstract: A partial wave analysis of pion photoproduction has been obtained in the framework of fixed-t dispersion relations valid from threshold up to 500 MeV. In the resonance region we have precisely determined the electromagnetic properties of the \Delta(1232) resonance, in particular the E2/M1 ratio R_{EM}=(-2.5 +- 0.1) %. For pion electroproduction recent experimental data from Mainz, Bates and JLab for Q^2 up to 4.0 (GeV/c)^2 have been analyzed with two different models, an isobar model (MAID) and a dynamical model. The E2/M1 ratios extracted with these two models show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and become positive with increasing Q^2. This is a possible indication of a very slow approach toward the pQCD region. The C2/M1 ratio near the photon point is found as R_{SM}(0)=(-6.5 +- 0.5) %. At high Q^2 the absolute value of the ratio is strongly increasing, a further indication that pQCD is not yet reached.
Unitary ambiguity in the extraction of the E2/M1 ratio for the $γ N\leftrightarrowΔ$ transition  [PDF]
P. Wilhelm,Th. Wilbois,H. Arenhoevel
Physics , 1996, DOI: 10.1103/PhysRevC.54.1423
Abstract: The resonant electric quadrupole amplitude in the transition $\gamma N\leftrightarrow\Delta(1232)$ is of great interest for the understanding of baryon structure. Various dynamical models have been developed to extract it from the corresponding photoproduction multipole of pions on nucleons. It is shown that once such a model is specified, a whole class of unitarily equivalent models can be constructed, all of them providing exactly the same fit to the experimental data. However, they may predict quite different resonant amplitudes. Therefore, the extraction of the E2/M1($\gamma N\leftrightarrow\Delta$) ratio (bare or dressed) which is based on a dynamical model using a largely phenomenological $\pi N$ interaction is not unique.
Hints on the quadrupole deformation of the $Δ$(1232)  [PDF]
C. Fernandez-Ramirez,E. Moya de Guerra,J. M. Udias
Physics , 2006, DOI: 10.1103/PhysRevC.73.042201
Abstract: 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 Watson's theorem. The obtained EMR value, EMR$=(-1.30\pm0.52)$%, 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.
Analysis of the quadrupole deformation of $Δ$(1232) within an effective Lagrangian model for pion photoproduction from the nucleon  [PDF]
C. Fernandez-Ramirez,E. Moya de Guerra,J. M. Udias
Physics , 2006, DOI: 10.1140/epja/i2006-10198-1
Abstract: We present an extraction of the E2/M1 ratio of the $\Delta$(1232) from experimental data applying an effective Lagrangian model. We compare the result obtained with different nucleonic models and we reconcile the experimental results with the Lattice QCD calculations.
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