A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice

Abstract

Using the non-relativistic effective field theory framework in a finite volume, we discuss the extraction of the $\Delta N{\gamma }^{\ast }$ transition form factors from lattice data. A counterpart of the Lüscher approach for the matrix elements of unstable states is formulated. In particular, we thoroughly discuss various kinematic settings, which are used in the calculation of the above matrix element on the lattice. The emerging Lüscher-Lellouch factor and the analytic continuation of the matrix elements into the complex plane are also considered in detail. A full group-theoretical analysis of the problem is made, including the partial-wave mixing and projecting out the invariant form factors from data.

29 pages, 5 figures. Right-hand side of Eq. (4.13) is corrected by the normalization factor $V^{-1/2}$ and all related formulas namely, Eqs. (4.15), (4.16), (4,17), (4.21), (4.36), (5.1), (5.3) accordingly

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• Electromagnetic excitation of the Delta(1232)-resonance
• Scalar mesons in a finite volume
• Scalar mesons moving in a finite volume and the role of partial wave mixing
• The nucleon to Delta electromagnetic transition form factors in lattice QCD
• Nucleon to Delta transition form factors with $N_F=2+1$ domain wall fermions
• Non leptonic two-body decay amplitudes from finite volume calculations
• Photodisintegration of a Bound State on the Torus
• The three-particle system on a torus

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