Resonances in an external field: the 1+1 dimensional case

Abstract

Using non-relativistic effective field theory in 1+1 dimensions, we generalize Lüscher's approach for resonances in the presence of an external field. This generalized approach provides a framework to study the infinite-volume limit of the form factor of a resonance determined in lattice simulations.

Scalar mesons in a finite volume

“…Moreover, from the phase shift determined on the lattice, one may (in principle) extract the position and width of the elastic resonances. A further generalization of the approach allows one to address the measurement of the resonance form factors [50]. For an alternative method to directly extract the resonance position in the complex plane from the measured two-point function at finite times, see ref.…”

Matrix elements of unstable states

“…Moreover, as shown in ref. [30] (in case of 1 + 1 dimensions), the matrix elements measured for any given level follow a similar pattern. For example, the magnetic moment tends to the sum of the magnetic moments of the free particles in the limit L → ∞.…”

“…(5.2) becomes a relation that defines L. Our first task is to find all η nR . It is instructive to begin from the 1+1-dimensional case [30]. The counterpart of eq.…”

“…Finally, we would like to note that the problem is milder in the case of 1+1 dimensions, see ref. [30]. First, there are no finite fixed points and no ambiguity emerges.…”

“…[30] it has been shown that the problematic contributions in 1+1 dimensions can be fit by a polynomial in p (not p 2 ) with n-dependent coefficients, so the analytic continuation still can be performed (although it is a more subtle affair now, see ref. [30] for the details). No similar statement exists in the case of 3+1 dimensions.…”