Abstract
We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. In addition, we discuss possible extensions of our approach and, as an example application, prospects for applying the formalism to study the onset of deep-inelastic scattering. More details are given in the published version of this work, Ref. [1].
Highlights
In Lattice QCD, low-energy properties of the strong force are calculated numerically in a finite, discretized spacetime box
With total three-momentum projected to zero, as the box size is increased (L → ∞) the pole position in the corresponding finite-volume Euclidean correlator approaches the infinite-volume value with exponentially small corrections as EQ(L) = MQ + O(e−MπL), where Mπ is the physical mass of the lightest degree of freedom, the pion in QCD, and MQ the mass of the particle with quantum numbers Q [2]
K is the finite-volume spectral function. Substituting this sum of delta functions into Eq (9) and evaluating the integral immediately gives back Eq (8). We emphasize at this stage that, while the infinitevolume spectral function gives direct access to the decay width, in the finite volume we have a sum of delta peaks
Summary
In Lattice QCD, low-energy properties of the strong force are calculated numerically in a finite, discretized spacetime box. In theories with a mass gap, like QCD, it is possible to define single-particle, finite-volume states that smoothly approach their infinite-volume counterparts For such states, with total three-momentum projected to zero, as the box size is increased (L → ∞) the pole position in the corresponding finite-volume Euclidean correlator approaches the infinite-volume value with exponentially small corrections as EQ(L) = MQ + O(e−MπL), where Mπ is the physical mass of the lightest degree of freedom, the pion in QCD, and MQ the mass of the particle with quantum numbers Q [2].
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