Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion

Abstract

The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. The formalism allows one to determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled channels directly from Lattice Quantum Chromodynamics. We show that the extension to more than two channels is straightforward and present the result for three channels. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes is extracted. In the non-relativistic case, we pay close attention to processes that mix the 1S0-3S1 two-nucleon states, e.g. proton-proton fusion (pp -> d+ e^+ + nu_e), and show how to determine the transition amplitude of such processes directly from lattice QCD.

20 pages, 3 figures

References in corpus (14)

• Multiple-channel generalization of Lellouch-Luscher formula
• Evidence for a Bound H-dibaryon from Lattice QCD
• K^- p scattering length from scattering experiments
• The Deuteron and Exotic Two-Body Bound States from Lattice QCD
• Scalar mesons in a finite volume
• Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD
• On the Strangeness -1 S-wave Meson-Baryon Scattering
• Rummukainen-Gottlieb's formula on two-particle system with different mass
• Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD
• The $KD$, $\eta D_s$ interaction in finite volume and the nature of the $D_{s^{\ast }0}(2317)$ resonance
• Scattering of unstable particles in a finite volume: the case of pi rho scattering and the a1(1260) resonance
• Strategy to find the two $\Lambda (1405)$ states from lattice QCD simulations
• The $DN$, $\pi {\Sigma }_c$ interaction in finite volume and the ${\Lambda }_c(2595)$ resonance
• Chiral unitary theory of scalar mesons in a finite volume

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