Generalizing the relativistic quantization condition to include all three-pion isospin channels
- European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.
- Univ. of Valencia (Spain). Inst. for Corpuscular Physics (IFIC)
- Univ. of Washington, Seattle, WA (United States). Physics Dept.
We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed energies, En(L), in a given cubic volume with side-length L. This function depends on an intermediate three-body quantity, denoted which can thus be constrained from lattice QCD in- put. The second step is a set of integral equations relating to the physical scattering amplitude, M3. Both of the key relations, En(L) ↔ and are shown to be block-diagonal in the basis of definite three-pion isospin, Iπππ , so that one in fact recovers four independent relations, corresponding to Iπππ = 0, 1, 2, 3. We also provide the generalized threshold expansion of for all channels, as well as parameterizations for all three-pion resonances present for Iπππ = 0 and Iπππ = 1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for Iπππ = 0, focusing on the quantum numbers of the ω and h1 resonances.
- Research Organization:
- Univ. of Washington, Seattle, WA (United States); Univ. of Valencia (Spain)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); Generalitat Valenciana; European Union (EU)
- Grant/Contract Number:
- SC0011637; PROMETEO/2019/083; 713673
- OSTI ID:
- 1646656
- Alternate ID(s):
- OSTI ID: 1774010
- Journal Information:
- Journal of High Energy Physics (Online), Vol. 2020, Issue 7; ISSN 1029-8479
- Publisher:
- Springer BerlinCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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