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Analytic continuation of the relativistic three-particle scattering amplitudes

Journal Article · · Physical Review. D.
 [1];  [2];  [3]
  1. University of Washington, Seattle, WA (United States); University of Washington
  2. Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  3. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
+ Show Author Affiliations

We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the nonrelativistic three-body scattering theory, we provide a detailed and general prescription for solving and analytically continuing integral equations describing the three-body reactions. We use these techniques to study a system with zero angular momenta described by a single scattering length leading to a bound state in a two-body subchannel. We obtain bound-state-particle and three-particle amplitudes in the previously unexplored kinematical regime; in particular, for real energies below elastic thresholds and complex energies in the physical and unphysical Riemann sheets. We extract positions of three-particle bound-states that agree with previous finite-volume studies, providing further evidence for the consistency of the relativistic finite-volume three-body quantization conditions. We also determine previously unobserved virtual bound states in this theory. Lastly, we find numerical evidence of the breakdown of the two-body finite-volume formalism in the vicinity of the left-hand cuts and argue for the generalization of the existing formalism.

Research Organization:
University of Washington, Seattle, WA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0011637; SC0019229
OSTI ID:
1997556
Alternate ID(s):
OSTI ID: 1999300
Journal Information:
Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 3 Vol. 108; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (27)

Figure 1(p. 3)figure Figure 1
Figure 2(p. 8)figure Figure 2
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Figure 12(p. 24)figure Figure 12
Table I(p. 24)table Table I
Figure 13(p. 25)figure Figure 13
Figure 14(p. 26)figure Figure 14
Figure 15(p. 26)figure Figure 15
Figure 16(p. 27)figure Figure 16
Table II(p. 27)table Table II
Figure 17(p. 28)figure Figure 17
Table III(p. 28)table Table III
Figure 18(p. 31)figure Figure 18
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Figure 20(p. 34)figure Figure 20
Table IV(p. 35)table Table IV
Figure 21(p. 37)figure Figure 21
Figure 22(p. 39)figure Figure 22
Figure 23(p. 40)figure Figure 23

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Bound states
Few-body systems
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Lattice field theory
Nuclear forces
Scattering amplitudes