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Universality of low-energy scattering in (2+1)-dimensions

Apr, 1998
22 pages
Published in:
  • Phys.Rev.D 58 (1998) 025014
e-Print:
DOI:
Report number:
  • CERN-TH-98-129,
  • RU-98-3-B,
  • LAPTH-683-98,
  • LPTHE-ORSAY-98-31,
  • CERN-TH-98-129-RU98-3-B-LAPTH683-98-LPTHE-ORSAY-98-31
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Abstract: (arXiv)
We prove that, in (2+1) dimensions, the S-wave phase shift, δ0(k) \delta_0(k), k being the c.m. momentum, vanishes as either δ0→cln⁡(k/m)orδ0→O(k2)\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2) as k→0k\to 0. The constant cc is universal and c=π/2c=\pi/2. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in ϕ34\phi_3^4 and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like (ln⁡k)n(\ln k)^n as k→0k\to 0, while the full amplitude vanishes as (ln⁡k)−1(\ln k)^{-1}. We show how these two facts can be reconciled.
  • scattering amplitude: universality
  • partial wave
  • potential
  • dimension: 2
  • field theory: massive
  • axiomatic field theory
  • threshold
  • dimension: 3
  • phi**n model: 4
  • perturbation theory: higher-order