Abstract:
Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity, analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions of nonlinear recurrence relations relevant for field theory applications. We introduce a new class of quantum field theories (quasirenormalizable field theories) in which resumming leading logarithms for 2→22→2 scattering amplitudes yields a possibly infinite number of Landau poles.
Keywords:
renormalization group, effective field theory, leading logarithm, Landau pole, Dixon elliptic function.
The research of M. V. Polyakov and
K. M. Semenov-Tian-Shansky was supported by the DFG (Grant No. CRC110).
The research of A. O. Smirnov was supported by the Russian Foundation for Basic Research (Grant No. 18-51-18007).
Citation:
M. V. Polyakov, K. M. Semenov-Tian-Shansky, A. O. Smirnov, A. A. Vladimirov, “Quasirenormalizable quantum field theories”, TMF, 200:2 (2019), 290–309; Theoret. and Math. Phys., 200:2 (2019), 1176–1192
This publication is cited in the following 3 articles:
B. Ananthanarayan, M. S. A. A. Khan, D. Wyler, “Chiral perturbation theory: reflections on effective theories of the standard model”, Indian J. Phys., 97:11 (2023), 3245
L. V. Bork, D. I. Kazakov, “UV divergences, RG equations and high energy behaviour of the amplitudes in the Wess-Zumino model with quartic interaction”, J. High Energ. Phys., 2022:6 (2022)
J. Linzen, M. V. Polyakov, K. M. Semenov-Tian-Shansky, N. S. Sokolova, “Exact summation of leading logs around T¯TT¯¯¯¯T deformation of O(N+1)O(N+1) -symmetric 2D2D Qfts”, J. High Energy Phys., 2021, no. 5, 266