S-matrix bootstrap for resonances

Journal of High Energy Physics, Sep 2018

Abstract We study the 2 → 2 S-matrix element of a generic, gapped and Lorentz invariant QFT in d = 1 + 1 space time dimensions. We derive an analytical bound on the coupling of the asymptotic states to unstable particles (a.k.a. resonances) and its physical implications. This is achieved by exploiting the connection between the S-matrix phase-shift and the roots of the S-matrix in the physical sheet. We also develop a numerical framework to recover the analytical bound as a solution to a numerical optimization problem. This later approach can be generalized to d = 3 + 1 spacetime dimensions.

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S-matrix bootstrap for resonances

Journal of High Energy Physics September 2018, 2018:52 | Cite as S-matrix bootstrap for resonances AuthorsAuthors and affiliations N. DoroudJ. Elias Miró Open Access Regular Article - Theoretical Physics First Online: 10 September 2018 Received: 04 May 2018 Accepted: 29 July 2018 13 Downloads Abstract We study the 2 → 2 S-matrix element of a generic, gapped and Lorentz invariant QFT in d = 1 + 1 space time dimensions. We derive an analytical bound on the coupling of the asymptotic states to unstable particles (a.k.a. resonances) and its physical implications. This is achieved by exploiting the connection between the S-matrix phase-shift and the roots of the S-matrix in the physical sheet. We also develop a numerical framework to recover the analytical bound as a solution to a numerical optimization problem. This later approach can be generalized to d = 3 + 1 spacetime dimensions. Keywords Field Theories in Lower Dimensions Nonperturbative Effects Integrable Field Theories  ArXiv ePrint: 1804.04376 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [2] V.S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions, Phys. Rev. D 80 (2009) 045006 [arXiv:0905.2211] [INSPIRE].ADSMathSciNetGoogle Scholar [3] F. Caracciolo and V.S. Rychkov, Rigorous Limits on the Interaction Strength in Quantum Field Theory, Phys. Rev. D 81 (2010) 085037 [arXiv:0912.2726] [INSPIRE].ADSGoogle Scholar [4] S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].ADSzbMATHGoogle Scholar [5] F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping Mixed Correlators in the 3D Ising Model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar [6] S. Ferrara, A.F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [7] A.M. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz. 66 (1974) 23 [INSPIRE].Google Scholar [8] M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE]. [9] M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap II: two dimensional amplitudes, JHEP 11 (2017) 143 [arXiv:1607.06110] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [10] M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix Bootstrap III: Higher Dimensional Amplitudes, arXiv:1708.06765 [INSPIRE]. [11] D. Mazac and M.F. Paulos, The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices, arXiv:1803.10233 [INSPIRE]. [12] S. Weinberg, Reminiscences of the Standard Model, lecture at ICTP, Trieste, Italy, 17 October 2017, https://www.youtube.com/watch?v=mX2R8-nJhLQ, min. 27–30 and min. 73. [13] R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix, Cambridge University Press, Cambridge U.K. (1966) [INSPIRE].zbMATHGoogle Scholar [14] J.L. Miramontes, Hermitian analyticity versus real analyticity in two-dimensional factorized S-matrix theories, Phys. Lett. B 455 (1999) 231 [hep-th/9901145] [INSPIRE].ADSCrossRefGoogle Scholar [15] A.B. Zamolodchikov, Exact S-Matrix of Quantum sine-Gordon Solitons, JETP Lett. 25 (1977) 468 [INSPIRE].ADSGoogle Scholar [16] I. Arefeva and V. Korepin, Scattering in two-dimensional model with Lagrangian L = (1/γ)[(1/2)(∂μu)2 +m 2(cos u − 1)], Pisma Zh. Eksp. Teor. Fiz. 20 (1974) 680 [INSPIRE].Google Scholar [17] L.D. Landau and E.M. Lifshits, Course of Theoretical Physics. Volume 3: Quantum Mechanics: Non-Relativistic Theory, Butterworth-Heinemann, Oxford U.K. (1991) [INSPIRE]. [18] G. Mussardo and P. Simon, Bosonic type S-matrix, vacuum instability and CDD ambiguities, Nucl. Phys. B 578 (2000) 527 [hep-th/9903072] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [19] F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [20] M. Lüscher and U. Wolff, How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [21] M. Creutz (...truncated)


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N. Doroud, J. Elias Miró. S-matrix bootstrap for resonances, Journal of High Energy Physics, 2018, pp. 52, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)052