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Graviton emission in Einstein-Hilbert gravity. (English) Zbl 1309.83053

Summary: The five-point amplitude for the scattering of two distinct scalars with the emission of one graviton in the final state is calculated in exact kinematics for Einstein-Hilbert gravity. The result, which satisfies the Steinmann relations, is expressed in Sudakov variables, finding that it corresponds to the sum of two gauge invariant contributions written in terms of a new two scalar - two graviton effective vertex. A similar calculation is carried out in Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one extra gluon in the final state. The effective vertices which appear in both cases are then evaluated in the multi-Regge limit reproducing the well-known result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex can be written as the product of two QCD gluon emission vertices, up to corrections to preserve the Steinmann relations.

MSC:

83C45 Quantization of the gravitational field
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
81V05 Strong interaction, including quantum chromodynamics
81U35 Inelastic and multichannel quantum scattering

Software:

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References:

[1] J.M. Maldacena, The large-\[ \mathcal{N}\] limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2 (1998) 231 [Int. J. Theor. Phys.38 (1999) 1133 ] [hep-th/9711200] [INSPIRE]. · Zbl 0914.53047
[2] S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [INSPIRE]. · Zbl 1355.81126
[3] E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE]. · Zbl 0914.53048
[4] Z. Bern, J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The complete four-loop four-point amplitude in \[\mathcal{N} = {4}\] super-Yang-Mills theory, Phys. Rev.D 82 (2010) 125040 [arXiv:1008.3327] [INSPIRE].
[5] Z. Bern, L.J. Dixon, D. Dunbar, M. Perelstein and J. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys.B 530 (1998) 401 [hep-th/9802162] [INSPIRE].
[6] Z. Bern, J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The ultraviolet behavior of \[\mathcal{N} = {8}\] supergravity at four loops,Phys. Rev. Lett.103(2009) 081301 [arXiv:0905.2326] [INSPIRE].
[7] J.F. Donoghue, General relativity as an effective field theory: the leading quantum corrections, Phys. Rev.D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
[8] N. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum gravitational corrections to the nonrelativistic scattering potential of two masses, Phys. Rev.D 67 (2003) 084033 [Erratum ibid.D 71 (2005) 069903] [hep-th/0211072] [INSPIRE].
[9] J.F. Donoghue and T. Torma, Infrared behavior of graviton-graviton scattering, Phys. Rev.D 60 (1999) 024003 [hep-th/9901156] [INSPIRE].
[10] D.C. Dunbar and P.S. Norridge, Calculation of graviton scattering amplitudes using string based methods, Nucl. Phys.B 433 (1995) 181 [hep-th/9408014] [INSPIRE].
[11] Z. Bern, D.C. Dunbar and T. Shimada, String based methods in perturbative gravity, Phys. Lett.B 312 (1993) 277 [hep-th/9307001] [INSPIRE].
[12] Z. Bern and D.C. Dunbar, A mapping between Feynman and string motivated one loop rules in gauge theories, Nucl. Phys.B 379 (1992) 562 [INSPIRE].
[13] S.-Q. Su, Graviton bremsstrahlung at high energies, Doctoral Thesis, Katholieke Universiteit Leuven, Leuven Belgium (1982).
[14] J. Geris and S.-Q. Su, Single bremsstrahlung processes in quantum gravity, Commun. Theor. Phys.8 (1987) 325 [INSPIRE].
[15] J.F. Donoghue, Introduction to the effective field theory description of gravity, gr-qc/9512024 [INSPIRE].
[16] L. Lipatov, Effective action for the Regge processes in gravity, arXiv:1105.3127 [INSPIRE]. · Zbl 1274.81230
[17] M.T. Grisaru, P. van Nieuwenhuizen and C. Wu, Reggeization and the question of higher loop renormalizability of gravitation, Phys. Rev.D 12 (1975) 1563 [INSPIRE].
[18] M.T. Grisaru and H.J. Schnitzer, Dynamical calculation of bound state supermultiplets in \[\mathcal{N} = {8}\] supergravity, Phys. Lett.B 107 (1981) 196 [INSPIRE].
[19] L. Lipatov, Graviton reggeization, Phys. Lett.B 116 (1982) 411 [INSPIRE].
[20] L. Lipatov, Multi-Regge processes in gravitation, Sov. Phys. JETP55 (1982) 582 [Zh. Eksp. Teor. Fiz.82 (1982) 991] [INSPIRE].
[21] L. Lipatov, High-energy scattering in QCD and in quantum gravity and two-dimensional field theories, Nucl. Phys.B 365 (1991) 614 [INSPIRE].
[22] L. Lipatov, Reggeization of the vector meson and the vacuum singularity in non-Abelian gauge theories, Sov. J. Nucl. Phys.23 (1976) 338 [INSPIRE].
[23] V.S. Fadin, E. Kuraev and L. Lipatov, On the Pomeranchuk singularity in asymptotically free theories, Phys. Lett.B 60 (1975) 50 [INSPIRE].
[24] E. Kuraev, L. Lipatov and V.S. Fadin, Multi-reggeon processes in the Yang-Mills theory, Sov. Phys. JETP44 (1976) 443 [INSPIRE].
[25] E. Kuraev, L. Lipatov and V.S. Fadin, The Pomeranchuk singularity in non-Abelian gauge theories, Sov. Phys. JETP45 (1977) 199 [INSPIRE].
[26] I. Balitsky and L. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys.28 (1978) 822 [INSPIRE].
[27] J.M. Martın-García, xPerm: fast index canonicalization for tensor computer algebra, Comput. Phys. Commun.179 (2008) 597 [arXiv:0803.0862]. · Zbl 1197.15002
[28] Z. Bern, Perturbative quantum gravity and its relation to gauge theory, Living Rev. Rel.5 (2002)5 [gr-qc/0206071] [INSPIRE]. · Zbl 1023.83010
[29] J.J.M. Carrasco and H. Johansson, Generic multiloop methods and application to \[\mathcal{N} = {4}\] super-Yang-Mills, J. Phys.A 44 (2011) 454004 [INSPIRE]. · Zbl 1232.81054
[30] R. Gastmans and T.T. Wu, The ubiquitous photon: helicity method for QED and QCD, Clarendon, Oxford U.K. (1990) [INSPIRE].
[31] Z. Xu, D.-H. Zhang and L. Chang, Helicity amplitudes for multiple bremsstrahlung in massless non-Abelian gauge theories, Nucl. Phys.B 291 (1987) 392 [INSPIRE].
[32] O. Steinmann, Über den Zusammenhang zwischen den Wightmanfunktionen und der retardierten Kommutatoren (in German), Helv. Phys. Acta33 (1960) 257. · Zbl 0131.44201
[33] O. Steinmann, Wightman-Funktionen und retardierten Kommutatoren. II (in German), Helv. Phys. Acta33 (1960) 347. · Zbl 0131.44202
[34] L. Lipatov, High-energy asymptotics of multicolor QCD and two-dimensional conformal field theories, DESY-93-055, DESY, Zeuthen Germany April 1993 [Phys. Lett.B 309 (1993) 394 ] [INSPIRE].
[35] L. Lipatov, The bare Pomeron in quantum chromodynamics, Sov. Phys. JETP63 (1986) 904 [Zh. Eksp. Teor. Fiz.90 (1986) 1536] [INSPIRE].
[36] J. Bartels, High-energy behavior in a non-Abelian gauge theory. 2. First corrections to T(n→m) beyond the leading LNS approximation, Nucl. Phys.B 175 (1980) 365 [INSPIRE].
[37] J. Kwiecinski and M. Praszalowicz, Three gluon integral equation and odd c singlet Regge singularities in QCD, Phys. Lett.B 94 (1980) 413 [INSPIRE].
[38] L. Lipatov, Duality symmetry of Reggeon interactions in multicolor QCD, Nucl. Phys.B 548 (1999) 328 [hep-ph/9812336] [INSPIRE].
[39] L. Lipatov, High-energy asymptotics of multicolor QCD and exactly solvable lattice models, Padua preprint DFPD-93-TH-70, unpublished, University of Padua, Padua Italy October 1993 [hep-th/9311037] [INSPIRE].
[40] L. Lipatov, Asymptotic behavior of multicolor QCD at high energies in connection with exactly solvable spin models, JETP Lett.59 (1994) 596 [Pisma Zh. Eksp. Teor. Fiz.59 (1994)571] [INSPIRE].
[41] L. Faddeev and G. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett.B 342 (1995) 311 [hep-th/9404173] [INSPIRE].
[42] L. Lipatov, Integrability of scattering amplitudes in \[\mathcal{N} = {4}\] SUSY, J. Phys.A 42 (2009) 304020 [arXiv:0902.1444] [INSPIRE]. · Zbl 1176.81062
[43] J. Bartels, L. Lipatov and A. Prygarin, Integrable spin chains and scattering amplitudes, J. Phys.A 44 (2011) 454013 [arXiv:1104.0816] [INSPIRE]. · Zbl 1270.81131
[44] J. Bartels, L. Lipatov and A. Sabio Vera, BFKL Pomeron, reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev.D 80 (2009) 045002 [arXiv:0802.2065] [INSPIRE].
[45] J. Bartels, L. Lipatov and A. Sabio Vera, N = 4 supersymmetric Yang-Mills scattering amplitudes at high energies: the Regge cut contribution, Eur. Phys. J.C 65 (2010) 587 [arXiv:0807.0894] [INSPIRE].
[46] A. Romagnoni and A. Sabio Vera, A hidden \[BFKL/XX{X_{{ - \frac{1}{2}}}}\] spin chain mapping, arXiv:1111.4553 [INSPIRE].
[47] Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett.105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
[48] Z. Bern, T. Dennen, Y.-T. Huang and M. Kiermaier, Gravity as the square of gauge theory, Phys. Rev.D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
[49] Z. Bern and T. Dennen, A color dual form for gauge-theory amplitudes, arXiv:1103.0312 [INSPIRE].
[50] L.D. Landau and E.M. Lifshitz, The classical theory of fields, 3rd revised edition, Pergamon, London U.K. (1971). · Zbl 0043.19803
[51] B.S. DeWitt, Quantum theory of gravity. 3. Applications of the covariant theory, Phys. Rev.162 (1967) 1239 [INSPIRE]. · Zbl 0161.46501
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