×

Compton-like scattering of a scalar particle with \(N\) photons and one graviton. (English) Zbl 1472.81250

Summary: Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number \(N\) of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a “tree replacement” rule to construct the reducible parts of the amplitude which involve irreducible pure \(N\)-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary \(N\).

MSC:

81U10 \(n\)-body potential quantum scattering theory
81V80 Quantum optics
83C45 Quantization of the gravitational field
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Elvang, H.; Huang, Y.t., Scattering Amplitudes in Gauge Theory and Gravity (2015), Cambridge University Press · Zbl 1332.81010
[2] Feynman, R. P., An operator calculus having applications in quantum electrodynamics, Phys. Rev., 84, 108 (1951) · Zbl 0044.23304
[3] Bern, Z.; Kosower, D. A., Efficient calculation of one loop QCD amplitudes, Phys. Rev. Lett., 66, 1669 (1991)
[4] Bern, Z.; Kosower, D. A., The computation of loop amplitudes in gauge theories, Nucl. Phys. B, 379, 451 (1992)
[5] Bern, Z.; Dunbar, D. C.; Shimada, T., String-based methods in perturbative gravity, Phys. Lett. B, 312, 277 (1993)
[6] Strassler, M. J., Field theory without Feynman diagrams: one loop effective actions, Nucl. Phys. B, 385, 145 (1992)
[7] Schubert, C., Perturbative quantum field theory in the string inspired formalism, Phys. Rep., 355, 73 (2001) · Zbl 0988.81108
[8] Schmidt, M. G.; Schubert, C., Worldline Green functions for multiloop diagrams, Phys. Lett. B, 331, 69 (1994)
[9] Schmidt, M. G.; Schubert, C., Multiloop calculations in the string inspired formalism: the single spinor loop in QED, Phys. Rev. D, 53, 2150 (1996)
[10] Adler, S. L.; Schubert, C., Photon splitting in a strong magnetic field: recalculation and comparison with previous calculations, Phys. Rev. Lett., 77, 1695 (1996)
[11] Reuter, M.; Schmidt, M. G.; Schubert, C., Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals, Ann. Phys., 259, 313 (1997) · Zbl 0988.81523
[12] Gies, H.; Sanchez-Guillen, J.; Vazquez, R. A., Quantum effective actions from nonperturbative worldline dynamics, J. High Energy Phys., 0508, Article 067 pp. (2005)
[13] Dunne, G. V.; Schubert, C., Worldline instantons and pair production in inhomogeneous fields, Phys. Rev. D, 72, Article 105004 pp. (2005)
[14] Bastianelli, F.; Zirotti, A., Worldline formalism in a gravitational background, Nucl. Phys. B, 642, 372 (2002) · Zbl 0998.81064
[15] Bastianelli, F.; Bonezzi, R., One-loop quantum gravity from a worldline viewpoint, J. High Energy Phys., 1307, Article 016 pp. (2013) · Zbl 1342.83075
[16] Bastianelli, F.; Bonezzi, R.; Corradini, O.; Latini, E., One-loop quantum gravity from the \(N = 4\) spinning particle, J. High Energy Phys., 1911, Article 124 pp. (2019)
[17] Bastianelli, F.; Schubert, C., One loop photon-graviton mixing in an electromagnetic field: part 1, J. High Energy Phys., 0502, Article 069 pp. (2005)
[18] Gies, H.; Langfeld, K.; Moyaerts, L., Casimir effect on the worldline, J. High Energy Phys., 0306, Article 018 pp. (2003)
[19] Bastianelli, F.; Corradini, O.; Latini, E., Higher spin fields from a worldline perspective, J. High Energy Phys., 0702, Article 072 pp. (2007)
[20] Bastianelli, F.; Bonezzi, R.; Corradini, O.; Latini, E., Effective action for higher spin fields on (A)dS backgrounds, J. High Energy Phys., 1212, Article 113 pp. (2012) · Zbl 1397.81189
[21] Bastianelli, F.; Corradini, O.; Pisani, P. A.G., Worldline approach to quantum field theories on flat manifolds with boundaries, J. High Energy Phys., 0702, Article 059 pp. (2007)
[22] Corradini, O.; Edwards, J. P.; Huet, I.; Manzo, L.; Pisani, P., Worldline formalism for a confined scalar field, J. High Energy Phys., 1908, Article 037 pp. (2019) · Zbl 1421.83107
[23] Bonezzi, R.; Corradini, O.; Vinas, S. A. Franchino; Pisani, P. A.G., Worldline approach to noncommutative field theory, J. Phys. A, 45, Article 405401 pp. (2012) · Zbl 1255.81219
[24] Ahmadiniaz, N.; Schubert, C., A covariant representation of the Ball-Chiu vertex, Nucl. Phys. B, 869, 417 (2013) · Zbl 1262.81185
[25] Ahmadiniaz, N.; Schubert, C., QCD gluon vertices from the string-inspired formalism, Int. J. Mod. Phys. E, 25, Article 1642004 pp. (2016)
[26] Daikouji, K.; Shino, M.; Sumino, Y., Bern-Kosower rule for scalar QED, Phys. Rev. D, 53, 4598 (1996)
[27] Ahmadiniaz, N.; Bashir, A.; Schubert, C., Multiphoton amplitudes and generalized Landau-Khalatnikov-Fradkin transformation in scalar QED, Phys. Rev. D, 93, Article 045023 pp. (2016)
[28] Ahmad, A.; Ahmadiniaz, N.; Corradini, O.; Kim, S. P.; Schubert, C., Master formulas for the dressed scalar propagator in a constant field, Nucl. Phys. B, 919, 9 (2017) · Zbl 1361.81163
[29] Ahmadiniaz, N.; Bastianelli, F.; Corradini, O., Dressed scalar propagator in a non-Abelian background from the worldline formalism, Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, 93, 4, Article 049904 pp. (2016), Addendum:
[30] Berezin, F. A.; Marinov, M. S., Particle spin dynamics as the Grassmann variant of classical mechanics, Ann. Phys. (N. Y.), 104, 336 (1977) · Zbl 0354.70003
[31] Gershun, V. D.; Tkach, V. I., Classical and quantum dynamics of particles with arbitrary spin, JETP Lett., 29, 288 (1979)
[32] Bonezzi, R.; Meyer, A.; Sachs, I., Einstein gravity from the \(N = 4\) spinning particle, J. High Energy Phys., 1810, 025 (2018) · Zbl 1402.83019
[33] Fradkin, E. S.; Gitman, D. M., Path integral representation for the relativistic particle propagators and BFV quantization, Phys. Rev. D, 44, 3230 (1991)
[34] Ahmadiniaz, N.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C., One-particle reducible contribution to the one-loop spinor propagator in a constant field, Nucl. Phys. B, 924, 377 (2017) · Zbl 1373.81401
[35] N. Ahmadiniaz, V.M. Banda, F. Bastianelli, O. Corradini, J.P. Edwards, C. Schubert, in preparation.
[36] Goebel, C. J.; Halzen, F.; Leveille, J. P., Angular zeros of Brown, Mikaelian, Sahdev, and Samuel and the factorization of tree amplitudes in gauge theories, Phys. Rev. D, 23, 11, 2682 (1981)
[37] Choi, S. Y.; Shim, J. S.; Song, H. S., Factorization and polarization in linearized gravity, Phys. Rev. D, 51, 2751 (1995)
[38] Holstein, B. R., Factorization in graviton scattering and the ‘natural’ value of the g factor, Phys. Rev. D, 74, Article 085002 pp. (2006)
[39] Bastianelli, F.; Corradini, O.; Dávila, J. M.; Schubert, C., On the low-energy limit of one-loop photon-graviton amplitudes, Phys. Lett. B, 716, 345 (2012)
[40] Bjerrum-Bohr, N. E.J.; Holstein, B. R.; Planté, L.; Vanhove, P., Graviton-photon scattering, Phys. Rev. D, 91, 6, Article 064008 pp. (2015)
[41] Ahmadiniaz, N.; Corradini, O.; Dávila, J. M.; Schubert, C., Gravitational Compton scattering from the worldline formalism, Int. J. Mod. Phys. Conf. Ser., 43, Article 1660201 pp. (2016)
[42] Bastianelli, F.; van Nieuwenhuizen, P., Path Integrals and Anomalies in Curved Space (2006), Cambridge University Press: Cambridge University Press Cambridge, U.K. · Zbl 1120.81057
[43] Dai, P.; Huang, Y.t.; Siegel, W., Worldgraph approach to Yang-Mills amplitudes from N=2 spinning particle, J. High Energy Phys., 0810, Article 027 pp. (2008) · Zbl 1245.81286
[44] F.M. Balli, Wordline Computation of Tree-level QED and QCD Amplitudes and Transversality, unpublished M.Sc. thesis.
[45] Bastianelli, F.; Corradini, O.; van Nieuwenhuizen, P., Dimensional regularization of nonlinear sigma models on a finite time interval, Phys. Lett. B, 494, 161 (2000) · Zbl 0976.81035
[46] Bastianelli, F., The path integral for a particle in curved spaces and Weyl anomalies, Nucl. Phys. B, 376, 113 (1992)
[47] Bastianelli, F.; van Nieuwenhuizen, P., Trace anomalies from quantum mechanics, Nucl. Phys. B, 389, 53 (1993)
[48] Weinberg, S., Photons and gravitons in S-matrix theory: derivation of charge conservation and equality of gravitational and inertial mass, Phys. Rev., 135, Article B1049 pp. (1964) · Zbl 0144.23702
[49] Cachazo, F.; Strominger, A., Evidence for a new soft graviton theorem
[50] Strominger, A., Lectures on the infrared structure of gravity and gauge theory · Zbl 1408.83003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.