### Abstract

We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j±1| and the same mass as the target. The second sum rule applies if the theory at hand possesses intermediate narrow resonances with masses different from the mass of the scatterer. These sum rules are generalizations of the Gerasimov-Drell-Hearn-Weinberg sum rule. Along with the requirement of tree level unitarity, they relate different low energy couplings in the theory. Using these sum rules, we show that in certain cases the gyromagnetic ratio can differ from the "natural" value g = 2, even at tree level, without spoiling perturbative unitarity. These sum rules can be used as constraints applicable to all supergravity and higher-spin theories that contain particles charged under some U(1) gauge field. In particular, applied to four dimensional N = 8 supergravity in a spontaneously broken phase, these sum rules suggest that for the theory to have a good ultraviolet behavior, additional massive states need to be present, such as those coming from the embedding of the N = 8 supergravity in type II superstring theory. We also discuss the possible implications of the sum rules for QCD in the large-N
_{c} limit.

Original language | English (US) |
---|---|

Article number | 048 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 7 |

DOIs | |

State | Published - 2012 |

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### Keywords

- Scattering amplitudes
- Sum rules
- Supergravity models

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(7), [048]. https://doi.org/10.1007/JHEP07(2012)048

**New sum rules from low energy Compton scattering on arbitrary spin target.** / Grigoryan, Hovhannes R.; Porrati, Massimo.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2012, no. 7, 048. https://doi.org/10.1007/JHEP07(2012)048

}

TY - JOUR

T1 - New sum rules from low energy Compton scattering on arbitrary spin target

AU - Grigoryan, Hovhannes R.

AU - Porrati, Massimo

PY - 2012

Y1 - 2012

N2 - We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j±1| and the same mass as the target. The second sum rule applies if the theory at hand possesses intermediate narrow resonances with masses different from the mass of the scatterer. These sum rules are generalizations of the Gerasimov-Drell-Hearn-Weinberg sum rule. Along with the requirement of tree level unitarity, they relate different low energy couplings in the theory. Using these sum rules, we show that in certain cases the gyromagnetic ratio can differ from the "natural" value g = 2, even at tree level, without spoiling perturbative unitarity. These sum rules can be used as constraints applicable to all supergravity and higher-spin theories that contain particles charged under some U(1) gauge field. In particular, applied to four dimensional N = 8 supergravity in a spontaneously broken phase, these sum rules suggest that for the theory to have a good ultraviolet behavior, additional massive states need to be present, such as those coming from the embedding of the N = 8 supergravity in type II superstring theory. We also discuss the possible implications of the sum rules for QCD in the large-N c limit.

AB - We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j±1| and the same mass as the target. The second sum rule applies if the theory at hand possesses intermediate narrow resonances with masses different from the mass of the scatterer. These sum rules are generalizations of the Gerasimov-Drell-Hearn-Weinberg sum rule. Along with the requirement of tree level unitarity, they relate different low energy couplings in the theory. Using these sum rules, we show that in certain cases the gyromagnetic ratio can differ from the "natural" value g = 2, even at tree level, without spoiling perturbative unitarity. These sum rules can be used as constraints applicable to all supergravity and higher-spin theories that contain particles charged under some U(1) gauge field. In particular, applied to four dimensional N = 8 supergravity in a spontaneously broken phase, these sum rules suggest that for the theory to have a good ultraviolet behavior, additional massive states need to be present, such as those coming from the embedding of the N = 8 supergravity in type II superstring theory. We also discuss the possible implications of the sum rules for QCD in the large-N c limit.

KW - Scattering amplitudes

KW - Sum rules

KW - Supergravity models

UR - http://www.scopus.com/inward/record.url?scp=84864481063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864481063&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2012)048

DO - 10.1007/JHEP07(2012)048

M3 - Article

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 048

ER -