Lamb shift and the gravitational binding energy for binary black holes

Lamb shift and the gravitational binding energy for binary black holes We show that the correction to the gravitational binding energy for binary black holes due to the tail effect resembles the Lamb shift in the Hydrogen atom. In both cases a conservative effect arises from interactions with radiation modes, and moreover an explicit cancelation between near and far zone divergences is at work. In addition, regularization scheme-dependence may introduce “ambiguity parameters.” This is remediated—within an effective field theory approach—by the implementation of the zero-bin subtraction. We illustrate the procedure explicitly for the Lamb shift, by performing an ambiguity-free derivation within the framework of nonrelativistic electrodynamics. We also derive the renormalization group equations from which we reproduce Bethe logarithm (at order αe5logαe), and likewise the contribution to the gravitational potential from the tail effect (proportional to v8logv). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Lamb shift and the gravitational binding energy for binary black holes

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Lamb shift and the gravitational binding energy for binary black holes

Abstract

We show that the correction to the gravitational binding energy for binary black holes due to the tail effect resembles the Lamb shift in the Hydrogen atom. In both cases a conservative effect arises from interactions with radiation modes, and moreover an explicit cancelation between near and far zone divergences is at work. In addition, regularization scheme-dependence may introduce “ambiguity parameters.” This is remediated—within an effective field theory approach—by the implementation of the zero-bin subtraction. We illustrate the procedure explicitly for the Lamb shift, by performing an ambiguity-free derivation within the framework of nonrelativistic electrodynamics. We also derive the renormalization group equations from which we reproduce Bethe logarithm (at order αe5logαe), and likewise the contribution to the gravitational potential from the tail effect (proportional to v8logv).
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.024063
Publisher site
See Article on Publisher Site

Abstract

We show that the correction to the gravitational binding energy for binary black holes due to the tail effect resembles the Lamb shift in the Hydrogen atom. In both cases a conservative effect arises from interactions with radiation modes, and moreover an explicit cancelation between near and far zone divergences is at work. In addition, regularization scheme-dependence may introduce “ambiguity parameters.” This is remediated—within an effective field theory approach—by the implementation of the zero-bin subtraction. We illustrate the procedure explicitly for the Lamb shift, by performing an ambiguity-free derivation within the framework of nonrelativistic electrodynamics. We also derive the renormalization group equations from which we reproduce Bethe logarithm (at order αe5logαe), and likewise the contribution to the gravitational potential from the tail effect (proportional to v8logv).

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jul 15, 2017

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