Point-particle effective field theory III: relativistic fermions and the Dirac equation

Burgess, C.P.; Hayman, P.; Rummel, Markus; Zalavari, Laszlo

doi:10.1007/jhep09(2017)007

Cited by 15 publications

(51 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Linearity in the microscopic scale is unlike standard contributions to energy shifts due to nuclear finite-size effects [51][52][53]. It is intriguing that for plausible nuclear values of this energy shift is similar to what is seen experimentally in comparisons between energy levels for electrons and muons bound to nuclei, though (alas) similar-sized contributions do not also arise in the Dirac equation appropriate for spin-half particles [4].…”

Section: Jhep07(2017)072mentioning

confidence: 80%

“…In particular, for hydrogen-like states both of these effects imply s-wave states are shifted in energy by amounts that depend differently on mass than does the normal (Zα) 4 r 2 p m 3 charge-radius term (where α is the usual fine-structure constant). Unfortunately 4 these effects seem not to be shared by spin-half pariticles [4], and so their experimental verification requires more precise measurements for the energies of π-or K-mesic atoms than are presently possible.…”

Section: Jhep07(2017)072mentioning

confidence: 99%

“…As we see above (and is argued in [1]), this opens the possibility for cross sections being much larger than geometric in size provided the matching in the UV provides a coupling h 0 in the right range. This leaves open (see, however, [4]) why the standard arguments associated with monopole catalysis of baryon-number violation [6,7] provide the microscopic UV boundary conditions required to enhance scattering cross sections, thereby allowing classical RG evolution to provide a simple explanation for the unexpectedly large size of these cross sections.…”

Section: Jhep07(2017)072mentioning

confidence: 99%

See 2 more Smart Citations

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Burgess

Hayman

Rummel

et al. 2017

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We apply point-particle effective field theory (PPEFT) to compute the leading shifts due to finite-sized source effects in the Coulomb bound energy levels of a relativistic spinless charged particle. This is the analogue for spinless electrons of calculating the contribution of the charge-radius of the source to these levels, and our calculation disagrees with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size, one of which captures the standard charge-radius contribution. The other effective operator is a contact interaction whose leading contribution to δE arises linearly (rather than quadratically) in the small length scale, , characterizing the finite-size effects, and is suppressed by (Zα) 5 . We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting particle's mass. Its contribution turns out to be crucial if the charge radius satisfies (Zα) 2 a B , where a B is the Bohr radius, because then relativistic effects become important for the boundary condition. We show how the problem is equivalent to solving the Schrödinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts (and is responsible for its being linear in the source size). We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, such as those with large scattering lengths and perhaps also catalysis of reactions through scattering with monopoles. Experimental observation of these effects would require more precise measurement of energy levels for mesonic atoms than are now possible.

show abstract

Section: Jhep07(2017)072mentioning

confidence: 80%

Section: Jhep07(2017)072mentioning

confidence: 99%

Section: Jhep07(2017)072mentioning

confidence: 99%

See 1 more Smart Citation

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Burgess

Hayman

Rummel

et al. 2017

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, much of the previous discussion is made relatively easy by mapping the radial part of the Teukolsky equation [20] into a radial Schrödinger equation. By doing so we show how the above black-object story directly maps onto arguments coming from point-particle effective field theories (PPEFTs), used elsewhere to describe the influence of small central sources (like nuclei) on much larger orbits (like those for atomic electrons) described using the Schrödinger [19], Klein-Gordon [21] and Dirac equation [22]. (For related discussions of inverse-square potentials and conformal properties in the near-horizon limit see [23,24].…”

Section: • Rg-invariant Relations Between Couplings and Observablesmentioning

confidence: 99%

Effective field theory of black hole echoes

Burgess

Plestid

Rummel

2018

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

Gravitational wave 'echoes' during black-hole merging events have been advocated as possible signals of modifications to gravity in the strong-field (but semiclassical) regime. In these proposals the observable effect comes entirely from the appearance of nonzero reflection probability at the horizon, which vanishes for a standard black hole. We show how to apply EFT reasoning to these arguments, using and extending earlier work for localized systems that relates choices of boundary condition to the action for the physics responsible for these boundary conditions. EFT reasoning applied to this action argues that linear 'Robin' boundary conditions dominate at low energies, and we determine the relationship between the corresponding effective coupling (whose value is the one relevant low-energy prediction of particular modifications to General Relativity for these systems) and the phenomenologically measurable near-horizon reflection coefficient. Because this connection involves only near-horizon physics it is comparatively simple to establish, and we do so for perturbations in both the Schwarzschild geometry (which is the one most often studied theoretically) and the Kerr geometry (which is the one of observational interest for post-merger ring down). In passing we identify the renormalization-group evolution of the effective couplings as a function of a regularization distance from the horizon, that enforces how physics does not depend on the precise position where the boundary conditions are imposed. We show that the perfect-absorber/perfectemitter boundary conditions of General Relativity correspond to the only fixed points of this evolution. Nontrivial running of all other RG evolution reflects how modifications to gravity necessarily introduce new physics near the horizon. arXiv:1808.00847v2 [gr-qc]

show abstract

“…novel perspectives on computations within the Standard Model; for a recent example see Refs. [139][140][141].…”

Section: Motivating Searches For New Phenomenamentioning

confidence: 99%

Review of experimental and theoretical status of the proton radius puzzle

Hill

2017

EPJ Web Conf.

View full text Add to dashboard Cite

Abstract. The discrepancy between the measured Lamb shift in muonic hydrogen and expectations from electron-proton scattering and regular hydrogen spectroscopy has become known as the proton radius puzzle, whose most "mundane" resolution requires a > 5σ shift in the value of the fundamental Rydberg constant. I briefly review the status of spectroscopic and scattering measurements, recent theoretical developments, and implications for fundamental physics.

show abstract

Point-particle effective field theory III: relativistic fermions and the Dirac equation

Cited by 15 publications

References 74 publications

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Effective field theory of black hole echoes

Review of experimental and theoretical status of the proton radius puzzle

Contact Info

Product

Resources

About