Reduced theoretical error for He+4 spectroscopy

Abstract

We apply point-particle effective field theory (PPEFT) to electronic and muonic 4 He + ions, and use it to identify linear combinations of spectroscopic measurements for which the theoretical uncertainties are much smaller than for any particular energy levels. The error is reduced because these combinations are independent of all short-range physics effects up to a given order in the expansion in the small parameters R/aB and Zα (where R and aB are the ion's nuclear and Bohr radii). In particular, the theory error is not limited by the precision with which nuclear matrix elements can be computed, or compromised by the existence of any novel short-range interactions, should these exist. These combinations of 4 He measurements therefore provide particularly precise tests of QED. The restriction to 4 He arises because our analysis assumes a spherically symmetric nucleus, but the argument used is more general and extendable to both nuclei with spin, and to higher orders in R/aB and Zα. * cburgess@perimeterinstitute.ca † haymanpf@mcmaster.ca ‡ rummelm@mcmaster.ca § zalavarl@mcmaster.ca arXiv:1708.09768v3 [hep-ph] 23 Oct 2018 1 Our metric has (− + ++) signature, so γ 0 is anti-hermitian while the spatial γ i are hermitian.

Fall to the centre in atom traps and point-particle EFT for absorptive systems

“…This qualitative feature is present for any singular potential, including the 1/x 4 potential experienced by polarizable atoms in the presence of an ion. Likewise, PPEFT can be successfully applied to parameterize nuclear effects in precision hydrogen spectroscopy where relativistic effects can induce singular potentials [48].…”

Influence through mixing: hotspots as benchmarks for basic black-hole behaviour

“…Including this coupling is not simply an intellectual exercise because its presence is often required to renormalize divergences that arise because fields like φ diverge at the hotspot position once couplings are turned on there. As is well-known from other contexts [76][77][78][79][80][81][82][83][84][85][86][87] having fields divergence at the position of a source like this is fairly generic -the simplest example being the Coulomb potential diverging at the position of a source charge. From an EFT perspective the presence of couplings like λ is often compulsory, because the requirement that UV divergences drop out of physical observables causes the couplings to run and λ = 0 need not be a fixed point of this renormalization-group (RG) flow.…”

“…But the example of the Coulomb field for a small charge distribution also suggests that evaluating the 1/r divergence at r = 0 is really an artefact of trying to extrapolate to zero an external solution that is not actually appropriate in the microscopic theory within which the source's structure can be resolved. A general EFT treatment of these issues is possible [10,[80][81][82][83][84] (and tested in detail calculating nuclear finite-size effects in atoms [85][86][87]), and shows how all such divergences get renormalized by the effective couplings in JHEP09(2021)006…”

Point-Particle Catalysis

“…using the definitions (4.9). Equations (4.14) (together with (4.7), (4.12), (2.10), and past work [8]) suggests the integration constants can each be characterized by a unique RG-invariant length-scale. To see how this works, define the scales ǫ 1 , ǫ 2 , and ǫ 3 by the following relations:…”

“…Second, that parameterization is completely general, and inherently includes all possible interactions, including any potential new physics. Some obvious examples that have been explored are cross-sections and bound-state energies of electrons in terms of nuclear charge radii [7,8]. In this work, we ask the question: how do the small nuclear properties enter into physical quantities when there are multiple channels of interaction with the point-particle?…”