Pionless Effective Field Theory Evaluation of Nuclear Polarizability in Muonic Deuterium

Chen Ji; Lucas Platter; Samuel B. Emmons

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Pionless Effective Field Theory Evaluation of Nuclear Polarizability in Muonic Deuterium

Samuel B. Emmons, Chen Ji, Lucas Platter

Nuclear Theory · Submitted 17 Sep 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find agreement with previous calculations and explain the accuracy of our calculation.

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arXiv ID2009.08347 (version 1)

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CitationChen Ji, Lucas Platter, Samuel B. Emmons. "Pionless Effective Field Theory Evaluation of Nuclear Polarizability in Muonic Deuterium." arXiv:2009.08347 (2020). https://pith.science/paper/FOYXXPY2

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We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory. We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron. We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift. We also discuss the impact of relativistic and other higher-order effects. We find agreement with previous calculations and explain the accuracy of our calculation.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory.	contribution 0.76	0.96	0.07	asserted 1.00
s1	We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron.	contribution 0.66	0.88	0.28	hedged possibility 0.51
s2	We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift.	contribution 0.84	0.96	0.14	asserted 1.00
s3	We also discuss the impact of relativistic and other higher-order effects.	contribution 0.86	0.70	0.04	unclear 0.58
s4	We find agreement with previous calculations and explain the accuracy of our calculation.	result 0.74	0.89	0.48	asserted 1.00

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Original abstract

We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory. We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron. We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift. We also discuss the impact of relativistic and other higher-order effects. We find agreement with previous calculations and explain the accuracy of our calculation.

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6 arXiv papers cite this in 7 sentences

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Our result here is compatible with the earlier N3LO $χ$ET result [ref] , as well as with that obtained from the N2LO / deuteron longitudinal response function in the point-nucleon limit [ref] .

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory · Inelastic Contribution · 1.00
The value obtained by us is appreciably smaller than the N2LO / result of Emmons et al. [ref] , which is not unexpected, given that the nucleon-size effects, included in our calculation but not in Ref. [ref] , suppress the magnitude of the $2γ$-exchange correction.

A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO · Inelastic $2γ$ Exchange · 0.98

What it cites · 13 sentences without a confident label

Uses the method or tool of 3 papers

In this work, we make use of the work of Rosenfelder and Leidemann [ref] and thereby also more recent calculations that use a state-of-the-art nuclear Hamiltonian [ref] .

Probing uncertainties of nuclear structure corrections in light muonic atoms · Introduction · 0.90
[equation] where $E$ is the two-nucleon energy in the center of mass frame and $_0$ indicates the loop integral defined in Eq. [ref]. $_0$ is solved using the PDS scheme [ref] and its dependence on the renormalization scale $μ$ is given in Eq. [ref].

A New Expansion for Nucleon-Nucleon Interactions · Leading order nucleon-nucleon amplitude · 0.99
In the power-divergence-subtraction (PDS) scheme, the expanded LECs of Eq. [ref] are given by [ref] [equation] where $μ$ is the PDS renormalization scale.

Nucleon-Nucleon Effective Field Theory Without Pions · Lagrangian and Feynman rules · 0.85

Uses data or values from 2 papers

To obtain the $η$-expansion results of the relativistic $δ^A_pol,L$ in ZRA (or $χ$EFT), we need to add an additional relativistic correction $0.037$ meV from Ref. [ref] (or $0.030$ meV from Ref. [ref] ) to the non-relativistic value.

Ab initio calculation of nuclear structure corrections in muonic atoms · Numerical results for TPE contribution to Lamb shift · 0.96
The deuteron charge form factor $F_E(q^2)$ has been evaluated using $π$EFT in Ref. [ref] .

Nucleon-Nucleon Effective Field Theory Without Pions · Theory of two-photon exchange contributions · 0.88

Compares with 1 paper

We also shown the comparison with Ref. [ref] in the table, where the calculations were done using two different expansion methods, named $η$-less method and $η$-expansion method respectively.

Probing uncertainties of nuclear structure corrections in light muonic atoms · Numerical results for TPE contribution to Lamb shift · 1.00

Cites as background 1 paper

The effects of TPE on $μ$-d observables were originally calculated in Refs. [ref] and were recently revisited with improved accuracy using different nuclear models [ref] .

Probing uncertainties of nuclear structure corrections in light muonic atoms · Introduction · 0.91

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