Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory

Astrid Hiller Blin; Vadim Lensky; Vladimir Pascalutsa

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Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory

Vadim Lensky, Astrid Hiller Blin, Vladimir Pascalutsa

Nuclear Theory · Submitted 16 Sep 2021

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

The authors' main claim The calculated unpolarised VVCS amplitude provides a high-precision model-independent input for a future calculation of the two-photon-exchange correction to the Lamb shift of muonic deuterium.

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arXiv ID2109.08223 (version 2)

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CitationAstrid Hiller Blin, Vadim Lensky, Vladimir Pascalutsa. "Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory." arXiv:2109.08223 (2021). https://pith.science/paper/57ISGT4S

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We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalised polarisabilities of the deuteron. The calculated unpolarised VVCS amplitude provides a high-precision model-independent input for a future calculation of the two-photon-exchange correction to the Lamb shift of muonic deuterium.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude.	contribution 0.96	0.96	0.16	asserted 1.00
s1	The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO.	method 0.87	0.92	0.12	asserted 1.00
s2	We also study the lowest spin-independent generalised polarisabilities of the deuteron.	contribution 0.96	0.93	0.07	asserted 0.97
s3	The calculated unpolarised VVCS amplitude provides a high-precision model-independent input for a future calculation of the two-photon-exchange correction to the Lamb shift of muonic deuterium.	interpretation 0.86	0.75	0.41	asserted 0.94

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Original abstract

We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalised polarisabilities of the deuteron. The calculated unpolarised VVCS amplitude provides a high-precision model-independent input for a future calculation of the two-photon-exchange correction to the Lamb shift of muonic deuterium.

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5 arXiv papers cite this in 39 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 28 sentences without a confident label

Uses its method or tool 2 papers

We employ / to evaluate the VVCS amplitude, as detailed in Ref. [ref] , computing the longitudinal amplitude to next-to-next-to-next-to-leading order (N3LO), and the transverse amplitude up to next-to-leading order (NLO) in the $z$-parametrisation scheme [ref] .

Deuteron VVCS and nuclear structure effects in muonic deuterium at N3LO in pionless EFT · Introduction and Summary · 0.85
The basis for our PE-exchange calculation is provided in Ref. [ref] , where closed analytic expressions for the unpolarized amplitudes of forward doubly-virtual Compton scattering (VVCS) off the deuteron are derived.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory · Introduction · 0.89

Uses its data or values 2 papers

Our present work is based on the recent N3LO evaluation of the deuteron charge form factor (FF) and the forward longitudinal amplitude of doubly-virtual Compton scattering (VVCS) [ref] , from which we derive all of the nuclear effects at $O(α^5)$, as well as their interference with the eVP.

A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO · Introduction · 0.84
Taking the N3LO result for $G_C(Q^2)$ in Ref. [ref] and expanding in Eq. [ref] also to N3LO results in [equation] This neglects the magnetic and quadrupole FFs, whose contributions are subleading in the / counting and are indeed numerically very small, see below in Table [ref].

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory · Elastic Contribution · 0.97

Compares with it 2 papers

For comparison, the pink dashed line shows the result of the $Z$-parameterization calculation at n2lo [ref] and the experimental data is taken from Ref. [ref] .

Renormalization group analysis of electromagnetic properties of the deuteron · Charge form factor · 0.98
The agreement between the N3LO / and N4LO $χ$ET calculations, see Ref. [ref] for a detailed comparison of the FFs, is not entirely surprising as both these EFTs are expected to well reproduce low-momenta/long-range properties of the deuteron, and both calculations are of sufficiently high orders in the respective expansions.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory · Elastic Contribution · 0.87

Cites it as support 1 paper

This motivated us to calculate the longitudinal amplitude up to N3LO in Ref. [ref] .

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory · Unpolarized Deuteron VVCS in Pionless EFT · 0.96

What it cites · 66 sentences without a confident label

Contests 2 papers

As a cross-check, we calculated the $P$-wave contribution to the $np→dγ$ cross section, also getting a result twice smaller than obtained in Ref. [ref] .

Precision Calculation of n+p->d+gamma Cross Section for Big-Bang Nucleosynthesis · Deuteron (generalised) polarisabilities · contest 0.75
We note that two of the RG equations for the N3LO two-nucleon one-photon contact terms obtained by us are at variance with those obtained in Ref. [ref] .

n+p -> d+gamma for Big-Bang Nucleosynthesis · Conclusion · contest 0.73

Uses the method or tool of 14 papers

Specifically, we employ the pionless EFT (/) [ref] , where the pions are heavy and hence the nucleon-nucleon ($NN$) interaction is described by contact interactions organized in powers of nucleon three-momentum $P$.

Universality in Few-body Systems with Large Scattering Length · Introduction · 0.92
Specifically, we employ the pionless EFT (/) [ref] , where the pions are heavy and hence the nucleon-nucleon ($NN$) interaction is described by contact interactions organized in powers of nucleon three-momentum $P$.

Effective Field Theory for Few-Nucleon Systems · Introduction · 0.92
Specifically, we employ the pionless EFT (/) [ref] , where the pions are heavy and hence the nucleon-nucleon ($NN$) interaction is described by contact interactions organized in powers of nucleon three-momentum $P$.

Low-Energy Universality in Atomic and Nuclear Physics · Introduction · 0.92

Uses data or values from 7 papers

The value of the RG-invariant quantity in Eq. [ref] can be fitted to, e.g., data on $np→dγ$; we use the result from Ref. [ref] that found, also in the $z$-parametrisation, [equation] The value of $L_2^M1_S$ is fitted to the deuteron magnetic moment, obtaining [ref] [equation] this result is the same at NLO both in the $z$- and in the $ρ$-parametrisation.

Precision Calculation of n+p->d+gamma Cross Section for Big-Bang Nucleosynthesis · NLO · 0.98
The value of the RG-invariant quantity in Eq. [ref] can be fitted to, e.g., data on $np→dγ$; we use the result from Ref. [ref] that found, also in the $z$-parametrisation, [equation] The value of $L_2^M1_S$ is fitted to the deuteron magnetic moment, obtaining [ref] [equation] this result is the same at NLO both in the $z$- and in the $ρ$-parametrisation.

Nucleon-Nucleon Effective Field Theory Without Pions · NLO · 0.98
The value of the RG-invariant quantity in Eq. [ref] can be fitted to, e.g., data on $np→dγ$; we use the result from Ref. [ref] that found, also in the $z$-parametrisation, [equation] The value of $L_2^M1_S$ is fitted to the deuteron magnetic moment, obtaining [ref] [equation] this result is the same at NLO both in the $z$- and in the $ρ$-parametrisation.

A Perturbative Calculation of the Electromagnetic Form Factors of the Deuteron · NLO · 0.98

Compares with 12 papers

The expression for $α_E1$ reproduces the N3LO result obtained in Ref. [ref] using the $np→γd$ cross section calculated in Ref. [ref] , however, our $P$-wave contribution is a factor of $2$ smaller.

Improving the Convergence of NN Effective Field Theory · Deuteron (generalised) polarisabilities · 0.90
The expression for $α_E1$ reproduces the N3LO result obtained in Ref. [ref] using the $np→γd$ cross section calculated in Ref. [ref] , however, our $P$-wave contribution is a factor of $2$ smaller.

Precision Calculation of n+p->d+gamma Cross Section for Big-Bang Nucleosynthesis · Deuteron (generalised) polarisabilities · 0.90
The numerical value is also in a very good agreement with the N3LO $χ$EFT result of Ref. [ref] , $β_M1=0.0715(15) fm^3$; this agreement is remarkable, given that this is a relatively low-order calculation.

Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory · Deuteron (generalised) polarisabilities · 0.99

Cites as background 2 papers

The rest of generalities is also very much analogous to the nucleon case (see, e.g., Refs. [ref] ).

Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom · Unpolarised VVCS amplitudes · 0.96
The rest of generalities is also very much analogous to the nucleon case (see, e.g., Refs. [ref] ).

Dispersion relations in real and virtual Compton scattering · Unpolarised VVCS amplitudes · 0.96

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