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Judith A. McGovern

Publications and source records attributed to Judith A. McGovern.

At least 19 recordsLinked to original sources
arXiv2024

Compton Scattering on 4He with Nuclear One- and Two-Body Densities

We present the first \emph{ab initio} calculation of elastic Compton scattering from 4He. It is carried out to $\mathcal{O}(e^2 δ^3)$ [N3LO] in the $δ$ expansion of $χ$EFT. At this order and for this target, the only free parameters are the scalar-isoscalar electric and magnetic dipole polarisabilities of the nucleon. Adopting current values for these yields a parameter-free prediction. This compares favourably with the world data from HI$γ$S, Illinois and Lund for photon energies $50\;\mathrm{MeV}\lesssimω\lesssim120\;\mathrm{MeV}$ within our theoretical uncertainties of $\pm10\%$. We predict a cross section up to 7 times that for deuterium. As in 3He, this emphasises and tests the key role of meson-exchange currents between np pairs in Compton scattering on light nuclei. We assess the sensitivity of the cross section and beam asymmetry to the nucleon polarisabilities, providing clear guidance to future experiments seeking to further constrain them. The calculation becomes tractable by use of the Transition Density Method. The one- and two-body densities generated from 5 chiral potentials and the AV18$+$UIX potential are available using the python package provided at \url{https://pypi.org/project/nucdens/}.

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arXiv2023

Calculation of Dynamical Response Functions Using a Bound-state Method

We investigate a method to extract response functions (dynamical polarisabilities) directly from a bound-state approach applied to calculations of perturbation-induced reactions. The use of a square-integrable basis leads to a response in the form of a sum of $δ$ functions. We integrate this over energy and fit a smooth function to the resulting stepwise-continuous one. Its derivative gives the final approximation to the physical response function. We show that the method reproduces analytical results where known, and analyse the details for a variety of models. We apply it to some simple models, using the Stochastic Variational Method as the numerical method. Although we find that this approach, and other numerical techniques, have some difficulties with the threshold behaviour in coupled-channel problems with multiple thresholds, its stochastic nature allows us to extract robust results even for such cases.

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arXiv2020

Scattering Observables from One- and Two-Body Densities: Formalism and Application to $γ\,{}^3$He Scattering

We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on $^3$He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like $^4$He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our $^3$He densities can be used to evaluate any $^3$He elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga.

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arXiv2018

Polarisabilities from Compton Scattering on 3He

This executive summary of recent theory progress in Compton scattering off 3He focuses on determining neutron polarisabilities; see ref. [2] and references therein for details and a better bibliography. Prepared for the Proceedings of the 22nd International Conference on Few-Body Problems in Physics, Caen 9-13 July 2018.

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arXiv2018

Comment on "Nucleon spin-averaged forward virtual Compton tensor at large Q^2"

In recent work, Hill and Paz apply the operator product expansion to forward doubly virtual Compton scattering. The resulting large-$Q^2$ form of the amplitude $W_1(0,Q^2)$ is compatible with the one we obtain by extrapolation of low-$Q^2$ results from a chiral effective field theory, providing support for our approach. That paper also presents a result for the two-photon contribution to the Lamb shift in muonic hydrogen that has a much larger uncertainty than in previous work. We show that this an overestimate arising from the inclusion of the proton pole term in the subtracted dispersion relation for $W_1$.

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arXiv2018

Elastic Compton Scattering from 3He and the Role of the Delta

We report observables for elastic Compton scattering from $^3$He in Chiral Effective Field Theory with an explicit $Δ(1232)$ degree of freedom ($χ$EFT) for energies between 50 and 120 MeV. The $γ\,{}^3$He amplitude is complete at N3LO, $\mathcal{O}(e^2δ^3)$, and in general converges well order by order. It includes the dominant pion-loop and two-body currents, as well as the Delta excitation in the single-nucleon amplitude. Since the cross section is two to three times that for deuterium and the spin of polarised $^3$He is predominantly carried by its constituent neutron, elastic Compton scattering promises information on both the scalar and spin polarisabilities of the neutron. We study in detail the sensitivities of 4 observables to the neutron polarisabilities: the cross section, the beam asymmetry and two double asymmetries resulting from circularly polarised photons and a longitudinally or transversely polarised target. Including the Delta enhances those asymmetries from which neutron spin polarisabilities could be extracted. We also correct previous, erroneous results at N2LO, i.e.~without an explicit Delta, and compare to the same observables on proton, neutron and deuterium targets. An interactive Mathematica notebook of our results is available from hgrie@gwu.edu.

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arXiv2018

Comprehensive Study of Observables in Compton Scattering on the Nucleon

We present an analysis of $13$ observables in Compton scattering on the proton. Cross sections, asymmetries with polarised beam and/or targets, and polarisation-transfer observables are investigated for energies up to the $Δ(1232)$ resonance to determine their sensitivity to the proton's dipole scalar and spin polarisabilities. The Chiral Effective Field Theory Compton amplitude we use is complete at N$^4$LO, $\mathcal{O(}e^2δ^4)$, for photon energies $ω\sim m_π$, and so has an accuracy of a few per cent there. At photon energies in the resonance region it is complete at NLO, $\mathcal{O}(e^2δ^0)$, and so its accuracy there is about $20$\%. We find that for energies from pion-production threshold to about $250\;\mathrm{MeV}$, multiple asymmetries have significant sensitivity to presently ill-determined combinations of proton spin polarisabilities. We also argue that the broad outcomes of this analysis will be replicated in complementary theoretical approaches, e.g., dispersion relations. Finally, we show that below the pion-production threshold, $6$ observables suffice to reconstruct the Compton amplitude, and above it $11$ are required. Although not necessary for polarisability extractions, this opens the possibility to perform "complete" Compton-scattering experiments. An interactive Mathematica notebook, including results for the neutron, is available from judith.mcgovern@manchester.ac.uk .

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arXiv2016

Nucleon Polarisabilities at and Beyond Physical Pion Masses

We examine the results of Chiral Effective Field Theory ($χ$EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of $m_π$. This provides chiral extrapolations for lattice-QCD polarisability computations. We include both the leading and sub-leading effects of the nucleon's pion cloud, as well as the leading ones of the $Δ(1232)$ resonance and its pion cloud. The analytic results are complete at N$^2$LO in the $δ$-counting for pion masses close to the physical value, and at leading order for pion masses similar to the Delta-nucleon mass splitting. In order to quantify the truncation error of our predictions and fits as $68$\% degree-of-belief intervals, we use a Bayesian procedure recently adapted to EFT expansions. At the physical point, our predictions for the spin polarisabilities are, within respective errors, in good agreement with alternative extractions using experiments and dispersion-relation theory. At larger pion masses we find that the chiral expansion of all polarisabilities becomes intrinsically unreliable as $m_π$ approaches about $300\;$MeV---as has already been seen in other observables. $χ$EFT also predicts a substantial isospin splitting above the physical point for both the electric and magnetic scalar polarisabilities; and we speculate on the impact this has on the stability of nucleons. Our results agree very well with emerging lattice computations in the realm where $χ$EFT converges. Curiously, for the central values of some of our predictions, this agreement persists to much higher pion masses. We speculate on whether this might be more than a fortuitous coincidence.

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arXiv2016

Impact of the Delta (1232) resonance on neutral pion photoproduction in chiral perturbation theory

We present an ongoing project to assess the importance of D-waves and the $Δ(1232)$ resonance for descriptions of neutral pion photoproduction in Heavy Baryon Chiral Perturbation Theory. This research has been motivated by data published by the A2 and CB-TAPS collaborations at MAMI [1]. This data has reached unprecedented levels of accuracy from threshold through to the $Δ$ resonance. Accompanying the experimental work, there has also been a series of publications studying the theory that show that, to go beyond an energy of $E_γ=170$ MeV, it is necessary to include other aspects, in particular the $Δ(1232)$ as a degree of freedom [2] and possibly higher partial waves [3].

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arXiv2016

Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $\{α_{E1},\,β_{M1}\}_p=\{11.2(0.7),\,3.9(0.7)\}\times10^{-4}$fm$^3$, and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $\{α_{E2},\,β_{M2}\}_p=\{17.3(3.9),\,-15.5(3.5)\}\times10^{-4}$fm$^5$, $\{α_{E1ν},\,β_{M1ν}\}_p=\{-1.3(1.0),\,7.1(2.5)\}\times10^{-4}$fm$^5$, and $\{γ_{E1E1},\,γ_{M1M1},\,γ_{E1M2},\,γ_{M1E2}\}_p=\{-3.3(0.8),\,2.9(1.5),\,0.2(0.2),\,1.1(0.3)\}\times10^{-4}$fm$^4$. The results for the scalar polarisabilities are in significant disagreement with semi-empirical analyses based on dispersion relations, however the results for the spin polarisabilities agree remarkably well. Results for proton Compton-scattering multipoles and polarised observables up to the Delta(1232) resonance region are presented too. The asymmetries $Σ_3$ and $Σ_{2x}$ reproduce the experimental data from LEGS and MAMI. Results for $Σ_{2z}$ agree with a recent sum rule evaluation in the forward kinematics. The asymmetry $Σ_{1z}$ near the pion production threshold shows a large sensitivity to chiral dynamics, but no data is available for this observable. We also provide the predictions for the polarisabilities of the neutron: $\{α_{E1},\,β_{M1}\}_n=\{13.7(3.1),\,4.6(2.7)\}\times10^{-4}$fm$^3$, $\{α_{E2},\,β_{M2}\}_n=\{16.2(3.7),\,-15.8(3.6)\}\times10^{-4}$fm$^5$, $\{α_{E1ν},\,β_{M1ν}\}_n=\{0.1(1.0),\,7.2(2.5)\}\times10^{-4}$fm$^5$, and $\{γ_{E1E1},\,γ_{M1M1},\,γ_{E1M2},\,γ_{M1E2}\}_n=\{-4.7(1.1),\,2.9(1.5),\,0.2(0.2),\,1.6(0.4)\}\times10^{-4}$fm$^4$. The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching dynamical and static polarisabilities.

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arXiv2014

Theory Viewpoint on Extracting Nucleon Polarisabilities in Low-Energy Compton Scattering

During the workshop "Compton Scattering off Protons and Light Nuclei: pinning down the nucleon polarisabilities" (ECT*, Trento, Italy, 29 July -- 2 August 2013, http://www.ectstar.eu/node/98), recent developments had been reviewed in experimental and theoretical studies of real and virtual Compton scattering, static and generalized dipole scalar and spin polarisabilities of nucleons, as well as related phenomena in physics of muonic atoms. A vivid topic at the workshop was pathways towards the most precise extraction of the static polarisabilities from low-energy Compton cattering---including pertinent theoretical uncertainties. Being asked by our experimental colleagues, we prepared during the workshop a short letter with conclusions of the discussion, emphasising future prospects.

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arXiv2014

Proton polarisabilities from Compton data using Covariant Chiral EFT

We present a fit of the spin-independent electromagnetic polarisabilities of the proton to low-energy Compton scattering data in the framework of covariant baryon chiral effective field theory. Using the Baldin sum rule to constrain their sum, we obtain $α=[10.6\pm0.25$(stat)$\pm0.2$(Baldin)$\pm0.4$(theory)$]\times10^{-4}$fm$^3$ and $β=[3.2\mp0.25$(stat)$\pm0.2$(Baldin)$\mp0.4$(theory)$]\times10^{-4}$fm$^3$, in excellent agreement with other chiral extractions of the same quantities.

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arXiv2013

Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom

We analyse the proton Compton-scattering differential cross section for photon energies up to 325 MeV using Chiral Effective Field Theory and extract new values for the electric and magnetic polarisabilities of the proton. Our EFT treatment builds in the key physics in two different regimes: photon energies around the pion mass ("low energy") and the higher energies where the Delta(1232) resonance plays a key role. The Compton amplitude is complete at N4L0, O(e^2 delta^4), in the low-energy region, and at NLO, O(e^2 delta^0), in the resonance region. Throughout, the Delta-pole graphs are dressed with pi-N loops and gamma-N-Delta vertex corrections. A statistically consistent database of proton Compton experiments is used to constrain the free parameters in our amplitude: the M1 gamma-N-Delta transition strength b_1 (which is fixed in the resonance region) and the polarisabilities alpha and beta (which are fixed from data below 170 MeV). In order to obtain a reasonable fit we find it necessary to add the spin polarisability gammaM1 as a free parameter, even though it is, strictly speaking, predicted in chiral EFT at the order to which we work. We show that the fit is consistent with the Baldin sum rule, and then use that sum rule to constrain alpha+beta. In this way we obtain alpha=[10.65+/-0.35(stat})+/-0.2(Baldin)+/-0.3(theory)]10^{-4} fm^3, and beta =[3.15-/+0.35(stat)-/+0.2(Baldin)-/+0.3(theory)]10^{-4} fm^3, with chi^2 = 113.2 for 135 degrees of freedom. A detailed rationale for the theoretical uncertainties assigned to this result is provided.

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arXiv2012

Using EFT to analyze low-energy Compton scattering from protons and light nuclei

We discuss the application of an effective field theory (EFT) which incorporates the chiral symmetry of QCD to Compton scattering from the proton and deuteron. We describe the chiral EFT analysis of the proton Compton scattering database presented in our recent review (arXiv:1203.6834), which gives: alpha^{(p)}=10.5 +/- 0.5(stat) +/- 0.8(theory); beta^{(p)}= 2.7 +/- 0.5(stat) +/- 0.8(theory), for the electric and magnetic dipole polarizability of the proton. We also summarize the chiral EFT analysis of the world data on coherent Compton scattering from deuterium presented in arXiv:1203.6834. That yields: alpha^{(s)}=10.5 +/- 2.0(stat) +/- 0.8(theory); beta^{(s)}=3.6 +/- 1.0(stat) +/- 0.8(theory).

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arXiv2012

Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory

We calculate the amplitude T_1 for forward doubly-virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the gammaNDelta form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.

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