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Harald W. Griesshammer

Publications and source records attributed to Harald W. Griesshammer.

At least 19 recordsLinked to original sources
arXiv2025

On Two Nucleons Near Unitarity with Perturbative Pions

We explore the impact of perturbative pions on the Unitarity Expansion in the two-nucleon S-waves of Chiral Effective Field Theory at next-to-next-to leading order. Pion exchange explicitly breaks the nontrivial fixed point's universality and invariance under conformal and Wigner-$\SU(4)$ spin-isospin transformations. This Chiral Effective Field Theory applies tothe Unitarity Window (45deg 100MeV are remedied by taking only the central part of the pion's N2LO contribution. In contradistinction to the tensor part, it is invariant under Wigner-SU(4)symmetry and hence identical in 1S0 and 3S1. NLO pions are Wigner-invariant. Both channels describe PWAs and pole parameters well within mutually consistent quantitative theory uncertainty estimates. Pionic effects are small, even for k>mpi. Empirically determined breakdown scales agree well with $Λ_{NN}=\frac{16πf_π^2}{g_A^2M}=300\;$MeV where iterated OPE is not suppressed. We therefore conjecture: The footprint of both scale invariance and Wigner-symmetry in the Unitarity Expansion shows persistence,i.e. both dominate even for k=mpi and are more relevant than chiral symmetry,so that the tensor/Wigner-SU(4) symmetry-breaking part of OPE does not enter before N3LO. We also discuss the potential relevance of entanglement power and possible resolution of a conflict with the strength of the tensor interaction in the large-Nc expansion.

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arXiv2025

The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas

In the Unitarity Limit, the NN S-wave binding energies are zero, the scattering lengths infinite, Physics is universal, i.e. insensitive to details of the interactions, and observables display richer symmetries, namely invariance under both scaling and Wigner's combined SU(4) transformation of spin and isospin. This presentation is a digest of the first quantitative exploration of corrections to this picture when pions are included [1] (see there for a more comprehensive list of references). Since the pion mass and decay constant introduce dimensionful scales in the NN system, they explicitly break the symmetries of the Unitarity fixed point. In $χ$EFT, these symmetries must therefore be classified as emergent. This text focuses on the $χ$EFT variant with Perturbative ("KSW") Pions at next-to-next-to leading order (N2LO). This leads to the Hypothesis that both scale invariance and Wigner-SU(4) symmetry in the Unitarity Expansion show persistence, i.e. the footprint of both combined dominates even for $k\gtrsim m_π$ and is more relevant than chiral symmetry, so that the tensor/Wigner-SU(4) symmetry-breaking part of OPE is suppressed and does not enter before N3LO. Included are also ideas about underlying mechanisms and LO results of $χ$EFT with Nonperturbative Pions in the expansion about Unitarity.

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arXiv2025

Scattering Observables from Few-Body Densities and Compton Scattering on 6Li

The dynamics of scattering on light nuclei is numerically expensive using standard methods. Fortunately, recent developments allow one to factor the relevant quantities for a given probe into a convolution of an $n$-body Transition Density Amplitude (TDA) and the interaction kernel for a given probe. These TDAs depend only on the target, and not the probe; they are calculated once for each set of kinematics and can be used for different interactions. The kernels depend only on the probe, and not on the target; they can be reused for different targets and different kinematics. The calculation of TDAs becomes numerically difficult for more than four nucleons, but we discuss a new solution through the use of a Similarity Renormalization Group transformation, and a subsequent back-transformation. This technique allows for extending the TDA method to heavier nuclei such as 6Li. We present preliminary results for Compton scattering on 6Li and compare with available data, anticipating an upcoming, more thorough study. We also discuss ongoing extensions to pion-photoproduction and other reactions on light nuclei.

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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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arXiv2024

Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda

Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio $ξ:=2r_0/a$ once $|r_0|$ is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion [1]. At leading order, no three-body interaction is needed. A ground state exists only in the range $0.366\ldots\geξ\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$.

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arXiv2023

Universality of Three Identical Bosons with Large, Negative Effective Range

"Resummed-Range Effective Field Theory'' is a consistent nonrelativistic effective field theory of contact interactions with large scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative. Its observables are universal, i.e.~they depend only on the dimensionless ratio $ξ:=2r_0/a$, with the overall distance scale set by $|r_0|$. In the two-body sector, the position of the two shallow $S$-wave poles in the complex plane is determined by $ξ$. We investigate three identical bosons at leading order for a two-body system with one bound and one virtual state ($ξ\le0$), or with two virtual states ($0\leξ<1$). Such conditions might, for example, be found in systems of heavy mesons. We find that no three-body interaction is needed to renormalise (and stabilise) Resummed-Range EFT at LO. A well-defined ground state exists for $0.366\ldots\geξ\ge-8.72\ldots$. Three-body excitations appear for even smaller ranges of $ξ$ around the ``quasi-unitarity point'' $ξ=0$ ($|r_0|\ll|a|\to\infty$) and obey discrete scaling relations. We explore in detail the ground state and the lowest three excitations and parametrise their trajectories as function of $ξ$ and of the binding momentum $κ_2^-$ of the shallowest \twoB state from where three-body and two-body binding energies are identical to zero three-body binding. As $|r_0|\ll|a|$ becomes perturbative, this version turns into the ``Short-Range EFT'' which needs a stabilising three-body interaction and exhibits Efimov's Discrete Scale Invariance. By interpreting that EFT as a low-energy version of Resummed-Range EFT, we match spectra to determine Efimov's scale-breaking parameter $Λ_*$ in a renormalisation scheme with a ``hard'' cutoff. Finally, we compare phase shifts for scattering a boson on the two-boson bound state with that of the equivalent Efimov system.

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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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arXiv2022

What Can Possibly Go Wrong?

A lot. [In this hard, unbiased and objective look at some past and continuing blunders in following Weinberg's suggestions to arrive at a comprehensive description of Nuclear Physics using Effective Field Theories, some names and citations are withheld to protect the innocent.]

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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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arXiv2020

A Consistency Test of EFT Power Countings from Residual Cutoff Dependence

A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented. The Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the breakdown scale of an EFT, on the low-momentum scales, and on the order of the calculation. Passing this test is a necessary but not sufficient consistency criterion for a suggested power counting whose exact nature is disputed. In Chiral Effective Field Theory (ChiEFT) with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the convergence pattern in results. This led to proposals which predict different sets of Low Energy Coefficients (LECs) at the same chiral order, and at times even predict a different ordering long-range contributions. The method may independently check whether an observable is renormalised at a given order, and proves estimates of both the breakdown scale and the momentum-dependent order-by-order convergence pattern. Conversely, it helps identify those LECs (and long-range pieces) which ensure renormalised observables at a given order. I also discuss assumptions and the relation to Wilson's Renormalisation Group; useful observable and cutoff choices; the momentum window with likely best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting LECs to data; and caveats as well as limitations. Since the test is designed to minimise the use of data, it quantitatively falsifies if the EFT has been renormalised consistently. This complements other tests which quantify how an EFT compares to experiment. Its application in particular to the 3P0 and P2-3F2 partial waves of NN scattering in ChiEFT may elucidate persistent power-counting issues.

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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

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

Dissecting Deuteron Compton Scattering I: The Observables with Polarised Initial States

A complete set of linearly independent observables in Compton scattering with arbitrarily polarised real photons off an arbitrarily polarised spin-1 target is introduced, for the case that the final-state polarisations are not measured. Adopted from the one widely used e.g. in deuteron photo-dissociation, it consists of 18 terms: the unpolarised cross section, the beam asymmetry, 4 target asymmetries and 12 asymmetries in which both beam and target are polarised. They are expressed by the helicity amplitudes and -- where available -- related to observables discussed by other authors. As application to deuteron Compton scattering, their dependence on the (isoscalar) scalar and spin dipole polarisabilities of the nucleon is explored in Chiral Effective Field Theory with dynamical Delta(1232) degrees of freedom at order $e^2δ^3$. Some asymmetries are sensitive to only one or two dipole polarisabilities, making them particularly attractive for experimental studies. At a photon energy of 100 MeV, a set of 5 observables is identified from which one may be able to extract the spin polarisabilities of the nucleon. These are experimentally realistic but challenging and mostly involve tensor-polarised deuterons. Relative to Compton scattering from a nucleon, sensitivity to the "mixed" spin polarisabilities $γ_{E1M2}$ and $γ_{M1E2}$ is increased because of interference with the D wave component of the deuteron and with its pion-exchange current. An interactive Mathematica 9.0 notebook with results for all observables at photon energies up to 120 MeV is available from hgrie@gwu.edu. Note May 2017/April 2018: This arXiv version presents the article including the corrections in the Errata Eur. Phys. J. A53 (2017) 113 and A54 (2018) 57 to ibid. A49 (2013) 100. This affects Eqs. (2.12) to (2.14), Figs. 4, 7 to 10, 12, 14 to 16, 18 to 20, 22 and 23, and the corresponding, related text.

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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

Assessing Theory Uncertainties in EFT Power Countings from Residual Cutoff Dependence

I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the EFT breakdown scale, low-momentum scales, and the order of the calculation. Passing this test is a necessary but not sufficient consistency criterion for a suggested power counting whose exact nature is disputed. For example, in ChiEFT with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the relation between convergence pattern and numerical results, and led to proposals which predict different numbers of Low Energy Coefficients at the same chiral order. The method may provide an independent check whether an observable is renormalised at a given order, and of both the breakdown scale and the momentum-dependent order-by-order convergence pattern of an EFT. Conversely, it may help identify LECs which produce renormalised observables at a given order. I also discuss its underlying assumptions and relation to the RG Equation; useful choices for observables and cutoffs; the momentum window in which the test provides best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting Low Energy Coefficients to data in different or the same channel; caveats and limitations. Since the test is designed to minimise the use of data, it allows one to quantitatively falsify if the EFT has been renormalised consistently, rather than quantifying how an EFT compares to experiment. Its application in particular to the 3P0 and 3P2-3F2 partial waves of NN scattering in ChiEFT may elucidate persistent power-counting issues. Details and a better bibliography can be found in an upcoming publication.

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