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Harald W. Griesshammer

Publications and source records attributed to Harald W. Griesshammer.

At least 55 records · Page 3Linked to original sources
arXiv2005

A nucleon in a tiny box

We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ mβ<< 1) as well as in the "p-regime" (mL ~ mβ>> 1). Based on the two leading orders, we discuss the convergence of the expansion as a function of the lattice size and quark masses. This result can be used to extrapolate lattice results obtained from lattice sizes smaller than the pion cloud, avoiding the numerical simulation of physics under theoretical control. An extraction of the low-energy coefficient c_3 of the chiral Lagrangean from lattice simulations at small volumes and a ``magic'' ratio β=1.22262 L might be possible.

hep-lat↗
arXiv2004

Nucleon Polarisabilities from Compton Scattering off the One- and Few-Nucleon System

These proceedings sketch how combining recent theoretical advances with data from the new generation of high-precision Compton scattering experiments on both the proton and few-nucleon systems offers fresh, detailed insight into the Physics of the nucleon polarisabilities. A multipole-analysis is presented to simplify their interpretation. Predictions from Chiral Effective Field Theory with special emphasis on the spin-polarisabilities can serve as guideline for doubly-polarised experiments below 300 MeV. The strong energy-dependence of the scalar magnetic dipole-polarisability $β_{M1}$ turns out to be crucial to understand the proton and deuteron data. Finally, a high-accuracy determination of the proton and neutron polarisabilities shows that they are identical within error-bars. For details and a better list of references, consult the given references.

nucl-th↗
arXiv2004

Deuteron Compton Scattering: A Random Walk

In this sketch, some recent developments in Compton scattering off the deuteron are reviewed. The strong energy-dependence of the scalar magnetic dipole polarisability β_M1 turns out to be crucial to understand the data from Saskatoon at 94 MeV. Chiral Effective Field Theory is used to extract the static iso-scalar dipole polarisabilities as \barα^s=12.6\pm1.4_{stat}\pm1.0_{wavefu} and \barβ^s=2.3\pm1.7_{stat}\pm0.8_{wavefu}, in units of 10^{-4} fm^3. Therefore, proton and neutron polarisabilities are identical within error bars. For details and a better list of references, consult the given references.

nucl-th↗
arXiv2004

Improved Convergence in the Three-Nucleon System at Very Low Energies

Neutron-deuteron scattering in the context of ``pion-less'' Effective Field Theory at very low energies is investigated to next-to-next-to-leading order. Convergence is improved by fitting the two-nucleon contact interactions to the tail of the deuteron wave-function, a procedure known as Z-parameterisation and extended here to the three-nucleon system. The improvement is particularly striking in the doublet-S wave (triton) channel, where better agreement to potential-model calculations and better convergence from order to order in the power counting is achieved for momenta as high as \sim 120 MeV. Investigating the cut-off dependence of the phase-shifts, one confirms numerically the analytical finding that the first momentum-dependent three-body force enters at N2LO. The other partial waves converge also substantially faster. Effective-range parameters of the nd-system are determined, e.g. for the quartet-S-wave scattering length a_q=[6.35\pm0.02] fm, which compares favourably both in magnitude and uncertainty with recent high-precision potential-model determinations. Differential cross-sections up to E_{lab}\approx 15 MeV agree with data.

nucl-th↗
arXiv2004

Compton Scattering off Nucleons: Focus on the Nucleonic Low-Energy Degrees of Freedom

In this sketch, I focus on Physics and formalism behind dynamical polarisabilities, a new tool to test and interpret quantitative predictions about the low-energy degrees of freedom inside the nucleon from the multipoles of Compton scattering for photon energies below 300 MeV. A way to extract them from double-polarised precision experiments is sketched. Predictions from Chiral Effective Field Theory, both on the proton and on the neutron, serve as guideline for forthcoming experiments. Special interest is put on the rôle of the nucleon spin-polarisabilities. For details and a complete list of references, consult Refs. [1,2,3].

nucl-th↗
arXiv2003

Spin Polarizabilities of the Nucleon from Polarized Low Energy Compton Scattering

As guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross sections in low energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the Delta(1232) resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.

nucl-th↗
arXiv2003

Signatures of Chiral Dynamics in Low Energy Compton Scattering off the Nucleon

We present a projector formalism which allows to define dynamical polarizabilities of the nucleon from a multipole expansion of the nucleon Compton amplitudes. We give predictions for the energy dependence of these dynamical polarizabilities both from dispersion theory and from leading-one-loop chiral effective field theory. Based on the good agreement between the two theoretical frameworks, we conclude that the energy dependence of the dynamical polarizabilities is dominated by chiral dynamics, except in those multipole channels where the first nucleon resonance Delta(1232) can be excited. Both the dispersion theory framework and a chiral effective field theory with explicit Delta(1232) degrees of freedom lead to a very good description of the available low energy proton Compton data. We discuss the sensitivity of the proton Compton cross section to dynamical polarizabilities of different multipole content and present a fit of the static electric and magnetic dipole polarizabilities from low-energy Compton data up to omega=170 MeV, finding alpha_E=(11.04+-1.36)*10^(-4) fm^3, beta_M =(2.76-+1.36)*10^(-4) fm^3.

nucl-th↗
arXiv2002

Low Energy Expansion in the Three Body System to All Orders and the Triton Channel

We extend and systematise the power counting for the three-body system, in the context of the ``pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalisation issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations.

nucl-th↗
arXiv2002

The S Wave Pion Deuteron Scattering Length in Effective Field Theory

The S wave pion deuteron scattering length is presented at NLO in the Effective Field Theory formulation of the two nucleon system with perturbative pions. At this order, this observable is determined by the iso-scalar S wave pion nucleon scattering length a^+, by pion re-scattering contributions inside the deuteron and by two nucleon two pion contact interactions that involve two unknown parameters which renormalise the appearing divergences. By choosing their values accordingly and in agreement with their natural sizes predicted by the power counting, we are able to accommodate the available experimental data. However, a^+ cannot be determined from pion deuteron scattering directly. An ongoing experiment at PSI aiming to reduce the error bars by an order of magnitude will make it possible to pin down the size of these counter terms more accurately. We compare our findings to an approach in which pions are treated non-perturbatively.

nucl-th↗
arXiv2002

Learning from Dispersive Effects in the Nucleon Polarisabilities

A cartoon is drawn how and why to define and extract the energy dependence of the nucleon polarisabilities from low energy Compton scattering on the nucleon. The information dynamical polarisabilities contain about the low energy degrees of freedom inside the nucleon is extracted by comparing the chiral effective field theory calculation with dispersion theory results. Dynamical polarisabilities do not contain more or less information than the corresponding Compton scattering amplitudes, but as with any multipole decomposition, the facts are more readily accessible and easier to interpret. Stringent constraints for models and model-independent power countings of a low energy effective field theory of the nucleon follow from their analysis.

nucl-th↗
arXiv2002

Dispersion Effects in Nucleon Polarisabilities

We present a formalism to extract the dynamical nucleon polarisabilities defined via a multipole expansion of the structure amplitudes in nucleon Compton scattering. In contradistinction to the static polarisabilities, dynamical polarisabilities gauge the response of the internal degrees of freedom of a composed object to an external, real photon field of arbitrary energy. Being energy dependent, they therefore contain additional information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances and meson production thresholds of the nucleon. We give explicit formulae to extract the dynamical electric and magnetic dipole as well as quadrupole polarisabilities from low energy nucleon Compton scattering up to the one pion production threshold and discuss the connection to the definition of static nucleon polarisabilities. As a concrete example, we examine the results of leading order Heavy Baryon Chiral Perturbation Theory for the four leading spin independent iso-scalar polarisabilities of the nucleon. Finally, we consider the possible r{ô}le of energy dependent effects in low energy extractions of the iso-scalar dipole polarisabilities from Compton scattering on the deuteron.

nucl-th↗
arXiv2001

An Introduction to Few Nucleon Systems in Effective Field Theory

Progress in the Effective Field Theory of two and three nucleon systems is sketched, concentrating mainly on the low energy version in which pions are integrated out as explicit degrees of freedom. Examples given are: the extraction of nucleon polarisabilities from deuteron Compton scattering at very low energies; the energy dependence of the nucleon polarisabilities; three body forces and the triton; and $\mathrm{nd}$ partial waves at momenta below the pion cut.

nucl-th↗
arXiv2000

Nucleon Polarisabilities from Compton Scattering on the Deuteron

An analytic calculation of the differential cross section for elastic Compton scattering on the deuteron at photon energies ωin the range of 25-50 MeV is presented to next-to-next-to-leading order, i.e. to an accuracy of \sim 3%. The calculation is model-independent and performed in the low energy nuclear Effective Field Theory without dynamical pions. The iso-scalar, scalar electric and magnetic nucleon polarisabilities α_0 and β_0 enter as free parameters with a theoretical uncertainty of about 20%. Using data at $ω_{Lab}=49 MeV$ we find $α_0=8.4\pm 3.0(exp)\pm 1.7(theor)$, $β_0=8.9\pm 3.9(exp)\pm 1.8(theor)$, each in units of $10^{-4} fm^3$. With the experimental constraint for the iso-scalar Baldin sum rule, $α_0=7.2\pm 2.1(exp)\pm 1.6(theor)$, $β_0=6.9\mp 2.1(exp)\mp 1.6(theor)$. A more accurate result can be achieved by: (i) better experimental data, and (ii) a higher order theoretical calculation including contributions from a couple of so far undetermined four-nucleon-two-photon operators.

nucl-th↗
arXiv2000

Effective Field Theory with Two and Three Nucleons

Progress in the Effective Field Theory of two and three nucleon systems is sketched, concentrating on the low energy version in which pions are integrated out as explicit degrees of freedom. Examples given are calculations of deuteron Compton scattering, three body forces and the triton, and nd partial waves.

nucl-th↗
arXiv2000

A Tale of Two and Three Bodies

This presentation is a concise teaser for the Effective Field Theory (EFT) of two and three nucleon systems as it emerged in the last three years, using a lot of words and figures, and a few cheats.

nucl-th↗
arXiv2000

Higher Partial Waves in an Effective Field Theory Approach to nd Scattering

The phase shifts for the higher partial waves (l\ge 1) in the spin quartet and doublet channel of nd scattering at centre-of-mass energies up to 15 MeV are presented at next-to-leading and next-to-next-to-leading order in an effective field theory in which pions are integrated out. As available, the results agree with both phase shift analyses and potential model calculations.

nucl-th↗
arXiv1999

A Sketch of Two and Three Bodies

A cartoon of the Effective Field Theory of many nucleon systems is drawn, concentrating on Compton scattering in the two nucleon system, and on $nd$ scattering in the three body system.

nucl-th↗