Compton scattering from the proton: An analysis using the delta expansion up to N3LO

We report on a chiral effective field theory calculation of Compton scattering from the proton. Our calculation includes pions, nucleons, and the Delta(1232) as explicit degrees of freedom. It uses the "delta expansion", and so implements the hierarchy of scales m_pi < M_Delta-M_N < Lambda_chi. In this expansion the power counting in the vicinity of the Delta peak changes, and resummation of the loop graphs associated with the Delta width is indicated. We have computed the nucleon Compton amplitude in the delta expansion up to N3LO for photon energies of the order of m_pi. This is the first order at which the proton Compton scattering amplitudes receive contributions from contact operators which encode contributions to the spin-independent polarisabilities from states with energies of the order of Lambda_chi. We fit the coefficients of these two operators to the experimental proton Compton data that has been taken in the relevant photon-energy domain, and are in a position to extract new results for the proton polarisabilities alpha and beta.Comment: 6 pages. Proceeding of Sixth International Workshop on Chiral Dynamics, Bern (Switzerland), 6th -- 10th July 2009. To be published in Po

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).Comment: 5 pages. Invited talk, presented by Phillips at the 11th Conference on the Intersections of Nuclear and Particle Physics (CIPANP 2012), St. Petersburg, FL, May 201

Nucleon Polarisabilities at and Beyond Physical Pion Masses

We examine the results of Chiral Effective Field Theory ($\chi$EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of $m_\pi$. 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 $\Delta(1232)$ resonance and its pion cloud. The analytic results are complete at N$^2$LO in the $\delta$-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 $m_\pi$ approaches about $300\;$MeV---as has already been seen in other observables. $\chi$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 $\chi$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.Comment: 39 pages LaTeX2e (pdflatex) including 12 figures as 16 .pdf files using includegraphics. Version approved for publication in EPJA includes modifications, clarifications and removal of typographical errors in refereeing and publication proces

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.Comment: 36 pages, 15 figures Version 2 is shortened for publication; version 1 is more self-contained. Results section unchange

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 $\Delta(1232)$ 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, $\mathcal{O(}e^2\delta^4)$, for photon energies $\omega\sim m_\pi$, and so has an accuracy of a few per cent there. At photon energies in the resonance region it is complete at NLO, $\mathcal{O}(e^2\delta^0)$, 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 [email protected] .Comment: 75 pages LaTeX2e (pdflatex) including 37 figures as .pdf files using includegraphics; minor corrections. Text-identical to published version but including the Online Supplement. Higher-resolution figures are available at http://home.gwu.edu/~hgrie/Compton/one-N-comprehensive-observables-delta4.v2.0.high-resolution-figures.tg

Compton Scattering and Nucleon Polarisabilities in Chiral EFT: Update and Future

We review theoretical progress and prospects for determining the nucleon's static dipole polarisabilities from Compton scattering on few-nucleon targets, including new values; see Refs. [1-5] for details and a more thorough bibliography.Comment: 6 pages LaTeX2e (pdflatex) including 11 figures as .pdf files. First presented by Griesshammer at the 12th Conference on the Intersections of Nuclear and Particle Physics CIPANP2015, 19-24 May 2015, Vail (CO), USA; updated for 22nd International Spin Symposium (SPIN 2016), University of Illinois, Urbana (USA), 26-30 September 2016. Corrected 2 figures, added clarifying tex

What different variants of chiral EFT predict for the proton Compton differential cross section - and why

We compare the predictions of different variants of chiral effective field theory for the gamma-p elastic scattering differential cross section. We pay particular attention to the role of pion loops, and the impact that a heavy-baryon expansion has on the behavior of those loops. We also correct erroneous results for these loops that were published in Phys. Rev. C 67, 055202 (2003) [ arXiv:nucl-th/0212024 ].Comment: 4 pages, 2 figure

Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei

Compton scattering provides important insight into the structure of the nucleon. For photons up to about 300 MeV, it is parameterised by six dynamical dipole polarisabilities which characterise the response of the nucleon to a monochromatic photon of fixed frequency and multipolarity. Their zero-energy limit yields the well-known static electric and magnetic dipole polarisabilities \alpha and \beta, and the four dipole spin polarisabilities. Chiral Effective Field Theory (ChiEFT) describes nucleon, deuteron and 3-He Compton scattering, using consistent nuclear currents, rescattering and wave functions. It can thus also be used to extract useful information on the neutron amplitude from Compton scattering on light nuclei. We summarise past work in ChiEFT on all of these reactions and compare with other theoretical approaches. We also discuss all proton experiments up to about 400 MeV, as well as the three modern elastic deuteron data sets, paying particular attention to precision and accuracy of each set. Constraining the Delta(1232) parameters from the resonance region, we then perform new fits to the proton data up to omega(lab)=170 MeV, and a new fit to the deuteron data. After checking in each case that a two-parameter fit is compatible with the respective Baldin sum rules, we obtain, using the sum-rule constraints in a one-parameter fit, \alpha=10.7\pm0.3(stat)\pm0.2(Baldin)\pm0.8(theory), \beta=3.1\mp0.3(stat)\pm0.2(Baldin)\pm0.8(theory), for the proton polarisabilities, and \alpha =10.9\pm 0.9(stat)\pm0.2(Baldin)\pm0.8(theory), \beta =3.6\mp 0.9(stat)\pm0.2(Baldin)\pm0.8(theory), for the isoscalar polarisabilities, each in units of 10^(-4) fm^3. We discuss plans for polarised Compton scattering, their promise as tools to access spin polarisabilities, and other future avenues for theoretical and experimental investigation.Comment: 82 pages LaTeX2e including 24 figures as .eps file embedded with includegraphicx; review for Prog. Part Nucl Phys. Final version identical to published areticle; spelling and grammar correcte

Non-degree Recital: Maria Phillips, soprano

Maria Phillips is a Senior pursuing a Bachelor of Music in Music Education. Ms. Phillips studies voice with Leah Partridge.https://digitalcommons.kennesaw.edu/musicprograms/1798/thumbnail.jp

Enlightenment, education and entertainment : a study of the Chautauqua movement in Kentucky.

The Chautauqua movement has been called culture under canvas and the university of the people. What began as a training camp for Sunday School teachers on the shores of Lake Chautauqua in western New York State in the 1870\u27s, grew and spread over the midwest for the next fifty years. There were some other permanent Chautauqua establishments, but none seemed to last as long as the original. What did last were traveling tent shows called Chautauquas that brought enlightenment, education, and entertainment to thousands of people over the summer months until the movement died because of technological advancements such as talking movies, radio, and the automobile. The circuit Chautauquas were quite well known in Iowa, Kansas, Missouri, and Illinois, but newspaper accounts show that they also spread into many states of the Ohio Valley and the South. Although there was a standard Chautauqua pattern that evolved over the years, each state and even each town added its own particular flavor to the pattern. Chautauqua in Kentucky was similar to Chautauqua in other states, and while it was not a major cultural phenomenon, it did have an impact on people who lived in rural and mountainous regions and thus were isolated from metropolitan areas and all that they had to offer. As the various circuits traveled throughout Kentucky from June through September, lecturers brought ideas, world news, and culture to those who might not otherwise have been exposed to such informative refinement. The Chautauquas faded away and as a cultural influence had little lasting impact on Kentuckians, except in individual memories. However, one cannot say that the Chautauquas were, therefore, unimportant; they were significant but primarily only during the times they were popular