arXiv subjects
Publications and source records attributed to Thomas R. Hemmert.
We compute corrections to both the isovector anomalous magnetic moment and the isovector electromagnetic current of the nucleon to $O(p^3)$ in the framework of covariant two-flavor Baryon Chiral Perturbation Theory. We then apply these corrections to lattice data for the anomalous magnetic moment from the LHPC, RBC & UKQCD and QCDSF collaborations.
Within the framework of two-flavor covariant baryon chiral perturbation theory we have expressed the Chernyak-Zhitnitsky, Ioffe and Dosch currents in terms of chiral fields to provide leading one-loop extrapolation formulae for the leading and next-to-leading twist normalization constants $f_N$, $λ_1$ and $λ_2$. Finite volume effects due to pion loops have been taken into account. The occurring low energy constants are fitted to data obtained from recent lattice QCD simulations in order to extract the values at the physical point.
We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100 MeV, using state-of-the-art deuteron wave functions and NN-potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green's functions in order to ensure gauge invariance and the correct Thomson limit. With this Green's-function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use Chiral Effective Field Theory with explicit Δ(1232) degrees of freedom within the Small Scale Expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic $γd$ data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find α_E^s= (11.3+-0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and β_M^s = (3.2-+0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are essentially the same.
We discuss the first moments of the parity-even Generalized Parton Distributions (GPDs) in a nucleon, corresponding to six (generalized) vector form factors. We evaluate these fundamental properties of baryon structure at low energies, utilizing the methods of covariant Chiral Perturbation Theory in the baryon sector (BChPT). Our analysis is performed at leading-one-loop order in BChPT, predicting both the momentum and the quark-mass dependence for the three (generalized) isovector and (generalized) isoscalar form factors, which are currently under investigation in lattice QCD analyses of baryon structure. We also study the limit of vanishing four-momentum transfer where the GPD-moments reduce to the well known moments of Parton Distribution Functions (PDFs). For the isovector moment _{u-d} our BChPT calculation predicts a new mechanism for chiral curvature, connecting the high values for this moment typically found in lattice QCD studies for large quark masses with the smaller value known from phenomenology. Likewise, we analyze the quark-mass dependence of the isoscalar moments in the forward limit and extract the contribution of quarks to the total spin of the nucleon. We close with a first glance at the momentum dependence of the isoscalar C-form factor of the nucleon.
We apply the methods of Chiral Perturbation Theory to the analysis of the first moments of the Generalized Parton Distributions in a Nucleon, usually known as generalized form factors. These quantities are currently also under investigation in Lattice QCD analyses of baryon structure, providing simulation results at large quark masses to be extrapolated to the "real world" via Chiral Effective Field Theory. We have performed a leading-one-loop calculation in the covariant framework of Baryon Chiral Perturbation Theory (BChPT), predicting both the momentum and the quark-mass dependence for all the vector and axial (generalized) form factors. In particular we discuss the results for the limit of vanishing four-momentum transfer where the GPD-moments reduce to the well known moments of Parton Distribution Functions (PDFs). We fit our results to available lattice QCD data, extrapolating down to the physical point. We conclude by presenting outstanding results from a combined fit to different GPDs-moments.
We present a calculation of the three complex form factors parametrizing the nucleon to Delta transition matrix element in the framework of chiral effective field theory with explicit Delta degrees of freedom. The interplay between short and long range physics is discussed and estimates for systematic uncertainties due to higher order effect are given.
Utilizing the methods of chiral effective field theory we present an analysis of the electromagnetic $NΔ$-transition current in the framework of the non-relativistic "small scale expansion" (SSE) to leading-one-loop order. We discuss the momentum dependence of the magnetic dipole, electric quadrupole and coulomb quadrupole transition form factors up to a momentum transfer of $Q^2<0.3$ GeV$^2$. Particular emphasis is put on the identification of the role of chiral dynamics in this transition. Our analysis indicates that there is indeed non-trivial momentum dependence in the two quadrupole form factors at small $Q^2<0.15$ GeV$^2$ arising from long distance pion physics, leading for example to negative radii in the (real part of the) quadrupole transition form factors. We compare our results with the EMR($Q^2$) and CMR($Q^2$) multipole-ratios from pion-electroproduction experiments and find a remarkable agreement up to four-momentum transfer of $Q^2\approx 0.3$ GeV$^2$. Finally, we discuss the chiral extrapolation of the three transition form factors at $Q^2=0$, identifying rapid changes in the (real part of the) quark-mass dependence of the quadrupole transition moments for pion masses below 200 MeV, which arise again from long distance pion dynamics. Our findings indicate that dipole extrapolation methods currently used in lattice QCD analyses of baryon form factors are not applicable for the chiral extrapolation of $NΔ$ quadrupole transition form factors.
We calculate the nucleon and the delta mass to fourth order in a covariant formulation of the small scale expansion. We analyze lattice data from the MILC collaboration and demonstrate that the available lattice data combined with our knowledge of the physical values for the nucleon and delta masses lead to consistent chiral extrapolation functions for both observables up to fairly large pion masses. This holds in particular for very recent data on the delta mass from the QCDSF collaboration. The resulting pion-nucleon sigma term is sigma_{piN} = 48.9 MeV. This first quantitative analysis of the quark-mass dependence of the structure of the Delta(1232) in full QCD within chiral effective field theory suggests that (the real part of) the nucleon-delta mass-splitting in the chiral limit, Delta_0 = 0.33 GeV, is slightly larger than at the physical point. Further analysis of simultaneous fits to nucleon and delta lattice data are needed for a precision determination of the properties of the first excited state of the nucleon.
We examine elastic Compton scattering off the deuteron for photon energies between 50 MeV and 100 MeV in the framework of chiral effective field theories to next-to-leading order. We compare one theoretical scheme with only pions and nucleons as explicit degrees of freedom to another in which the Delta(1232) resonance is treated as an explicit degree of freedom. Whereas pion degrees of freedom suffice to describe the experimental data measured at about 70 MeV, the explicit Delta(1232) gives important contributions that help to reproduce the angular dependence at higher energies. The static isoscalar dipole polarizabilities alpha_E^s and beta_M^s are fitted to the available data, giving results for the neutron polarizabilities alpha_E^n=(14.2+-2.0(stat)+-1.9(syst))*10^(-4)fm^3, beta_M^n=(1.8+-2.2(stat)+-0.3(syst))*10^(-4)fm^3. These values are in good agreement with previous experimental analyses. Comparing them to the well-known proton values we conclude that there is currently no evidence for significant differences between the proton and neutron electromagnetic dipole polarizabilities.
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.
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.
We discuss the use of cutoff methods in chiral perturbation theory. We develop a cutoff scheme based on the operator structure of the effective field theory that allows to suppress high momentum contributions in Goldstone boson loop integrals and by construction is free of the problems traditional cutoff schemes have with gauge invariance or chiral symmetries. As an example, we discuss the chiral expansion of the nucleon mass. Contrary to other claims in the literature we show that the mass of a nucleon in heavy baryon chiral perturbation theory has a well behaved chiral expansion up to effective Goldstone boson masses of 400 MeV when one utilizes standard dimensional regularization techniques. With the help of the here developed cutoff scheme we can demonstrate a well-behaved chiral expansion for the nucleon mass up to 600 MeV of effective Goldstone Boson masses. We also discuss in detail the prize, in numbers of additional short distance operators involved, that has to be paid for this extended range of applicability of chiral perturbation theory with cutoff regularization, which is usually not paid attention to. We also compare the fourth order result for the chiral expansion of the nucleon mass with lattice results and draw some conclusions about chiral extrapolations based on such type of representation.
We study the quark mass expansion of the axial-vector coupling constant g_A of the nucleon. The aim is to explore the feasibility of chiral effective field theory methods for extrapolation of lattice QCD results - so far determined at relatively large quark masses corresponding to pion masses larger than 0.6 GeV - down to the physical value of the pion mass. We compare two versions of non-relativistic chiral effective field theory: One scheme restricted to pion and nucleon degrees of freedom only, and an alternative approach which incorporates explicit Delta(1230) resonance degrees of freedom. It turns out that, in order to approach the physical value of g_A in a leading-one-loop calculation, the inclusion of the explicit Delta(1230) degrees of freedom is crucial. With information on important higher order couplings constrained from analyses of inelastic pion production processes, a chiral extrapolation function for g_A is obtained, which works well from the chiral limit across the physical point into the region of present lattice data. The resulting enhancement of our extrapolation function near the physical pion mass is found to arise from an interplay between long- and short- distance physics.
We present a Lorentz-invariant formulation of baryon chiral perturbation theory including spin-3/2 fields. Particular attention is paid to the projection on the spin-3/2 components of the delta fields. We also discuss the nucleon mass and the pion-nucleon sigma term.
We report on recent work about the study of quark mass dependence of nucleon magnetic moments and axial-vector coupling constant. We examine the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD data obtained at relative large pion masses down to the physical values.
We summarize developments concerning the quark mass dependence of nucleon magnetic moments and the axial-vector coupling constant g_A. The aim is to explore the feasibility of chiral effective field theory methods for the extrapolation of lattice QCD results, from the relatively large quark masses that can be handled in such computations down to the physically relevant range.
The spin structure of the nucleon is analyzed in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. The structure functions of doubly virtual Compton scattering are calculated to one-loop accuracy (fourth order in the chiral expansion). We discuss the generalization of the Gerasimov-Drell-Hearn sum rule, the Burkhardt-Cottingham sum rule and moments of these. We give predictions for the forward and the longitudinal-transverse spin polarizabilities of the proton and the neutron at zero and finite photon virtuality. A detailed comparison to results obtained in heavy baryon chiral perturbation theory is also given.
We study the chiral loop corrections to the generalized Gerasimov-Drell-Hearn sum rule of the nucleon for finite photon virtuality in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. We perform a complete one-loop calculation and obtain significant differences to previously found results based on the heavy baryon approach for the proton and neutron spin-dependent forward Compton amplitudes.