The isovector time-reversal- and parity-violating pion-nucleon coupling $\bar{g}_π^{(1)}$ is uniquely sensitive to dimension six interactions between right-handed light quarks and the Standard Model Higgs doublet that naturally arises in left-right symmetric models. Recent work has used the $\bar{g}_π^{(1)}$-induced one-loop contribution to the neutron electric dipole moment $d_n$, together with the present experimental $d_n$ bound, to constrain the CP-violating parameters of the left-right symmetric model. We show that this and related analyses are based on an earlier meson theory $d_n$ computation that is not consistent with the power-counting appropriate for an effective field theory. We repeat the one-loop calculation using heavy baryon chiral perturbation theory and find that the resulting $d_n$ sensitivity to $\bar{g}_π^{(1)}$ is suppressed, implying more relaxed constraints on the parameter space of the left-right symmetric model. Assuming no cancellations between this loop contribution and other contributions, such as the leading order EDM low-energy constant, the present limit on $d_n$ implies $|\bar{g}_π^{(1)}| \lesssim 1.1\times 10^{-10}$.
The isovector GMO sum rule for zero energy forward pion-nucleon scattering is critically studied to obtain the charged pion-nucleon coupling constant using the precise negatively charged pion-proton and pion-deuteron scattering lengths deduced recently from pionic atom experiments. This direct determination leads to a pseudoscalar charged pion-nucleon coupling constant of 14.23 +- 0.09 (statistic) +- 0.17 (systematic). We obtain also accurate values for the pion-nucleon scattering lengths.
We study the in-medium modification of the isovector pi N amplitude using a non-linear representation of the sigma model but keeping the scalar degree of freedom. We check that our result does not depend on the representation. We discuss the connection with other approaches based on chiral perturbation theory.
We calculate the two-pion continuum contribution to the nucleon isovector spectral functions drawing upon the new high statistics measurements of the pion form factor by the CMD-2, KLOE, and SND collaborations. The general structure of the spectral functions remains unchanged, but the magnitude increases by about 10%. Using the updated spectral functions, we calculate the contribution of the two-pion continuum to the nucleon isovector form factors and radii. We compare the isovector radii with simple rho-pole models and illustrate their strong underestimation in such approaches. Moreover, we g…
Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods how to include pion rescattering are compared: (a) solving the Muskhelishvili-Omnes (MO) equation and (b) using an N/D approach. It turns out that the resu…
The empirical value of the real part of the pion-deuteron scattering length can be well understood in terms of the dominant isovector $πN$-double scattering contribution. We calculate in chiral perturbation theory all one-pion loop corrections to this double scattering term which in the case of $πN$-scattering close the gap between the current-algebra prediction and the empirical value of the isovector threshold T-matrix $T_{πN}^-$. In addition to closing this gap there is in the $πd$-system a loop-induced off-shell correction for the exchanged virtual pion. Its coordinate space representation…
The unitarity relations for isovector nucleon form factors in the two-pion approximation for the intermediate states are analytically extended in a model independent way from the real half-axis t > 4 $μ^2$ ($μ$ is the pion mass) to the whole complex t-plane. As a result, the explicit integral representations for the nucleon form factors are constructed in terms of the pion form factor and imaginary parts of the t-channel p-wave piN-scattering amplitudes at t < 0. New method based on the explicit integral representations is developed for numerical evaluation of the two-pion contribution to the …
We present the first lattice-QCD calculation of the nucleon isovector unpolarized parton distribution functions (PDFs) at the physical-continuum limit using Large-Momentum Effective Theory (LaMET). The lattice results are calculated using ensembles with multiple sea pion masses with the lightest one around 135~MeV, 3 lattice spacings $a\in[0.06,0.12]$~fm, and multiple volumes with $M_πL$ ranging 3.3 to 5.5. We perform a simultaneous chiral-continuum extrapolation to obtain RI/MOM renormalized nucleon matrix elements with various Wilson-link displacements in the continuum limit at physical pion…
We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: $(\vec \nabla ρ_p- \vec \nabla ρ_n)^2 G_d(ρ)+ (\vec \nabla ρ_p- \vec \nabla ρ_n)\cdot(\vec J_p-\vec J_n) G_{so(ρ)+(\vec J_p-\vec J_n)^2 G_J(ρ)$ pertaining to different proton and neutron densities. Our calculation treats systematically the effects from $1π$-exchange, iterated $1π$-exchange, and irreducible $2π$-exchange with intermediate $Δ$-isobar excitations, including Pauli-blocking corrections up to three-loop order.…
The one-pion exchange current corrections to isoscalar and isovector magnetic moments of double-closed shell nuclei plus and minus one nucleon with $A=15,17,39$ and 41 have been studied in the relativistic mean field (RMF) theory and compared with previous relativistic and non-relativistic results. It has been found that the one-pion exchange current gives a negligible contribution to the isoscalar magnetic moments but a significant correction to the isovector ones. However, the one-pion exchange current doesn't improve the description of nuclear isovector magnetic moments for the concerned nu…
We present a state-of-the-art calculation of the isovector quark helicity Bjorken-$x$ distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta $P_z \in \{2.2, 2.6, 3.0\}$~GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET). We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and system…
Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent isovector nuclear spin-orbit strength $V_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy $Σ_{spin} = {i\over 2} \vec σ\cdot (\vec q \times\vec p)[U_{ls}(p,k_f)- V_{ls}(p,k_f)τ_3 δ] $ of a nucleon scattering off weakly inhomogeneous isospin-asymmetric nuclear matter. We find that iterated $1π$-exchange generates at saturation density, $k_{f0}=272.7 $MeV, an isovector nuclear spin-orbit strength at $p=0$ of $V_{ls}(0,k_{f0}) \simeq 50$ MeVf…
Current status of nucleon structure calculations with joint RBC and UKQCD 2+1-flavor dynamical domain-wall fermions (DWF) lattice QCD is reported: Two ensembles with pion mass of about (m_π=170) MeV and 250 MeV are used. The lattice cutoff is set at about 1.4 GeV, allowing a large spatial volume of about (L=4.6) fm across while maintaining a sufficiently small residual breaking of chiral symmetry with the dislocation-suppressing-determinant-ratio (DSDR) gauge action. We calculate all the isovector form factors and some low moments of isovector structure functions. We confirm the finite-size ef…
The scalar-isoscalar, scalar-isotensor and vector-isovector pion-pion partial wave amplitudes are analyzed. Preliminary results indicate that only the scalar-isoscalar amplitude fitted to the "down-flat" data satisfies Roy's equations and consequently crossing symmetry.
We extend a recent calculation of the nuclear energy density functional in the systematic framework of chiral perturbation theory by computing the isovector spin-orbit terms: $(\vec \nabla ρ_p- \vec \nabla ρ_n)\cdot(\vec J_p-\vec J_n) G_{so}(k_f)+ (\vec J_p-\vec J_n)^2 G_J(k_f)$. The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange Hartree and Fock diagrams. From these few leading order contributions in the small momentum expansion one obtains already a good equation of state of isospin-symmetric nuclear matter. We find that the parameterfree results f…
Processes of one- and two-pion production in $NN$ collisions are considered in connection with excitation of intermediate dibaryon resonances. In particular, relative contributions of the conventional meson-exchange and dibaryon excitation mechanisms in the reaction $pp \to d π^+$ are investigated in detail. Inclusion of the intermediate isovector dibaryon resonances is shown to essentially improve the description of experimental data for this reaction, provided the soft meson-baryon form factors consistent with $πN$ elastic scattering are used. Manifestation of the intermediate isoscalar and …
We examine the potential energy contribution to the symmetry energy (in the parabolic approximation) arising from the isovector mesons, π, ρ, and δ. The significance of a microscopic model which incorporates all important mesons is revealed. In particular, we demonstrate the importance of the pion for a realistic investigation of isospin-sensitive systems.
The isospin breaking in the nucleon isovector axial charge, $g_A^3$, are calculated within the external field QCD sum-rule approach. The isospin violations arising from the difference in up and down current quark masses and in up and down quark condensates are included; electromagnetic effects are not considered. We find $δg^3_A/g^3_A \approx (0.5-1.0)\times 10^{-2}$, where $δg^3_A = (g^3_A)_p + (g^3_A)_n$ and $ g^3_A = [(g^3_A)_p - (g^3_A)_n]/2$. Using the Goldberger-Treiman relation, we also obtain an estimate of the isospin breaking in the pion-nucleon coupling constant, $(g_{ppπ_0}-g_{nnπ_…
We derive novel low--energy theorems for single pion production off nucleons through the isovector axial current. We find that the $k^2$-dependence of the multipole $L_{0+}^{(+)}$ at threshold is given by the nucleon scalar form factor, namely $σ(k^2-M_π^2 ) /(3 πM_πF_π)$. The relation to PCAC results for soft pions including electroweak form factors is also clarified.
We explore the structure of the spin-1/2 flavor-octet baryons (hyperons) through their electromagnetic transverse densities. The transverse densities describe the distribution of charge and magnetization at fixed light-front time and enable a spatial representation of the baryons as relativistic systems. At peripheral distances b~1/M_pi the transverse densities are computed using a new method that combines chiral effective field theory and dispersion analysis. The peripheral isovector densities arise from two-pion exchange, which includes the rho-meson resonance through elastic unitarity. The …
We evaluate the two--pion contribution to the nucleon electromagnetic form factors by use of dispersion analysis and chiral perturbation theory. After subtraction of the rho--meson component, we calculate the distributions of charge and magnetization in coordinate space, which can be interpreted as the effects of the pion cloud. We find that the charge distribution of this pion cloud effect peaks at distances of about 0.3 fm. Furthermore, we calculate the contribution of the pion cloud to the isovector charges and radii of the nucleon.
Earlier work suggested that the in-medium $πN$ threshold isovector amplitude $b_1(ρ)$ gets renormalized in pionic atoms by about 30% away from its $ρ=0$ free-space value, relating such renormalization to the leading low-density decrease of the in-medium quark condensate $<\bar q q>$ and the pion decay constant $f_π$ in terms of the pion-nucleon $σ$ term $σ_{πN}$. Accepting the validity of this approach, we extracted $σ_{πN}$ from a large-scale fit of pionic-atom level shift and width data across the periodic table. Our fitted value $σ_{πN}=57\pm 7$ MeV is robust with respect to variation of $π…
We calculate the imaginary parts of the isoscalar scalar and isovector electromagnetic form factors of the nucleon up to two-loop order in chiral perturbation theory. Particular attention is paid on the correct behavior of Im $σ_N(t)$ and Im $G_{E,M}^V(t)$ at the two-pion threshold $t_0=4 m_π^2$ in connection with the non-relativistic 1/M-expansion. We recover the well-known strong enhancement near threshold originating from the nearby anomalous singularity at $t_c = 4m_π^2-m_π^4/M^2 = 3.98 m_π^2$. In the case of the scalar spectral function Im $σ_N(t)$ one finds a significant improvement in c…
Parity- and time reversal-violating (PVTV) pion-nucleon couplings govern the magnitude of long-range contributions to nucleon and atomic electric dipole moments. When these couplings arise from chiral symmetry-breaking CP-violating operators, such as the QCD $θ$-term or quark chromoelectric dipole moments, one may relate hadronic matrix elements entering the PVTV couplings to nucleon and pion mass shifts by exploiting the corresponding chiral transformation properties at leading order (LO) in the chiral expansion. We compute the higher-order contributions to the lowest order relations arising …
We present an analysis of isospin-breaking effects in threshold pion-nucleon scattering due to the light quark mass difference and the dominant virtual photon effects. We discuss the deviation from various relations, which are exact in the isospin limit. The size of the isospin-violating effects in the relations involving the isovector $πN$ amplitudes is typically of the order of one percent. We also find a new remarkably large effect $(\sim 40%)$ in an isoscalar triangle relation connecting the charged and neutral pion scattering off protons.
Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the $Δ$(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass m$^*_Δ\approx$ 0.45. For the isovector component only a constraint between the potential's strength at saturation and the isovec…
The CALTECH gamma-transition experiment testing time reversal symmetry via the E2/M1 mulipole mixing ratio of the 122 keV gamma-line in Fe-57 has already been performed in 1977. Extending an earlier analysis in terms of an effective one-body potential, this experiment is now analyzed in terms of effective one boson exchange T-odd P-even nucleon nucleon potentials. Within the model space considered for the Fe-57 nucleus no contribution from isovector rho-type exchange is possible. The bound on the coupling strength phi_A from effective short range axial-vector type exchange induced by the exper…
The procedure for deriving the Ward-Takahashi identity is applied to the pseudovector coupling pion-nucleon system in which the isovector and axial-vector current does not conserved. The relation is given in closed form although it is more complicated than that of the quantum electrodynamics. The application to the propagator has revealed the interesting results.
We derive the parity- and time-reversal-violating nuclear interactions stemming from the QCD theta term and quark/gluon operators of effective dimension 6: quark electric dipole moments, quark and gluon chromo-electric dipole moments, and two four-quark operators. We work in the framework of two-flavor chiral perturbation theory, where a systematic expansion is possible. The different chiral-transformation properties of the sources of time-reversal violation lead to different hadronic interactions. For all sources considered the leading-order potential involves known one-pion exchange, but its…
Based on the framework of an extended multiphase transport model with mean-field potentials in both the partonic phase and the hadronic phase, we explain the elliptic flow difference between $π^+$ and $π^-$ in the beam-energy scan program at the relativistic heavy-ion collider by incorporating the vector-isovector potential for quarks and antiquarks with different isospins. It is found that the isospin splitting of pion elliptic flow favors a strong vector-isovector interaction, and thus serves as a probe of the quark matter equation of state as well as the QCD phase structure at finite baryon…
We evaluate the S-wave pion--nucleon scattering length $a^-$ in the framework of heavy baryon chiral perturbation theory up--to--and--including terms of order $M_π^4$. We show that the order $M_π^4$ piece of the isovector amplitude at threshold, $T^-_{\rm thr}$, vanishes exactly. We predict for the isovector scattering length, $0.088 \, M_{π^+}^{-1} \le a^- \le 0.096 \, M_{π^+}^{-1}$.
Analyses on possible systematics in some isovector nucleon observables in the RBC+UKQCD 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD are presented. The vector charge, axial charge, quark momentum and helicity fractions, and transversity are discussed using mainly the Iwasaki\(\times\)DSDR ensemble at pion mass of 170 MeV. No autocorrelation issue is observed in the vector charge and quark momentum and helicity fractions. Blocked Jack-knife analyses expose significant growth of estimated error for the axial charge with increasing block sizes that are similar to or larger than the …
Using chiral perturbation theory, we calculate the density-dependent spin-orbit coupling generated by the two-pion exchange three-nucleon interaction involving virtual $Δ$-isobar excitation. From the corresponding three-loop Hartree and Fock diagrams we obtain an isoscalar spin-orbit strength $F_{\rm so}(k_f)$ which amounts at nuclear matter saturation density to about half of the empirical value of $90 $MeVfm$^5$. The associated isovector spin-orbit strength $G_{\rm so}(k_f)$ comes out about a factor of 20 smaller. Interestingly, this three-body spin-orbit coupling is not a relativistic effec…
The separated isovector spin-longitudinal and spin-transverse responses from a recent (p,n) quasifree experiment at 494 MeV are analyzed in a Glauber theory framework up to two-step contributions. Nuclear correlations are treated in the continuum random phase approximation, accounting for the spreading width of the particle-hole states. A good description of the spin-longitudinal response is achieved, hinting at some evidence of pionic effects in the quasielastic region. The spin-transverse response is underestimated and we show that multistep contributions, while sizable, are not sufficient t…
We report a state-of-the-art lattice calculation of the isovector quark transversity distribution of the proton at the physical pion mass. Within the framework of large-momentum effective theory (LaMET), we compute the transversity quasi-distributions using clover valence fermions on 2+1+1-flavor (up/down, strange, charm) HISQ-lattice configurations with boosted proton momenta as large as 3.0~GeV. The relevant lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and systematically matched to the physical transversity dist…
We critically evaluate the isovector GMO sum rule for forward pion-nucleon scattering using the recent precision measurements of negatively charged pion-proton and pion-deuteron scattering lengths from pionic atoms. We deduce the charged-pion-nucleon coupling constant, with careful attention to systematic and statistical uncertainties. This determination gives, directly from data a pseudoscalar coupling constant of 14.11+-0.05(statistical)+-0.19(systematic) or a pseudovector one of 0.0783(11). This value is intermediate between that of indirect methods and the direct determination from backwar…
We study the imaginary parts of the isoscalar electromagnetic and isovector axial form factors of the nucleon close to the $3π$-threshold in covariant baryon chiral perturbation theory. At the two-loop level, the contributions arising from leading and next-to-leading order chiral $πN$-vertices, as well as pion-induced excitations of virtual $Δ(1232)$-isobars, are calculated. It is found that the heavy baryon treatment overestimates substantially these $3π$-continua. From a phenomenological analysis, that includes the narrow $ω(783)$-resonance or the broad $a_1$-resonance, one can recognize sma…
The nucleon-nucleon interaction arising from the exchange of three pions and the excitation of $Δ(1232)$-isobars in intermediate states is studied. Approximating the $Δ$-propagator by the inverse $Δ$N mass-splitting, analytical expressions are derived for the spectral-functions of the isoscalar and isovector central, spin-spin and tensor NN-potentials in momentum-space. A trans- lation of the spectral-functions into coordinate-space potentials reveals that the main effect of these specific exchange and excitation mechanisms is a repulsive isoscalar central NN-potential.
We report the first Lattice QCD calculation using the almost physical pion mass mpi=149 MeV that agrees with experiment for four fundamental isovector observables characterizing the gross structure of the nucleon: the Dirac and Pauli radii, the magnetic moment, and the quark momentum fraction. The key to this success is the combination of using a nearly physical pion mass and excluding the contributions of excited states. An analogous calculation of the nucleon axial charge governing beta decay has inconsistencies indicating a source of bias at low pion masses not present for the other observa…
Parity-violating quasielastic electron scattering is studied within the context of the relativistic Fermi gas and its extensions to include the effects of pionic correlations and meson-exchange currents. The work builds on previous studies using the same model; here the part of the parity-violating asymmetry that contains axial-vector hadronic currents is developed in detail using those previous studies and a link is provided to the transverse vector-isovector response. Various integrated observables are constructed from the differential asymmetry. These include an asymmetry averaged over the …
We evaluate the isovector nucleon electromagnetic form factors in quenched and full QCD on the lattice using Wilson fermions. In the quenched theory we use a lattice of spatial size 3 fm at beta=6.0 enabling us to reach low momentum transfers and a lowest pion mass of about 400 MeV. In the full theory we use a lattice of spatial size 1.9 fm at beta=5.6 and lowest pion mass of about 380 MeV enabling comparison with the results obtained in the quenched theory. We compare our lattice results to the isovector part of the experimentally measured form factors.
We derive a novel model-independent result for the pion susceptibility in QCD via the isovector-pseudoscalar vacuum polarisation. In the neighbourhood of the chiral-limit, the pion susceptibility can be expressed as a sum of two independent terms. The first expresses the pion-pole contribution. The second is identical to the vacuum chiral susceptibility, which describes the response of QCD's ground-state to a fluctuation in the current-quark mass. In this result one finds a straightforward explanation of a mismatch between extant estimates of the pion susceptibility.
A recent calculation of the nuclear energy density functional from chiral two- and three-nucleon forces is extended to the isovector terms pertaining to different proton and neutron densities. An improved density-matrix expansion is adapted to the situation of small isospin-asymmetries and used to calculate in the Hartree-Fock approximation the density-dependent strength functions associated with the isovector terms. The two-body interaction comprises of long-range multi-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition, the leading …
From recent charge exchange measurements in the extreme forward direction, an independent and precise determination of the pion nucleon coupling constant is possible. This determination has reopened the debate on the value of this fundamental coupling constant of nuclear physics. Precise measurements of charge exchange observables at forward angles below 900 MeV/c would also give a better understanding of the long range part of the two-pion exchange potential. For example, the confirmation of the coherence of the tensor forces from the pion exchange and the isovector two-pion exchange would be…
The isoscalar and isovector scattering lengths (b_0,b_1) are determined using a unitarized coupled channel approach based on chiral Lagrangians. Using experimental values of pionic hydrogen and deuterium as well as low energy pi N scattering data, the free parameters of the model are calculated. Isospin violation is incorporated to a certain extent by working with physical particle masses. For the deuterium scattering length a_{pi-d} new significant corrections concerning real and imaginary parts are evaluated, putting new constraints from pi-d scattering on the values of (b_0,b_1). In particu…
The electric dipole form factor (EDFF) of the nucleon stemming from the QCD theta term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analytic contribution from the pion cloud. In the case of the theta term, the expected lower bound on the deuteron electric dipole moment is |d_d| > 1.4 10^(-4) θe fm. The momentum dependence of the isovector EDFF is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for mom…
Nuclear electric dipole moments of $^{3}He$ and $^{3}H$ are calculated using Time Reversal Invariance Violating (TRIV) potentials based on the meson exchange theory, as well as the ones derived by using pionless and pionful effective field theories, with nuclear wave functions obtained by solving Faddeev equations in configuration space for the complete Hamiltonians comprising both TRIV and realistic strong interactions. The obtained results are compared with the previous calculations of $^{3}He$ EDM and with time reversal invariance violating effects in neutron-deuteron scattering.
We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The ch…
We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up-to-and-including order $1/m^2$ with fixed and free coefficients. As an application, we discuss in detail pion-nucleon scattering. In particular, we show that the $1/m$ expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirica…
Neutrino-induced pion and photon production from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, and these processes are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo \textit{et al.} (MiniBooNE Collaboration), Phys.\ Rev.\ Lett.\ {\bf 100}, 032301 (2008)]. Pion and photon production are investigated at intermediate energies, where the $Δ$ resonance becomes important. The Lorentz-covariant effective field theory contains nucleons, pions, Deltas, isoscalar scalar ($σ$) and vector ($ω$) fields, and isovector vector ($ρ$) fie…
We present a calculation of the pi^- d scattering length with an accuracy of a few percent using chiral perturbation theory. For the first time isospin-violating corrections are included consistently. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion-nucleon scattering lengths and obtain a^+=(7.6 +/- 3.1) x 10^{-3} mpi^{-1} and a^-=(86.1 +/- 0.9) x 10^{-3} mpi^{-1}. Via the Goldberger-Miyazawa-Oehme sum rule, this leads to a charged-pion-nucleon coupling constant g_c^2/4 pi = 13.69 +/- 0.20.
We calculate in chiral perturbation theory the dominant next-to-leading order correction to the $πγ$-exchange NN-potential proportional to the large isovector magnetic moment $κ_v = 4.7$ of the nucleon. The corresponding spin-spin and tensor potentials $\widetilde V_{S,T}(r)$ in coordinate space have a very simple analytical form. At long distances $r \simeq 2$ fm these potentials are of similar size (but opposite in sign) as the leading order $πγ$-exchange potentials. We consider also effects from virtual $Δ$-isobar excitation as well as other isospin-breaking contributions to the $2π$-exchan…
We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_π\approx200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations…
We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3 $MeV at $r=1.0 $fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $πN$-scatter…
We present the first lattice calculation of the nucleon isovector unpolarized generalized parton distribution (GPD) at the physical pion mass using a lattice ensemble with 2+1+1 flavors of highly improved staggered quarks (HISQ) generated by MILC Collaboration, with lattice spacing $a\approx 0.09$~fm and volume $64^3\times 96$. We use momentum-smeared sources to improve the signal at nucleon boost momentum $P_z \approx 2.2$ GeV, and report results at nonzero momentum transfers in $[0.2,1.0]\text{ GeV}^2$. Nonperturbative renormalization in RI/MOM scheme is used to obtain the quasi-distribution…
A modified linear sigma model that allows for $g_A = 1.26$ by addition of vector and pseudovector $πN$ coupling terms was discussed by Bjorken and Nauenberg and by Lee. In this extended linear sigma model the elastic $π$N scattering amplitudes satisfy the relevant chiral low-energy theorems, such as the Weinberg-Tomozawa relation for the isovector scattering length and in some cases Adler's "consistency condition". The agreement of the isospin symmetric $πN$ scattering length with experiment is substantially improved in this extended sigma model as compared with the original one. We show that …
We calculate the nucleon form factors G_A and G_P of the isovector axial-vector current and the pion-nucleon form factor G_piN in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order O(p^4). In addition to the standard treatment including the nucleon and pions, we also consider the axial-vector meson a_1 as an explicit degree of freedom. This is achieved by using the reformulated infrared renormalization scheme. We find that the inclusion of the axial-vector meson effectively results in one additional low-energy coupling constant that we determine by a fit t…
The generalized parton distributions (GPDs) offer a window on three-dimensional imaging of the nucleon, providing understanding of how the fundamental properties of the nucleon, such as its mass and spin, arise from the underlying quark and gluon degrees of freedom. In this work, we present the first lattice calculation of the nucleon isovector helicity GPD at physical pion mass, using an $a \approx 0.09$ fm lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by MILC Collaboration. We perform the GPD calculation in Breit frame using averaged nucleon boost momentum…
