We present results on the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{Δu-Δd}$, and the transversity moment, $\langle x \rangle_{δu-δd}$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC collaboration using $2+1+1$-flavors of dynamical highly improved staggered quarks (HISQ). The correlation functions are calculated using the Wilson-Clover action and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI${}^\prime$-MOM scheme. The data have been collected at lattice spacings $a \approx 0.15,\ 0.12,\ 0.09,$ and 0.06 fm and $M_π\approx 310,\ 220$ and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the $\overline{MS}$ scheme at 2 GeV, are $\langle x \rangle_{u-d} = 0.173(14)(07)$, $\langle x \rangle_{Δu-Δd} = 0.213(15)(22)$ and $\langle x \rangle_{δu-δd} = 0.208(19)(24)$, where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.
We use vector flavor symmetry to relate form factors of isospin changing operators to isovector form factors. Flavor twisted boundary conditions in lattice QCD thus allow isovector form factors of twist-two operators, e.g, to be computed at continuous values of the momentum transfer. These twisted boundary conditions, moreover, are implemented only in the valence sector. Effects of the finite volume must be addressed to extract isovector moments and radii at zero lattice momentum. As an example, we use chiral perturbation theory to assess the volume effects in extracting the isovector magnetic…
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…
The current status is reported of joint lattice numerical calculations by LHP and RBC collaborations of isovector nucleon form factors using 2+1-flavor physical-mass domain-wall fermions ensemble at a lattice cutoff $a^{-1}$ of 1.730(4) GeV and spatial volume of $(La=\mbox{\rm 5.471(13)fm})^3$ generated jointly by RBC and UKQCD collaborations.
We present an update on the status of the calculations of isovector and flavor-diagonal charges of the nucleon. The calculations of the isovector charges are being done using ten $2+1+1$-flavor HISQ ensembles generated by the MILC collaboration covering the range of lattice spacings $a \approx$ 0.12, 0.09, 0.06 fm and pion masses $M_π\approx$ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and three-states fits to the three-point correlators. The calculations of the disconnected diagrams needed to estimate flavor-diagonal charges …
The current status of the LHP and RBC joint calculations of the nucleon isovector form factors and low moments of structure functions with a 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD ensemble at the physical pion mass generated by RBC and UKQCD Collaborations with a momentum cutoff of 1.730(4) GeV and lattice spatial extent of 5.476(12) fm is reported. About ten percent of the statistics reported in Lattice 2014 were found with an incorrect boundary condition in time but correcting for it resulted in less than one-percent difference.
We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham's formula is corrected and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find δM_{p-n}^γ= 1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with addi…
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 …
In this letter, we report the results for the isovector polarized quark quasi-distribution functions $Δu(x,v) - Δd(x,v)$ in the large $N_c$, calculated within the chiral quark-soliton model. It is shown that the polarized quark quasi-distributions present good convergence to the light-cone PDFs in the limit of the nucleon boost momentum $P_N \to \infty$ (or the velocity $v \to 1$), compared to the case of the unpolarized isosinglet distributions.
We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges $g_S^{u-d}$, $g_A^{u-d}$, and $g_T^{u-d}$. We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited-states compared to use of a single, loc…
Systematics in nucleon isovector vector, $g_V$, and axialvector, $g_A$, charges calculated on a 2+1-flavor dynamical domain-wall-fermions (DWF) ensemble at physical mass jointly generated by RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with lattice cut off of 1.730(4) GeV, are analyzed. Both are calculated with about a percent or less statistical errors. A few standard-deviation systematics seen in vector charge is consistent with possible $O(a^2)$ discretization error through small excited-state contamination. Axialvector charge is found with three to nine standard-deviation systematic d…
We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\langle x\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \times 64$ lattice at $m_π = 330$ MeV with lattice spacing $a = 0.114$ fm.
Nucleon isovector vector- and axialvector-current form factors, the renormalized isovector transversity and scalar charge, and the bare quark momentum and helicity moments of isovector structure functions are reported with improved statistics from two recent RBC+UKQCD 2+1-flavor dynamical domain-wall fermions ensembles: Iwasaki\(\times\)DSDR gauge \(32^3\times64\) at inverse lattice spacing of 1.38 GeV and pion mass of 249 and 172 MeV.
The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We present a lattice QCD calculation of this form factor, introducing a new method to directly extract its z-expansion from lattice correlators. Our final parameterization of the form factor, which extends up to spacelike virtualities of 0.7 GeV^2 with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.
The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We perform a lattice-QCD based calculation of this form factor, introducing a new method to directly extract its $z$-expansion from lattice correlators. Our final parametrization of the form factor, which extends up to spacelike virtualities of $0.7\,{\rm GeV}^2$ with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.
We present our recent high precision calculations (Phys. Rev. D102 (2020) no.5, 054512 and JHEP 04 (2021) 044, JHEP 21 (2020) 004) of the first moment of nucleon isovector polarized, unpolarized and transversity distributions, i.e., momentum fraction, helicity and transversity moment, respectively. We use the standard method for the calculation of these moments (via matrix elements of twist two operators), and carry out a detailed analysis of the sources of systematic uncertainty, in particular of excited state contributions. Our calculations have been performed using two different lattice set…
We report nucleon mass, isovector vector and axial-vector charges, and tensor and scalar couplings, calculated using two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD collaborations. These ensembles were generated with Iwasaki $\times$ dislocation-suppressing-determinant-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV. The nucleon mass extrapolates to a value $m_N = 0.950(5)$ GeV at physical point. The isovector vector charge renormalizes to unity in th…
Nucleon isovector form factors calculated on a 2+1-flavor domain-wall-fermions ensemble with strange and degenerate up and down quarks at physical mass and lattice cut off, $a^{-1}$, of about 1.730(4) GeV, are reported. The ensemble was generated jointly by RBC and UKQCD collaborations with a spatial extent of $48a$ or about 5.5 fm. The form factors are calculated in collaboration with LHP collaboration as well. The resulting shape parameters of the form factors, such as vector-charge mean squared radius, $\langle r_1^2\rangle$, or anomalous magnetic moment, $F_2(0)$ appear less dependent on p…
We present the current status of our analysis of nucleon structure observables including isovector charges and twist-2 matrix elements as well as the nucleon mass. Results are computed on a large set of CLS $N_f=2+1$ gauge ensembles with $M_π\approx0.130\mathrm{MeV}\ldots 350\mathrm{MeV}$, four values of the lattice spacing $a=0.05\mathrm{fm}\ldots 0.09\mathrm{fm}$ and covering a large range of physical volumes. Compared to the results presented at last year's conference we have added data on a very fine and large box at small light quark mass ($T\times L^3=192 \times 96^3$, $M_π=172\mathrm{Me…
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 present the analysis of isovector axial vector nucleon form factors on a set of $N_f=2+1$ CLS ensembles with $\mathcal O(a)$-improved Wilson fermions and Lüscher-Weisz gauge action. The set of ensembles covers a pion mass range of $130-353\,$MeV with lattice spacings between $0.05\,$fm and $0.09\,$fm. In particular, the set includes a $L/a=96$ ensemble at the physical pion mass. For the purpose of the form factor extraction, we employ both the summed operator insertion method (summation method) and explicit two-state fits in order to account for excited-state contributions to the nucleon co…
In this work we present the isovector flavor combination for the nucleon tensor charge extracted from lattice QCD simulations using overlap fermions on $N_f=2+1$ domain-wall configurations. The pion mass dependence is studied using six valence quark masses, each reproducing a value for the pion mass in the valence sector between 147 and 330 MeV. We investigate and eliminate systematic uncertainties due to contamination by excited states, by employing several values for the source-sink separation that span from 1 fm to 1.6 fm. We apply a chiral extrapolation in the valence sector using a quadra…
We present results on the axial, scalar and tensor isovector-couplings of the nucleon from 2+1 flavor lattice QCD with physical light quarks ($m_π$ = 135 MeV) in large spatial volume of (10.8 fm)$^3$. The calculations are carried out with the PACS10 gauge configurations generated by the PACS Collaboration with the stout-smeared $\mathcal{O}(a)$ improved Wilson fermions and Iwasaki gauge action at $β=1.82$ corresponding to the lattice spacing of 0.084 fm. For the renormalization, we use the RI/SMOM scheme, a variant of Rome-Southampton RI/MOM scheme with reduced systematic errors, as the interm…
We present high-statistics results for the isovector and flavor diagonal charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the isospin symmetric limit, results for the neutron are given by the $u \leftrightarrow d$ interchange. A chiral-continuum fit with leading order corrections was made to extract the connected and disconnected contributions in the continuum limit and at $M_π=135$ MeV. All results are given in the $\overline{MS}$ scheme at 2 GeV. The isovector charges, $g_A^{u-d} = 1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$, are use…
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…
The extraction of the magnetic form factor of the nucleon at zero momentum transfer is usually performed by adopting a parametrization for its momentum dependence and fitting the results obtained at finite momenta. We present position space methods that rely on taking the derivative of relevant correlators to extract directly the magnetic form factor at zero momentum without the need to assume a functional form for its momentum dependence. These methods are explored on one ensemble using $N_f=2+1+1$ Wilson twisted mass fermions.
Preliminary results are presented for nucleon isovector charges and twist-2 matrix elements which have been obtained employing an improved analysis strategy to deal with excited-state contamination. The set of CLS $N_f=2+1$ gauge ensembles in this study has been extended compared to our 2018 calculation, including an ensemble at physical quark masses. Besides the addition of new ensembles, the number of gauge configurations and measurements has been increased on several of the existing ensembles and the analysis has been extended to include additional source-sink separations. The ensembles cov…
We compute the axial, scalar, tensor and pseudoscalar isovector couplings of the nucleon as well as the induced tensor and pseudoscalar charges in lattice simulations with $N_f=2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions. The simulations are carried out down to a pion mass of 150 MeV and linear spatial lattice extents of up to 4.6 fm at three different lattice spacings ranging from approximately 0.08 fm to 0.06 fm. Possible excited state contamination is carefully investigated and finite volume effects are studied. The couplings, determined at these la…
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…
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.
We present results for the scalar and tensor isovector-couplings ($g_S$ and $g_T$) of the nucleon measured at the physical point ($M_π=135$ MeV) with a single lattice spacing of $0.085\ \mathrm{fm}$ in 2+1 flavor QCD. Our calculations are carried out with two ensembles of gauge configurations generated by the PACS Collaboration with nonperturbatively ${\cal O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\ {\rm fm})^4$ and $(5.5\ {\rm fm})^4$ lattices, where the finite-size effect on the nucleon mass was not shown at the level of the statistical precision less than 0.5%. …
We present high-statistics estimates of the isovector charges of the nucleon from four 2+1-flavor ensembles generated using Wilson-clover fermions with stout smearing and tree-level tadpole improved Symanzik gauge action at lattice spacings $a=0.114$ and $0.080$ fm and with $M_π\approx 315$ and 200 MeV. The truncated solver method with bias correction and the coherent source sequential propagator construction are used to cost-effectively achieve $O(10^5)$ measurements on each ensemble. Using these data, the analysis of two-point correlation functions is extended to include four states in the f…
We calculate the nucleon isovector scalar charge in lattice QCD using overlap fermions on five ensembles of gauge configurations generated by the RBC/UKQCD collaboration using the domain-wall quark action with $2+1$ dynamical flavors. The five ensembles cover five pion masses, $m_π\approx$ 139, 171, 302, 337 and 371 MeV, and four lattice spacings, $a \approx $ 0.06, 0.08, 0.11 and 0.14 fm. Three to six valence quark masses are computed on each ensemble to investigate the pion mass dependence. The extrapolation to the physical pion mass, continuum and infinite volume limits is obtained by a glo…
We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling $g^3_A$ with overlap valence on $2+1$-flavor Domain Wall Fermion sea. Using the equality of $g^3_A$ from the spatial and temporal components of the axial-vector current as a normalization condition, we find that $g_A^3$ is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges $g_A^{3}(24I)=1.22(4)$ and $g_A^{3}(3…
We present preliminary results for the axial, scalar and tensor charges of the nucleon measured in 2+1 flavor QCD with the physical light quarks ($m_π=135$ MeV). Our simulations are carried out with gauge configurations generated by the PACS Collaboration with the stout-smeared $O(a)$ improved Wilson fermions and Iwasaki gauge action at a single lattice spacing of $0.085\ (\mathrm{fm})$. There are two lattice ensembles of the PACS gauge configurations, which have physical lattice sizes over $(10\ \mathrm{fm})^4$ and $(5\ \mathrm{fm})^4$, respectively. We compute the nucleon three-point correla…
We calculate the quark mass dependence of both isovector and isoscalar anomalous magnetic moments of the nucleon in a chiral effective field theory with explicit pion, nucleon and Delta(1232) degrees of freedom to leading-one-loop order. In the isovector sector we fit 3 unknown couplings of the effective Lagrangian to available lattice data and obtain a surprisingly well-behaved extrapolation function connecting the chiral limit, experimental data and the lattice simulations. We also discuss the polynomial quark mass dependence in the isoscalar sector and finally compare with the Pade formula …
We report on numerical lattice QCD calculations of some of the low moments of the nucleon structure functions. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain wall fermions and the Iwasaki gauge action ($β= 2.13$). The inverse lattice spacing is $a^{-1} = 1.73$ GeV, and two spatial volumes of ((2.7{\rm fm})^3) and ((1.8 {\rm fm})^3) are used. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange mass is about 12 % heavier than the physical one. The…
We present high statistics results for the isovector charges $g^{u-d}_A$, $g^{u-d}_S$ and $g^{u-d}_T$ of the nucleon. Calculations were carried out on eleven ensembles of gauge configurations generated by the MILC collaboration using highly improved staggered quarks (HISQ) action with 2+1+1 dynamical flavors. These ensembles span four lattice spacings $a \approx$ 0.06, 0.09, 0.12 and 0.15 fm and light-quark masses corresponding to $M_π\approx$ 135, 225 and 315 MeV. Excited-state contamination in the nucleon 3-point correlation functions is controlled by including up to three-states in the spec…
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 present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Non-perturbative renormalization of the relevant quark currents is performed where necessary. The inverse lattice spacing, $a^{-1}$, is about 1.7 GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2 the strange quark mass. The physical volume of the lattice is abou…
Properties of the proton and the neutron are explored in partially-quenched chiral perturbation theory with two non-degenerate light flavors. Masses, magnetic moments, matrix elements of isovector twist-2 operators and axial-vector currents are computed at the one-loop level in the chiral expansion.
We describe a procedure for extracting momentum derivatives of nucleon matrix elements on the lattice directly at $Q^2=0$. This is based on the Rome method for computing momentum derivatives of quark propagators. We apply this procedure to extract the nucleon isovector magnetic moment and charge radius as well as the isovector induced pseudoscalar form factor at $Q^2=0$ and the axial radius. For comparison, we also determine these quantities with the traditional approach of computing the corresponding form factors, i.e. $G^v_E(Q^2)$ and $G_M^v(Q^2)$ for the case of the vector current and $G_P^…
Nucleon isovector vector, $g_V$, and axialvector, $g_A$, charges calculated on a 2+1-flavor dynamical domain-wall-fermions (DWF) ensemble at physical mass jointly generated by RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with lattice cut off of 1.730(4) GeV, are reported with about a percent statistical errors, along with isovector ``scalar,'' $g_S$, and ``tensor charges,'' $g_T$, with larger statistical errors. Nucleon mass is estimated as 947(6) MeV. A few standard-deviation systematics is seen in the vector charge, likely from $O(a^2)$ discretization error through small excited-state c…
We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $ππ$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric rad…
We report the current status of RBCK calculations on nucleon structure with both quenched and unquenched lattice QCD. The combination of domain wall fermions and DBW2 gauge action works well for isovector vector and axial charges, and moments of structure functions <x>_q, d_1, and <1>_{δq}.
We present a theoretical parametrization of the nucleon electromagnetic form factors (FFs) based on a combination of chiral effective field theory and dispersion analysis. The isovector spectral functions on the two-pion cut are computed using elastic unitarity, chiral pion-nucleon amplitudes, and timelike pion FF data. Higher-mass isovector and isoscalar t-channel states are described by effective poles, whose strength is fixed by sum rules (charges, radii). Excellent agreement with the spacelike proton and neutron FF data is achieved up to Q^2 \sim 1 GeV^2. Our parametrization provides prope…
We present lattice-QCD results on the nucleon isovector axial, scalar and tensor charges, the isovector electromagnetic Dirac and Pauli form factors, and the connected parts of the isoscalar charges. The calculations have been done using two ensembles of HISQ lattices generated by the MILC Collaboration with 2+1+1 dynamical flavors at a lattice spacing of 0.12 fm and with light-quark masses corresponding to pions with masses 310 and 220 MeV. We perform a systematic study including excited-state degrees of freedom and examine the dependence of the extracted nucleon matrix elements on source-sin…
We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings $a=\{0.098,0.085,0.064,0.049\}$~fm and various pion masses ranging between $220$ and $350$ MeV, with proton momenta up to $2.8$ GeV. The result is non-perturbatively renormalized in the hybrid scheme with self renormalization which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass and in…
We present recent developments in lattice QCD simulations as applied in the study of hadron structure. We discuss the challenges and perspectives in the evaluation of benchmark quantities such as the nucleon axial charge and the isovector parton momentum fraction, as well as, in the computation of the nucleon $σ$-terms, which involve the calculation of disconnected quark loop contributions.
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 bary…
With twisted boundary conditions on the quark fields, we study nucleon matrix elements of the axial current utilizing twisted heavy baryon chiral perturbation theory. One can explore the momentum transfer dependence of the axial form factors more easily than by using ordinary lattice quantized momenta alone. As examples, we derive expressions for the nucleon axial radius and pseudoscalar form factor.
We re-analyze the flavor decomposition of the pion-nucleon $σ$-term in the framework of baryon chiral perturbation to fourth order. We employ a covariant and the heavy baryon framework including also the low-lying decuplet. Using only continuum data, we find a small strangeness content of the proton. The uncertainties are, however, large and might be overcome by dedicated lattice QCD calculations.
We determine generalized form factors of the nucleon from lattice simulations with $N_f = 2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions down to a pion mass of 150 MeV. We also present the resulting isovector quark angular momentum. Possible excited-state contaminations are investigated with correlated simultaneous fits.
Precision Sum Rule for Nucleon Isovector Polarizabilities and the Proton-Neutron Mass Difference
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School for Theoretical Physics, School of Physics and Electronics, Hunan University（湖南大学物理与电子学院理论物理学院）；Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University（湖南大学高能标物理与应用湖南省重点实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
