Massimiliano Procura
We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical guidance for chiral extrapolations of lattice QCD results with dynamical fermions.
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Chiral corrections to the delta axial charge are determined using heavy baryon chiral perturbation theory. Knowledge of this axial coupling is necessary to assess virtual-delta contributions to nucleon and delta observables. We give isospin relations useful for a lattice determination of the axial coupling. Furthermore we detail partially quenched chiral corrections, which are relevant to address partial quenching and/or mixed action errors in lattice calculations of the delta axial charge.
The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these proceedings, we present preliminary results on a blinded calculation of $g_A$ and the axial form factor using HISQ staggered baryons with 2+1+1 flavors of sea quarks. Calculations are done using physical light quark masses and are absolutely normalized. We discuss fitting form factor data with the model-independent $z$ expansion parametrization.
The extrapolation of nucleon axial charge $g_A$ is investigated within the framework of heavy baryon chiral effective field theory. The intermediate octet and decuplet baryons are included in the one loop calculation. Finite range regularization is applied to improve the convergence in the quark-mass expansion. The lattice data from three different groups are used for the extrapolation. At physical pion mass, the extrapolated $g_A$ are all smaller than the experimental value.
The axial N-> Delta(1232) transition form factors are calculated within the light cone QCD sum rules method. A comparison of our results with predictions of lattice theory and quark model calculations is pre- sented.
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 analyze the nucleon axial-vector coupling to two loops in chiral perturbation theory. We show that chiral extrapolations based on this representation require lattice data with pion masses below 300 MeV.
It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation functions, the corresponding relation for form factors (sometimes called the generalized Goldberger-Treiman relation in the literature) is broken rather badly. In this work we trace this difference back to excited state contributions and propose a new projection method that resolves this problem. We demonstrate the efficacy of this method by computing the axial a…
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.
Lattice results on the N to Delta electromagnetic, axial-vector and pseudoscalar form factors are evaluated using dynamical staggered sea quarks and domain wall valence quarks for pion masses in the range of 580-350 MeV, as well as, dynamical and quenched Wilson fermions for similar pion masses.
We discuss electro-magnetic and weak production of pions on nucleons and show how results of experiments and their interpretation in terms of chiral quark models with explicit meson degrees of freedom combine to reveal the ground-state axial form factors and axial N-Delta transition amplitudes.
We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at N$^3$LO for…
It is shown that the strong volume-dependence of the axial charge of the nucleon seen in lattice QCD calculations can be understood quantitatively in terms of the pion-induced interactions between neighbouring nucleons. The associated wave function renormalization leads to an increased suppression of the axial charge as the strength of the interaction increases, either because of a decrease in lattice size or in pion mass.
A relativistic quark model and a new set of wave functions of nucleon and Delta have been used to study the electromagnetic propertities of (1/2)^+ baryons and photoelectric production of Delta(1236).
We present a quenched lattice calculation of the nucleon isovector vector and axial-vector charges gV and gA. The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order O(a^2). The DBW2 gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and perfo…
The N-Delta axial form factors are determined from neutrino induced pion production ANL & BNL data by using a state of the art theoretical model, which accounts both for background mechanisms and deuteron effects. We find violations of the off diagonal Goldberger-Treiman relation at the level of 2 sigma which might have an impact in background calculations for T2K and MiniBooNE low energy neutrino oscillation precision experiments.
We present data for the axial coupling constant g_A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g_A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattic…
Results for the isovector axial form factors of the proton from a lattice QCD calculation are presented for both point-split and local currents. They are obtained on a quenched $16^{3} \times 24$ lattice at $β= 6.0$ with Wilson fermions for a range of quark masses from strange to charm. We determine the finite lattice renormalization for both the local and point-split currents of heavy quarks. Results extrapolated to the chiral limit show that the $q^2$ dependence of the axial form factor agrees reasonably well with experiment. The axial coupling constant $g_A$ calculated for the local and the…
We examine the role of the Delta-Delta intermediate state in low energy NN scattering using effective field theory. Theories both with and without pions are discussed. They are regulated with dimensional regularization and MSbar subtraction. We find that the leading effects of the Delta-Delta state can be absorbed by a redefinition of the contact terms in a theory with nucleons only. It does not remove the requirement of a higher dimension operator to reproduce data out to moderate momentum. The explicit decoupling of the Delta-Delta state is shown for the theory without pions.
We discuss electro-magnetic and weak axial N-Delta transition amplitudes in the linear sigma-model and the Cloudy-Bag Model as typical representatives of chiral quark models. We show that good qualitative understanding of the transition can be obtained in models which, in addition to the pion cloud, incorporate a fluctuating sigma-field inside the baryon.
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 calculate the hypercharge and flavor singlet axial couplings related to the spin of the nucleon in a constituent quark model. In addition to the standard one-body axial currents, the model includes two-body axial exchange currents. The latter are necessary to satisfy the Partial Conservation of Axial Current (PCAC) condition. For both axial couplings we find significant corrections to the standard quark model prediction. Exchange currents reduce the valence quark contribution to the nucleon spin and afford an interpretation of the missing nucleon spin as orbital angular momentum carried by …
A covariant quark model, based both on the spectator formalism and on vector meson dominance, and previously calibrated by the physical data, is here extended to the unphysical region of the lattice data by means of one single extra adjustable parameter - the constituent quark mass in the chiral limit. We calculated the Nucleon (N) and the gamma N -> Delta form factors in the universe of values for that parameter described by quenched lattice QCD. A qualitative description of the Nucleon and gamma N -> Delta form factors lattice data is achieved for light pions.
We evaluate the N to Delta axial transition form factors in lattice QCD in the quenched theory, with two degenerate flavors of dynamical Wilson fermions and using domain wall valence fermions with staggered sea quark configurations. We predict the ratio $C_5^A(q^2)/C_3^V(q^2)$ relevant to the parity violating asymmetry and check the validity of the off-diagonal Goldberger-Treiman relation.
We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing and the quark masses to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We s…
The axial strange form factor $F^s_A$ of the nucleon is assumed to be dominated at low momentum transfer by the isoscalar axial vector mesons $f_1(1285)$ and $f_1(1420)$. The importance of the $a_0πN$-triangular vertex correction is demonstrated.
We report a theoretical study of the axial Nucleon to Delta(1232) ($N\toΔ$) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the $Δ$ couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble chamber data and in quark models.
We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the nonperturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike…
An expansion of the electromagnetic form factors of the nucleon and Delta(1232) in small momentum transfer and pion mass is performed in a manifestly-covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and Delta(1232) electromagnetic form factors, charge radii, and electromagnetic moments in the framework of SU(2) baryon chiral perturbation theory, with nucleon and Delta(1232)-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and elec…
We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework.
It is shown that the specific space distribution of the nucleon axial charge may lead to the significant reduction of the cross section of the reaction $p+p\to D+e^++ν$ and may provide the mechanism to explain observed deficit of solar neutrinos.
We review some basic properties of the N-Delta transition axial amplitudes and relate them to the strong pi-N-Delta form-factor. In models with the pion cloud we derive a set of constraints on the pion wave function which guaranty the correct behaviour of the amplitudes in the vicinity of the pion pole. Corrections due to the spurious center-of-mass motion are calculated to the leading order in the inverse baryon mass. We give explicit expressions for the amplitudes in the Cloudy Bag Model and show that they rather strongly underestimate the experimental values.
We have analyzed axial-vector current-current correlation functions between one-nucleon states to calculate the singlet axial-vector coupling constant of the nucleon. The octet-octet and the octet-singlet current correlators, investigated in this work, do not require any use of instanton effects. The QCD and hadronic parameters used for the evaluation of correlators have been varied by (10 - 20)%. The value of the singlet axial-vector coupling constant of the nucleon obtained from this analysis is consistent with its current determination from experiments and QCD theory.
Measurements of the polarization of the final proton in elastic e-p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. Here we present our results of the calculation of the polarization of the final nucleon in charged current quasi-elastic neutrino nucleon scattering. Relations which connect the axial form factor with the polarization, the cross section and the electromagnetic form factors of the nucleon are derived. Measurements of the polarization of the nucleon in the high-statistics short baseline neutrino experiments (or in near detectors of…
We present results on the nucleon scalar, axial and tensor charges, as well as, on the first moments of the unpolarized, polarized and transversity parton distributions using $N_f=2$ and $N_f=2+1+1$ twisted mass fermions. These include an ensemble that yields the physical value of the ratio of the nucleon to the pion mass. Results on the axial charges of hyperons and charmed baryons are also presented for a range of pion masses including the physical one.
We report lattice QCD results on the axial charges of ground and excited nucleon states of both parities. This is the first study of these quantities with approximately chiral (CI) fermions. Two energy levels in the range of the negative parity resonances N*(1535) and N*(1650) are observed and we determine the axial charge for both. We obtain a small axial charge for one of them, which is consistent with the chiral symmetry restoration in this state as well as with the small axial charge of the N*(1535) predicted within the quark model. This result agrees with the findings of Takahashi et al. …
We study the axial amplitudes for the N-Delta transition in models with quarks and chiral mesons. A set of constraints on the pion field is imposed which enforces PCAC and the off-diagonal Goldberger-Treiman relation. The quark contribution to the amplitudes in general strongly underestimates the C^A_5 amplitude as well as the piNDelta strong coupling constant. We show that the results are considerably improved in models that, in addition to the pion cloud, incorporate a fluctuating sigma field inside the baryon.
In a world with two quark flavors and a large number of colors (N_c), the polarized and unpolarized quark distributions in the delta are completely determined by those in the nucleon up to {\cal O}(1/N_c). In particular, we find q_Δ(x) =[(1\pm 2T_z)u_N(x)+ (1\mp 2T_z)d_N(x)]/2 and Δq_Δ(x) =[(5\pm 2T_z)Δu_N(x) + (5\mp 2T_z)Δd_N(x)]/10, where q = u, d and $T_z$ the charge state of a delta. The result can be used to estimate the leading chiral-logarithmic corrections to the quark distributions in the nucleon.
The axial charges of the nucleon and the well-established N* resonances are studied within a consistent framework. For the first time the axial charges of the N* resonances are produced for the relativistic constituent quark model. The axial charge of the nucleon is predicted close to experiment, and the ones of N*(1535) and N*(1650), the only cases where such a comparison is possible, agree well with results from quantum chromodynamics on the lattice that have recently become available. The relevance of the magnitudes of the N* axial charges for the low-energy behavior of quantum chromodynami…
Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We det…
It is shown that the QCD anomaly may lead to an abnormal mixing behavior of the axial vector mesons similar to the pseudoscalar mesons. These mixing effects, involving a gluonic axial vector state, generate a non-vanishing strange quark component in the nucleon. They reduce the matrix element of the singlet axial vector in comparison to the value obtained in a naive quark model. The results are in agreement with the data obtained in the polarized lepton-nucleon scattering experiments.
Using the most general form of the baryon current, nucleon form factors, induced by isovector and isoscalar axial-vector currents, are studied in the framework of light cone QCD sum rule approach. Comparison of our results on form factors with the existing results and lattice calculations are presented.
We have calculated the polarization of the final nucleon in charged current quasi-elastic ν-N scattering. We show that the longitudinal and transverse polarizations, as well as their ratio exhibit simple dependence on the axial form factor and their sensitivity to the axial mass is much stronger than that of the cross section. This suggests that measurements of the polarization of the nucleon in the high-statistics neutrino experiments could provide important information on the axial form factor.
We present a calculation of the polarized rho meson cloud in a nucleon using time-ordered perturbation theory in two different variants advocated in the literature. We calculate the induced difference between the distributions Delta d^bar(x) and Delta u^bar(x). We use a recent lattice calculation to motivate an ansatz for the polarized valence quark distribution of the rho meson. Our calculations show that the two theoretical approaches give vastly different results. We conclude that Delta d^bar(x) - Delta u^bar(x) can be of relevant size with important consequences for the combined fits of po…
We report on our calculation of the nucleon axial and tensor charges in 2+1-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated at a single lattice spacing 0.12 fm and at a strange quark mass close to its physical value. We employ the all-mode-averaging technique to calculate the relevant nucleon correlation functions, and the disconnected quark loop is efficiently calculated by using the all-to-all quark propagator. We present our preliminary results for the isoscalar and isovector charges obtained at pion masses $m_π$ = 450 and 540 MeV.
We apply the perturbative chiral quark model (PCQM) at one loop to analyze the axial form factor of the nucleon. This chiral quark model is based on an effective Lagrangian, where baryons are described by relativistic valence quarks and a perturbative cloud of Goldstone bosons as dictated by chiral symmetry. We apply the formalism to obtain analytical expressions for the axial form factor of the nucleon, which is given in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, strong pion-nucleon form factor) and of only one model parameter (radius of the …
Influence of the effects of the pion-nucleon and nucleon-nucleon re-scattering on the polarization observables of the reaction gamma + d = p + p + pi- in Delta - isobar region is investigated. Pion-nucleon and nucleon-nucleon re-scattering are studied in the diagrammatic approach. Relativistic-invariant forms of the pion photoproduction and pion-nucleon scattering operators are used. The unitarization procedure in K-matrix approach is applied for the resonance partial amplitudes. It is shown a considerable influence of the re-scattering effects on the polarization observables of this reaction …
We perform a relativistic chiral effective-field theory calculation of the pion electroproduction off the nucleon ($e^- N \to e^- N π$) in the Delta(1232)-resonance region. After fixing the three low-energy constants, corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) $γNΔ$ couplings, our calculation provides a prediction for the momentum-transfer and pion-mass dependence of the $γNΔ$ form factors. The prediction for the pion-mass dependence resolves the discrepancy between the recent lattice QCD results and the experimental value for the "C2/M1 ratio" at low $Q^2$.
We study the axial-vector form factor of the nucleons at constant and homogenous isospin chemical potential using holographic QCD. Nucleon mass splitting in such isospin medium is taken into account. According to AdS/CFT correspondence, the critical value of the isospin chemical potential μ_I equals to UV- boundary value of the time component of the bulk gauge field. We calculate the axial-vector form factor of the proton and neutron in such background in the framework of the hard-wall model and plot the form factors for the isospin chemical potential critical value μ_I=m_π.
Renormalization of the axial vector currents due to Goldstone loops is studied in a simple extension of Manohar - Georgi chiral quark model which incorporates $U(1)_A$ anomaly effects. The polarized strage quark sea in the polarized nucleon results from different renormalization of the flavor singlet and octet currents and is in reasonable agreement with the experiment.
The nucleon axial charge is calculated as a function of the pion mass in full QCD. Using domain wall valence quarks and improved staggered sea quarks, we present the first calculation with pion masses as light as 354 MeV and volumes as large as (3.5 fm)^3. We show that finite volume effects are small for our volumes and that a constrained fit based on finite volume chiral perturbation theory agrees with experiment within 7% statistical errors.
We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.
The strange and flavor-singlet axial form factors of the nucleon from lattice QCD
本文利用格点QCD方法确定核子单态轴型因子G^{u+d+s}_A(Q^2)及其奇异贡献G^s_A(Q^2)，并关注断开贡献的处理，以提取奇异部分，全面研究不同味通道的核子轴结构。
The theoretical and experimental status of the isovector axial-vector current form factors G_A(q^2) and G_P(q^2) of the nucleon is reviewed. We also describe a new calculation of these form factors in manifestly Lorentz-invariant chiral perturbation theory (ChPT) with the inclusion of axial-vector mesons as explicit degrees of freedom.
We study the N-Delta-gamma transition in the Dyson-Schwinger approach. The nucleon and Delta baryons are treated as quark-diquark bound states, where the ingredients of the electromagnetic transition current are computed self-consistently from the underlying dynamics in QCD. Although our approach does not include pion-cloud effects, we find that the electric and Coulomb quadrupole form-factor ratios R_EM and R_SM show good agreement with experimental data. This implies that the deformation from a spherical charge distribution inside both baryons can be traced back to the appearance of p waves …
Nucleon matrix elements of axial anomaly, axial currents and pseudoscalar currents in the QCD sum rule
利用QCD求和规则，分析核子与轴反常、轴流及赝标量流耦合常数，表达为夸克、胶子及部分子分布矩的矩阵元，并考虑非对角贡献。
The axial-vector form factor of the nucleons is considered in the framework of hard-wall model of holographic QCD. A new interaction term between the bulk gauge and matter fields was included into the interaction Lagrangian. We obtain the axial-vector form factor of nucleons in the boundary QCD from the bulk action using AdS/CFT correspondence. The momentum square dependence of the axial-vector form factor is analysed numerically.
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
The complete spin structure of the pion-nucleon-loop contribution to the delta self-energy and dressed propagator is calculated in vacuum, with the most general form of the pion-nucleon-delta vertex. The imaginary parts of the ten Lorentz-scalar coefficients are calculated in closed form, while the real parts are obtained numerically from a dispersion relation. The effect of the pion-nucleon-delta coupling constants and form-factor on the pion-nucleon phase-shift in the spin-3/2 isospin-3/2 channel is studied.
We establish relations which express the generalized parton distributions (GPDs) describing the $N\to Δ$ transition in terms of the nucleon GPDs. These relations are based on the known large-$N_c$ relation between the $N\to Δ$ electric quadrupole moment and the neutron charge radius, and a newly derived large-$N_c$ relation between the electric quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Namely, in the large-$N_c$ limit we find $C2=E2$. The resulting relations among the nucleon and $N\toΔ$ GPDs provide predictions for the $N\toΔ$ electromagnetic form factors which are found to…
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