Nucleon Matrix Elements Research Articles

Revisiting scalar and pseudoscalar couplings with nucleons

Certain dark matter interactions with nuclei are mediated possibly by a scalar or pseudoscalar Higgs boson. The estimation of the corresponding cross sections requires a correct evaluation of the couplings between the scalar or pseudoscalar Higgs boson and the nucleons. Progress has been made in two aspects relevant to this study in the past few years. First, recent lattice calculations show that the strange-quark sigma term σs and the strange-quark content in the nucleon are much smaller than what are expected previously. Second, lattice and model analyses imply sizable SU(3) breaking effects in the determination on the axial-vector coupling constant $ g_A^8 $ that in turn affect the extraction of the isosinglet coupling $ g_A^0 $ and the strange quark spin component Δs from polarized deep inelastic scattering experiments. Based on these new developments, we re-evaluate the relevant nucleon matrix elements and compute the scalar and pseudoscalar couplings of the proton and neutron. We also find that the strange quark contribution in both types of couplings is smaller than previously thought.

Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

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 pole structure of the quark-antiquark vertices that enters the nucleon matrix elements and determines the momentum dependence of the form factors. Our result for the axial charge underestimates the experimental value by 20-25% which might be a signal of missing pion-cloud contributions. The axial and pseudoscalar form factors agree with phenomenological and lattice data in the momentum range above Q^2 ~ 1...2 GeV^2.

Precision study of excited state effects in nucleon matrix elements

We present a dedicated analysis of the influence of excited states on the calculation of nucleon matrix elements. This calculation is performed at a fixed value of the lattice spacing, volume and pion mass that are typical of contemporary lattice computations. We focus on the nucleon axial charge, g A , for which we use about 7500 measurements, and on the average momentum of the unpolarized isovector parton distribution, 〈 x 〉 u − d , for which we use about 23 , 000 measurements. All computations are done employing N f = 2 + 1 + 1 maximally-twisted-mass Wilson fermions and using non-perturbatively calculated renormalization factors. Excited state effects are shown to be negligible for g A , whereas they lead to an O ( 10 % ) downward shift for 〈 x 〉 u − d .

Twist-4 contributions to the azimuthal asymmetry in semi-inclusive deeply inelastic scattering

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering process ${e}^{\ensuremath{-}}+N\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+q+X$ in leading order of perturbative QCD and up to twist-4 in power corrections and study, in particular, the azimuthal asymmetry $⟨\mathrm{cos}2\ensuremath{\phi}⟩$. The final results are expressed in terms of transverse momentum dependent parton matrix elements of the target nucleon up to twist-4. We also apply it to ${e}^{\ensuremath{-}}+A\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry $⟨\mathrm{cos}2\ensuremath{\phi}⟩$ by using a Gaussian ansatz for the transverse momentum dependent parton matrix elements.

Anomalous tensor magnetic moments and form factors of the proton in the self-consistent chiral quark-soliton model

We investigate the form factors of the chiral-odd nucleon matrix element of the tensor current. In particular, we aim at the anomalous tensor magnetic form factors of the nucleon within the framework of the SU(3) and SU(2) chiral quark-soliton model. We consider $1/N_c$ rotational corrections and linear effects of SU(3) symmetry breaking with the symmetry-conserving quantization employed. We first obtain the results of the anomalous tensor magnetic moments for the up and down quarks: $\kappa_{T}^{u}=3.56$ and $\kappa_{T}^{d}=1.83$, respectively. The strange anomalous tensor magnetic moment is yielded to be $\kappa_{T}^{s}=0.2\sim -0.2$, that is compatible with zero. We also calculate the corresponding form factors $\kappa_{T}^{q}(Q^{2})$ up to a momentum transfer $Q^{2}\leq 1\,\mathrm{GeV}^{2}$ at a renormalization scale of $0.36\,\mathrm{GeV}^{2}$.

Connecting the Breit frame to the infinite momentum light front frame: HowGEturns intoF1

We investigate the connection between the Breit and infinite momentum frames and show that when the nucleon matrix element of the time component of the electromagnetic current, which yields ${G}_{E}$ in the Breit frame, is boosted to the infinite momentum (or light-front) frame, the quantity ${F}_{1}$ is obtained.

Nucleon matrix elements and baryon masses in the Dirac orbital model

Using the expansion of the baryon wave function in a series of products of single quark bispinors (Dirac orbitals), the nonsinglet axial and tensor charges of a nucleon are calculated. The leading term yields $g_A = 1.27$ in good agreement with experiment. Calculation is essentially parameter-free and depends only on the strong coupling constant value $\alpha_s$. The importance of lower Dirac bispinor component, yielding 18% to the wave function normalization is stressed. As a check, the baryon decuplet masses in the formalism of this model are also computed using standard values of the string tension $\sigma$ and the strange quark mass $m_s$; the results being in a good agreement with experiment.

Flavor twisted boundary conditions and the nucleon vector current

Using flavor twisted boundary conditions, we study nucleon matrix elements of the vector current. We twist only the active quarks that couple to the current. Finite volume corrections due to twisted boundary conditions are determined using partially twisted, partially quenched, heavy baryon chiral perturbation theory, which we develop for the graded group $SU(7|5)$. Asymptotically these corrections are exponentially small in the volume, but can become pronounced for small twist angles. Utilizing the Breit frame does not mitigate volume corrections to nucleon vector current matrix elements. The derived expressions will allow for better controlled extractions of the isovector magnetic moment and the electromagnetic radii from simulations at zero lattice momentum. Our formalism, moreover, can be applied to any nucleon matrix elements.

Nucleon form factors from quenched lattice QCD with domain wall fermions

We present a quenched lattice calculation of the weak nucleon form factors: vector [${F}_{V}({q}^{2})$], induced tensor [${F}_{T}({q}^{2})$], axial vector [${F}_{A}({q}^{2})$] and induced pseudoscalar [${F}_{P}({q}^{2})$] form factors. Our simulations are performed on three different lattice sizes ${L}^{3}\ifmmode\times\else\texttimes\fi{}T={24}^{3}\ifmmode\times\else\texttimes\fi{}32$, ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$, and ${12}^{3}\ifmmode\times\else\texttimes\fi{}32$ with a lattice cutoff of ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.3\text{ }\text{ }\mathrm{GeV}$ and light quark masses down to about $1/4$ the strange quark mass (${m}_{\ensuremath{\pi}}\ensuremath{\approx}390\text{ }\text{ }\mathrm{MeV}$) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about $(3.6\text{ }\text{ }\mathrm{fm}{)}^{3}$, where the finite volume effects on form factors become negligible and the lower momentum transfers (${q}^{2}\ensuremath{\approx}0.1\text{ }\text{ }{\mathrm{GeV}}^{2}$) are accessible. The ${q}^{2}$ dependences of form factors in the low ${q}^{2}$ region are examined. It is found that the vector, induced tensor, and axial-vector form factors are well described by the dipole form, while the induced pseudoscalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling ${g}_{A}/{g}_{V}={F}_{A}(0)/{F}_{V}(0)=1.219(38)$ and the pseudoscalar coupling ${g}_{P}={m}_{\ensuremath{\mu}}{F}_{P}(0.88{m}_{\ensuremath{\mu}}^{2})=8.15(54)$, where the errors are statistical errors only. These values agree with experimental values from neutron $\ensuremath{\beta}$ decay and muon capture on the proton. However, the root mean-squared radii of the vector, induced tensor, and axial vector underestimate the known experimental values by about 20%. We also calculate the pseudoscalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.

Probing nucleon structure on the lattice

The QCDSF/UKQCD collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320 MeV.

Minimal dark matter

A few multiplets that can be added to the SM contain a lightest neutral component which is automatically stable and provides allowed DM candidates with a non-standard phenomenology. Thanks to coannihilations, a successful thermal abundance is obtained for well defined DM masses. The best candidate seems to be a SU ( 2 ) L fermion quintuplet with mass 4.4 TeV, accompanied by a charged partner 166 MeV heavier with life-time 1.8 cm , that manifests at colliders as charged tracks disappearing in π ± with 97.7% branching ratio. The cross section for usual NC direct DM detection is σ SI = f 2 1.0 × 10 −43 cm 2 where f ∼ 1 is a nucleon matrix element. We study prospects for CC direct detection and for indirect detection.

Hadron Phenomenology from Quenched Overlap Fermions

We compute hadron masses and nucleon matrix elements in quenched QCD using overlap fermions.

Algebraic approach to bare nucleon matrix elements of quark operators

An algebraic method for evaluating bare nucleon matrix elements of quark operators is proposed. Thereby, bare nucleon matrix elements are traced back to vacuum matrix elements. The method is similar to the soft pion theorem. Matrix elements of two-quark, four-quark and six-quark operators inside the bare nucleon are considered.

Flavor twisted boundary conditions and the nucleon axial current

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.

Strange form factors and Chiral Perturbation Theory

We review the contributions of Chiral Perturbation Theory to the theoretical understanding or not-quite-yet-understanding of the nucleon matrix elements of the strange vector current.

Recent results on moments of parton distribution functions

We report on recent results for the pion and nucleon matrix element of the twist-2 operator corresponding to the average momentum of non-singlet quark densities. We discuss finite size effects for the nucleon matrix element and present first preliminary results for the non-perturbative renormalisation from full dynamical simulations.

Baryon axial charge in a finite volume

We compute finite-volume corrections to nucleon matrix elements of the axial-vector current. We show that knowledge of this finite-volume dependence --as well as that of the nucleon mass-- obtained using lattice QCD will allow a clean determination of the chiral-limit values of the nucleon and Delta-resonance axial-vector couplings.

Finite size effects of a pion matrix element

We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when compared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation.

QCD sum rules for hyperon-nucleon interactions

We investigate the hyperon-nucleon interactions in the QCD sum rule starting from the nucleon matrix element of the hyperon correlation function. Through the dispersion relation, the correlation function in the operator product expansion (OPE) is related with its integral over the physical energy region. The dispersion integral around the hyperon-nucleon $(YN)$ threshold is identified as a measure of the interaction strength in the $YN$ channel. The Wilson coefficients of the OPE for the hyperon correlation function are calculated. The obtained sum rules relate $YN$ interaction strengths to the nucleon matrix elements of the quark-gluon composite operators, which include strange quark operators as well as up and down quark operators. It is found that the $YN$ interaction strengths are smaller than the $NN$ interaction strength since the nucleon matrix elements of strange quark operators are smaller than those of up and down quark operators. Among $YN$ channels $\ensuremath{\Lambda}N$ channel has stronger interaction than $\ensuremath{\Sigma}N$ and $\ensuremath{\Xi}N$ channels. It is also found that the interaction strength is greater in the ${\ensuremath{\Sigma}}^{+}p\phantom{\rule{0.3em}{0ex}}({\ensuremath{\Xi}}^{0}p)$ channel than in the ${\ensuremath{\Sigma}}^{\ensuremath{-}}p\phantom{\rule{0.3em}{0ex}}({\ensuremath{\Xi}}^{\ensuremath{-}}p)$ channel since the nucleon matrix elements of up quark operators are greater than those of down quark operators. The spin-dependent part is much smaller than the spin-independent part in the $YN$ and $NN$ channels. The results of the sum rules are compared with those of the phenomenological meson-exchange models.

Quark spectra and light hadron phenomenology from overlap fermions with improved gauge field action

We present first results from a simulation of quenched overlap fermions with improved gauge field action. Among the quantities we study are the spectral properties of the overlap operator, the chiral condensate and topological charge, quark and hadron masses, and selected nucleon matrix elements. To make contact with continuum physics, we compute the renormalization constants of quark bilinear operators in perturbation theory and beyond.