Pion-nucleon Coupling Constant Research Articles

QCD analysis of ΔS = 0 hadronic parity violation

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (ΔS=0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the W to the O(2GeV) energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the W mass scale from QCD operator mixing effects form a closed set, and they result in a 12×12 anomalous dimension matrix. Computing the resulting effective Hamiltonian and comparing to earlier results, we affirm the importance of operator mixing effects and find, as an example, that the parity-violating pion-nucleon coupling constant, using the factorization Ansatz and an assessment of the pertinent quark charge of the nucleon in lattice QCD at the 2 GeV scale, is in better agreement with recent experiments.

Nucleon axial-vector and pseudoscalar form factors and PCAC relations

We use a continuum quark+diquark approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, $G_A$ and $G_P$, and unify them with the pseudoscalar form factor $G_5$ or, equivalently, the pion-nucleon form factor $G_{\pi NN}$. We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge $g_A=G_A(0)=1.25(3)$ and a mass-scale $M_A = 1.23(3) m_N$, where $m_N$ is the nucleon mass, can accurately describe the pointwise behaviour of $G_A$. Concerning $G_P$, we obtain the pseudoscalar charge $g_p^\ast = 8.80(23)$, and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, $g_{\pi NN}/m_N =14.02(33)/{\rm GeV}$ is consistent with recent precision determinations.

Precision Determination of Pion-Nucleon Coupling Constants Using Effective Field Theory.

The pion-nucleon coupling constants determine the strength of the long-range nuclear forces and play a fundamental part in our understanding of nuclear physics. While the charged- and neutral-pion couplings to protons and neutrons are expected to be very similar, owing to the approximate isospin symmetry of the strong interaction, the different masses of the up and down quarks and electromagnetic effects may result in their slightly different values. Despite previous attempts to extract these coupling constants from different systems, our knowledge of their values is still deficient. In this Letter, we present a precision determination of these fundamental observables with fully controlled uncertainties from neutron-proton and proton-proton scattering data using chiral effective field theory. To achieve this goal, we use a novel methodology based on the Bayesian approach and perform, for the first time, a full-fledged partial-wave analysis of nucleon-nucleon scattering up to the pion production threshold in the framework of chiral effective field theory, including a complete treatment of isospin-breaking effects and our own determination of mutually consistent data. The resulting values of the pion-nucleon coupling constants are accurate at the percent level and show no significant charge dependence. These results mark an important step toward developing a precision theory of nuclear forces and structure.

On the Breakdown of Charge Independence and Charge Symmetry of the Pion—Nucleon Coupling Constant

A simple, physically validated, model of charge-independence and charge-symmetry breaking is proposed for the pion-nucleon coupling constant. Within this model, the pion-nucleon coupling constants are assumed to be in direct proportion to the masses of nucleons and pions involved in the interaction. The charge dependence of the pion-nucleon coupling constants and low-energy parameters of nucleon-nucleon scattering in the 1S0 spin-singlet state is studied on the basis of Yukawa’s meson theory. By using the value of $$f_{pp\pi^0}^2=0.0749(7)$$ established reliably for the pseudovector pion-nucleon coupling constant, which characterizes the strength of the nuclear proton-proton interaction, the values of $$f_c^2=0.0802(7)$$ and $$f_0^2=0.0750(7)$$ were calculated for, respectively, the charged and neutral pion-nucleon coupling constants, along with the value of $$f_{nn\pi^0}^2=0.0751(7)$$, which characterizes the strength of the nuclear neutron-neutron interaction. The values calculated for the low-energy parameters of neutron-proton and neutron-neutron scattering with the aid of the above constants agree well with experimental data.

Precise determination of charge-dependent pion-nucleon-nucleon coupling constants

We undertake a covariance error analysis of the pion-nucleon-nucleon coupling constants from the Granada-2013 np and pp database comprising a total of 6720 scattering data below LAB energy of 350 MeV. Assuming a unique pion-nucleon coupling constant in the One Pion Exchange potential above a boundary radius $r_c=3 {\rm fm}$ we obtain $f^2=0.0763(1)$. The effects of charge symmetry breaking on the $^3P_0$, $^3P_1$ and $^3P_2$ partial waves are analyzed and we find $f_{p}^2 = 0.0761(4)$, $f_{0}^2 = 0.0790(9)$ and $f_{c}^2 = 0.0772(6)$ with a strong anti-correlation between $f_c^2$ and $f_0^2$. We successfully test normality for the residuals of the fit. Potential tails in terms of different boundary radii as well as chiral Two-Pion-Exchange contributions as sources of systematic uncertainty are also investigated.

Up, down, and strange nucleon axial form factors from lattice QCD

We report a calculation of the nucleon axial form factors $G_A^q(Q^2)$ and $G_P^q(Q^2)$ for all three light quark flavors $q\in\{u,d,s\}$ in the range $0\leq Q^2\lesssim 1.2\text{ GeV}^2$ using lattice QCD. This work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $G_A^q(Q^2)$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $G_P^{u-d}(Q^2)$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We find that the disconnected contributions to $G_P$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.

Lattice QCD spectroscopy for hadronic CP violation

The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion-nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion-nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU(2) and SU(3) chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.

Relation between the charged and neutral pion–nucleon coupling constants in the Yukawa model

In the Yukawa model for nuclear forces, a simple relation between the charged and neutral pion-nucleon coupling constants is derived. The relation implies that the charged pion-nucleon coupling constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion-nucleon constant shows a very good agreement with one of the recent experimental values. The relative splitting between the charged and neutral pion-nucleon coupling constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.

Three pion nucleon coupling constants

There exist four pion nucleon coupling constants, [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] which coincide when up and down quark masses are identical and the electron charge is zero. While there is no reason why the pion–nucleon–nucleon coupling constants should be identical in the real world, one expects that the small differences might be pinned down from a sufficiently large number of independent and mutually consistent data. Our discussion provides a rationale for our recent determination [Formula: see text] based on a partial wave analysis of the [Formula: see text] self-consistent nucleon–nucleon Granada-2013 database comprising 6713 published data in the period 1950–2013.

О нарушении изоспиновой инвариантности константы пион-нуклонной связи и длины нуклон-нуклонного рассеяния

О нарушении изоспиновой инвариантности константы пион-нуклонной связи и длины нуклон-нуклонного рассеяния

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at gπ2±/4π = 14.55(13). This value is in perfect agreement with the experimental value of gπ2±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is gπ2 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.

The effect of finite temperature and chemical potential on nucleon properties in the logarithmic quark sigma model

The logarithmic quark sigma model is applied to study the nucleon properties at finite temperature and chemical potential. The field equations have been solved numerically in the mean-field approximation by using the extended iteration method at finite temperature and baryon chemical potential. Baryon properties are investigated, such as the hedgehog mass, the magnetic moments of the proton and neutron, and the pion-nucleon coupling constant. We find that the hedgehog mass and the magnetic moments of the proton and neutron increase with increasing temperature and chemical potential, while the pion-nucleon coupling constant decreases. A comparison with the original sigma model and QCD sum rules is presented. We conclude that the logarithmic quark sigma model successfully describes baryon properties of a hot and dense medium.

О зарядовой зависимости константы пион-нуклонной связи

О зарядовой зависимости константы пион-нуклонной связи

Parity violation in neutron capture on the proton: Determining the weak pion–nucleon coupling

We investigate the parity-violating analyzing power in neutron capture on the proton at thermal energies in the framework of chiral effective field theory. By combining this analysis with a previous analysis of parity violation in proton–proton scattering, we are able to extract the size of the weak pion–nucleon coupling constant. The uncertainty is significant and dominated by the experimental error which is expected to be reduced soon.

The Chiral Quark-Sigma Model with Modified Logarithmic Potential for Nucleon Properties

A modified logarithmic mesonic potential which based on some aspects of quantum chromodynamics (QCD) theory is investigated. The modified logarithmic mesonic potential is far from the singularity point which comes at vanishing of pion and sigma-meson contributions ( σ2 +π2 = 0 ) . The field equations have been solved in the mean-field approximation using the iteration method. The obtained results of nucleon properties are improved in comparison with the original quark-sigma model and other models. In particular, the nucleon and delta masses, the pion-nucleon coupling constant, and the sigma term are in good agreement with experimental data. In addition, A comparison with the recent quark models such as the extended Skyrme model and the perturbative quark model is discussed. We conclude that the modified logarithmic quark model successfully predicts nucleon properties and avoid difficulty that found in the previous works.

THE EFFECT OF FINITE TEMPERATURE ON THE NUCLEON PROPERTIES IN THE EXTENDED LINEAR SIGMA MODEL

The extended quark sigma model, which includes higher-order mesonic interactions is applied at finite temperature. The field equations are solved using the mean-field approximation. Nucleon properties such as the nucleon mass, the magnetic moments of the proton and neutron, and the pion-nucleon coupling constant are examined as functions of temperature. The obtained results indicate that the deconfinement phase transition conditions are satisfied in the present work at higher values of temperature. A comparison with other models is presented.

Corrections for the polarization-dependent efficiency and new neutron-proton analyzing power data at 7.6 MeV

We present new corrections for the polarization-dependent efficiency (PDE), which introduces a false asymmetry into measurements of $n\text{\ensuremath{-}}p$ analyzing power ${A}_{y}(\ensuremath{\theta})$ caused by double scattering in the neutron side detectors. To accomplish this, we created a new database of $^{12}\mathrm{C}$$(\mathrm{nP\vec},n)$ ${A}_{y}(\ensuremath{\theta})$ by using a combination of fits to data, phase-shift analysis, and $R$-matrix analysis. Our recorrection for PDE of previously reported $n\text{\ensuremath{-}}p$ ${A}_{y}(\ensuremath{\theta})$ data at 7.6 and 12.0 MeV and new data at 7.6 MeV indicate that we have achieved a superior representation of $^{12}\mathrm{C}$$(\mathrm{nP\vec},n)$. Our results continue to suggest a possible charge dependence of the pion-nucleon coupling constant.

A connection between the high energy-scale evolution of the P- and T-odd πNN coupling constant and the strong πNN interaction

The large energy-scale behaviour of the parity and time-reversal violating (PTV) pion–nucleon coupling constant is analysed in a model combining renormalization-group techniques and the dressing of the PTV vertex with a pion loop. With the strong πNN vertex as a mixture of the pseudovector and pseudoscalar couplings, we show that depending on the admixture parameter, two qualitatively distinct types of behaviour are obtained for the PTV coupling constant at high energy scales: an asymptotic freedom or a fixed point. We find a critical value of the admixture parameter which delineates these two scenarios. Several examples of the high-energy scale behaviour of the PTV πNN constant are considered, corresponding to realistic hadronic models of the strong pion–nucleon interaction.

Neutron–proton analyzing power at 12 MeV and inconsistencies in parametrizations of nucleon–nucleon data

We present the most accurate and complete data set for the analyzing power Ay(θ) in neutron–proton scattering. The experimental data were corrected for the effects of multiple scattering, both in the center detector and in the neutron detectors. The final data at En=12.0 MeV deviate considerably from the predictions of nucleon–nucleon phase-shift analyses and potential models. The impact of the new data on the value of the charged pion–nucleon coupling constant is discussed in a model study.

Hadronic parity violation in [formula omitted] with effective field theory

The parity-violating nucleon–nucleon (NN) potential is considered up to next-to-next-to leading order in heavy-baryon chiral perturbation theory. We include one-pion exchange at leading order and the two-pion exchange and two-nucleon contact terms at next-to-next-to-leading order. The effects of intermediate (two-pion exchange) and short-range (two-nucleon contact) terms are probed by calculating the photon asymmetry Aγ in n→p→dγ employing Siegert's theorem and an accurate phenomenological potential for the parity-conserving NN interaction. We explore in detail the uncertainties due to the parameters that control the contribution of the short-range interaction. We obtain about 20% uncertainty in the value of Aγ up to the next-to-next-to leading order. We discuss the implication of this uncertainty for the determination of the weak pion–nucleon coupling constant and how the uncertainty can be reduced.