The simple model describing charge independence and charge symmetry breaking of the pion-nucleon coupling constant is proposed. The model, which has simple physical meaning and foundation, suggests directly proportional dependence of the pion-nucleon coupling constants on the masses of interacting nucleons and pions. Charge dependence of the pion-nucleon coupling constant and the $^{1}S_{0}$-state low-energy nucleon-nucleon ($NN$) scattering parameters are studied on the basis of the Yukawa meson theory. The values of the $np$ and $nn$ interaction characteristics calculated by the proposed model agree quite well with the experimental data.
I discuss recent results regarding the influence of pion-nucleon and and nucleon-resonance physics on the (spin-) polarizabilities of the nucleon as measured in (polarized) Compton scattering.
We study relationship between the physical quantities that characterize pion-nucleon and nucleon-nucleon interaction on the basis of the fact that nuclear forces in the nucleon-nucleon system at low energies are mainly determined by the one-pion exchange mechanism. By making use of the recommended proton-proton low-energy scattering parameters, we obtain the following value for the charged pion-nucleon coupling constant g$_{π^{\pm }}^{2}/4π=14.55(13)$. Calculated value of this quantity is in excellent agreement with the experimental result g$_{π^{\pm }}^{2}/4π=14.52(26)$ of the Uppsala Neutron…
A perturbative QCD treatment of the pion wave function is applied to computing the scattering amplitude for coherent high relative momentum di-jet production from a nucleon.
The isovector GMO sum rule for zero energy forward pion-nucleon scattering is critically studied to obtain the charged pion-nucleon coupling constant using the precise negatively charged pion-proton and pion-deuteron scattering lengths deduced recently from pionic atom experiments. This direct determination leads to a pseudoscalar charged pion-nucleon coupling constant of 14.23 +- 0.09 (statistic) +- 0.17 (systematic). We obtain also accurate values for the pion-nucleon scattering lengths.
The Nucleon-Nucleon interaction in the singlet ($^1 S_0$) and triplet ($^3 S_1$) channels have been studied in the framework of Relativistic Harmonic Model using the Resonating Group Method in Born-Oppenheimer approximation. The full Hamiltonian consists of the kinetic energy, two body confinement potential, confined one gluon exchange potential and one pion exchange potential. Contribution of Confined One Gluon Exchange Potential and One Pion Exchange Potential to the adiabatic nucleon-nucleon interaction potential is discussed.
The pion-nucleon and kaon-nucleon scattering lengths are studied in the QCD sum rule. We show that the leading and next-to-leading order terms of the OPE give rise to the Tomozawa-Weinberg and sigma terms, respectively. We also show that in the kaon-nucleon system the $Λ(1405)$ contribution has to be subtracted from the OPE side in order to obtain the scattering length. The odd components of the $T$-matrices are in agreement with the experimental values not only in the pion-nucleon channel but also in the kaon-nucleon channel after the $Λ(1405)$ contribution subtracted. The even components dis…
Making use of the quasi-coherent state developed by Eriksson et al., we can find a nucleon solution accompanied by the pion field with trivial topology. We compare our approach with other related works, and examine a coherent state description of pions in the baryon structure. Our solution suggests a kind of nucleon resonance due to the topological change of pion field without the usual quark excitation.
A chiral invariant effective Lagrangian may be used to calculate the three-body interactions among low-energy pions and nucleons in terms of known parameters. This method is illustrated by the calculation of the pion-nucleus scattering length.
The renormalized pion-nucleon Lagrangian is calculated to O(p^3) in heavy baryon chiral perturbation theory. By suitably chosen transformations of the nucleon field, the Lagrangian is brought to a standard form.
The pion-nucleon sigma term is shown to be equal to the Goldberger-Treiman discrepancy at tree level. Its value estimated this way is very sensitive to the pion-nucleon coupling constant g_{pi NN}. This relation, when combined with the pion-nucleon S-wave scattering lengths, yields a new determination of g_{pi NN} at tree level. The results of a one-loop analysis are also summarized determining an allowed range for the induced pseudoscalar coupling constant g_P.
Next to leading order effective field theory calculations are performed for $ {}^1S_0$ NN scattering using subtractive renormalization procedure. One pion exchange and contact interaction potentials are iterated using Lippman-Schwinger equation. Satisfactory fit to the Nijmegen data is obtained for the momenta up to 300 MeV in the centre of mass frame. Phase shifts are also compared with the results of KSW approach where pions are included perturbatively.
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.
Owing to the Kubo relation, the shear viscosities of pionic and nucleonic components have been evaluated from their corresponding retarded correlators of viscous stress tensor in the static limit, which become non-divergent only for the non-zero thermal widths of the constituent particles. In the real-time thermal field theory, the pion and nucleon thermal widths have respectively been obtained from the pion self-energy for different meson, baryon loops and the nucleon self-energy for different pion-baryon loops. We have found a non-monotonic momentum distributions of pion and nucleon thermal …
A chiral pion-nucleon amplitude supplemented by the HJS subthreshold coefficients is used to calculate the the long range part of the two-pion exchange nucleon-nucleon potential. In our expressions the HJS coefficients factor out, allowing a clear identification of the origin of the various contributions. A discussion of the configuration space behaviour of the loop integrals that determine the potential is presented, with emphasis on cancellations associated with chiral symmetry. The profile function for the scalar-isoscalar component of the potential is produced and shown to disagree with th…
The effect of the non-perturbative term is investigated for the pion-nucleon scattering. Including the self-energy of nucleon the cross section of the elastic scattering results in a constant value at the laboratory momentum $p_L \to \infty$. The amplitude of the forward direction is applied to the dispersion relation.
We study the mass of a nucleon in a nucleus using a model recently introduced for a nucleon current with a pion cloud component. The method of QCD sum rules is used to determine the mass shifts for nucleons to first order in nuclear density in oxygen-16 and calcium-40, with the pion propagator determined by an optical potential for pion-nucleus scattering. Mass shifts due to the pionic contributions range from negligible in oxygen to -100 MeV in calcium at central nuclear density, with larger shifts in the nuclear surface. The consistency of this model with chiral perturbation theory is demons…
The leading divergences of the generating functional for Green functions of quark currents between one--nucleon states are calculated with heat kernel techniques. The results allow for a chiral invariant renormalization of all two--nucleon Green functions of the pion--nucleon system to $O(p^3)$ in the low--energy expansion.
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.
In the real-time thermal field theory, the standard expression of shear viscosity for the nucleonic constituents is derived from the two point function of nucleonic viscous stress tensors at finite temperature and density. The finite thermal width or Landau damping is traditionally included in the nucleon propagators. This thermal width is calculated from the in-medium self-energy of nucleon for different possible pion-baryon loops. The dynamical part of nucleon-pion-baryon interactions are taken care by the effective Lagrangian densities of standard hadronic model. The shear viscosity to entr…
We evaluate the two--pion contribution to the nucleon electromagnetic form factors by use of dispersion analysis and chiral perturbation theory. After subtraction of the rho--meson component, we calculate the distributions of charge and magnetization in coordinate space, which can be interpreted as the effects of the pion cloud. We find that the charge distribution of this pion cloud effect peaks at distances of about 0.3 fm. Furthermore, we calculate the contribution of the pion cloud to the isovector charges and radii of the nucleon.
We compute the light-cone momentum distributions of pions in the nucleon in chiral effective theory using both pseudovector and pseudoscalar pion-nucleon couplings. For the pseudovector coupling we identify δ-function contributions associated with end-point singularities arising from the pion-nucleon rainbow diagrams, as well as from pion bubble and tadpole diagrams which are not present in the pseudoscalar model. Gauge invariance is demonstrated, to all orders in the pion mass, with the inclusion of Kroll-Ruderman couplings involving operator insertions at the πNN vertex. The results pave the…
We study the third order pion-nucleon scattering amplitude obtained from heavy baryon chiral perturbation theory inside the Mandelstam triangle. We reconstruct the pion-nucleon amplitude in the unphysical region by use of dispersion relations and determine the pertinent low-energy constants by a fit to this amplitude. A detailed comparison with values obtained from phase shift analysis is given. Our analysis leads to a pion-nucleon sigma-term of sigma(0) = 40 MeV based on the Karlsruhe partial wave analysis. We have repeated the same procedure using the latest solution of the VPI group and fin…
The 1S0, 3S1, and 3D1 nucleon-nucleon scattering phase shifts are calculated at next-to-next-to-leading order (NNLO) in an effective field theory. Predictions for the 1P1, 3P0, 3P1, 3P2, 1D2, 3D2, and 3D3 phase shifts at this order are also compared with data. The calculations treat pions perturbatively and include the NNLO contributions from order $Q_r^3$ and $Q_r^4$ radiation pion graphs. In the 3S1, 3D1, 3P0, and 3P2 channels we find large disagreement with the Nijmegen partial wave analysis at NNLO. These spin triplet channels have large corrections from graphs with two potential pion exch…
We analyze elastic-pion nucleon scattering to third order in the so-called small scale expansion. It is based on an effective Lagrangian including pions, nucleons and deltas as active degrees of freedom and counting external momenta, the pion mass and the nucleon-delta mass splitting as small parameters. The fermion fields are considered as very heavy. We present results for phase shifts, threshold parameters and the sigma term. We discuss the convergence of the approach. A detailed comparison with results obtained in heavy baryon chiral perturbation theory to third and fourth order is also gi…
An explicit pionic component of the nucleon may be identified by measuring polarized $Δ^{++}$ fragments produced in deep-inelastic scattering off polarized protons. The pion-exchange model predicts highly correlated polarizations of the $Δ^{++}$ and target proton, in marked contrast with the competing diquark fragmentation process.
In a recent Letter, Alberg and Miller presented a calculation of the pion contributions to the self-energy of the nucleon computed from a pseudoscalar (PS) pion-nucleon interaction, with the claim that the result would be equivalent to that with the pseudovector (PV) form. We demonstrate that the PV and PS pion-nucleon couplings do in fact lead to different results for the self-energy. In particular, for the model-independent, leading nonanalytic behavior of the self-energy, the PV theory yields the well-known m_π^3 dependence in the chiral limit, while the PS interaction involves an additiona…
For interactions involving two or more nucleons it is useful to divide pions into three classes: potential, radiation, and soft. The momentum threshold for the production of radiation pions is $Q_r = \sqrt{M_N m_π}$. We show that radiation pions can be included systematically with a power counting in $Q_r$. The leading order radiation pion graphs which contribute to NN scattering are evaluated in the PDS and OS renormalization schemes and are found to give a small contribution. The power counting for soft pion contributions is also discussed.
We study pion--nucleon scattering with a chiral lagrangian of pions, nucleons, and $Δ$-isobars. The scattering amplitude is evaluated to one-loop $Q^3$ order, where $Q$ is a generic small momentum, using a new approach which is equivalent to heavy baryon chiral perturbation theory. We obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to 100 MeV. A sigma term greater than 45 MeV is favored, but the value is not well determined.
We study pion-nucleon scattering at tree level with a chiral lagrangian of pions, nucleons, and $Δ$-isobars using a K-matrix unitarization procedure. Evaluating the scattering amplitude to order $Q^2$, where $Q$ is a generic small momentum scale, we obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to $50 $MeV. The fit can be extended to 150 MeV when we include the order-$Q^3$ contributions. Our results are independent of the off-shell $Δ$ parameter.
We give reasons in support of the use of an effective intensity-dependent pion-nucleon coupling Hamiltonian for describing the properties of the pion multiplicity distribution and the corresponding factorial moments within the thermal-density matrix approach.We explain the appearance of the negative-binomial (NB) distribution for pions and the well-known empi- rical relation of Wroblewski.Our model Hamiltonian is written as a linear combination of the generators of the SU(1,1) group.We find the generating function for the pion multiplicity distribution at finite temperature T and discuss the p…
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
We construct the complete effective chiral pion-nucleon Lagrangian in the presence of virtual photons to one loop. As an application, we consider strong and electromagnetic isospin violation for scattering of neutral pions off nucleons. We show that for the scattering lengths these isospin violating terms are of the same size as the purely hadronic ones. We also analyze isospin-violating effects for the $σ$--term. These can be as large as 10% for the absolute value but are negligible for the shift to the Cheng-Dashen point.
I discuss low-energy pion-nucleon scattering in the framework of chiral perturbation theory. I argue that using this theoretical method one is able to handle the in some cases tremendous experimental accuracy (for the low partial waves). I then show how strong and electromagnetic isospin violation can be treated simultaneously. Some first results for neutral pion scattering and the $σ$-term are given.
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory. The so-called triangle relation is found to be violated by about 1.5 %. We encounter a substantial isospin-breaking correction to neutral-pion-nucleon scattering beyond Weinberg's prediction due to a cusp effect. Finally, the application to hadronic atoms is briefly discussed.
By using the soft pion theorem in the inclusive reactions, soft pions' contribution to the structure function $F_2$ in the nucleon is estimated. It is shown that this contribution produces such a large flavor asymmetry in the light sea quark distributions that it gives about $30\sim 50 %$ of the NMC deficit in the Gottfried sum.
We study pion--nucleon scattering with a chiral lagrangian of pions, nucleons, and $Δ$-isobars to order $Q^3$, where $Q$ is a generic small momentum. We compare the results from heavy baryon chiral perturbation theory with those from the infrared regularization scheme. While the former provides a reasonable fit to the data out to a pion c.m. kinetic energy of 100 MeV, the latter is only able to fit up to 40 MeV and even then the parameters obtained are unreasonable. Difficulties with the infrared scheme in the $u$-channel are discussed.
We analyse elastic-pion nucleon scattering to fourth order in heavy baryon chiral perturbation theory, extending the third order study published in Nucl. Phys. A640 (1998) 199. We use various partial wave analyses to pin down the low-energy constants from data in the physical region. The S-wave scattering lengths are consistent with recent determinations from pionic hydrogen and deuterium. We find an improved description of the P-waves. We also discuss the pion-nucleon sigma term and problems related to the prediction of the subthreshold parameters.
Virtual Compton scattering off nucleons and pions at low energies is discussed. Predictions for the generalized polarizabilities of the nucleon are presented within the framework of heavy-baryon chiral perturbation theory and the linear sigma model. First results for the generalized polarizabilities of the charged pion in chiral perturbation theory at ${\cal O}(p^4)$ are shown.
The amplitudes for the pion-nucleon charge exchange reaction of the Karlsruhe-Helsinki and the George-Washington-University partial wave analyses are compared with those of a Regge-cut model with the aim to explore the possibility to provide high energy constraints for theoretical baryon resonance analyses in the energy region above 2 GeV.
In this paper, we show that the low energy theorem (LET) of the threshold pion-photoproduction can be fully recovered in the quark model. An essential result of this investigation is that the quark-pion operators are obtained from the effective chiral Lagrangian, and the low energy theorem does not require the constraints on the internal structures of the nucleon. The pseudoscalar quark-pion coupling generates an additional term at order $μ=m_π/M$ only in the isospin amplitude $A^{(-)}$. The role of the transitions between the nucleon and the resonance $P_{33}(1232)$ and P-wave baryons are als…
We have calculated coupling constants of a neutral pion with the lowest two nucleon resonances. This includes both the diagonal as well as non-diagonal coupling constants involving a nucleon resonance and a nucleon. For this, we first calculate vacuum-to-pion correlation function of the interpolating fields of two nucleons and then take its matrix elements with respect to a nucleon spinor and/or a nucleon resonance spinor(s). Using different QCD sum rules obtained from different matrix elements we eliminate unwanted coupling constants and solve for the desired ones. This is a simple extension …
We analyze the $γN\toπN$ process in the negative parity channel with Hamiltonian effective filed theory which is successful in studying the nucleon resonances associated with the meson-nucleon scattering and lattice QCD simulations. We provide the scattering amplitude of pion photoproduction and extract the electric dipole amplitudes $E_{0+}$. The triquark component in $N^*(1535)$ is important for improving the consistence between our results and the experimental data.
The pion nucleon vertex function at finite temperature is studied in the framework of: (a) the thermal (linear) sigma model to leading (one-loop) order, and (b) a thermal QCD-Finite Energy Sum Rule. Results from both methods indicate that the strength of the pion-nucleon coupling decreases with increasing T, vanishing at a critical temperature. The associated mean-square radius is a monotonically increasing function of T, diverging at the critical temperature. This is interpreted as (analytical) evidence for the quark-gluon deconfinement phase transition.
Inclusive cross section for pion production in proton - proton collisions are calculated based on unintegrated parton distribution functions (uPDFs). In addition to purely gluonic terms the present approach includes also quark degrees of freedom. Phenomenological fragmentation functions from the literature are used. The new mechanisms are responsible for $π^+$ - $π^-$ asymmetry. In contrast to standard collinear approach, application of 2 $\to$ 1 $k_t$ - factorization approach can be extended towards much lower transverse momenta, both at mid and forward rapidity region. The results of the cal…
Low energy phenomena involving two nucleons can be successfully described using effective field theory. Because of the relatively large expansion parameter, it is only at next-to-next-to-leading order (NNLO) where one can expect to see agreement with experiment at the few percent level. The first part of this talk will focus on radiation pion effects, which first appear at NNLO. The power counting for radiation pions is simple for center of mass momentum p~\sqrt{M m_pi}=Q_r, the threshold for pion production. We explain how graphs calculated with the Q_r power counting scale for p~m_π. The Q_r…
We present a simple description of pion-nucleon ($πN$) scattering taking into account the full complexity of pion absorption and creation on the nucleon. To do this we solve Dyson-Schwinger equations within the framework of Time-Ordered Perturbation Theory. This enables us to construct partial wave separable $ πN$ t matrices that can be useful in models of nuclear processes involving fully dressed nucleons. At the same time, our approach demonstrates features of Quantum Field Theory, like particle dressing, renormalisation, and the use of Dyson-Schwinger equations, in a non-relativistic contex…
In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion-nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking corrections both in pion-nucleon and pion-deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion-deuteron system, and discuss the subtleties regarding the definition of the pion-nucleon scattering lengths in the presence of electromagnetic interactions by comparing to …
Elastic pion-pion and pion-nucleon scattering are reviewed in the context of chiral perturbation theory. Theoretical results from systematic low-energy expansions to O(p^6) for pion-pion and to O(p^3) for pion-nucleon scattering are compared with experimental data. Possible future developments are outlined.
We extend the study of a JP=2+, I=3/2 pion-Lambda-nucleon quasibound state [Phys. Rev. D 78, 014013 (2008)] by solving nonrelativistic Faddeev equations, using 3S1-3D1, Lambda N - Sigma N coupled channels Chiral Quark Model local interactions, and pion-nucleon and coupled pion-Lambda - pion-Sigma separable interactions fitted to the position and decay parameters of the Delta(1232) and Sigma(1385) resonances, respectively. The results exhibit a strong sensitivity to the p-wave pion-hyperon interaction, with a pion-Lambda-nucleon quasibound state persisting over a wide range of acceptable parame…
The pion-nucleon $σ$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3σ$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.
The uncoupled $P$-wave channels of nucleon-nucleon scattering are studied in an effective field theory (EFT) including a perturbative dibaryon field and perturbative pions. Good agreement between EFT results and the Nijmegen partial wave analysis is observed up to a center-of-mass momentum $k \approx 400$ MeV. Using a method that combines renormalization and fitting together, the long-standing convergence problem of EFTs in these channels with perturbative pions, for momenta above the pion mass is addressed from a new perspective.
We have searched for bound states in the pion-Lambda-nucleon system by solving the nonrelativistic Faddeev equations, as well as a relativistic version, with input separable pion-nucleon, pion-Lambda, and Lambda-nucleon interactions. A bound-state solution, driven by the Delta(1232) and Sigma(1385) p-wave meson-baryon resonances, was found in the channel (I,JP)=(3/2,2+), provided the Lambda lab momentum at which the Lambda-nucleon S=1,L=0,J=1 phase shift becomes negative is larger than about 750-800 MeV/c. Other strange and charmed pion-baryon-baryon systems that might have bound states of a s…
We calculate pion mass, pion decay constant, PCAC quark mass and nucleon mass in two flavour lattice QCD with unimproved Wilson fermion and gauge actions. Simulations are performed using DD-HMC algorithm at two lattice spacings and two volumes for several values of the quark mass. The cutoff effects in pion mass and nucleon mass for the explored region of parameter space are found to be negligible. The chiral behaviours of pion mass, pion decay constant and quark condensate are found to be qualitatively consistent with NLO chiral perturbation theory.
The pion-mass dependence of the nucleon mass within the covariant SU(2) baryon chiral perturbation theory both without and with explicit Delta(1232) degrees of freedom up to order p^4 is investigated. By fitting to lattice QCD data in 2 and 2+1 flavors from several collaborations, for pion masses M_pi < 420 MeV, we obtain low energy constants of natural size and compatible with pion nucleon scattering data. Our results are consistent with the rather linear pion-mass dependence showed by lattice QCD. In the 2 flavor case we have also performed simultaneous fits to the nucleon mass and pion-nucl…
We present a general representation for the nucleon distribution amplitudes and for the nucleon to pion transition distribution amplitudes in terms of light-cone wave functions. We apply our formalism to a light-cone constituent quark model giving some numerical results for both the classes of observables.
The longest-range part of the nuclear force due to the one-pion exchange governs the energy dependence of the scattering amplitude in the near-threshold region and imposes correlations between the coefficients in the effective range expansion. These correlations may be regarded as low-energy theorems and are known to hold to a high accuracy in the neutron-proton 3S1 partial wave. We generalize the low-energy theorems to the case of unphysical pion masses and provide results for the correlations between the coefficients in the effective range expansion in this partial wave for pion masses up to…
