Nucleon-delta Mass Research Articles

Nucleon polarisabilities at and beyond physical pion masses

We examine the results of Chiral Effective Field Theory ($\chi$EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of $m_\pi$. This provides chiral extrapolations for lattice-QCD polarisability computations. We include both the leading and sub-leading effects of the nucleon's pion cloud, as well as the leading ones of the $\Delta(1232)$ resonance and its pion cloud. The analytic results are complete at N$^2$LO in the $\delta$-counting for pion masses close to the physical value, and at leading order for pion masses similar to the Delta-nucleon mass splitting. In order to quantify the truncation error of our predictions and fits as $68$\% degree-of-belief intervals, we use a Bayesian procedure recently adapted to EFT expansions. At the physical point, our predictions for the spin polarisabilities are, within respective errors, in good agreement with alternative extractions using experiments and dispersion-relation theory. At larger pion masses we find that the chiral expansion of all polarisabilities becomes intrinsically unreliable as $m_\pi$ approaches about $300\;$MeV---as has already been seen in other observables. $\chi$EFT also predicts a substantial isospin splitting above the physical point for both the electric and magnetic scalar polarisabilities; and we speculate on the impact this has on the stability of nucleons. Our results agree very well with emerging lattice computations in the realm where $\chi$EFT converges. Curiously, for the central values of some of our predictions, this agreement persists to much higher pion masses. We speculate on whether this might be more than a fortuitous coincidence.

Pion production in nucleon-nucleon collisions in chiral effective field theory withΔ(1232) degrees of freedom

A calculation of the pion-production operator up to next-to-next-to-leading order for s-wave pions is performed within chiral effective field theory. In the previous study [Phys. Rev. C 85, 054001 (2012)] we discussed the contribution of the pion-nucleon loops at the same order. Here we extend that study to include explicit Delta degrees of freedom and the 1/m_N^2 corrections to the pion-production amplitude. Using the power counting scheme where the Delta-nucleon mass difference is of the order of the characteristic momentum scale in the production process, we calculate all tree-level and loop diagrams involving Delta up to next-to-next-to-leading order. The long-range part of the Delta loop contributions is found to be of similar size to that from the pion-nucleon loops which supports the counting scheme. The net effect of pion-nucleon and Delta loops is expected to play a crucial role in understanding of the neutral pion production data.

Baryon structure in the global color symmetry model of QCD

Baryons are considered as solitons in the global color symmetry model (GCM) of QCD. With both the scalar and pseudoscalar chiral fields being included and the Hedgehog approximation being taken, we obtain a GCM soliton profile whose mass and radius are quite close to the experimental data of a nucleon. We then quantize the angular momentum and isospin with the collective quantization method and obtain a nucleon-Delta mass split comparable with experimental data.

Quark mass dependence of baryon properties: Foundations and applications

I discuss the quark mass dependence of various baryon properties derived from chiral perturbation theory. Such representations can eventually be used as chiral extrapolation functions when lattice data at sufficiently small quark masses become available. The quark mass dependence is encoded in loop and contact term contributions, the latter given in terms of low-energy constants. I stress the importance of utilizing phenomenological input to constrain a certain class of low-energy constants and discuss the ensuing theoretical uncertainty for various baryon observables. Examples are the nucleon and the baryon octet masses, the nucleon isovector anomalous magnetic moment and the axial-vector coupling of the nucleon. I stress the role of resonance decoupling and present first results for the delta mass based on an effective field theory in which the nucleon-delta mass splitting is counted as a small parameter. I also discuss breifly the pion mass dependence of the nuclear force as derived from chiral nuclear effective field theory.

Pion–nucleon scattering in an effective chiral field theory with explicit spin- [formula omitted] fields

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 given.

Self-Consistent Pushing and Cranking Corrections to the Meson Fields of the Chiral Quark-Loop Soliton

We study translational and spin-isospin symmetry restoration for the two-flavor chiral quark-loop soliton. Instead of a static soliton at rest we consider a boosted and rotating hedgehog soliton. Corrected classical meson fields are obtained by minimizing a corrected energy functional which has been derived by semi-classical methods (variation after projection). We evaluate corrected meson fields in the region 300 MeV ≤ M≤ 600 MeV of constituent quark masses M and compare them with the uncorrected fields. We study the effect of the corrections on various expectation values of nuclear observables such as the root-mean square radius, the axial-vector coupling constant, magnetic moments and the delta-nucleon mass splitting.

Systematic [formula omitted] expansion for spin [formula omitted] particles in baryon chiral perturbation theory

Starting from a relativistic formulation of the pion-nucleon-delta system, the most general structure of 1 M corrections for a heavy baryon chiral lagrangian including spin 3 2 resonances is given. The heavy components of relativistic nucleon and delta fields are integrated out and their contributions to the next-to-leading order lagrangians are constructed explicitly. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass m π and the delta-nucleon mass difference Δ. As an application, we consider neutral pion photoproduction at threshold to third order in this small scale expansion.

On size and shape of the average meson fields in the semibosonized Nambu & Jona-Lasinio model

We consider a two-flavor Nambu \& Jona-Lasinio model in Hartree approximation involving scalar-isoscalar and pseudoscalar-isovector quark-quark interactions. Average meson fields are defined by minimizing the effective Euklidean action. The fermionic part of the action, which contains the full Dirac sea, is regularized within Schwinger's proper-time scheme. The meson fields are restricted to the chiral circle and to hedgehog configurations. The only parameter of the model is the constituent quark mass $M$ which simultaneously controls the regularization. We evaluate meson and quark fields self-consistently in dependence on the constituent quark mass. It is shown that the self-consistent fields do practically not depend on the constituent quark mass. This allows us to define a properly parameterized reference field which for physically relevant constituent masses can be used as a good approximation to the exactly calculated one. The reference field is chosen to have correct behaviour for small and large radii. To test the agreement between self-consistent and reference fields we calculate several observables like nucleon energy, mean square radius, axial-vector constant and delta-nucleon mass splitting in dependence on the constituent quark mass. The agreement is found to be very well. Figures available on request.

The Sigma Term: Leading Non-Analytic Behaviour Of Decuplet Contributions

We examine the analytic structure, in powers of the quark mass (m), of the chiral loop corrections to the pion-nucleon sigma term arising from coupling to the lowest mass baryon decuplet. The leading non-analytic term is found to go like m2 In(m/2a) (with a the delta-nucleon mass splitting), and to be quite significant numerically.

Chiral Corrections for Lattice QCD

We show that in the quenched approximation, lattice QCD calculations miss important corrections to the mass of hadrons. For example, we argue that the nucleon mass is overestimated by up to 30% while the nucleon-delta mass splitting is underestimated by a similar amount. As the quenched approximation is relaxed, the quark mass decreased and the lattice size increased, these errors should go away. A systematic method of monitoring the size of the residual error is suggested.

Gluonic contributions in the chiral hyperbag

We incorporate into a non-perturbative chiral bag model scheme the gluons and the η' in a perturbative fashion. We analyze in this context the proton matrix element for the flavor singlet axial current, where due account is taken of the anomaly, and the delta-nucleon mass difference. Our results show that the contribution due to the gluons is significant for large bag radii and that they are crucial in order to establish the Cheshire cat principle.

Medium effects on Δ properties and N-Δ transition form factors

The properties of the Δ(1232) isobar immersed in a nuclear medium are investigated in a chiral quark-meson theory. To this end the Nambu-Jona-Lasinio model is used to evaluate the pion decay constant, the pion mass and the sigma mass at finite medium density. These values serve to fix the parameters of the Gell-Mann-Lévi sigma model. The latter is then solved in a variational mean-field and projection approach in order to obtain the static delta properties and γNΔ and πNΔ vertices. At the nuclear matter density both the mass of the delta and the nucleon-delta mass splitting are reduced by about 20%, the radii show swelling and the form factors get noticeably reduced at finite momentum transfers relevant for charge-exchange reactions and electron scattering.

BAG INDEPENDENT RELATION FOR SPIN-ISOSPIN PROJECTED BARYONS IN THE CHIRAL BAG PLUS SKYRMION HYBRID MODEL

We propose an approximate spin-isospin projection method with collective coordinates. We perform the collective rotation in the coordinate space instead of the isospin space and construct a local Lorentz boosted quark field as an approximated solution of the collective rotation. In this projection scheme, we find that the moment of inertia of the quark is expressed by one body operator as the baryon number and the Casimir energy. After the quantization of the rotation, we find for the chiral bag model also the bag independent relations between the magnetic moments and the nucleon-delta mass difference, which have been derived for the Skyrmion.

Tensor polarization of the elastice−2H scattering and the scaling behavior of six-quark dynamics

Tensor polarization, ${t}_{20}$, of elastic electron-deuteron scattering is calculated with the resonating group method applied to the six-quark system. We stress the role of baryon size for short-range nuclear correlations, such as the short-range repulsion due to the color magnetic interaction, through the six-quark dynamics. Correct sizes of the delta-nucleon mass splitting and the binding energy of the deuteron are the restrictions imposed on the model Hamiltonian for each different choice of the three-quark cluster size b. An interesting scaling behavior for ${t}_{20}$ is observed with regard to the momentum transfer q and b, for different models of the medium-range attractive force. An asymptotic equation predicted by the perturbative quantum chromodynamics, i.e., ${\mathrm{lim}}_{\mathrm{q}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathrm{t}}_{20}$(q)=const, is examined within the present framework, and the momentum transfer for this condition turns out to be quite large, q=4--6 GeV/c. Magnetic effects are seen to be important at large q.

Gluons and the spin of the proton

The recent observation that constituent quark helicities carry very little of the spin of the proton, in contrast with naive quark model expectations, can be understood by taking into account non-perturbative aspects of QCD, such as chiral symmetry breaking and confinement. We compute the non-strange quark contribution Δu+ Δd to the proton spin in a chiral field-theoretical model of quark and gluon confinement. Our mean field computations include self-consistently the effects of gluon exchange between constituent quarks. When the parameters of the model, including the effective strong fine structure constant α s, are adjusted to reproduce as far as possible the experimental mean nucleon-delta mass and the relative nucleon-delta mass splitting, we obtain Δu+Δd⋍0.26, which is only one third of the α s=0 value. We show that this implies that all the proton spin is in fact orbital angular momentum.

CRANKING THE CHIRAL SOLITON BAG MODEL: GLUONIC EFFECTS

The nucleon-delta mass difference is computed in the chiral soliton bag model with soft confinement of gluons by the cranking method. The resulting value of the effective strong fine structure constant is αs≃0.7.

CRANKING THE CHIRAL SOLITON BAG MODEL: QUANTUM CORRECTIONS

The generation of physical states from mean field hedgehogs by cranking is extended to coherent hedgehogs, thus improving the agreement between the cranking and coherent state projection methods, and enabling us to correct simultaneously for translational and rotational fluctuations. These corrections lead to a drastic reduction in the mean nucleon-delta mass which, for the physical values of mπ and Fπ, is lower than, or approximately equal to, the experimental value.

Self-consistent one-gluon exchange in soliton bag models

The treatment of soliton bag models as two-point boundary value problems is extended to include self-consistent one-gluon exchange interactions. The colour-magnetic contribution to the nucleon-delta mass splitting is calculated self-consistently in the mean-field, one-gluon-exchange approximation for the Friedberg-Lee and Nielsen-Patkos models. Small glueball mass parameters ( m GB∼500 MeV) are favoured. Comparisons with previous calculations are made.

GLUONIC CONTRIBUTION TO THE NUCLEON-DELTA MASS DIFFERENCE IN A CHIRAL SOLITON BAG MODEL

A generalization of the Friedberg-Lee model, which minimally incorporates soft confinement of quarks and gluons and approximate chiral symmetry, is presented and applied to the computation of the gluonic contribution to the nucleon-delta mass difference. The value of the effective strong fine structure constant is estimated to be αs= 0.65.

Rotation of the chiral bag

Cranking of the chiral bag model is carried out in order to generate the correct quantum numbers for SU(2) baryons. The moment of inertia of the system is found to be divided between the meson and quark sectors. A numerical evaluation of the contributions to the moment of inertia from valence quarks and from mesons is presented. Finally, a discussion is given of the nucleon-delta mass splitting predicted in the chiral bag model.