Octet and decuplet magnetic and axial couplings from one-loop self-consistent perturbation theory

Octet and decuplet wave functions, obtained in a recent precision fit to the spectrum using one-loop self-consistent perturbation theory of mesons and gluons interacting with bagged relativistic quarks, are used to evaluate axial couplings and magnetic moments. Results are fully competitive with other models and provide further support to one-loop self-consistent perturbation theory as a useful model of baryon structure.     

Strong contribution to octet baryon mass splittings

We calculate the _md−_mu$m_d-m_u$ contribution to the mass splittings in baryonic isospin multiplets using SU(3) chiral perturbation theory and lattice QCD. Fitting isospin-averaged perturbation theory functions to PACS-CS and QCDSF-UKQCD Collaboration lattice simulations of octet baryon masses, and using the physical light-quark mass ratio _mu/_md$m_u/m_d$ as input, allows _Mn−_Mp$M_n-M_p$, _MΣ−−_MΣ+$M_{{\Sigma }^{-}}-M_{{\Sigma }^{+}}$ and _MΞ−−_MΞ0$M_{{\Xi }^{-}}-M_{{\Xi }^0}$ to be evaluated from the full SU(3) theory. The resulting values for each mass splitting are consistent with the experimental values after allowing for electromagnetic corrections. In the case of the nucleon, we find _Mn−_Mp=2.9±0.4 MeV$M_n-M_p=2.9\pm 0.4\text{MeV}$, with the dominant uncertainty arising from the error in _mu/_md$m_u/m_d$.     

Generalized heavy baryon chiral perturbation theory

Standard SU(2) Heavy Baryon Chiral Perturbation Theory is extended in order to include the case of small or even vanishing quark condensate. The effective lagrangian is given to in its most general form and to in the scalar sector. A method is developed to efficiently construct the relativistic baryonic effective lagrangian for chiral SU(2) to all orders in the chiral expansion. As a first application, mass- and wave-function renormalization as well as the scalar form factor of the nucleon is calculated to . The result is compared to a dispersive analysis of the nucleon scalar form factor adopted to the case of a small quark condensate. In this latter analysis, the shift of the scalar form factor between the Cheng-Dashen point and zero momentum transfer is found to be enhanced over the result assuming strong quark condensation by up to a factor of two, with substantial deviations starting to be visible for . Received: 22 July 1998 / Revised version: 2 September 1998 / Published online: 2 November 1998     

Two-nucleon problem in semi-relativistic baryon chiral perturbation theory

We consider a symmetry-preserving approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Within this framework the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively.     

Some recent results in baryon chiral perturbation theory

I present and discuss recent results on elastic pion-nucleon scattering and near-threshold neutral-pion electroproduction off deuterium obtained in the framework of chiral perturbation theory.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.75.Gx Pion-baryon interactions - 25.30.Rw Electroproduction reactions - 12.39.Fe Chiral Lagrangians     

Sigma-terms in heavy baryon chiral perturbation theory revisited

The -terms are calculated at next-to-leading order in heavy baryon chiral perturbation theory by employing a cutoff regularization. The results do not depend on the cutoff value to the order we are working . The baryon masses and are used to perform a least-squares fit to the three appearing low-energy constants and predictions for the two KN -terms and the strange contribution to the nucleon mass are made. The lack of convergence in the chiral expansions of these quantities when regularized dimensionally is overcome in the cutoff scheme. The -term shifts to the pertinent Cheng-Dashen points are calculated. We also include the spin-3/2 decuplet in the effective theory. Received: 21 July 1998 / Revised version: 31 August 1998 / Published online: 25 January 1999     

Time-dependent self-consistent perturbation theory and applications to molecules

The two most intense bands of the 370 nm electronic band system of tropolone have been rotationally analysed. They are separated by 18·93 cm^-1 and it has been shown that the high wavenumber band is the 0^--0^- (H₁ ¹) transition in what is almost certainly the internal hydrogen-bonding vibration v _H : the low wavenumber band is the 0⁺-0⁺ (0₀ ⁰) transition. A rotational contour analysis of both bands shows that there is an intensity alternation in K _a″ such that the ratio K _a″ even : odd is 10 : 6 in the 0⁺-0⁺ band and 6 : 10 in the 0^--0^- band. The intensity alternation, the nearly equal intensities of the 0⁺-0⁺ and 0^--0^- bands, the separation of these two bands and the anharmonic behaviour of v _H show that the separation of the 0⁺ and 0^- levels is small in the ground electronic state (probably less than 50 cm^-1) and is 18·93 cm^-1 larger in the excited electronic state.

The 0⁺-0⁺ and 0^--0^- bands are both type B showing that the electronic transition is à ¹ B ₂-X ¹ A ₁ and therefore π*-π rather than π*-n. The π*-n transition is probably shifted to high wavenumber by the internal hydrogen-bonding.     

Wave function renormalization in heavy baryon chiral perturbation theory

We establish exact relations between relativistic form factors and amplitudes for single-baryon processes and the corresponding quantities calculated in the framework of heavy baryon chiral perturbation theory. A crucial ingredient for the proper matching is the first complete treatment of baryon wave function renormalization in heavy baryon chiral perturbation theory.     

NN scattering in higher-derivative formulation of baryon chiral perturbation theory

We consider a new approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Starting with a Lorentz-invariant form of the effective Lagrangian we work out a new symmetry-preserving framework where the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively. Analogously to the KSW approach, the (leading) renormalization scale dependence to any finite order is absorbed in the redefinition of a finite number of parameters of the effective potential at given order. On the other hand, analogously to Weinberg’s power counting, the one-pion-exchange potential is of leading order and is treated non-perturbatively.     

Generalized polarizabilities of the nucleon in baryon chiral perturbation theory

The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron–proton bremsstrahlung (\(ep\rightarrow ep\gamma \)) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (B\(\chi \)PT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations – all done in heavy-baryon \(\chi \)PT (HB\(\chi \)PT) – and discuss the differences between B\(\chi \)PT and HB\(\chi \)PT responsible for these discrepancies.     

Heavy baryon chiral perturbation theory and the weak nonleptonic p-wave decays of the baryon octet

Considerable confusion in the literature about heavy baryon chiral perturbation theory, its convergence properties, and appropriate calculational techniques, make it timely to discuss the nonleptonic p-wave decays of the octet of baryons. We present model independent results.     

Probing the convergence of perturbative series in baryon chiral perturbation theory

Using the examples of pion-nucleon scattering and the nucleon mass we analyze the convergence of perturbative series in the framework of baryon chiral perturbation theory. For both cases we sum up sets of an infinite number of diagrams by solving equations exactly and compare the solutions with the perturbative contributions.     

The absence of cut-off effects for the fixed-point action in one-loop perturbation theory

In order to support the formal renormalization group arguments that the fixed-point action of an asymptotically free model gives cut-off independent physical predictions in one-loop perturbation theory, we calculate the finite-volume mass gap m(L) in the non-linear σ-model. No cut-off effect of the type g⁴ (a/L)ⁿ is seen for any n. The results are compared with those of the standard and tree level improved symanzik actions.     

Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.