Search results for "PERTURBATION"
showing 10 items of 811 documents
A dispersion relation for the pion-mass dependence of hadron properties
2010
We present a dispersion relation in the pion-mass squared, which static quantities (nucleon mass, magnetic moment, etc.) obey under the assumption of analyticity in the entire complex $m_\pi^2$ plane modulo a cut at negative $m_\pi^2$ associated with pion production. The relation is verified here in a number of examples of nucleon and $\Delta$-isobar properties computed in chiral perturbation theory up to order $p^3$. We outline a method to obtain relations for other mass-dependencies, and illustrate it on a two-loop example.
Finite volume corrections to forward Compton scattering off the nucleon
2021
We calculate the spin-averaged amplitude for doubly virtual forward Compton scattering off nucleons in the framework of manifestly Lorentz invariant baryon chiral perturbation theory at complete one-loop order $O(p^4)$. The calculations are carried out both in the infinite and in a finite volume. The obtained results allow for a detailed estimation the finite-volume corrections to the amplitude which can be extracted on the lattice using the background field technique.
Chiral perturbation theory of hyperfine splitting in muonic hydrogen
2016
We present the leading-order prediction of baryon chiral perturbation theory for the proton polarizability contribution to the 2S hyperfine splitting in muonic hydrogen, and compare with the results of dispersive calculations.
Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory
2017
We perform a complete and systematic calculation of the octet-baryon form factors within the fully covariant approach of SU(3) chiral perturbation theory at O(p^3). We use the extended on-mass shell renormalization scheme, and include explicitly the vector mesons and the spin-3/2 decuplet intermediate states. Comparing these predictions with data including magnetic moments, charges, and magnetic radii, we determine the unknown low-energy constants, and give predictions for yet unmeasured observables, such as the magnetic moment of the Sigma^0, and the charge and magnetic radii of the hyperons.
Meson-Baryon Interactions in Unitarized Chiral Perturbation Theory
2002
Meson-Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The $s-$wave meson-baryon scattering amplitude is analyzed in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic reson…
Spin-dependent sum rules connecting real and virtual Compton scattering verified
2017
We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly-virtual Compton scattering. For example, the polarizability $\delta_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability $\gamma_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.
Improved description of the pion-nucleon scattering phenomenology in covariant baryon chiral perturbation theory
2014
We highlight some of the recent advances in the application of chiral effective field theory (chiral EFT) with baryons to the $\pi N$ scattering process. We recall some problems that cast doubt on the applicability of chiral EFT to $\pi N$ and show how the relativistic formalism, once the $\Delta(1232)$-resonance is included as an explicit degree of freedom, solves these issues. Finally it is shown how this approach can be used to extract the $\sigma$-terms from phenomenological information.
η(′)→π+π−γ(*) in large- Nc chiral perturbation theory
2021
We present a calculation of the decays ${\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\gamma}}^{(*)}$ at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-${N}_{c}$ chiral perturbation theory. The numerical evaluation of the results is performed successively at LO, NLO, and NNLO, fitting the relevant low-energy constants to the available experimental data. We discuss the widths and decay spectra of ${\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ as well as ${\ensuremath{…
Two-photon decays and transition form factors of π0 , η , and η′ in large- Nc chiral perturbation theory
2020
We present a calculation of $P\ensuremath{\rightarrow}{\ensuremath{\gamma}}^{(*)}{\ensuremath{\gamma}}^{(*)}$ processes, where $P={\ensuremath{\pi}}^{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$, at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-${N}_{c}$ chiral perturbation theory. The results are numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants are determined through fits to the available experimental data. We investigate the decay widths to real photons, the single-virtual transition form factors, and the widths of $P\ensuremath{\rightarrow}\ensuremath{\gamma}{l}^{+}{l}^{\ensuremath{-}}$, where…
Proton polarizabilities: status, relevance, prospects
2013
This is a brief review of the status of understanding the proton polarizabilities in chiral perturbation theory and of their relevance to the `proton charge radius puzzle'.