Search results for " Perturbation theory"
showing 10 items of 358 documents
Higher-Order Corrections to Sirlin's Theorem inO(p6)Chiral Perturbation Theory
1997
We present the results of the first two-loop calculation of a form factor in full $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral perturbation theory. We choose a specific linear combination of ${\ensuremath{\pi}}^{+}$, ${K}^{+}$, ${K}^{0}$, and $K\ensuremath{\pi}$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order ${p}^{6}$ operators with unknown constants. For the charge radii, the corrections to the previous one-loop result turn out to be significant. To clearly identify the two-loop effects, more accurate measurements of the kaon and pion electromagnetic charge radii would be desirable.
Neutral Pion Threshold Production atQ2=0.05GeV2/c2and Chiral Perturbation Theory
2001
New data are presented on the $p({e,e}^{\ensuremath{'}}p){\ensuremath{\pi}}^{0}$ reaction at threshold at a four-momentum transfer of ${Q}^{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.05{\mathrm{GeV}}^{2}{/c}^{2}$. The data were taken with the three-spectrometer setup of the A1 Collaboration at the Mainz Microtron MAMI. The complete center of mass solid angle was covered up to a center of mass energy of 4 MeV above threshold. Combined with measurements at three different values of the virtual photon polarization $\ensuremath{\epsilon}$, the structure functions ${\ensuremath{\sigma}}_{T}$, ${\ensuremath{\sigma}}_{L}$, ${\ensuremath{\sigma}}_{\mathrm{TT}}$, and ${\ensuremath{\sigma…
Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
2018
We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent …
Accurate Test of Chiral Dynamics in theγ→p→π0pReaction
2013
A precision measurement of the differential cross sections dσ/dΩ and the linearly polarized photon asymmetry Σ≡(dσ⊥-dσ∥)/(dσ⊥+dσ∥) for the γp→π0p reaction in the near-threshold region has been performed with a tagged photon beam and almost 4π detector at the Mainz Microtron. The Glasgow-Mainz photon tagging facility along with the Crystal Ball/TAPS multiphoton detector system and a cryogenic liquid hydrogen target were used. These data allowed for a precise determination of the energy dependence of the real parts of the S- and all three P-wave amplitudes for the first time and provide the most stringent test to date of the predictions of chiral perturbation theory and its energy region of a…
Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
1996
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well …
A pedagogical approach to the Magnus expansion
2010
Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.
Low-energy constants from resonance chiral theory
2008
I discuss the recent attempts to build an effective chiral Lagrangian incorporating massive resonance states. A useful approximation scheme to organize the resonance Lagrangian is provided by the large-Nc limit of QCD. Integrating out the resonance fields, one recovers the usual chiral perturbation theory Lagrangian with explicit values for the low-energy constants, parameterized in terms of resonance masses and couplings. The resonance chiral theory generates Green functions that interpolate between QCD and chiral perturbation theory. Analyzing these Green functions, both for large and small momenta, one gets QCD constraints on the resonance couplings and, therefore, information on the low…
Improved description of the -scattering phenomenology at low energies in covariant baryon chiral perturbation theory
2013
Abstract We present a novel analysis of the π N scattering amplitude in covariant baryon chiral perturbation theory up to O ( p 3 ) within the extended-on-mass-shell renormalization scheme and including the Δ ( 1232 ) explicitly in the δ -counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the π N scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger–Treiman relation, the pion–nucleon sigma term and the extrapolation on…
Chiral perturbation theory: Introduction and recent results in the one-nucleon sector
2009
We provide an introduction to the basic concepts of chiral perturbation theory and discuss some recent developments in the manifestly Lorentz-invariant formulation of the one-nucleon sector.
Towards a determination of the chiral couplings at NLO in 1/N-C: L-8(r)(μ) and C-38(r)(μ)
2007
14 pages.-- ISI Article Identifier: 000244120200039.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0610290