Search results for "dispersion relation"
showing 10 items of 140 documents
Anomalous magnetic moment of the muon in a dispersive approach
2014
We present a new general dispersive formalism for evaluating the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. In the suggested approach, this correction is related to the imaginary part of the muon's electromagnetic vertex function. The latter may be directly related to measurable hadronic processes by means of unitarity and analyticity. As a test we apply the introduced formalism to the case of meson pole exchanges and find agreement with the direct two-loop calculation.
Dispersive analysis of the γγ⁎ → ππ process
2019
Abstract We present a theoretical study of the γ γ ⁎ → π + π − , π 0 π 0 processes from the threshold through the f 2 ( 1270 ) region in the ππ invariant mass. We adopt the Omnes representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the f 0 ( 980 ) resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.
Dispersion relation formalism for virtual Compton scattering and the generalized polarizabilities of the nucleon
2000
A dispersion relation formalism for the virtual Compton scattering (VCS) reaction on the proton is presented, which for the first time allows a dispersive evaluation of 4 generalized polarizabilities at a four-momentum transfer $Q^2 \leq$ 0.5 GeV$^2$. The dispersive integrals are calculated using a state-of-the-art pion photo- and electroproduction analysis. The dispersion formalism provides a new tool to analyze VCS experiments above pion threshold, thus increasing the sensitivity to the generalized polarizabilities of the nucleon.
Nucleon strangeness and unitarity
1996
The strange-quark vector current form factors of the nucleon are analyzed within the framework of dispersion relations. Particular attention is paid to contributions made by $K\bar{K}$ intermediate states to the form factor spectral functions. It is shown that, when the $K\bar{K}\to N\bar{N}$ amplitude is evaluated in the Born approximation, the $K\bar{K}$ contributions are identical to those arising from a one-loop calculation and entail a serious violation of unitarity. The mean square strangeness radius and magnetic moment are evaluated by imposing unitarity bounds on the kaon-nucleon partial wave amplitudes. The impact of including the kaon's form factor in the dispersion integrals is a…
Dispersion relation analysis of neutral pion photoproduction and electroproduction at threshold
2002
Neutral pion photoproduction and electroproduction at threshold is analyzed in the framework of dispersion relations. For this purpose, we evaluate the real threshold amplitudes in terms of Born contributions and dispersion integrals determined by the imaginary parts of the multipoles of the unitary isobar model (MAID) and the phenomenological partial-wave analysis (SAID). The results show considerable cancellations between Born terms and resonance contributions. Good agreement with the data is found for photoproduction. While our dispersion analysis suggests considerable discrepancies for electroproduction, the present state of the experimental multipole analysis at finite ${Q}^{2}$ does n…
Virtual Compton scattering and the generalized polarizabilities of the proton atQ2=0.92and 1.76 GeV2
2012
Virtual Compton Scattering (VCS) on the proton has been studied at Jefferson Lab using the exclusive photon electroproduction reaction (e p --> e p gamma). This paper gives a detailed account of the analysis which has led to the determination of the structure functions P{sub LL}-P{sub TT}/epsilon and P{sub LT}, and the electric and magnetic generalized polarizabilities (GPs) alpha{sub E}(Q{sup 2}) and beta{sub M}(Q{sup 2}) at values of the four-momentum transfer squared Q{sup 2} = 0.92 and 1.76 GeV{sup 2}. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q{sup 2}-…
Sterile neutrinos with altered dispersion relations revisited
2020
In this paper we investigate neutrino oscillations with altered dispersion relations in the presence of sterile neutrinos. Modified dispersion relations represent an agnostic way to parameterize new physics. Models of this type have been suggested to explain global neutrino oscillation data, including deviations from the standard three-neutrino paradigm as observed by a few experiments. We show that, unfortunately, in this type of models new tensions arise turning them incompatible with global data.
Role of correlated two-pion exchange in $K^+ N$ scattering
1995
A dynamical model for S-- and P--wave correlated $2 \pi$ (and $K \bar K$) exchange between a kaon and a nucleon is presented, starting from corresponding $N \bar N \rightarrow K \bar K$ amplitudes in the pseudophysical region, which have been constructed from nucleon, $\Delta$--isobar and hyperon ($\Lambda$, $\Sigma$) exchange Born terms and a realistic meson exchange model of the $\pi \pi \rightarrow K \bar K$ and $K \bar K \rightarrow K \bar K$ amplitude. The contribution in the s--channel is then obtained by performing a dispersion relation over the unitarity cut. In the $\rho$--channel, considerable ambiguities exist, depending on how the dispersion integral is performed. Our model, sup…
Electromagnetic investigations of nucleon resonances and sum rules
2000
Abstract Pion photoproduction is analyzed by dispersion relations at fixed t . The results for s-wave production at threshold and p-wave production in the Δ(1232) resonance region are compared to the experimental data. These investigations are extended to the case of pion electroproduction in the framework of the Unitary Isobar Model. Recent developments to explore the spin structure of the nucleon by double-polarization observables are summarized, and new results for the spin polarizability, the Gerasimov-Drell-Hearn and related sum rules are presented.
The Pion Velocity in Dense Skyrmion Matter
2003
We have developed a field theory formalism to calculate $in$-$medium$ properties of hadrons within a unified approach that exploits a single Lagrangian to describe simultaneously both matter background and meson fluctuations. In this paper we discuss the consequences on physical observables of a possible phase transition of hadronic matter taking place in the chiral limit. We pay special attention to the pion velocity $v_\pi$, which controls, through a dispersion relation, the pion propagation in the hadronic medium. The $v_\pi$ is defined in terms of parameters related to the matrix element in matter of the axial-vector current, namely, the in-medium pion decay constants, $f_t$ and $f_s$. …