Search results for "dispersion relation"
showing 10 items of 140 documents
ϒ photoproduction on the proton at the Electron-Ion Collider
2020
We present a dispersive analysis with the aim to extract the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ scattering length from $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}p$ experiments. In this framework, the imaginary part of the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ forward scattering amplitude is obtained from $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}p$ cross section measurements and is constrained at high energies from existing HERA and LHC data. Its real part is calculated through a once-subtracted dispersion relation, and the subtraction constant is proportional to the $\mathrm{\ensuremath{\…
Dispersion theoretical analysis of the nucleon spin polarizabilities
1999
The spin polarizabilities of the nucleon have been calculated from pion photoproduction data using forward dispersion relations. The feasibility of an experimental determination of these structure constants is discussed by focusing on polarization observables of the reaction \( \vec{\gamma }\vec{p} \to \gamma p \)→ γ p.
Unitarity, analyticity and duality constraints in η and π photoproduction
2019
We report an update of the isobar model EtaMAID. A new approach is proposed to avoid double counting in the overlap region of Regge and resonances. Dispersion relation is applied on top of the isobar model, and both models describe the data equally well. Application of these ideas to pion photoproduction is discussed.
Dispersive analysis of the γ*γ*→ππ process
2020
We present a dispersive analysis of the double-virtual photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this process is very sensitive to hadronic final-state interaction. For the $s$-wave, we use a coupled-channel $\ensuremath{\pi}\ensuremath{\pi}$, $K\overline{K}$ analysis which allows for a simultaneous description of both ${f}_{0}(500)$ and ${f}_{0}(980)$ resonances. For higher energies, ${f}_{2}(1270)$ shows up as a dominant structure which we approximate by a single-channel $\ensuremath{\pi}\ensuremath{\pi}$ rescattering in the $d$-wave. In the dispersive approach, the latter requires taking into account $t$- and $u$-channel vector-meson exchange left-hand cuts …
Reduced hadronic uncertainty in the determination of $V_{ud}$
2018
We analyze the universal radiative correction $\Delta_R^V$ to neutron and superallowed nuclear $\beta$ decay by expressing the hadronic $\gamma W$-box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the $\gamma W$ interference structure function $F_3^{(0)}$. By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of $\Delta_R^V = 0.02467(22)$, wherein the hadronic uncertainty is reduced. Assuming other Standard Model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of $|V_{ud}| = 0.97366(15)$, raising tension with …
Higher-order proton structure corrections to the Lamb shift in muonic hydrogen
2011
The recent conundrum with the proton charge radius inspires reconsideration of the corrections that enter into determinations of the proton size. We study the two-photon proton-structure corrections, with special consideration of the non-pole subtraction term in the dispersion relation, and using fits to modern data to evaluate the energy contributions. We find that individual contributions change more than the total, and present results with error estimates.
Data-driven dispersive analysis of the ππ and πK scattering
2021
We present a data-driven analysis of the resonant $S$-wave $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K\ensuremath{\rightarrow}\ensuremath{\pi}K$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $\ensuremath{\pi}\ensuremath{\pi}$ scattering we present both a single- and a coupled-channel analysis by including additionally the $K\overline{K}$ channel. For the latter the central result is the Omn\`es m…
Bulk-plasmon dispersion relations in metals
1991
En utilisant une technique de la regle de somme dans l'approximation de la phase aleatoire etendue, on examine la relation de dispersion des plasmons en volume, en introduisant les effets de la correlation et de l'echange dans le modele du jellium. Les resultats obtenus sont compares aux resultats experimentaux. On souligne le role cle que jouent les effets de la correlation et de l'echange dans l'amelioration de l'accord entre la theorie et l'experience. On calcule egalement la polarisabilite statique en fonction de 9. Les formules peuvent etre facilement modifiees pour incorporer les effets de la structure de bandes (a travers une masse effective electronique intrabande) et les effets de …
Comments on the dispersion relation method to vector–vector interaction
2019
We study in detail the method proposed recently to study the vector-vector interaction using the $N/D$ method and dispersion relations, which concludes that, while for $J=0$, one finds bound states, in the case of $J=2$, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for $N$ and $D$ and a subtracted dispersion relation for $D$ is used, with subtractions made up to a polynomial of second degree in $s-s_\mathrm{th}$, matching the expression to $1-VG$ at threshold. We study this in detail for the $\rho - \rho$ interaction and to see the convergence of the method we make an extra subtraction matching $1-VG$ at threshold…
Integrated photoabsorption strength and sum rules for a bound Dirac particle
1985
Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a…