The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and ...gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to
m
QED
p
-
n
=
0.58
±
0.16
MeV
.
The Cottingham formula expresses the electromagnetic part of the mass of a particle in terms of the virtual Compton scattering amplitude. At large photon momenta, this amplitude is dominated by short ...distance singularities associated with operators of spin 0 and spin 2. In the difference between proton and neutron, chiral symmetry suppresses the spin 0 term. Although the angular integration removes the spin 2 singularities altogether, the various pieces occurring in the standard decomposition of the Cottingham formula do pick up such contributions. These approach asymptotics extremely slowly because the relevant Wilson coefficients only fall off logarithmically. We rewrite the formula in such a way that the leading spin 2 contributions are avoided ab initio. Using a sum rule that follows from Reggeon dominance, the numerical evaluation of the e.m. part of the mass difference between proton and neutron yields mQED=0.58±0.16MeV. The result indicates that the inelastic contributions are small compared to the elastic ones.
We study the scattering of the light-flavor pseudoscalar mesons (
π
,
K
,
η
) off the ground-state charmed mesons (
D
,
D
s
) within chiral effective field theory. The recent lattice simulation ...results on various scattering lengths and the finite-volume spectra both in the moving and center-of-mass frames, most of which are obtained at unphysical meson masses, are used to constrain the free parameters in our theory. Explicit formulas to include the
S
- and
P
-wave mixing to determine the finite-volume energy levels are provided. After a successful reproduction of the lattice data, we perform a chiral extrapolation to predict the quantities with physical meson masses, including phase shifts, inelasticities, resonance pole positions and the corresponding residues from the scattering of the light pseudoscalar and charmed mesons.
An explicit expression for the finite-volume energy shift of shallow three-body bound states for nonidentical particles is obtained in the unitary limit. The inclusion of the higher partial waves is ...considered. To this end, the method of Meißner, Rìos, and Rusetsky Phys. Rev. Lett. 114, 091602 (2015) is generalized for the case of unequal masses and arbitrary angular momenta. It is shown that in the S-wave and in the equal-mass limit, the result from Meißner, Rìos, and Rusetsky is reproduced.
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the ...Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.
We investigate the a0(980) resonance within chiral effective field theory through a three-coupled-channel analysis, namely, πη, KK¯, and πη′. A global fit to recent lattice finite-volume energy ...levels from πη scattering and relevant experimental data on a πη event distribution and the γγ→πη cross section is performed. Both the leading and next-to-leading-order analyses lead to similar and successful descriptions of the finite-volume energy levels and the experimental data. However, these two different analyses yield different πη scattering phase shifts for the physical masses for the π, K, η, and η′ mesons. The inelasticities, the pole positions in the complex energy plane, and their residues are calculated both for unphysical and physical meson masses.
Cottingham formula and nucleon polarisabilities Gasser, J.; Hoferichter, M.; Leutwyler, H. ...
The European physical journal. C, Particles and fields,
08/2015, Volume:
75, Issue:
8
Journal Article
Peer reviewed
Open access
The difference between the electromagnetic self-energies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the ...electroproduction cross sections – provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment.
We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the
T
-matrix. In ...a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the
T
-matrix created by this resummation. We test this alternative expansion for several model potentials and observe good convergence.
In this work, we present an explicit form of the Lüscher equation and consider the construction of the operators in different irreducible representations for the case of scattering of two vector ...particles. The formalism is applied to scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.
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