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 review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the ...determination of the light-quark masses, the form factor \f_+(0)\, arising in the semileptonic \K \rightarrow \pi \ transition at zero momentum transfer, as well as the decay constant ratio \f_K/f_\pi \ and its consequences for the CKM matrix elements \V_{us}\ and \V_{ud}\. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of \SU(2)_L\times SU(2)_R\ and \SU(3)_L\times SU(3)_R\ Chiral Perturbation Theory. We review the determination of the \B_K\ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for \m_c\ and \m_b\ (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant \\alpha _s\.
We demonstrate that near the threshold, the pi pi scattering amplitude contains a pole with the quantum numbers of the vacuum--commonly referred to as the sigma--and determine its mass and width ...within small uncertainties. Our derivation does not involve models or parametrizations but relies on a straightforward calculation based on the Roy equation for the isoscalar S wave.
We review lattice results related to pion, kaon,
D
- and
B
-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the ...determination of the light-quark masses, the form factor
f
+
(
0
)
, arising in the semileptonic
K
→
π
transition at zero momentum transfer, as well as the decay constant ratio
f
K
/
f
π
and its consequences for the CKM matrix elements
V
u
s
and
V
u
d
. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of
S
U
(
2
)
L
×
S
U
(
2
)
R
and
S
U
(
3
)
L
×
S
U
(
3
)
R
Chiral Perturbation Theory. We review the determination of the
B
K
parameter of neutral kaon mixing as well as the additional four
B
parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for
m
c
and
m
b
(also new compared to the previous review), as well as those for
D
- and
B
-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant
α
s
.
We review lattice results relevant for pion and kaon physics with the aim of making them easily accessible to the particle physics community. Specifically, we review the determination of the ...light-quark masses, the form factor
f
+
(0), relevant for the semileptonic
K
→
π
transition at zero momentum transfer as well as the ratio
f
K
/
f
π
of decay constants and discuss the consequences for the elements
V
us
and
V
ud
of the CKM matrix. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)
L
×SU(2)
R
and SU(3)
L
×SU(3)
R
Chiral Perturbation Theory and review the determination of the
B
K
parameter of neutral kaon mixing. We introduce quality criteria and use these when forming averages. Although subjective and imperfect, these criteria may help the reader to judge different aspects of current lattice computations. Our main results are summarized in Sect. 1.2, but we stress the importance of the detailed discussion that underlies these results and constitutes the bulk of the present review.
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.
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