Electromagnetic Mass Difference Of Pions Research Articles

Contribution of higher meson resonances to the electromagnetic pion-mass difference

Some modifications of the formula for calculating the electromagnetic pion-mass difference are proposed on the basis of the chiral-symmetry-restoration phenomenon at high energies and the operator-product expansion of quark densities for vector (ρ) and axial-vector (a 1) meson fields. All calculations are performed through taking into account higher meson resonances in the vector and axial-vector channels. It is shown that the inclusion of only the first ρ 0 and a 1 radial excitations improves the results of the calculation for the electromagnetic pion-mass difference in relation to the known ones. The electromagnetic ρ-and a 1-meson decay constants and the constant L 10 of the effective chiral Lagrangian are estimated with the aid of the generalized Weinberg sum rules.

Chiral sum rules and duality in QCD

The ALEPH data on the vector and axial-vector spectral functions, extracted from tau-lepton decays, is used in order to test local and global duality, as well as a set of four QCD chiral sum rules. These are the Das-Mathur-Okubo sum rule, the first and second Weinberg sum rules, and a relation for the electromagnetic pion mass difference. We find these sum rules to be poorly saturated, even when the upper limit in the dispersion integrals is as high as 3 GeV 2 . Since perturbative QCD, plus condensates, is expected to be valid for |q 2|≥ O(1 GeV 2) in the whole complex energy plane, except in the vicinity of the right hand cut, we propose a modified set of sum rules with weight factors that vanish at the end of the integration range on the real axis. These sum rules are found to be precociously saturated by the data to a remarkable extent. As a byproduct, we extract for the low energy renormalization constant L ̄ 10 the value −4 L ̄ 10=2.43×10 −2 , to be compared with the standard value −4 L ̄ 10=(2.73±0.12)×10 −2 . This in turn leads to a pion polarizability α E=3.7×10 −4 fm 3 .

Electromagnetic mass difference of pions at low temperature

We compute low temperature corrections to the electromagnetic mass difference of pions in the chiral limit. The computation is done in a model independent way in the framework of chiral perturbation theory, using the background field method and the hard thermal loop approximation. We also generalize at low temperature the sum rule of Das et al. We find that the mass difference between the charged and neutral pions decreases at low temperature $T$ with respect to the T=0 value. This is so in spite of the fact that charged particles always get a thermal correction to their masses of order $\sim eT$, where $e$ is the gauge coupling constant. Our result can be understood as a consequence of the tendency towards chiral symmetry restoration at finite temperature.

THE ELECTROMAGNETIC MASS DIFFERENCE OF PIONS FROM QCD

It is shown that the two point functions of definite class can be calculated, at small spacelike momenta, as subtraction constants in the Borel transformed QCD sum rules. Using the results of current algebra and PCAC, we obtain three different sum rules for determination of the electromagnetic mass difference of pions. The result is in a good agreement with experiment, and confirms the standard value for the four-quark vacuum condensate.

The role of resonances in chiral perturbation theory

The strong interactions of low-lying meson resonances (spin ⩽ 1) with the octet of pseudoscalar mesons ( π, K, η) are considered to lowest order in the derivative expansion of chiral SU(3). The resonance contributions to the coupling constants of the O( p 4) effective chiral lagrangian involving pseudoscalar fields only are determined. These low-energy coupling constants are found to be dominated by the resonance contributions. Although we do not treat the vector and axial-vector mesons as gauge bosons of local chiral symmetry, vector meson dominance emerges as a prominent result of our analysis. As a further application of chiral resonance couplings, we calculate the electromagnetic pion mass difference to lowest order in chiral perturbation theory with explicit resonance fields.

QCD sum rules versus experiment

We show the compatibility of Shifman, Vainshtein and Zakharov (SVZ) sum rules with the sum rules involving the electro-magnetic mass difference of pions and the axial form factor in radiative π± decay. In spite of good agreement between them, QCD sum rules are unable to explain clearly the experimental data of τ-decay in the axial channel.

π +−π 0 mass difference at finite temperature

The electromagnetic mass difference of pions at finite temperature is computed. The finite temperature contribution to δm 2 π ≡ m 2 π + − m 2 π 0 is obtained to be παT 2, neglecting the corrections due to the ϱ and A 1 mesons. It has the same sign as the zero temperature value and is comparable to it in magnitude around T ≈ 200 MeV. The calculation is also done in case of supersymmetric QCD where it is known that at T = 0 δm 2 π = 0. The results may have implications for cosmology and for relativistic heavy ion collisions.

The electromagnetic mass difference of pions from asymptotic QCD

We show how the asymptotic behaviour of an analytic amplitude can yield information on the amplitude at small space-like momenta. Applying this to QCD two-point functions, we are able to obtain low energy parameters without using resonance saturation. In the special case considered here, we have calculated the electromagnetic mass difference of pions using only the asymptotic QCD amplitude. The result, in very good agreement with experiment is\(\Delta m_\pi = 5.3 \pm 1.5MeV.\)

Current-algebra calculation of the electromagnetic mass difference of pions and quantum chromodynamics

The current-algebra calculation of the pion electromagnetic mass difference is reexamined in the light of quantum chromodynamics. The old analysis cannot be upheld because of the failure of the second Weinberg sum rule. After a straightforward modification based on Dashen's theorem we obtain a mass difference close to the experimental value.

Mass of the up quark

It is shown that the theoretical uncertainty connected with the PCAC formulas that relate quark masses to the pseudo-scalar meson masses, decay constants, wave function renormalization constants, and electromagnetic self-energy corrections permits the choice of a massless up quark without contradicting experiment at present. This choice, however, entails a sizable correction to Dashen's formula for the electromagnetic mass difference of pions and kaons.

Electromagnetic mass difference of pions and the radial excitations of the ρ-A1-π system

Electromagnetic mass difference of pions and the radial excitations of the ρ-A1-π system

Electromagnetic-mass difference of pions in unified gauge field theories

In the past few years several indications have been given on the presence of a logarithmically divergent term in the electromagnetic-mass shift of hard pions (1.2). Even in the case of soft pions the model-dependent second Weinberg sum rule (WSR) had to be assumed for the convergence (~). There is a possibility that these problems can be covered by quantum gravity (4). There exists, however, another natural way out and this is the cancellation of the electromagnetic and weak divergences in unified gauge field theories (for a list see (s)). In ref. (6) it has been shown that in the soft pion mass difference (PMD) the divergences coming from y and Z exchanges cancel out without using the second WSR. In the present paper we examine whether this was only a property of the Weinberg-Salam model (7.s). The understanding of the hard PMD is much more difficult due to our very limited knowledge on the scalar-meson-pion coupling. However, if we assume that the scalar mesons are decoupled from the pions, then only the y, W, Z contributions come in. In this approximation, keeping the hard pion and all the other contributions in the longitudinal spectral function and taking soft external pions, we get logarithmic and quadratic divergences to the mass shift. The logarithmic divergences can always be eliminated by the second WSR or its modifications. If the current-pion scattering scales and no operator Sehwinger term exists, then quadratic divergences are not expected (9) so that by treating all the hard-pion contributions they would cancel. In several models the choice of a fixed Weinberg angle may lead to a compensation, as is shown below. I t is also possible that the quadratic divergence is automatically removed in the complete hard PMD.

Finite electromagnetic mass difference of pions and tensor gravity

It is shown how the tensor gravity makes the electromagnetic mass splitting of pions finite without using any lagrangian model for the strong interaction. The mass splitting is sensitive to the spectral-function sum rules. A finite mass splitting does not lead to a unique modification of the second Weinberg sum rule. For the electromagnetic mass difference of pions good values are obtained by suitably chosen input data.

Electromagnetic mass difference of pions in the presence of scalar gravity

The electromagnetic mass difference of pions is calculated in gravity-modified quantum electrodynamics to second order of the electromagnetic interaction. The result is 3.9MeV which lies 0.7 MeV lower than the experimental value 4.6 MeV. We assume the vierbein description of the gravity.

An effective charge-dependent two-nucleon potential

An effective charge-dependent two-nucleon potential with a Yukawa radial dependence is obtained by a least-squares fit with the charge-dependent potential arising from the ρ-meson electromagnetic mass difference. The observed discrepancy between the neutron-proton and proton-proton scattering lengths and effective ranges in the singlet S-state is examined in terms of this potential. The finite size of nucleons, magnetic interactions, the electromagnetic mass difference of pions, Δπ = π +−π°, and the isospin mixing of various mesons contribute to the observed difference in scattering lengths by at most 50 %. The Coulomb and vacuum polarization potential corrected effective range for the proton-proton interaction shows also a small discrepancy with the neutron-proton effective range. The remaining part of these differences is attributed, in both cases, to the effective charge-dependent potential. In order to obtain agreement between neutron-proton and proton-proton scattering lengths and effective ranges we find Δρ = ρ +−ρ 0 = −2.8 to −6.1 MeV.

Virtual Photon-Photon Annihilation and the Pion Mass Difference

On the basis of current algebra and partial conservation of axial-vector current, a sum rule is derived which relates the electromagnetic pion mass difference to the differential cross section for charged-pion pair production near the threshold through virtual photon-photon annihilation in electron-electron (positron) collisions.

Theπ+−π0Mass Difference Using Gravity-Modified Hadron Electrodynamics

Computations of gravity-modified hadron electrodynamics are performed using nonpolynomial Lagrangian field-theory techniques. In particular, it is shown that the infinity encountered in a standard Lagrangian approach to the electromagnetic mass difference of pions is removed. The numerical value obtained for the mass shift is a little high, but consideration of the effects of tensor-meson dominance of gravity leads to a closer agreement with experiment.

Charge-dependent effects and low-energy nucleon-nucleon scattering

Abstract The observed discrepancy between the neutron-proton and proton-proton scattering lengths in the singlet state is examined in terms of short-range electromagnetic corrections to the two-nucleon potential. The finite size of nucleons, the magnetic interactions of neutron- proton, proton-proton systems, the electromagnetic mass difference of pions, Δm ( π ) = m ( π ∓)— m ( π °), and the isospin mixing of various mesons contribute to the observed difference at most 50 %. The remaining part is attributed to the very short-range charge-dependent potential stemming from the ϱ-meson exchange. In order to eliminate the discrepancy between neutron- proton and proton-proton scattering lengths we obtain Δm ( ρ ) = m ( ρ ∓)− m ( ρ ° ) = −1.4 to −3.1 MeV.

Effects of a Finite ρ Width on the Electromagnetic Mass Difference of Pions

Effects of a Finite ρ Width on the Electromagnetic Mass Difference of Pions

Sum rules and the electromagnetic mass difference of pions

Using the algebra of currents, we show that the electromagnetic pion mass-difference diverges in the soft-pion limit, if the usual spectral sum rules are assumed. We propose an altered sum rule which makes the result finite and in close agreement with experiment.