Relativistic effects in the pionium lifetime

Abstract

The pionium decay width is evaluated in the framework of chiral perturbation theory and the relativistic bound state formalism of constraint theory. Corrections of order O(α) are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses. Strong interaction corrections from second-order perturbation theory of the bound state wave equation are found to be of the order of 0.4%. Electromagnetic radiative corrections, due to pion-photon interactions, are estimated to be of the order of -0.1%. Electromagnetic mass shift insertions in internal propagators produce a correction of the order of 0.3%. The correction due to the passage from the strong interaction scattering amplitude evaluated with the mass parameter fixed at the charged pion mass to the amplitude evaluated with the mass parameter fixed at the neutral pion mass is found to be of the order of 6.4%.

47 pages, 4 figures, Latex, calls the FEYNMAN macropackage for drawing figures

References in corpus (4)

• A sum rule approach to the violation of Dashen's theorem
• Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to $\pi \pi$ scattering
• The extraction of hadronic parameters from experiments on pionium
• ππ, Kπand πN potential scattering and a prediction of a narrow σmeson resonance

Cited by in corpus (37)

• ππscattering
• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Decays of the pi+ pi- atom
• Electromagnetic corrections in hadronic processes
• Light Fermion Finite Mass Effects in Non-relativistic Bound States
• pi(-)p atom in ChPT: strong energy-level shift
• Aspects of meson-baryon scattering in three- and two-flavor chiral perturbation theory
• Integrating out strange quarks in ChPT
• On the Lifetime of the pi+pi- Atom
• Numerical analysis of the pi+pi- atom lifetime in ChPT
• Decay widths and energy shifts of pi pi and pi K atoms
• (Pi+Pi-) Atom in Chiral Perturbation Theory
• Effective Field Theory Approach to Pionium
• Isospin breaking corrections to low-energy pi-K scattering
• The pionium lifetime in generalized chiral perturbation theory
• Non-Relativistic Pion Interactions and the Pionium Lifetime
• Electromagnetic Corrections to Charged Pion Scattering at Low Energies
• Integrating out strange quarks in ChPT: terms at order p^6
• Detection of ${\pi }^{+}{\pi }^{-}$atoms with the DIRAC spectrometer at CERN
• Electromagnetic low-energy constants in ChPT
• Partial wave analysis of pbar-p to Lambdabar-Lambda
• Spectra and decays of pi pi and pi K atoms
• Relativistic corrections to the Pionium Lifetime
• Isospin violation in pion-kaon scattering
• Hadronic Atoms
• Effective Lagrangians in bound state calculations
• Hadronic potentials from effective field theories
• Isospin-Breaking quark condensates in Chiral Perturbation Theory
• On the question of current conservation for the Two-Body Dirac equations of constraint theory
• Exclusive photon-fusion production of even-spin resonances and exotic QED atoms in high-energy hadron collisions
• Size of Isospin Breaking in Charged K(L4) Decay
• First measurement of a long-lived ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory
• Energy and decay width of the pi-K atom
• Integrating out the heaviest quark in N--flavour ChPT
• Pionium lifetime and ππscattering lengths in generalized chiral perurbation theory
• Possible manifestation of the 2p pionium in particle physics processes