Effective Field Theory Approach to Pionium

Abstract

The various dynamical scales below the pion mass involved in ${\pi }^{+}$ ${\pi }^{-}$ atoms are sequentially integrated out using non-relativistic effective field theory techniques. This allows us to systematically organise the corrections to the energy levels and decay width. We present our results in terms of a single unknown constant which may be obtained by matching to the Chiral Lagrangian with electromagnetic interactions at two loops.

24 pages, 4 figures, uses feynmf.sty and feynmf.mf, minor corrections in a few formulas, the text and references

References in corpus (2)

• On the Lifetime of the pi+pi- Atom
• Relativistic corrections to the Pionium Lifetime

Cited by in corpus (26)

• ππscattering
• The QCD Potential at $O(1/m)$
• Ground-state energy of pionic hydrogen to one loop
• Cusps in K --> 3 pi decays
• The QCD potential at O(1/m^2): Complete spin-dependent and spin-independent result
• Kaon-nucleon scattering lengths from kaonic deuterium experiments
• Decays of the pi+ pi- atom
• The Threshold t-tbar Cross Section at NNLL Order
• Poincare' invariance constraints on NRQCD and potential NRQCD
• Non-resonant and electroweak NNLO correction to the $e^{+}{e}^{-}$ top anti-top threshold
• Decay widths and energy shifts of pi pi and pi K atoms
• Leading Chiral Logarithms to the Hyperfine Splitting of the Hydrogen and Muonic Hydrogen
• The $\sqrt{mΛ_{QCD}$ scale in heavy quarkonium
• Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD
• Electromagnetic Corrections to Charged Pion Scattering at Low Energies
• The nucleon-nucleon potential beyond the static approximation
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Hadronic Atoms
• Threshold singularities, dispersion relations and fixed-order perturbative calculations
• Hadronic potentials from effective field theories
• Breit Hamiltonian and QED Effects for Spinless Particles
• Energy and decay width of the pi-K atom
• Kaonic atoms in QCD
• Momentum Representation of Coulomb Wave Functions and Level Shifts in Bottomonium due to Charm Effects
• Kaon-Nucleon scattering lengths from the experiments on kaonic hydrogen and kaonic deuterium
• Electromagnetic Corrections to Low-Energy pi-pi Scattering