Axial resonances a 1(1260), b 1(1235) and their decays from the lattice

  • C.B. Lang
  • Luka LeskovecEmail author
  • Daniel Mohler
  • Sasa Prelovsek
Open Access


The light axial-vector resonances a 1(1260) and b 1(1235) are explored in N f = 2 lattice QCD by simulating the corresponding scattering channels ρπ and ωπ. Interpolating fields \( \overline{q}q \) and ρπ or ωπ are used to extract the s-wave phase shifts for the first time. The ρ and ω are treated as stable and we argue that this is justified in the considered energy range and for our parameters m π ⋍ 266 MeV and L ⋍ 2 fm. We neglect other channels that would be open when using physical masses in continuum. Assuming a resonance interpretation a Breit-Wigner fit to the phase shift gives the a 1(1260) resonance mass \( m_{{{a_1}}}^{\mathrm{res}}=1.435\left( {53} \right)\left( {_{-109}^{+0 }} \right) \) compared to \( m_{{{a_1}}}^{\exp }=1.230\left( {40} \right) \) GeV. The a 1 width \( {\varGamma_{{{a_1}}}}(s)\equiv {{{{g^2}p}} \left/ {s} \right.} \) is parametrized in terms of the coupling and we obtain \( {g_a}{{_{{_1}}}_{\rho}}_{\pi }=1.71\left( {39} \right) \) GeV compared to \( g_{{{a_1}\rho \pi}}^{\exp }=1.35\left( {30} \right) \) GeV derived from \( \Gamma_{{{a_1}}}^{\exp }=425\left( {175} \right) \) MeV. In the b 1 channel, we find energy levels related to π(0)ω(0) and b 1(1235), and the lowest level is found at E 1m ω + m π but is within uncertainty also compatible with an attractive interaction. Assuming the coupling \( {g_{{{b_1}\omega \pi }}} \) extracted from the experimental width we estimate \( m_{{{b_1}}}^{res }=1.414\left( {36} \right)\left( {_{-83}^{+0 }} \right) \)


Lattice QCD QCD 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • C.B. Lang
    • 1
  • Luka Leskovec
    • 2
    Email author
  • Daniel Mohler
    • 3
  • Sasa Prelovsek
    • 2
    • 4
  1. 1.Institute of PhysicsUniversity of GrazGrazAustria
  2. 2.Jozef Stefan InstituteLjubljanaSlovenia
  3. 3.Fermi National Accelerator LaboratoryBataviaU.S.A.
  4. 4.Department of PhysicsUniversity of LjubljanaLjubljanaSlovenia

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