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

Journal Article · Mon Apr 28 00:00:00 EDT 2014 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP04(2014)162 · OSTI ID:1128720

Lang, C. B. ^[1]; Leskovec, Luka ^[2]; Mohler, Daniel ^[3]; Prelovsek, Sasa ^[4]

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1. Univ. of Graz, Graz (Austria)
2. Jozef Stefan Institute, Ljubljana (Slovenia)
3. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
4. Jozef Stefan Institute, Ljubljana (Slovenia); Univ. of Ljubljana, Ljubljana (Slovenia)

The light axial-vector resonances $$a_1(1260)$$ and $$b_1(1235)$$ are explored in Nf=2 lattice QCD by simulating the corresponding scattering channels $$\rho\pi$$ and $$\omega\pi$$. Interpolating fields $$\bar{q} q$$ and $$\rho\pi$$ or $$\omega\pi$$ are used to extract the s-wave phase shifts for the first time. The $$\rho$$ and $$\omega$$ are treated as stable and we argue that this is justified in the considered energy range and for our parameters $$m_\pi\simeq 266~$$MeV and $$L\simeq 2~$$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 $$m_{a1}^{res}=1.435(53)(^{+0}_{-109})$$ GeV compared to $$m_{a1}^{exp}=1.230(40)$$ GeV. The $$a_1$$ width $$\Gamma_{a1}(s)=g^2 p/s$$ is parametrized in terms of the coupling and we obtain $$g_{a_1\rho\pi}=1.71(39)$$ GeV compared to $$g_{a_1\rho\pi}^{exp}=1.35(30)$$ GeV derived from $$\Gamma_{a1}^{exp}=425(175)$$ MeV. In the $$b_1$$ channel, we find energy levels related to $$\pi(0)\omega(0)$$ and $$b_1(1235)$$, and the lowest level is found at $$E_1 \gtrsim m_\omega+m_\pi$$ but is within uncertainty also compatible with an attractive interaction. Lastly, assuming the coupling $$g_{b_1\omega\pi}$$ extracted from the experimental width we estimate $$m_{b_1}^{res}=1.414(36)(^{+0}_{-83})$$.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: AC02-07CH11359
• OSTI ID: 1128720
• Report Number(s): FERMILAB-PUB--14-002-T; arXiv eprint number arXiv:1401.2088
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2014; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English