Journal
PHYSICAL REVIEW D
Volume 89, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.89.054008
Keywords
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Funding
- BMBF
- A.v. Humboldt foundation
- Fundamental Research Funds for the Central Universities
- National Natural Science Foundation of China [11005007]
- New Century Excellent Talents in University Program of Ministry of Education of China [NCET-10-0029]
- DFG Cluster of Excellence Origin and Structure of the Universe,
- DFG
- NSFC through the Sino-German CRC 110 Symmetries and Emergence of Structure in QCD.
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The Bethe-Salpeter equation in unitarized chiral perturbation theory is usually solved with the so-called onshell approximation. The underlying argument is that the off-shell effects can be absorbed by the corresponding coupling constants and physical masses, which has been corroborated by the success of unitarized chiral perturbation theory in describing a variety of physical phenomena. Such an approximation needs to be scrutinized when applied to study the light-quark mass evolution of physical observables, as routinely performed nowadays. In the present work, we propose to solve the Bethe-Salpeter equation with the full off-shell terms of the chiral potentials and apply this formalism to the description of the latest n(f) = 2 + 1 lattice QCD (LQCD) data on the scattering lengths of Nambu-Goldstone bosons off D mesons. It is shown that the LQCD data can be better described in this formalism than in the widely used on-shell approximation. On the other hand, no qualitative difference between the on-shell and off-shell approaches is observed for the light-quark mass evolution of the scattering lengths, given the limited LQCD data and their relatively large uncertainties. We also show that the light-quark mass dependence of the D-s0* (2317) remains essentially the same in both approaches.
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