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When hadrons become unstable: a novel type of non-analyticity in chiral extrapolations.

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http://dx.doi.org/10.1016/j.physletb.2011.08.022
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2011-09-20
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Elsevier Science BV
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Abstract
Hadron masses show a specific dependence on the quark masses. Therefore, the variation of these masses can cause a resonance in a hadronic scattering amplitude to become a bound state. Consequently, the amplitude exhibits a non analytic behavior at this transition. Crossed amplitudes, where the resonance can be exchanged in the t-channel, can be shown to exhibit the same phenomenon by s --> t analytic continuation. This entails possible kinks in lattice quark-mass extrapolations needed to compute hadronic observables.
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© 2011 Elsevier B.V. All rights reserved.We thank Stephan Durr and Akaki Rusetsky for useful discussions. This work was supported in part by grants provided by the HGF to the virtual institute "Spin and strong QCD" (VH-VI-231), the DFG (SFB/TR 16) and the EU I3HP "Study of Strongly Interacting Matter" under the Seventh Framework Program of the EU, FPA 2008-00592, 2007-29115-E, FIS2008-01323 (Spain) and 227431, HadronPhysics2 (EU). F.J.L.E. thanks the members of the Nuclear Theory Center at Forschungszentrum Julich for their hospitality during this work. U.G.M. also thanks the BMBF for support (Grant No. 06BN9006).
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