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Title Determination of crossing-symmetric p p scattering amplitudes and the quark mass evolution of the s constrained by lattice QCD
Authors Arkaitz Rodas, Jozef Dudek, Robert Edwards
JLAB number JLAB-THY-23-3791
LANL number (None)
Other number DOE/OR/23177-5982
Document Type(s) (Journal Article) 
Associated with EIC: No
Supported by Jefferson Lab LDRD Funding: No
Funding Source: Nuclear Physics (NP)
Other Funding:DE-SC0018416

Compiled for Physical Review D
Volume 109
Page(s) 034513
Publication Abstract: Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the $\sigma$, leading to large systematic uncertainties in the pole position. In this letter, we will show how dispersion relations can implement the additional constraints, using as input lattice--determined $\pi\pi$ partial wave scattering amplitudes with isospin--0,1,2. We will show that only certain combinations of amplitude parameterizations satisfy all constraints, and that when we restrict to these, the $\sigma$ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained $\sigma$ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance.
Experiment Numbers: other
Document: pdf
Accepted Manuscript: PhysRevD.109.034513.pdf
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