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Scalar radius of the pion and zeros in the form factor

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PHYSICS LETTERS B
卷 651, 期 2-3, 页码 139-146

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DOI: 10.1016/j.physletb.2007.06.023

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The quadratic pion scalar radius, (r(2))(s)(pi), plays an important role for present precise determinations of pi pi scattering. Recently, Yndurain, using S an Omnes representation of the null isospin (I) non-strange pion scalar form factor, obtains (r(2))(s)(pi) = 0.75 +/- 0.07 fm(2). This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omnes equations, (r(2))(s)(pi) = 0.61 +/- 0.04 fm(2). A large discrepancy between both values, given the precision, then results. We follow Yndurain's method and show that by requiring continuity of the resulting pion scalar form factor under tiny changes in the input pi pi phase shifts, the form factor obtained has a zero for some S-wave I = 0 T-matrices. Once this is accounted for, the resulting value is (r(2))(s)(pi) = 0.63 +/- 0.05 fm(2). The main source of error in our determination is present experimental uncertainties S in low energy S-wave I = 0 pi pi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD. (c) 2007 Elsevier B.V. All rights reserved.

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