Münster 2002 – scientific programme

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HK: Physik der Hadronen und Kerne

HK 9: Poster Session: Theory

HK 9.10: Poster

Tuesday, March 12, 2002, 10:30–12:45, Foyer Chemie

Chiral corrections to the double scattering term for the pion-deuteron scattering length — •Norbert Kaiser — Physik-Department T39, TU-München, 85747 Garching

The empirical value of real part of the pion-deuteron threshold T-matrix Re T_{π d} = 4π(1+m_π/M_d) Re  a_{π d}= −(0.496± 0.016)  fm can be well understood in terms of the dominant isovector π N double scattering contribution Re T_{π d} = −(T_{π N}⁻)²   <(π r)⁻¹>_d with <1/r>_d = ∫₀^∞dr [u²(r)+w²(r)]/r the inverse deuteron radius. However, since the leading order (Weinberg-Tomozawa) prediction for T_{π N}⁻ = m_π/2f_π² = 1.61 fm is about 13% below the empirical value the leading order chiral double scattering contribution to Re T_{π d} is also about 25% too small. We calculate in chiral perturbation theory all one pion-loop corrections to the double scattering term which in the case of π N-scattering close the gap between the current algebra prediction and the empirical value of T_{π N}⁻. In addition there is in the π d-system an off-shell correction for the exchanged virtual pion. Its coordinate space representation reveals that it is equivalent to 2π-exchange in the deuteron with a large distance behavior e^−2m_πr r^−5/2. When folded with the deuteron density its short distance singularity r⁻³ is regulated by introducing r_min=1/Λ= 0.23 fm with Λ a cutoff entering the chiral logarithm ln(m_π/2Λ) in T_{π N}⁻. We evaluate the chirally corrected double scattering term and the off-shell contribution with various realistic deuteron wave functions. We find that the off-shell correction contributes at most -8% and that the isovector double scattering term explains at least 90% of the empirical value of Re T_{π d}. Work supported in part by BMBF, DFG and GSI.