Abstract
We apply to nucleon decay the knowledge about the short-distance structure of baryon wave functions gleaned from QCD form factor calculations nd the J gY → p ̄ p decay rate. We review the uncertainties arising when current algebra and PCAC are used to relate N → ℓ + meson decay rates to 〈0| qqq|N〉 matrix elements. We show that the relevant matrix elements are not directly related to those of the leading twist operators “measured” in conventional high momentum transfer physics, but argue for an indirect based on models that fit both form factor and J Ψ decay data. We use these inputs to calculate the p → e + π 0 decay rate in minimal SU(5) and other grand unified theories (GUTs) for a specified value of the heavy vector boson mass m X . Our results combined with the recent experimental lower limit on this mode indicate that m X > 2 × 10 15 GeV in the minimal SU(5) GUT, and we derive analogous bounds for supersymmetric GUTs. Our calculated lifetime for a given value of m X is considerably shorter than previous estimates made using non-relativistic SU(6) or the bag model, a difference traceable to the different normalizations of 2 and 3 quark wave functions at short distances.
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