PCAC and the Deficit of Forward Muons in pi^+ Production by Neutrinos
Abstract
The K2K experiment, using a fine-grained detector in a neutrino beam of energy ~1.3 GeV has observed two-track events that can be interpreted as a coherent reaction \nu_\mu + \N -> \mu^- + \N + \pi^+ (\N = \rm{C}^{12}) or an incoherent process \nu_\mu + (p,n) \to \mu^- + \pi^+ + (p,n), the final nucleon being unobserved. The data show a significant deficit of forward-going muons in the interval Q^2 <~ 0.1 GeV^2, where a sizeable coherent signal is expected. We provide an explanantion of this effect, using a PCAC formula that includes the effect of the non-vanishing muon mass. The deficit is caused by a destructive interference of the axial vector and pseudoscalar (pion-exchange) amplitudes. No such effect occurs in the neutral current channels such as \nu_\mu + \N \to \nu_\mu + \pi^0 + \N.Keywords
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