PCAC and the Deficit of Forward Muons in pi^+ Production by Neutrinos
The K2K experiment, using a fine-grained detector in a neutrino beam of energy $ \sim 1.3 \mathrm{GeV}$ has observed two-track events that can be interpreted as a coherent reaction $ν_μ+ \N \to μ^- + \N + π^+ (\N = \rm{C}^{12})$ or an incoherent process $ν_μ+ (p,n) \to μ^- + π^+ + (p,n)$, the final nucleon being unobserved. The data show a significant deficit of forward-going muons in the interval $Q^2 \lesssim 0.1 \rm{GeV}^2$, where a sizeable coherent signal is expected. We attempt an explanantion of this effect, using a PCAC formula that includes the effect of the non-vanishing muon mass. A suppression of about 25 % is caused by a destructive interference of the axial vector and pseudoscalar (pion-exchange) amplitudes. The incoherent background is also reduced by 10 - 15 %. As a consequence the discrepancy between theory and observation is significantly reduced.