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 $<E>\sim 1.3\mathrm{GeV}$ has observed two-track events that can be interpreted as a coherent reaction ${\nu }_{\mu }+\mathbb{N}\to {\mu }^{-}+\mathbb{N}+{\pi }^{+}(\mathbb{N}={\mathrm{C}}^{12})$ 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 $Q^2\lesssim 0.1{\mathrm{GeV}}^2$, 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.

Comments: 4 pages including 1 figure, changes in abstract and text; version to appear in Phys.Lett. B