Explanation is given for observed sharp forward peaks in distributions of transverse momentum for hadrons produced in deeply inelastic hadron collisions. Small Q-value decay of peripherally produced nucleon resonances is the basic mechanism responsible for peaks in both ir and proton spectra. Implications of this result are discussed 0 Experimenters have recently made detailed measurements of cross section d 2 o/dpd$l for a single observed particle emergent from high-energy hadron-hadron interactions. 1 Particularly striking is structure at very small values of transverse momentum p T of the final pion in pp -77* + anything. 2 Indeed, as displayed in Fig. 3 of Ref. 2, for pion cm. longitudinal momentum p L = 0.6 GeV/c, data points for whichp T~2^0 .1 (GeV/c)"" 2 fall on a curve of form exp(-bp T 2 ) with 6~ 15 (GeV/c) 2 ; there is a break in the distribution, and at large p? a shallow curve [ocexp(-3^7-2 )] is measured. Suggestion of a similar forward peak is apparent also in data from PP *P + anything. 3 Because only one final particle is detected in these single-arm-spectrometer experiments, there is no empirical way to ascertain whether the observed particle is scattered directly or is the decay product of a resonance. Nevertheless, there is intuitive appeal to the idea that data at very small p T 2 are of the direct variety 3 ; in particular, the very steep forward peak might be thought to reflect simple exchange-model dynamics. In this note we develop very much the opposite point of view. Essentially, we assert that the steep forward peak in pp ^ir ± + anything is formed from TT ± which are decay products of nucleon resonances produced peripherally. The exact spin structure of nucleon resonances is not crucial, nor is it terribly important how strongly peripherally they are produced. Decisive factors are small Q value in resonance decay and small value of pion mass, which enters in the ratio (m Tes /m ll ) 2 .As a result, decay pions emerge with smaller (not larger I) p T tha,n parent resonances. 4 The same mechanism is responsible for protons with small p T , but the forward peak is predicted to be less steep than for pions. A consequence of our analysis is the important, if pessimistic, conclusion that it is impossible to isolate a direct-scattering component in deeply inelastic data obtained in single-arm experiments. Other implications and suggestions for further tests of our approach are listed at the end.Model. -Our mechanism is sketched in Fig. 1. We imagine a process in which resonance iV* is produced along with n other particles. Symbol X does not indicate any specific exchange mechanism but merely serves to represent peripheral production. (We need not specify details about the configuration of n particles produced with iV* other than to remark that in single-arm data an implicit sum is made over all possible multiplicities and particle types.) Resonance N* subsequently decays via N* ^n +N or sequentially as N* -n +Nf*. We are interested in the distribution in transverse momentum of decay pions.In ...