Why were some people studying “high pT” physics in the 1960s?

The quick answer is that they were looking for a “left handed” intermediate boson W±, the proposed carrier of the weak interaction [35]. Although the possibility of Fermi's point-like weak interaction of β decay [18,19] being transmitted by a boson field was originally discussed by Yukawa [222] and other authors, the modern concept of the parity-violating intermediate vector bosons W± as the quanta that transmit the weak interaction was introduced by Lee and Yang in the year 1960 [35, 36] to avoid a breakdown of unitarity in neutrino scattering at high energies if the weak interaction remained point-like [35]; and experiments were proposed to detect the intermediate bosons with high energy neutrinos [37, 38]. Neutrino beams at the new BNL-AGS and CERN-PS accelerators provided the first opportunity to study weak interactions at high energy, whereas previously weak interactions had only been studied via radioactive decay.

The first high energy neutrino experiment at the BNL-AGS [39] set a limit on the mass of the intermediate boson of roughly less than the mass of the proton MW ≲ Mp. However, much more importantly, this experiment discovered that the neutrinos from charged pion decay produced only muons.