# Theorie des tourbillons by Poincare H.

By Poincare H.

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Y5VL = VL These results are only true to the extent that E >> m. For massless neutrinos they are, of course, exactly true. 4) only involves left-handed neutrinos. 23) tells us that only left-handed quarks participate in ha(x). 2) when multiplied by y0 yields (1 2-15) = 0, Then using the fact that uR 2-15)2 uL (12-15) = UL. 3) that in fact only the left-handed parts of all the particles actually play a role in the weak currents. 5) but only when E >> m does UR/L really correspond to helicity ±2.

Even if we had an explicit expression for ha(x) we could not, in general, compute matrix elements of ha between hadron states, because the hadrons, being severely affected by the strong interactions, are far from being like bare free particles. 6) (pjh' In) -* up'Y'(Gv - GA-/5)U. 24. 6) is remarkable because that is the value of the coefficient of ya in la(x). Yet one might have thought that the effect of the strong interactions in the hadrons would give a drastically different value. The result is explained by the `conserved vector current' hypothesis (CVC) according to which the vector part Va(x) of ha(x) belongs to a triplet of conserved currents associated with the conservation of isospin in the hadronic reactions (Feynman and Cell-Mann, 1958).

8) Mw. However, the interaction is no longer point-like. The W exchange implies an interaction region of dimensions 1/MW and the angular dependence shows that more than just s-waves are participating. 9) so that lim a= k-oo G 2 MW22 = constant. 10) IT Despite this improved high energy behaviour, partial wave unitarity is still violated, albeit marginally. 11) w so that unitarity violation, ao > 1, occurs only at fantastically high ener- 2 The need for a gauge theory 26 w+ W Ve Fig. 3. Feynman diagram for vei/e -> W+W-.