What is transversity and transverse spin?

 P: 2,828 You are probing a hadron with a lepton, and you can work in the approximation where a single virtual photon is exchanged. Say the virtual photon is along the horizontal direction. Basically, transversity is the following quantity : So if your hadron is polarized upwards, it's the difference between the probability of finding a quark polarized upwards minus the probability of finding a quark polarized downwards. Transversity can be measured as a function of $x_B$ (x-Bjorken), the fraction of longitudinal momentum carried by the active quark. It can also be measured as a function of the resolution of your probe, or "wavelength" of the virtual photon, usually written $Q^2$, the opposite of the invariant mass of the virtual photon (it is positive in this regime). The point is that it will not be the same as if the green and red arrows above both point horizontally (the direction of the probe), because it is a relativistic effect and there is essentially an infinite boost along the horizontal direction (the Lorentz contraction make your hadron look like a pancake).