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Mandelstam VariablesIn theoretical physics, the Mandelstam variables are numerical quantities that encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion. For the usual case of two particles going to two particles, the momentum conservation implies: -
The outgoing four-momenta are taken to have a negative time-like component. The Mandelstam variables are then defined by -
t=(p_1+p_3)^2=(p_2+p_4)^2,\qquad u=(p_1+p_4)^2=(p_2+p_3)^2 Note that -
The letters are also used in the terms s-channel, t-channel, u-channel. These channels represent different Feynman diagrams or different possible scattering events where the interaction involves the exchange of an intermediate particle whose squared four-momentum equals , respectively. For example the s-channel corresponds to the particles 1,2 joining into an intermediate particle that eventually splits into 3,4: the s-channel is the only way how resonances and new unstable particles may be discovered unless their lifetime is long enough that they are directly detectable. The t-channel represents the process in which the particle 1 emits the intermediate particle and becomes the final particle 3, while the particle 2 absorbs the intermediate particle and becomes 4. The u-channel is the t-channel with the role of the particles 3,4 interchanged.
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