Phase Space Relativistic invariant phase-space element: d≈dp咖中中 E E Define pp or pp collision axis along z-axis Coordinates pu=(E, Px, px-Invariance with respect to boosts along z? 2 longitudinal components: E&p, (and dp E)NOT invariant 2 transverse components: px Py(and dpx, dpy) ARE invariant Boosts along Z-axis For convenience: define pu where only 1 component is not Lorentz invariant Choose pr, m, o as the transverse"(invariant)coordinates pr≡psin()andφ is the azimuthal angle For 4th coordinate define"rapidity How does it transform? E+p 2E p. p=E tanh y 13Jun2007 Tsinghua University13-Jun-2007 Tsinghua University 10 Phase Space • Relativistic invariant phase-space element: – Define pp or pp collision axis along z-axis: – Coordinates pm = (E,px ,py ,px ) – Invariance with respect to boosts along z? • 2 longitudinal components: E & pz (and dpz /E) NOT invariant • 2 transverse components: px py , (and dpx , dpy ) ARE invariant • Boosts along z-axis – For convenience: define pm where only 1 component is not Lorentz invariant – Choose pT , m, f as the “transverse” (invariant) coordinates • pT  psin(q) and f is the azimuthal angle – For 4th coordinate define “rapidity” (y) • …How does it transform? E dp dp dp E d p d x y z = = 3  z z E p E p y - +  ln 2 1 p E y z or = tanh