# The root second notation for collider energies

1. May 30, 2012

### welcomeblack

Every paper I read about cross-section measurements from colliders has a line saying (for example):

...positron-electron annihilations at $\sqrt{s}$ = 40 GeV are studied...

1) What does this mean? I'm guessing it means that in the CM frame, the energy of each beam is 40 GeV.

2) Why use that notation for energy? The square root of a second means nothing to me.

2. May 30, 2012

### Bill_K

s is one of the three Mandelstam variables s, t and u used to describe a collision in an invariant way. For a collision between particles A and B, s = (pA + pB)2. So √s is the center of mass energy.

3. May 30, 2012

### welcomeblack

Sweet. Thanks a bunch.