The root second notation for collider energies

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SUMMARY

The discussion clarifies the meaning of the root second notation, specifically \(\sqrt{s}\), in the context of collider energies, such as positron-electron annihilations at \(\sqrt{s} = 40 \text{ GeV}\). It establishes that this notation represents the center of mass energy, where \(s\) is one of the three Mandelstam variables used to describe particle collisions. The formula \(s = (p_A + p_B)^2\) is highlighted as essential for understanding these measurements. This notation is crucial for interpreting cross-section measurements in high-energy physics.

PREREQUISITES
  • Understanding of particle physics concepts, specifically collider experiments.
  • Familiarity with the Mandelstam variables: \(s\), \(t\), and \(u\).
  • Basic knowledge of center of mass energy calculations.
  • Experience with cross-section measurements in high-energy physics.
NEXT STEPS
  • Research the derivation and applications of Mandelstam variables in particle collisions.
  • Study the significance of center of mass energy in collider physics.
  • Explore the methods for measuring cross-sections in high-energy experiments.
  • Learn about the implications of different energy levels in particle collisions.
USEFUL FOR

Physicists, researchers in high-energy physics, and students studying particle collisions will benefit from this discussion, particularly those interested in understanding collider energy notations and their implications in experimental measurements.

welcomeblack
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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.
 
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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.
 
Sweet. Thanks a bunch.
 

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