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Relativistic Collisions and Mandelstam s

What you are seeing: compare a fixed-target experiment with a head-on collider for the same lab energy budget. The center-of-mass energy s\sqrt s grows only as Elab\sqrt{E_{lab}} for fixed target but linearly for symmetric colliders, justifying the LHC architecture.

Figure 1. Center-of-mass energy vs lab energy for fixed-target and collider geometries.
m1 (GeV)0.94
m2 (GeV)0.94
log10(E / GeV)3.00
geometry

WHAT TO TRY

  • Switch the geometry between fixed-target and symmetric collider: at the same beam energy the collider reaches a far higher sqrt(s), the invariant collision energy. The diagnostic shows why, collider sqrt(s) grows as E while fixed-target only grows as sqrt(E).
  • Raise the beam energy E: the collision fireball runs hotter and whiter and more outgoing tracks spray out, because the track multiplicity climbs as ln sqrt(s). That jet proliferation is what real detectors record.
  • Change the masses m1 and m2: the production threshold sqrt(s) = m1 + m2 shifts, so heavier beams need more energy to reach the same available collision energy above threshold.