Inputs
Beam configuration
Input variable
GeV
Collision frame
GeV/c²
GeV/c²
Default values use the proton mass. In collider mode, m₂ = m₁ is enforced.
Results
Kinematic quantities
Fixed-targetBeam momentum p
— GeV/c
Beam kinetic energy T
— GeV
Beam total energy E
— GeV
Velocity β = v/c
—
Lorentz factor γ
—
Beam rapidity ylab
—
Center-of-mass energy √s
— GeV
CM velocity βcm
—
CM Lorentz factor γcm
—
CM rapidity ycm in lab
—
Beam momentum p* in CM
— GeV/c
Beam energy E* in CM
— GeV
Beam kinetic energy T* in CM
— GeV
Beam rapidity ybeam in CM
—
Definitions in Natural units: c = 1.
E = T + m; p = √(E²−m²);
β = p/E; γ = E/m = 1/√(1−β²).
s = (p₁+p₂)². Fixed target: s =
m₁²+m₂²+2m₂E₁. Symmetric collider: √s = 2E.
For a fixed target, βcm =
p₁/(E₁+m₂), γcm = 1/√(1−βcm²), and ycm =
atanh(βcm). For a symmetric collider βcm=ycm=0.
E₁*=(s+m₁²−m₂²)/(2√s), p*=√(E₁*²−m₁²),
and T*=E₁*−m₁.
y = ½
ln[(E+pz)/(E−pz)] = atanh(βz). ylab
refers to the incident beam in the lab; ybeam is its CM-frame
rapidity.