Luminosity formula for LHC

L = F x n x N x N x f / (4 x Pi x s)

F= geometrical luminosity reduction factor
n = number of bunches
N = number of protons inside the bunch
f = revolution frequency of the bunch
s = transverse RMS beam size

LHC beam parameters

F = 0.84
n = 2808
N = 1.15 x 10^11
f = 11.245 x 10^3 Hz
Pi = 3.14
s = 16.7 x 10^-4 cm
L = 1.0 x 10^34 / cm^-2sec^-2

1 fb = 10^-39 cm^-2
1 year = 3.1563 x 10^7 s
Integrated luminosity for 1 year = 10^34 x 3.1563 x 10^7 cm^-2 = 3.1563 x 10^40 cm^-2 = 31.563 fb

Fundamental equation of high energy physics

N = L x s x e

N = event rate (s^-1)
L = luminosity (cm^-2s^-1)
s = cross section (cm^2)
e = efficiency

-- TaeJeongKim - 06 Mar 2009

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Topic revision: r2 - 2009-03-09 - TaeJeongKim
 
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