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B. J. Holzer et al.
luminosity:
L int =
T
0
L
t
dt
(6.35)
because it directly relates to the number of observed events:
L int · σ p = number of events of interest
(6.36)
The integral is taken over the sensitive time, i.e. excluding possible dead time.
The unit of the integrated luminosity is cm −2 and often expressed in inverse barn
(1 barn −1 = 10 24 cm −2 ).
Another important parameter for a beam with high luminosity and bunched
beams are the number of collisions per bunch crossing, the so-called pile up. In
particular for collisions with a large cross section this can become a problem. In
the case of the LHC, bunch crossings occur every 25 ns and the expected pile up is
more than 20 for proton-proton collisions. The challenge is to maximise the useful
luminosity while keeping the pile up to a level that can be handled by the particle
detectors.
6.4.5 Measurement and Calibration of Luminosity
To obtain the exact integrated luminosity, it has to be recorded continuously. It is
rather straightforward to obtain a counting rate directly proportional to the total
interaction rate dR/dt. This relative signal has to be calibrated to deliver the absolute
luminosity. We have already seen some effects that affect the absolute luminosity
and therefore to a large extent the luminosity measurement. In particular the
crossing angle and the luminous region are of importance since they have immediate
implications for the geometrical acceptance of the instruments.
In principle one can determine the absolute luminosity when all relevant beam
parameters are known, i.e. the bunch intensities, beam sizes (r.m.s. in case of
unknown beam profiles) and the exact geometry. However the precise measurement
of beam sizes is a challenge, in particular for hadron colliders when a nondestructive measurement is required. When the energy spread in the beams is large
(e.g. some e + e − colliders), a residual dispersion at the interaction point increases
significantly the beam size and must be included.
There exist other methods which relate the counting rate to well known processes
which can be used for calibration. We shall discuss several methods for both, lepton
and hadron colliders.
B. J. Holzer et al.
luminosity:
L int =
T
0
L
t
dt
(6.35)
because it directly relates to the number of observed events:
L int · σ p = number of events of interest
(6.36)
The integral is taken over the sensitive time, i.e. excluding possible dead time.
The unit of the integrated luminosity is cm −2 and often expressed in inverse barn
(1 barn −1 = 10 24 cm −2 ).
Another important parameter for a beam with high luminosity and bunched
beams are the number of collisions per bunch crossing, the so-called pile up. In
particular for collisions with a large cross section this can become a problem. In
the case of the LHC, bunch crossings occur every 25 ns and the expected pile up is
more than 20 for proton-proton collisions. The challenge is to maximise the useful
luminosity while keeping the pile up to a level that can be handled by the particle
detectors.
6.4.5 Measurement and Calibration of Luminosity
To obtain the exact integrated luminosity, it has to be recorded continuously. It is
rather straightforward to obtain a counting rate directly proportional to the total
interaction rate dR/dt. This relative signal has to be calibrated to deliver the absolute
luminosity. We have already seen some effects that affect the absolute luminosity
and therefore to a large extent the luminosity measurement. In particular the
crossing angle and the luminous region are of importance since they have immediate
implications for the geometrical acceptance of the instruments.
In principle one can determine the absolute luminosity when all relevant beam
parameters are known, i.e. the bunch intensities, beam sizes (r.m.s. in case of
unknown beam profiles) and the exact geometry. However the precise measurement
of beam sizes is a challenge, in particular for hadron colliders when a nondestructive measurement is required. When the energy spread in the beams is large
(e.g. some e + e − colliders), a residual dispersion at the interaction point increases
significantly the beam size and must be included.
There exist other methods which relate the counting rate to well known processes
which can be used for calibration. We shall discuss several methods for both, lepton
and hadron colliders.