IL NUOVO CIMENTO
DOI 10.1393/ncb/i2008-10528-4
Vol. 123 B, N. 3-4
Marzo-Aprile 2008
Luminosity measurements at LHC
S. de Capua(1 ), F. Ferro(2 ), M. De Gruttola(3 ) and M. Villa(4 )
(1 )
(2 )
(3 )
(4 )
CERN, CH-1211 - Gen`
eve 23, Switzerland
INFN, Sezione di Genova - via Dodecaneso 33, 16146 Genova, Italy
INFN, Sezione di Napoli - via Cintia, I-80126, Napoli, Italy
INFN, Sezione di Bologna - via Irnerio 46, 40126 Bologna, Italy
(ricevuto il 3 Giugno 2008; pubblicato online il 4 Agosto 2008)
Summary. — In this paper, we present the various techniques developed for measuring and monitoring the luminosity, both integrated than instantaneous, in p-p
collisions at the LHC. The investigated methods range from old and new techniques
for instantaneous luminosity measurement during dedicated runs, to the integrated
luminosity evaluation via the total and diﬀerential forward elastic cross-section measurement, to the oﬄine-integrated measurement using known channels, and ﬁnally
to the on-line techniques. A brief description of the detectors used for this purposes
is given when needed.
PACS 13.85.Lg – Total cross sections.
PACS 29.27.-a – Beams in particle accelerators.
1. – Introduction
A precise luminosity measurement and constant monitoring is essential to guarantee
the correct functioning of the accelerator and of course for any physical process crosssection determination. Therefore all the LHC experiments have been devoted many
eﬀorts to the construction of sub-detectors essentially dedicated to the luminosity measurement, and to the tuning of various experimental techniques.
In the following sections we present a brief discussion of all the experimental techniques to measure both the integrated and the instantaneous luminosity. These techniques can be divided in direct ones, when the luminosity is inferred from the bunch
properties, such as the in the well-known Van der Meers scan method or the newest
beam gas interaction method, and indirect methods, when oﬄine information of very
well-known channels, such as electroweak and electromagnetic “candles” processes, or
the total and forward diﬀerential elastic cross-section measurement are utilized.
A diﬀerent classiﬁcation can be made considering that the previous methods need
dedicated runs or oﬄine analyses after data collection, hence cannot be used during
relevant physical data collection, in contrast with all the on-line measurement monitoring
and control techniques, as described in the last section.
c Societ`
a Italiana di Fisica
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Fig. 1. – (Left) Schematic view of the typical layout of an IP and of the BRAN location. (Right)
Simulation of the beam-gas interactions reconstructed inside the Velo detector.
2. – Direct methods for luminosity measurements
Various methods have been developed in the past to measure the luminosity. In
this section we discuss two methods which measure directly the luminosity: the Van der
Meer scan method [1], developed for the LHC experiments, and the beam-gas interactions
method, speciﬁc to the LHCb experiment [2].
.
2 1. The Van der Meer scan method . – The method consists in moving the beams
transversely across each other and recording the relative luminosity (reaction rate). The
position for maximum luminosity is found and the absolute luminosity is inferred from
the measured beam overlap and the beam currents. This method was successfully applied
at the Intersecting Storage Rings (ISR) at CERN. Although the conditions at the LHC
will be drastically diﬀerent (bunched beam versus coasting beams, similar horizontal
and vertical beam sizes as opposed to widely diﬀerent sizes, bunch-to-bunch variations,
etc.), the BRAN project [3] aims to adopt the Van der Meer scan method to measure
the relative luminosity inside the four experimental detectors: ATLAS, ALICE, CMS
and LHCb. In the p-p collisions at the LHC many particles will be produced, including
neutral particles like neutrons and photons which will in general follow the trajectories
of the protons they descend from. Since the ﬂux of neutral particles is expected to be
suﬃcient to damage the bending magnet D2 in IP1 (ATLAS) and IP5 (CMS), where
the luminosity can reach 1034 cm−2 s−1 , an absorber made of copper of several meters of
length (TAN), is foreseen in front of D2 at about 140 m from the IP. At that location, the
two proton beams are separated by the bending magnets D1 and D2 by about 160 mm
and there is therefore a space of about 100 mm between the two vacuum chambers for
a detector to be placed. Hence the detector, inserted inside the TAN at the location of
the shower maximum, will monitor the rate of the neutral particles coming from the IP
(ﬁg. 1, left).
In order to monitor the neutral collision rate, the detectors must fulﬁl two main requirements: i) stand the high radiation dose, about 1 GGy for IP1 (ATLAS) and IP5
(CMS) and ii) perform bunch-by-bunch measurements (i.e. at a measurement speed
higher than 40 MHz). For this goal, two diﬀerent types of detectors are being developed:
LBNL is committed to deploy four fast ionization chambers (IC) in the TANs around
IP1 and IP5 in the framework of the US-LARP Collaboration [4], while CERN is aiming
to install solid-state cadmium telluride (CdTe) detectors [5, 6] developed by LETI laboratories [7] in the remaining two points (where the radiation dose expected is a bit
lower). These two technologies have good performances for what concerns one of the two
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LUMINOSITY MEASUREMENTS AT LHC
requirements: the IC is suﬃciently radiation hard, but will have diﬃculties meeting the
40 MHz requirement, while the CdTe can easily comply with the 40 MHz requirement,
but can only stand the lower dose expected at IP2 (ALICE) and IP8 (LHCb).
.
2 2. The beam-gas interactions method . – With the advent of precise microvertex
detectors, a novel method of measuring the absolute luminosity emerges [2]. The method
relies on the use of beam-gas interactions for measuring the individual beam shapes and
determining the beam overlap integral which enter the luminosity, by means of the vertex
locator detector (VeLo) [8] of the LHCb experiment. The method also allows the direct
measurement of beam crossing angles or beam oﬀsets. The proposed method is nondestructive: the target gas thickness required is much less than the integrated LHC
residual gas density, and the induced radiation is not larger than the one caused by
beam-gas collisions. The luminosity L for two counter-rotating bunches with density
function ρi (x, t) and uniform velocity vi is given by [9, 10]
2
L = f N1 N2
(v1 × v2 )
×
(v1 − v2 ) −
c2
2
ρ1 (x, t)ρ2 (x, t)d3 xdt,
where f is the revolution frequency and Ni the total number of particles in the bunches.
Assuming the velocities and the total number of particles in the bunches can be precisely
measured by independent means, the method aims at measuring the densities ρi from
beam-gas collisions. An estimation of the rate of inelastic pp collisions, taking xenon as
target gas, gives approximately 30 Hz, which will allow mapping the bunch proﬁle within
minutes with a statistical precision below 1%.
Figure 1 (right) shows the distributions along the z-axis of primary vertices with at
least 6 reconstructable tracks. For this plot, 10 k beam-gas inelastic events (for each
beam) were generated ﬂat in the range −1.2 m < zpv < 1.2 m, while 20 k beam-beam
inelastic events were generated assuming a Gaussian envelope centered on z = 0 and
with rms σzlum = 53 mm. Note that the exact distributions of each individual sample
can be obtained from separate analysis of a pure beam-gas experiment (for either beam)
and pure beam-beam experiments by running with gas but considering only non-colliding
bunches (or running with a single beam in the ring) and, respectively, by running without
target gas. This allows estimating precisely the contamination of a given sample by the
other samples without relying on models or Monte Carlo simulations.
Once calibrated by this method, any given reaction can be used later to measure the
absolute luminosity in a continuous way without the addition of target gas and at any
luminosity.
3. – Measurement of the integrated luminosity
.
3 1. Experimental apparatuses. – The TOTEM experiment [11] uses precision detectors (σ ∼ 30 μm) inserted in Roman Pots (movable sections of the vacuum chamber)
installed in the machine tunnel, at 147 and 220 m from the IP5, to measure the elastically and diﬀractively scattered protons close to the beam direction. Each Roman Pot
station counts for three Roman Pot units, equipped with ten planes of detectors. Two
units approach the beam vertically and one horizontally, providing also an overlap among
the detectors. In order to measure the elastic scattering to the smallest |t| values, the
detectors should be active as close to their physical edge as possible. In particular the
detectors will have to be eﬃcient up to a few tens of microns to their edge. In order to
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build the edgeless leading proton detectors, planar silicon detectors with current terminating structure, which provide a thin dead area of ∼ 50 μm, have been developed and
built at CERN.
The telescopes for the detection of the inelastic events (T1 and T2) have a good trigger
capability, provide tracking with a good angular resolution and allow the measurement of
the trigger eﬃciency. To discriminate beam-beam from beam-gas events, the telescopes
will identify the primary interaction vertex with an accuracy at the level of a cm by
reconstructing a few tracks from each side of the interaction point; the knowledge of the
full event is not needed.
The T1 telescope is made of 5 planes of 6 trapezoidal Cathode Strip Chambers
(CSC) [11] and will be placed in the CMS end-caps in the rapidity range 3.1 < |η| < 4.7
with a 2π azimuthal coverage. T2 is made of 20 half circular sectors of GEM [11] (Gas
Electron Multiplier) detectors; it will be placed in the shielding behind the CMS Hadronic
Forward (HF) calorimeter as a complement of the T1 telescope at larger η. With the
present dimension of the vacuum pipe, the T2 telescope will cover with good eﬃciency
the range 5.3 < |η| < 6.5.
The ATLAS experiment, in addition to the main detector, will install the so-called
ALFA system [12], which consists of scintillating ﬁber trackers located inside vertical
Roman Pots, similar to those developed for TOTEM, at a distance of 240 m from the
IP. The main characteristics of this tracker are a spatial resolution of ∼ 30 μm and no
signiﬁcant non-active edge region.
.
3 2. Total cross-section. – One of the most precise methods that can be used at the
LHC to measure the luminosity is to use the measurement of the total cross-section and
of the diﬀerential forward elastic cross-section, which are related by the optical theorem.
In this approach the measurement of the total cross-section does not depend on the
luminosity:
σtot =
16π(dNel /dt)t=0
,
(1 + ρ2 ) · (Nel + Ninel )
where Nel and Ninel are the observed rates of the elastic and inelastic interactions, respectively, (dNel /dt)t=0 is the extrapolation of the elastic rate to the optical point t = 0
(t is the momentum transfer) and ρ is the ratio of the real and imaginary part of the
forward amplitude. The precise measurement of σtot provides an absolute calibration of
the machine luminosity: L · σtot = Nel + Ninel .
TOTEM needs few one-day runs, with the special running conditions of a high β ∗ =
1540 m (nominal TOTEM optics) and a low luminosity of L ≈ 1028 cm−2 s−1 . The β
value at the interaction point (IP) requires zero crossing angle, due to the increase of the
beam size (proportional to β), and then a reduced number of bunches which is compatible
with the LHC injection scheme. The most likely conﬁguration is 36 proton bunches with
2.5 μs spacing.
Almost half of the total cross-section at the LHC is predicted to be from coherent
elastic scattering, single, double and central diﬀractive processes. At β ∗ = 1540 m, the
TOTEM experiment eﬃciently detects protons with −t > 0.004 GeV2 , i.e. 97% of all
the diﬀractively scattered protons, independently of their longitudinal momentum loss
in the range of 10−8 < Δp/p < 0.2. With the TOTEM acceptance extending up to the
pseudorapidities of 6.6, and with the eﬃcient proton detection capabilities close to the
LHC beams, the diﬀractively excited states with masses higher than 5 GeV/c2 are seen
LUMINOSITY MEASUREMENTS AT LHC
427
by the experiment. The leading proton, which will be used as an event trigger, will be
detected by the silicon detectors placed inside the Roman Pots, located symmetrically
with respect to the IP.
The inelastic rate will be measured with T1 and T2 telescopes which provide a fully
inclusive trigger with an expected uncertainty on the inelastic rate of the order of 1%,
after corrections.
Due to the very high cross-sections of the processes involved, a huge statistics can
be obtained in a short running time and the main error sources are the systematic
uncertainties coming from the beam parameters and from the diﬀerent theoretical model
which can be used to extrapolate the elastic rate to the optical point. For a review of
these models the reader can see, for example, [13-18].
.
3 3. Coulomb and nuclear interference. – The diﬀerent method used by ATLAS to
measure the luminosity consists in measuring the elastic scattering down to such small
t-values that the cross-section becomes sensitive to the electromagnetic amplitude via
the Coulomb interference term [12]. If the Coulomb region can be reached, an additional
constraint is available from the well-known electromagnetic amplitude that describes the
elastic scattering at small t values:
2
dN
2αEM
σtot
−b|t|/2
∼ Lπ −
+
(i + ρ)e
,
dt
|t|
4π
where the ﬁrst term corresponds to the Coulomb and the second to the strong-interaction
amplitude. Using this additional constraint together with the optical theorem allows the
determination of both luminosity and the total cross-section without a measurement of
the inelastic rate. The ALPHA detectors [12] will allow the measurement of t down to
|t|min = 0.0006 GeV2 , inside the region of interference. L will be determined from the ﬁt
of the measured rate to the above expression as well as the other parameters ρ, σtot , and
the slope parameter b.
Simulations show that with special beam optics (β ∗ = 2600 m which corresponds to
a luminosity of ∼ 1027 cm−2 s−1 ) more than 10 million events can be achieved with less
than 5 days running resulting in a statistical error on the luminosity < 2%. The main
source of uncertainty is originating from the alignment, the optical function and the
background subtraction which result in a total systematic error of about 2.5%, yielding
a total error of ∼ 3% [19].
.
3 4. Relative luminosity measurement. – Due to the limited acceptance of the leading
proton detectors with low β ∗ optics (β ∗ = 0.5 m in nominal LHC running conditions)
the measurement of the luminosity at L = 1033 –1034 cm−2 s−1 cannot be done directly
with the previous methods. As an example, the minimum |t| reached by TOTEM detectors would be 0.4 GeV2 and a precise measurement of the elastic rate as well as its
extrapolation at the optical point would be impossible. Moreover, the ﬁt made by the
COMPETE [20] Collaboration of the data taken in past experiments results in an error
on the prediction of the total cross-section at the LHC energy of 15–20%.
The solution to the problem consists in measuring the luminosity with the special
optics conditions and consider it as a calibration point. The relative measurement can
be achieved by measuring rates of speciﬁc processes or using speciﬁc trigger conditions;
in case of pile-up the zero-event counting approach can be used.
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Fig. 2. – Feynmann diagram and the kinematical variable deﬁnition for the two-photon pp → ppll
process.
4. – Integrated luminosity measurement using known channels
It will be possible to measure, or at least monitor, the luminosity of the LHC both at
the beginning and in regime conditions, using very well understood channels with huge
cross-sections and very clear experimental signature.
The main idea is to measure the rate of these well-known channels, taking care of
background subtraction, and hence to evaluate the luminosity costraining the crosssection to the theoretical value:
(1)
σ(L) =
exp
exp
Nsig+back
− Nback
×L
,
where the eﬃciency value takes into account geometry, trigger, reconstruction and selection of signal events.
At ATLAS, CMS and LHCb an oﬄine integrated-luminosity determination will be
provided with some “candle” channels such as Z/W decaying into leptons, and muons
(electrons) from double-γ exchange in proton collision, with the goal of reaching a luminosity measurement precision of ΔL/L ∼ 3% (surely not at the start-up, when the
systematic contribution from the detector needs to be investigated). Instead, an online
instantaneous luminosity will be provided via inelastic and QCD processes, with the
intention of reaching a precision of ΔL/L ∼ 1%.
In this section we discuss the method to obtain the oﬄine integrated luminosity, while
the following one focuses on online measurements.
.
4 1. Rate measurement of two-photon production of leptons pairs. – The process pp →
ppl l , where the muons (electrons) are produced both at central and forward rapidities,
can be recorded using the standard ATLAS/CMS/LHCb trigger and might provide an
attractive method of oﬄine integrated-luminosity determination. In ﬁg. 2 you can see
the Feynmann diagram and the kinematical variable deﬁnition of this process.
The process is very well understood: σ = 1.33 ± 0.01 pb for CMS/ATLAS and σ =
88 ± 1 pb for LHCb (the diﬀerence is, naturally, due to the diﬀerent angular acceptance)
and the signature very clear:
+ −
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LUMINOSITY MEASUREMENTS AT LHC
Fig. 3. – Plots discriminating signal leptons from double-γ exchange (top) from various backgrounds (bottom) at ATLAS (left) and LHCb (right).
– very little (few GeV) lepton pair invariant mass, dilepton tranverse momentum
∼ 5 GeV, and acoplanarity angle φ ∼ 2 mrad.
ppair
T
– |η l
+ −
l
| < 2.1 for ATLAS/CMS, and 1.6 < |η l
+ −
l
| < 5 for LHCb.
– Background (mainly Drell-Yan and semileptonic decay of heavy quarks) reduced
by oﬄine cut on tranverse momentum and acoplanarity to ∼ 17% of signal for
ATLAS/CMS and ∼ 10% for LHCb.
In ﬁg. 3 we show the plots discriminating signal from background: the left side shows
the distribution of pT and acoplanarity angle φ for signal and background events at
ATLAS [21] for 10 fb−1 ; instead in the right one it is plotted the dimuon invariant mass
(left) and dimuon tranverse momentum (right) for signal leptons from double-γ exchange
(top) and various backgrounds (bottom) at LHCb [22].
All the three experiments expect to measure the integrated luminosity from these
electromagnetic channels with a precision of ∼ 2%, but, as the cross-section is not very
high (especially at ATLAS and CMS), this will be a very important luminosity monitor
only after some fb−1 of data taking.
.
4 2. Rate measurement of the Z/W decaying into leptons pairs. – LHC will be a
Z/W-factory, so that both at start-up and at higher luminosities, plenty of electroweak
bosons will be produced: the Z(W) rate at L = 1034 cm−2 s−1 will be 20(200) Hz. The
experimental signature is also very clear:
– for Z → l+ l− : two isolated leptons with high transverse momentum (pT > 15,
20 GeV/c) at central(forward) rapidity for ATLAS/CMS (LHCb) with a dilepton
invariant mass closer to the nominal peak Z mass.
– for W → lν: a lepton with high tranverse momentum (pT > 15 GeV/c) and missing
transverse energy (ET > 50 GeV). In these events one evaluates the W transverse
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Fig. 4. – Left: distribution of reconstructed dimuon invariant mass for signal Z and various
background at CMS [23] for 10 fb−1 . Right: distribution of reconstructed W transverse mass
for signal muons and various background at CMS [23] for 10 fb−1 .
mass from
the lepton and the reconstructed neutrino according to the formula
W
mT = 2plT pνT (1 − cos Δφ), with φ the angle between lepton and neutrino in the
tranverse plane.
Therefore, it should be clear that a precise measurement of the integrated luminosity
can be done starting from Z/W rate at high luminosity when all detector, systematic
(lepton reconstruction eﬃciency, trigger, geometry, missing tranverse energy) and theoretical uncertainties (particle density function, initial state radiation) will be calibrated
and better understood (many of these issues will be reached using just these candle channels). Even at the beginning of the data taking the electroweak channels will be very
important as a monitor of the luminosity and a cross check with the other luminosity
measurement. In ﬁg. 4 we show two plots of the reconstructed Z mass and W tranverse
both with muons in the ﬁnal state, as expected for an integrated luminosity of 10 pb−1 .
It can be ﬁnally asserted that a precise measurement of the rate of Z/W will be
performed at LHC, and hence, assuming the cross-section equal to the theoretical value,
an accurate integrated-luminosity measurement can be provided. For example, in the
Z → μ+ μ− channel, the expected value (for sure not so obvious at the start-up) of the
uncertainty is
(2)
ΔN
(pp → Z/γ ∗ + X → μ+ μ− + X) = 0.005(stat.) + 0.01(ex.syst.) + 0.02(th.syst.)
N
5. – Run-time luminosity and experimental techniques
The luminosity measurement methods discussed previously are mainly referring to
measurements made on special runs (Van-der-Meer or beam gas methods or for σpp
measurements), or on already collected data (luminosity calibration on physics channels).
During physics data collection a completely diﬀerent approach has to be taken in order
to measure online luminosity.
LUMINOSITY MEASUREMENTS AT LHC
431
.
5 1. Instantaneous luminosity. – An essential aspect of a good physics data taking
in collider experiments concerns the stability of the beam conditions. Due to several
machine aspects actual beam conditions are not constant: the beam has a non-trivial
bunch structure with empty and ﬁlled bunches (typically out of 3564 bunches 2808 are
ﬁlled and 756 are empty), the ﬁlled bunches can have diﬀerent levels of ﬁlling and after
all the beam deteriorates with time (1% loss of luminosity every 10 minutes). Therefore
the average numbers of interaction and pile-up are not constant over time and this might
undermine the correct evaluation of the trigger, tracking and reconstruction eﬃciencies,
increasing signiﬁcantly to the total systematic error of cross-sections or branching fractions for the process of interest in LHC. A close monitoring of the number of interactions
is thus absolutely mandatory and this is the main (run-time) goal of the instantaneous
luminosity measurement. The rate of interactions (R) and the instantaneous luminosity
tot
tot
(L) are related by: Rate = Lσpp
, where σpp
is the total pp cross-section.
A luminosity control system should be able to follow the number of interactions on
a bunch-by-bunch basis (every 25 ns). The main goal of the detectors measuring the
instantaneous luminosity is to reach an accuracy of about 2–4%.
.
5 2. Detectors for instantaneous luminosity: lucid, hadron forward . – Several types of
forward detectors are usually employed in the instantaneous luminosity determination.
In ATLAS, the forward detectors [12] able to follow the luminosity on a bunch-bybunch basis are the BCM (Beam Condition Monitor, small diamond pixel sensor), LUCID
(a Cherenkov detector 5.6 < |η| < 6.2) and a Zero Degree Calorimeter (|η| > 10). The
main luminosity detector is the LUCID (LUminosity Cherenkov Integrating Detector):
this is composed by two vessels places around the beam-pipe at ±17 m from the interaction point. Each vessel houses 20 aluminum tubes (1.5 m long, 1.8 cm diameter) ﬁlled
with C4 F10 gas and pointing to the interaction point. When a charged particle coming
from the interaction point enters a tube, traveling almost parallel to its axis, it emits
Cherenkov photons in the gas. By internal reﬂections, the photons are conveyed to a
photomultiplier placed at a tube end. The signal amplitude is proportional to the number
of tracks coming from the IP that entered in the tube.
In CMS, the forward detectors [24] devoted to the luminosity measurements are the
PLT (Pixel Luminosity Telescope, small diamond pixel sensors), the Hadron Forward
calorimeter (HF) [25], CASTOR (a further calorimeter) [26] and the CMS/Totem roman
pot system. The main system for the luminosity measurement is the HF calorimeter
(3 < |η| < 5) whose active elements are the quartz rods where Cherenkov light from
electromagnetic or hadronic showers is produced and piped to photon detectors. The
two parts of the calorimeter are segmented in 864 individual towers which provide the
deposited energy (or transverse energy) in each tower. The number of towers above a
given threshold in transverse energy is some information directly related to the number
of interactions.
.
5 3. Measurement techniques. – Independently of the actual realization, all the instantaneous luminosity measurements share the same general aspects:
– the base quantities come from fast detectors able to provide a digital signal for each
beam crossing (BX); the detectors have to be read every 25 ns;
– dedicated electronic boards perform the luminosity measurements on-the-ﬂy, collecting statistics in a deﬁned time-slice and providing luminosity information for
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each bunch of the beam and a total one, i.e. 3564 diﬀerent luminosity measurements performed on data arriving at a rate of several GByte/s and processed every
25 ns;
– the electronic boards provide an “online” luminosity information available during
run-time and can be later calibrated, tuned and ﬁne-tuned with other methods.
The time-slices are called luminosity blocks and are deﬁned as a time interval for which
the luminosity can be considered as constant (≈ few minutes or 106 beam revolutions).
The actual measurement of the instantaneous luminosity is performed on inelastic
events. At LHC the average number of interactions μ in a given bunch crossing can
tot
be calculated as: μ = Lσpp
Δt, where Δt = 25 ns. Luminosity detectors are sensitive
to quantities (N ) proportional to μ as the number of hit tubes or the number of hit
towers: N ≈ kμε, where ε is an acceptance and eﬃciency factor and k is a calibration
factor. There are at least three diﬀerent methods to evaluate the luminosity L from the
measurement of N .
Direct method : This relies on the fact that N (and μ) is very low. Since for each
given BX the actual number of interactions is Poissonian distributed, in the case μ <
0.01, the probability of two or more interactions is negligible. Therefore it is necessary
to distinguish between no interaction and an interaction. Any simple deﬁnition of an
interaction can be used: i.e. a hit tower in CMS or a hit tube in ATLAS. By counting the
interactions in a given luminosity block, it is possible to provide a quantity proportional
to the luminosity. This method will be used when L < 1032 cm−2 s−1 .
Zero counting: When the probability of having two or more interactions become
not negligible, the luminosity is evaluated by count events without interactions (zero
counting), since their probability is related to N under the assumption of Poissonian
distribution of the interactions: P (0) = e−N . This method is usable in a range of
0.01 < N < 4.6 where the statistic uncertainty does not dominate the ﬁnal measurement.
Above this range, less than 1% of events are empty (zero-starvation region). When
N > 4.6 with the complete detectors (P (N ) < 0.01), it is possible to consider parts of
the detector (halves, quarters, single tubes or single towers) chosen so that for each part
N is in the range of indirect measurement (0.01 < N < 4.6).
Proportional methods: These are based on quantities roughly proportional to the luminosity, like number of hit tubes, number of hit towers, total transverse energy. Despite
the non-linearity problems [27] involved, they can provide ancillary information on time
scales longer than 25 ns. The physics measurements discussed in the previous section fall
in this category and will provide the absolute calibration of the online luminosity.
6. – Conclusions
Many eﬀorts will be devoted during the LHC data taking operation with the aim to
obtain a precise luminosity measurement in order to reduce the systematic contribution
due to the luminosity on the evaluation of any physics process. This contribution, with
the passing of time, and so with the tuning of the experiments will reduce from the
initial 10% to hopefully 1%. In this paper many ways of measuring the luminosity, both
instantaneous then integrated, have been presented and discussed.
Two methods to measure the absolute luminosity directly on bunch properties have
been presented. The van-der-Meer scan method aims to monitor the collision rates at
the four interaction points with an accuracy of about 10%, by means of two diﬀerent
detector technologies: a fast ionization chamber developed by LBNL and a solid-state
LUMINOSITY MEASUREMENTS AT LHC
433
CdTe detector developed by CERN and LETI. A further method relies instead on reconstruction of vertices from beam-gas interactions to measure the colliding bunch proﬁles
and to determine the beam overlap integral. A dedicated one-day-long running time
should be suﬃcient to carry out an absolute luminosity measurement with an accuracy
of 1% or better.
Measurements of the integrated luminosity have been shown to be feasible via the
measurement of the total cross-section and of the elastic scattering, using the optical
theorem or measuring directly the elastic cross-section inside the Coulomb-nuclear interference region. These methods can provide a precise measurement of the integrated
luminosity (5–10% uncertainty at the very beginning, 1–3% after) but require dedicated
runs with special accelerator optics.
At ATLAS, CMS and LHCb an oﬄine integrated-luminosity determination will be
provided by determining the cross-section of some “candle” channels such as Z/W decaying into leptons, and muons (electrons) from double-γ exchange in proton collision.
The latter channel will need a greater integrated luminosity, namely 1 fb−1 , to be used
as a tool for luminosity measurement, while the electroweak channels, due to the higher
cross-section will be the ﬁrst measured channels at LHC. Exploiting these channels a
luminosity measurement precision of ΔL/L ∼ 3% will be reached at regime condition
when the systematic contributions from the detector will be completely understood.
Eventually, in the last section we present the approach which has to be taken during
physics data collection in order to measure online (run-time) luminosity on a bunch-bybunch basis. The main goal of the detectors measuring the instantaneous luminosity
(LUCID in ATLAS, Hadron Forward Calorimeter in CMS) is to reach an accuracy of
about 2–4%. Only below these values the ﬁnal uncertainty on most of the measurable
cross-sections, branching ratios and coupling constants will not be limited by the accuracy
of the luminosity information.
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