The Large Hadron Collider

 The Large Hadron Collider (LHC) is the next generation collider at CERN. It will be built in the 27 km tunnel where the LEP collider is situated today and will start operation in June 2005. The collider will have two counter-rotating proton beams each with an energy of 7 TeV giving a total collision energy of 14 TeV. The LHC will take advantage of the existing accelerator complex at CERN to create the proton beams and accelerate them.

The Large Hadron Collider is the natural choice as the next step for particle physics. For the last many years discoveries of new particles have been dominated by hadron colliders extending the accessible energy range upwards. In this way the LHC can be seen as a discovery machine with a dynamic range of discovery from energy scales of 5 MeV in the case of B-physics to a few TeV for the discovery of new vector bosons or quark compositeness.

The theory for electroweak interactions had great success with the prediction and finally the discovery of the W and Z vector bosons at the proton-antiproton Sp $\bar{p}$S collider at CERN. In the electroweak theory it is, however, not sufficient with the four vector bosons responsible for the electroweak interactions since all particles in such a theory will be massless. The vector bosons can acquire mass by introducing a scalar doublet to break the symmetry between the four vector bosons. By assigning each fermion a coupling to the scalar field proportional to the mass of the particle the same scalar field can describe the masses of all known particles.

With the scalar field, the Higgs field, there is associated a Higgs particle which, if discovered, will be strong proof of this mass creation theory. However, the Higgs particle has not been seen and the field is open for discoveries at the LHC. While the standard model is a kind of minimal model there are many other models within the branch of supersymmetric theories which predict a forest of new particles within the range of the LHC.

To extent the reach of new physics to as high mass scales as possible and to increase the production cross section of the processes of interest as seen in fig. 1.1 it would be preferable to increase the centre of mass energy above the 14 TeV of the LHC. The magnetic field strength required to force the particle beams around in the collider increases linearly with the beam energy. The highest operational magnetic field for affordable superconducting magnets is 8.65 T which together with the requirement that the LHC has to fit inside the existing LEP tunnel gives the maximum energy of 7 TeV energy for the beams.

  

Figure: Expected cross section as a function of energy in the centre of mass system for proton-proton collisions. Note the difference between the total inelastic cross section and the cross section for physics processes like Higgs production. From [1].

With the beam energy limited, another way to increase the rate of events with interesting physics is to increase the luminosity. The event rate of a specific process is given as

 

$$\sigma_{x}^{}$$ (1)

where L is the luminosity and $\sigma_{x}^{}$ the cross section of the process. The cross section is at a given centre of mass energy a fixed number dependent on the specific physics process only while the luminosity is controlled by the parameters of the collider. The luminosity is for a collider

 

$${\textstyle\frac{1}{4\pi}} {\frac{N^2 f}{t A_{T}}}$$ (2)

where N is the number of protons in each bunch, t the time between individual bunches, A_T the transverse dimension of the bunches at the interaction points and f the fraction of bunch positions actually containing protons.

The time between the bunches is limited by the requirement that there should be no additional interactions on each side of the interaction region. For the LHC the bunch crossing time will be 25 ns corresponding to a bunch separation of 7.5 m. The transverse dimensions of the beam can at the interaction point be squeezed down to 15 $\mu$ m. To be able to fill new bunches into the LHC and operate the beam dump it is necessary to order the proton bunches in bunch trains followed by some empty bunches. In total 2835 of the 3557 available spaces with 25 ns separation will contain protons corresponding to f = 0.80 .

The only remaining way to increase the luminosity is to increase the number of protons in each bunch. This is limited by electromagnetic forces between the colliding bunches.

The maximal luminosity achievable will be close to 2 $\cdot$ 10³⁴ cm ^{- 2}s ^{- 1} but to be in a stable region the nominal luminosity is fixed at 10³⁴ cm ^{- 2}s ^{- 1}. For the first years of running it is foreseen to run at low luminosity L _low = 10³³ cm ^{- 2}s ^{- 1} and only gradually increasing it to the high luminosity L _high = 10³⁴ cm ^{- 2}s ^{- 1}.

The requirements on the luminosity from physics can be seen from fig. 1.1. The number of observed events is given as

 

$$\sigma \varepsilon$$ (3)

with T the effective time the machine is running, Br the branching ratio of the selected decay and $\varepsilon$ the detection efficiency. A standard year at the LHC is supposed to give a total running time of T = 10⁷ s. Taking as an example the creation of a 500 GeV Higgs particle, the cross section is 3 pb and the branching ratio for the favourable H $\rightarrow$ ZZ decay with the Z bosons decaying to leptons is around 0.1%. At low luminosity this gives just below 50 events a year before taking any detection efficiencies into account. Clearly a luminosity of 10³⁴ cm ^{- 2}s ^{- 1} or higher is required to identify a Higgs particle in this decay mode. The first years with the LHC can, however, be used for physics processes with higher cross sections such as B-physics, studies of the top quark and searches for supersymmetric particles.

The high requirement on luminosity is the reason for the choice of a proton-proton collider. For while a proton-antiproton collider has the advantage that both counter-rotating beams can be kept in the same beam pipe, producing the enormous amounts of antiprotons required for the high luminosity is not realistic and would be more expensive than the proton-proton solution with separate beam pipes. The charge asymmetry introduced with a proton-proton collider is not a serious problem for the physics analysis.

The number of simultaneous proton-proton inelastic interactions taken place in each bunch crossing is given as a Poisson distribution with an average of

 

$${\frac{{L} \sigma_{ie} t}{f}}$$ (4)

At high luminosity this gives an average of 22 simultaneous inelastic interactions in each event with an expected value of the inelastic cross section $\sigma_{ie}^{}$ = 70 mb. Each of the interactions give rise to many tracks from the interaction region thus giving events with many hundred tracks. The cross section from elastic scattering of the protons and diffractive events will not be seen by the detectors as it is only the inelastic scatterings that give rise to particles at sufficient high angles with respect to the beam axis.

The events with production of high mass objects such as vector bosons or Higgs particles are often called physics events. The term is misleading since all interactions of course contain physics but the dominating QCD-jet processes with low energy transfer are believed to contain little unknown physics and are thus regarded as background without any (new) physics information.

The difference between the total cross section and the cross section of the interesting physics is in many cases greater than ten orders of magnitude. The absolute majority of interactions, called minimum bias events, are fusion processes of gluons or quarks with a small energy transfer resulting in events with many hadrons of low momentum and nothing else. To identify the interesting events in the background requires some clear signatures. One of these is the identification of leptons with high transverse momentum. Leptons have a very low rate in minimum bias events but can be found in selected decay modes of most physics processes. The strong need for lepton identification has driven the design of the LHC detectors as will be seen in chapter 4.