The type of experiments that are to be carried out at TESLA demand high precision in the knowledge of the luminosity of the beam; unlike the case of LHC, the center of mass energy of a collision cannot be assumed to be twice the beam energy.
In practice, when the beam is run at given energy, some particles lose energy before the collision for several reasons. The range of collision energies is distributed in a spectrum, sharply peaked, with more than 65% of events with 0.1% of nominal energy: this distribution is referred to as the e+e- luminosity spectrum, ∂L/∂√S.
It is hoped that by using physics processes known as bhabha scattering, the energy spectrum can be reconstructed with an accuracy of 0.1%. This would be sufficient for top quark physics, whereas investigation of W mass would require an accuracy better by an order of magnitude: 0.01% in the luminosity spectrum.[cinabro jeju talk],[1miller boogert 02]
The three main processes that contribute to an energy loss are machine beamspread, beamstrahlung, and Initial State Radiation. They are detailed below:
This is the smallest source of energy loss. It is induced by the intrinsic energy spread of the e- and e+ produced by the machine, and it is an inescapable process.
Because of the process by which the electrons are used to produce the positrons, the latter will have a lower machine energy spread. The value for the positrons is 0.05%, and for the electrons it is 0.15%. This effect is unlikely to be gaussian.
We can already see the difficulty in reconstructing a spectrum to 0.1% accuracy, when the electrons have an intrinsic 0.15% energy spread.
Fig c: plot showing the relative energy losses
due to the three main processes [1miller boogert 02].
beamstrahlung is the name of the energy loss that electrons and positrons experience when the particles of one beam interact with the electromagnetic field of the opposite bunch. It is equivalent to brehmsstrahlung, which is caused by bending the trajectory of a charged particle, and has the same spectrum; in effect they are both caused by accelerating the particle.[1schulte thesis]
This is quite a large effect in an accelerator like TESLA[cinabro], as charges in the bunches are very concentrated due to small beam sizes.
Initial State Radiation (ISR) is a consequence of QED. At any given time, one of the beam particles can radiate a photon, thus losing energy.
It can be calculated to great accuracy, and would not need to be measured if it were the only effect present. To calculate it, some QCD cross sections have to be taken into account; we used BHWIDE, a wide angle bhabha scattering simulation program (fist developed in LEP[1bhwide page].)