Background vs Luminosity Optimisation
Guy Wormser, 22/1/1999
Since it is likely that BABAR can not properly at the full current that can be provided by the machine, a compromise between background level and luminosity will have to be made. There will be an optimal way to do that which will probably depend
somewhat of the daily status of PEP-II and BABAR so tuning will probably be necessary to find the optimal point. However, the simple guidelines given below can help to converge quicker to the optimum point.
Lumi=k* Nb *Ih*Il*f_transp(Ih / Il)*beambeam(Ih, Il)
Bckg=k’* Nb2*( Ih2*B+ Il2)+back_beambeam
Ib , Il are the currents in each bunch for the HER and LER respectively
Nb is the number of bunches.
f_transp(Ih / Il) denotes the energy transparency function. It could look like a narrow gaussian peaked at .35 but it needs to be measured.
Beambeam is the loss of luminosity due to beam-beam effects. It will make eventually the luminosity stop increasing for higher Ib , Il
B is the relative efficiency to produce background for HER and LER. It will depend of the subdetector, its location , its sensitivity, etc. ..It is usually between 1 and 3.
Back_beambeam is the extra background produced when the two beams are in collisions. No measurement of this exist yet.
Some initial guidelines
In the model above, and neglecting beam-beam induced backgrounds, it is obvious that the optimum is reached when the current in each bunch is maximized and the number of bunches minimized. In other words, once the machine has produced its optimal
luminosity, one would reduce simply the number of bunches to get the desired background level. One could gain for example a background reduction of 9 keep 1/3 of the luminosity.
If the f_transp function is not sharply peaked, one could even do better by reducing the current intensity in the LER which dominates the background if B<<10 and compensate by
increasing the current in the HER.
It remains to be seen how much beam-beam effects will distort this simple picture.