Birks Quenching

The current versions of hadronic string models (FTF & QGS) produce hadronic showers with (a few percent) higher energy response than the stable released (as used in LHC productions) version of these models. Test-beam and collider data seem to indicate lower energy response in hadronic showers than currently provided by Geant4 simulations. This is the main reason why the development versions of the string models were not released in two previous public versions of Geant4 (10.3 and 10.4), in spite of providing an overall better description of thin-target data. We think that the main reason why the simulation overshot the data regarding the energy response of hadronic showers is in fact due to an incorrect treatment of the quenching of the signal - the conversion from the energy deposited by ionizing particles in a sensitive detector to the observed electronic (readout) signal is not linear, with proportionally less signal for higher densities of deposited energy, for both scintillation light and ionization electron-hole/ion pairs. This quenching effect is traditionally described by the simple, phenomenological “law” suggested many years ago by Birks. Its main parameter is fitted from experimental data under the assumption that the observed energy is related to the incident particle energy loss. This does not consider delta-ray production which will result in lower energy deposit (density). As a result of this approximation, the density of deposited energy is overestimated, which implies that the Birks coefficient, as fitted from the experimental data, gets underestimated. Using this Birks coefficient in simulations where delta rays are emitted (and considered discretely), as in practice for all simulations of high-energy experiments, results in underestimating the quenching effect, and therefore predicting larger signals than in reality. The correct Birks coefficient to be used in a simulation depends on the production threshold which is chosen in the simulation, with lower thresholds producing a larger delta-ray component and therefore reducing the density of the energy deposition along the ionizing track, and hence requiring an even higher Birks coefficient. We suggest the following pragmatic approach to incorporating Birks quenching: The calibration of a calorimeter - i.e. the conversion from the electronic signal produced by a shower and the energy of the primary particle that initiates the shower - is typically done for test beam data with an electron of a given energy, e.g. 20 GeV. We suggest to add an extra step to this calibration, in which the Birks coefficient used in the simulation is tuned to reproduce the ratio of the energy response of a hadron (typically a charged pion or a proton) and the energy response of an electron of the same energy (this ratio is indicated as “h/e”). It is natural to consider the same beam energy used for the calibration, e.g. 20 GeV, but in principle it could be a different one; note also that the tuning of the Birks coefficient is idependent from the calibration constant, given that the latter cancels out from the ratio h/e. Of course, with the tuning of the Birks coefficient as suggested above we compensate also for some of the intrinsic inaccuracies in the modelling of hadronic interactions; however, this effect is valid uniquely at the energy where the tuning is done (e.g. 20 GeV), and limited only to the energy response. For other observables (energy resolution, longitudinal and lateral shower shapes), and for all other energies, this procedure has a minimal impact, i.e. should not reduce the prediction-power of the simulation.