1. Ivan Smiljanić Vinča Institute of Nuclear Sciences, Belgrade, Serbia Energy resolution and scale requirements for luminosity measurement

2. The aim of study The aim of this study is to optimize event selection taking into account following effects: beam-beam deflection and physics background, as well as to minimize sensitivity on detector energy resolution and scale.

3. Overview General information Event selection Luminosity vs. bias of the energy scale Luminosity vs. energy resolution using relative energy cut Luminosity vs. energy resolution using energy balance cut Conclusion

4. 1. Geometry: rmin = 80 mm rmax = 195 mm tungsten thickness = 3mm silicon thickness = 0.3mm Segmentation: 30 planes, 64 rings, 48 sectors z position = 2270 mm 2. Total cross section: (from BHLUMI) (from WHIZARD) 3. No crossing angle GALUGA gives muon cross section of 0,394±0,002nb (phone meeting from 31 st of January 2008, B. Pawlik’s presentation), while with WHIZARD we have 0,544±0,008nb, which means that the difference between two generators is about 38%, or that model/generator dependence is of order of magnitude of 2,8*10 -1. General information

5. Event selection Asymmetric cuts Asymmetric theta cuts are proposed by C. Rimbault and P. Bambade in order to accommodate to beam-beam deflection effects. Due to beam-beam deflection effects, Bhabha events become more accolinear, which results in reduction of the effective Bhabha cross section. To compensate for it, asymmetric theta cuts are proposed. These cuts are applied subsequently to forward and backward sides of the detector, in order to reduce systematics for the IP position and relative position of forward and backward detector. LCAL angular acceptance for geometry used is 35-87 mrad. Therefore, cuts are set as follows: cut 1: 39-80 mrad; cut 2: 35-87 mrad. Asymmetric cuts are applied in all results in this study! Relative energy cut Energy balance cut

6. Relative energy cut In following results, asymmetric cuts on theta are applied in a way explained earlier, together with the cut on relative energy (ERCUT), where relative energy is defined as a sum of energies of both particles belonging to a pair divided by twice the energy of the beam: This practically mean that the Bhabha particle carries E rel fraction of E beam.

7. Relative energy cut

8. This plot (thanks, Mila!) explains the sharp drops in background between 0 and 40 GeV and between 125 and 150 GeV. It seems that looser cut on relative energy (60% instead of 80% of relative energy, e. g. 150 GeV instead of 200 GeV) can be used together with asymmetric theta cut!

9. Bias of energy scale This plot is trying to answer what if there is some (known) bias in our energy measurement. According to these results, if there is an energy bias, it should be known with margin of ±148 MeV, if one wants to know luminosity at the 10 -4 level.

10. Energy resolution from the detector design Energy of particles in LCAL is measured through the calibration procedure, assuming both showers fully contained in the LCAL. Measured particle energy is, thus, affected by resolution effect. Since the detector is being calibrated under realistic beam conditions, the bias of energy scale can also be present. According to results presented at the phone conference on 31 st of January 2008 by I. Sadeh, energy resolution of 20%  GeV is taken in this study as a resolution that will be most probably achieved with the current LCAL design.

11. As mentioned, we assume the energy resolution of 20%  GeV with the current design. In order to check how well we have to control the resolution itself, a set of simulations has been done. In following simulations, a random number generator is used to smear, according to energy resolution, the actual energy of particles that caused a shower in the LCAL. Luminosity vs. E resolution using relative energy cut

12. For ERCUT=200 GeV, if one wants to achieve luminosity uncertainty below 10 -4, uncertainty of energy resolution at 20% should be about 1,5%. This is consistent with the value calculated by A. Stahl in his famous Note, though these two results are not fully comparable due to presence of additional asymmetric cuts on theta. But… Luminosity vs. E resolution using relative energy cut

13. For ERCUT=150 GeV, polynomial fit is not needed, a very simple linear fit looks quite fine. For luminosity uncertainty of 10 -4, we have to control energy resolution at the level of 25%, practically independent of resolution itself. Luminosity vs. E resolution using relative energy cut In both cases (cuts @ 200 and 150 GeV), we are dominated by the statistical dissipation (of order 10 -3 ) due to finite detector resolution.

14. Energy balance cut In following section, selection based on energy balance cut value (EBCUT) is studied. Energy balance is defined as the difference between energies of two particles from the pair divided by the energy of the particle with the lower energy: Asymmetric theta cuts are also applied.

15. Energy balance cut With the nominal ILC luminosity, we are practically insensitive to the statistical loss of signal due to selection efficiency. If the signal/background ratio can be controlled to the level of 10 -1, we can move from EBCUT=0,1 (used as default value so far) to EBCUT=0,2 and still to keep the uncertainty at the level of 10 -4.

16. For luminosity uncertainty of 10 -4, with this cut we have a very small margin to control energy resolution. For  E=20%, we have to know it at the level of 0,56%! In comparison with the relative energy cut at 150 GeV, where we are practically insensitive to the level we control energy resolution, this result indicates that energy balance cut should not be used instead of cut on relative energy. Luminosity vs. E resolution using energy balance cut

17. Conclusion Taking into account beam-beam deflection effects, presence of physics background from 4-fermion processes, energy resolution of the detector and possible biases of energy scale, we propose the following selection for luminosity measurement: asymmetric theta cuts; relative energy cut at 150 GeV (particles carry at least 60% of the beam energy). With such selection, systematics from all mentioned sources is kept below 10 -3, if we assume that we can really control the beam-beam deflection effects at the level of 10 -2 and physics background at the level of 10 -1. Energy resolution of the detector should (and certainly will) be controlled better than 25% and the possible bias of energy scale has to be known to approximately 150 MeV, or at the level of 10 -3.