Fast Luminosity Spectrum Measurement Aim Bhabha Beamstrahlung generator

Fast Luminosity Spectrum Measurement Aim Bhabha & Beamstrahlung generator Interface Luminosity Calorimeter Response matrix Parameters estimation technique Estimation result Unfolding Choice of regularisation parameter Summary Outlook Freddy Poirier - RHUL/JAI f. poirier@rhul. ac. uk Freddy Poirier – ILC-European workshop 2005

Fast luminosity spectrum measurement Aim: Measurement of luminosity spectrum using Bhabha scattering at low angle at the ILC. Determination of the effects (beamstr. & beam energy spread) modifying the luminosity spectrum. Determination of these effects is crucial in order to extract precision physics from threshold scans. Several groups are studying the lumi spectrum measurements using Bhabha scattering at large angle (Frary/Miller scheme, K. Moenig scheme) ISR If these effects are determined fast enough using Bhabha scattering it would become an interesting beam diagnostic. What is the potential of lumi spect. measurement at low angle? Freddy Poirier – ILC-European workshop 2005

Bhabha and Beamst. Generators -Bhabha generator: e+e- ( Bhwide 1. 04) Cross-section large at small angle All contributions to spectrum. ~7 nb between 23<θ<85 mrad at 500 Ge. V including ISR. LC parameters (TESLA TDR): -Interfaced with Beamstrahlung Generator CIRCE. 553 nm x 5 nm x 300 μm -Centre of mass energy is rescaled -Boost particle when beamstrahlung Angular distribution of electrons. Before and after inclusion of the interface with the beamstrahlung generator. Generation with larger angle than calorimeter angular acceptance. Freddy Poirier – ILC-European workshop 2005 Gaussian beam energy spread: 0. 18%

Luminosity Calorimeter • Measurement with luminosity calorimeter (geometry L* = 4. 05 m– head on collision) • Lumi. Cal – Angular acceptance 26. 2 to 82 mrad – ΔE/E = 25%/sqrt(E) – Molière radius ~ 9 mm* *This values correspond to one of the potential technology: (W. Lohmann et al. ) Silicon tungsten like calorimeter Freddy Poirier – ILC-European workshop 2005

Lumi. Cal. – Response Simple Cluster finding Response matrix R of the lumi. Cal. 1 cluster = highest energy particle in calo. + energies of other particles within 1 moliere radius. Typical Measured Spectrum 1 cluster in each calorimeter 48 x 106 generated events for R (true versus measured energy of the clusters) Freddy Poirier – ILC-European workshop 2005

Determination of Beamstr. Technique • CIRCE parameterizes beamstrahlung according to • By constructing a grid of spectra with the parameters modified by δak - here δak=10% one can obtained the derivative calculation • For Estimation of the parameters of a spectrum, a minimization of the chi 2 is performed (Based on K. Moenig’s technique) – The beam energy spread is included as a 4 th parameter. – This technique requires at least 8 generated spectrum. – Fits only applied to highest energy part (>200 Ge. V) Freddy Poirier – ILC-European workshop 2005

Parameter Determination Results • Technique applied on true (before detection and event selection) and simulated “measured” spectra. • 5 samples with a different random seed are used to investigate possible bias in estimation technique: – Each 0. 27 fb-1 – Run time = 2. 2 hours True The technique works on true spectra (errors are small – pull around unity) “Measured” Larger errors and pull >1 – get worse with worse energy resolution & efficiency < 100% Can we use unfolding to obtain better results than the measured ones? Freddy Poirier – ILC-European workshop 2005

Unfolding • • • The package in use for the Unfolding is GURU – SVD approach. The unfolding technique is to inverse the response matrix of the calorimeter and to “force” the unfolded spectrum to have a minimum bin to bin curvature (Tikhonov Method). This is done by adding a regularisation function to the least-square function applied on the unknown distribution. CIRCE + BHWIDE Calorimeter Unfolding Technique R ~R-1 parameter : t ANALYSIS Regularisation term Response matrix of calorimeter Unknown weight Reference distribution Witch acts as a smoothing function for the highly peaked spectrum. Nref is here made up of 48 *106 events and is a highly peaked distribution. Freddy Poirier – ILC-European workshop 2005

Choice of Regular. term • The strategy employed here is to fix the regularisation term for the set of spectra in our hand (5 samples – 0. 27 fb-1) Large stable region • Scan of the estimation of the parameters with respect to the regularisation term shows a large stable region. • Some systematic effects occurs at large tau. • At small tau, fluctuations in the unfolded spectrum limit the accuracy on the estimation. Tau=6*107 Freddy Poirier – ILC-European workshop 2005

Summary Unfolding helps drastically to gain in accuracy for the beam energy spread measurement. Larger mean errors in the estimated parameters for the unfolded results. Lumi. spectrum reconstructed correctly (not minimum χ2). Relative errors Freddy Poirier – ILC-European workshop 2005 Tau=6*107

Outlook • Results reveal that this method could be used to determine luminosity spectrum on an hourly basis to a precision of less than a percent. • Here only one cluster measurement was used. Using the two clusters, improvement can be expected (more statistics) and energy correlation can then be studied. • The question of background should be addressed, • Large grid should be built and several spectra with various parameters could then be studied, • At Snowmass accurate definition of forward calorimeter will be given and should be used for later unfolding. Freddy Poirier – ILC-European workshop 2005