Luminosity Spectrum Reconstruction - Impact of Detector Resolution Mismodelling Philipp Zehetner CERN Summer Student Supervised by Esteban Fullana and Andr´ e Sailer August 31, 2018
Preview 1. Short Introduction to Luminosity Spectra 2. Simulating the Luminosity Spectrum 3. Motivation for my Project 4. Analysis and Results 5. Outlook
What is the Luminosity Spectrum? dN/dE -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 0 500 1000 1500 E [GeV] Figure: Simulated CLIC luminosity spectrum for 3 TeV
Why is it not a delta-distribution?
Why is it not a delta-distribution? ◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the bunch. This is a property of the accelerator.
Why is it not a delta-distribution? ◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the bunch. This is a property of the accelerator. ◮ Pinch-effect Small beams generate large electrical fields. These fields squeeze the beam and defelct the particles towards the center.
Why is it not a delta-distribution? ◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the bunch. This is a property of the accelerator. ◮ Pinch-effect Small beams generate large electrical fields. These fields squeeze the beam and defelct the particles towards the center. ◮ Beamstrahlung Deflected particles radiate photons and thus reduce the particle’s energy.
Why is it not a delta-distribution? ◮ Beam-energy-spread Particles’ energy depend on their longitudinal position within the bunch. This is a property of the accelerator. ◮ Pinch-effect Small beams generate large electrical fields. These fields squeeze the beam and defelct the particles towards the center. ◮ Beamstrahlung Deflected particles radiate photons and thus reduce the particle’s energy. ◮ Correlation between energies If a particle collides with a particle at the front it is less likeley to have radiated beamstrahlung as it travelled less in the other particles’ field.
Beam-Energy-Spread 0.01 400 dN/dx Energy spread Beam E/E 300 ∆ 0 200 100 -0.01 0 -150 -100 -50 0 50 100 150 -0.004-0.002 0 0.002 0.004 x= E/E Z [ µ m] ∆ Beam (a) Energy dependece on (b) Beam-energy-spread as longitudinal position simulated by GuineaPig
Energy Correlation 1 Beam 3 10 /E 2 E 2 10 10 1 -1 10 0.5 0.5 1 E /E 1 Beam Energy spectrum simulated with GuineaPig for 3 TeV
Why do we care?
Why do we care? ◮ Cross-sections depend on the centre-of-mass energy Assuming that all particles have the nominal energy is just wrong and would yield large errors on the cross-sections which propagate in many other measurements
Why do we care? ◮ Cross-sections depend on the centre-of-mass energy Assuming that all particles have the nominal energy is just wrong and would yield large errors on the cross-sections which propagate in many other measurements ◮ Lorentz boost depends on energy difference and observables measured in the lab-frame depend on the Lorentz boost. If one particle has lost energy, lab frame and centre-of-mass frame are not identical anymore
How can we ’calculate’ it?
How can we ’calculate’ it? ◮ We can’t (at least not directly) The pinch effect and thus the Beamstrahlung highly depend on the exact geometry of the bunch which can’t be measured
How can we ’calculate’ it? ◮ We can’t (at least not directly) The pinch effect and thus the Beamstrahlung highly depend on the exact geometry of the bunch which can’t be measured ◮ It can be measured indirectly using Bhabha scattering E.g. as described in Luminosity Spectrum Reconstruction at Linear Colliders by St´ ephane Poss and Andr´ e Sailer .
The Model Peak Peak Arm1 Arm1 1.01 1.01 The model consists of four 2 2 x x -3 -3 10 10 different parts: 1 1 10 -4 10 -4 0.99 0.99 -5 -5 10 10 ◮ Peak : No particle 0.98 0.98 -6 -6 10 10 radiated beamstrahlung 0.97 10 -7 0.97 10 -7 0.97 0.98 0.99 1 1.01 0.97 0.98 0.99 1 1.01 x x 1 1 ◮ Body : Both particles Arm2 Arm2 Body Body 1.01 1.01 radiated beamstrahlung 2 2 x x 10 -3 10 -3 1 1 ◮ Arm1 : Particle 2 -4 -4 10 10 radiated beamstrahlung 0.99 0.99 -5 -5 10 10 ◮ Arm2 : Particle 1 0.98 0.98 10 -6 10 -6 radiated beamstrahlung -7 -7 0.97 10 0.97 10 0.97 0.98 0.99 1 1.01 0.97 0.98 0.99 1 1.01 x x 1 1
Mathematical Model x 1 ; [ p ] 1 � � L ( x 1 , x 2 ) = p Peak δ (1 − x 1 ) ⊗ BES Peak x 2 ; [ p ] 2 � � δ (1 − x 2 ) ⊗ BES Peak � x 1 ; [ p ] 1 � + p Arm 1 δ (1 − x 1 ) ⊗ BES Arm 1 x 2 ; [ p ] 2 Arm 1 , β Arm � � BB Limit (1) � x 1 ; [ p ] 1 Arm 2 , β Arm � + p Arm 2 BB Limit x 2 ; [ p ] 2 � � δ (1 − x 2 ) ⊗ BES Arm 2 � � Body , β Body x 1 ; [ p ] 1 + p Body BG Limit � � Body , β Body x 2 ; [ p ] 2 BG Limit ◮ 19 free parameters
Extracting the Luminosity Spectrum MC events Events simulated generated according with GuineaPig to the model later: Data
Extracting the Luminosity Spectrum MC events Events simulated generated according with GuineaPig to the model later: Data BHWIDE BHWIDE after Bhabha scattering after Bhabha scattering
Extracting the Luminosity Spectrum MC events Events simulated generated according with GuineaPig to the model later: Data BHWIDE BHWIDE after Bhabha scattering after Bhabha scattering Gaussian Gaussian Smearing Smearing Detector Level Detector Level
Extracting the Luminosity Spectrum MC events Events simulated generated according with GuineaPig to the model later: Data BHWIDE BHWIDE after Bhabha scattering after Bhabha scattering Gaussian Gaussian Smearing Smearing Detector Level Detector Level Fitted model as good approximation for the luminosity spectrum
Error Propagation ◮ Create 38 new luminosity spectra by shifting each parameter by ± σ ◮ The error on the top mass for each parameter is the difference between the nominal value and the one obtained by the shifted luminosity spectrum ◮ The total error is the square sum of the errors taking in account the covariance matrix
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