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Getting the Lumi-spectrum from Bhabha events

Getting the Lumi-spectrum from Bhabha events. Stewart Boogert and David Miller University College London ALCPG, IPBI/IR/MDI session, Victoria 29 th July 2004. Talk outline Bhabha acollinearity Simulation Reconstruction performance Fitting Luminosity spectrum Unfolding Top threshold

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Getting the Lumi-spectrum from Bhabha events

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  1. Getting the Lumi-spectrum from Bhabha events Stewart Boogert and David Miller University College London ALCPG, IPBI/IR/MDI session, Victoria 29th July 2004 Stewart Boogert & David Miller (UCL)

  2. Talk outline Bhabha acollinearity Simulation Reconstruction performance Fitting Luminosity spectrum Unfolding Top threshold Conclusions Luminosity spectrum Essential for all threshold scans at LC Best possible mass measurements of mt, MW or mSUSY Requires detailed understanding of dL/ds Top threshold as reference mt50-100 MeV (see Heinermeyer et al.) mt/mt  3. 10-4 Next 20 mins Stewart Boogert & David Miller (UCL)

  3. Sources of energy variation • Three source of energy variation • Linac energy spread • Typically ~0.1% • Gaussian(?!) shape • Beamstrahlung • 0.7% at 350 GeV • 1.7% at 800 GeV • Initial state radiation • Calculable to high precision in QED • Complicates measurement of beamstrahlung Stewart Boogert & David Miller (UCL)

  4. Bhabha acollinearity • Bhabha (e+e-e+e-n()) • High rate • Simple final state • Angular reconstruction • Calorimeter resolution insufficient to measure dL/ds • Assuming • Single photon radiation • Linac energy spread • Can have s’ >s (xt>1) • But only measure xm<1 as Bhabha acollinearity only sensitive to p. (but can “sign” x) • Luminosity weighted Stewart Boogert & David Miller (UCL)

  5. Bhabha simulation • Beam simulation • Circe/Guinea-Pig (modified) • Accelerator simulation (G. White) + Beam collision simulation • E0=175 GeV, simple scaling of accelerator parameters. • Guinea-Pig • TESLA TDR parameters scaled appropriately by energy (500 350GeV) • Bhabha scattering • BHWIDE (350 GeV, >7) Stewart Boogert & David Miller (UCL)

  6. Reconstruction of luminosity spectrum (xm) Reasonable agreement Definition of xt problematic due to overlap between ISR/FSR (future study “FS”) Difference between measured and true most serious close to x=1. Mean shift <xm-xt> 16.0510-4 Large due to asymmetric tails in xm-xt Reconstruction performance Stewart Boogert & David Miller (UCL)

  7. Reconstruction performance (2) • Failures/problems of the reconstruction • Multiple photon radiation • ISR/FSR factorisation (calo. vs tracking. FS) • Relationship between xt and xm quite complicated • Two methods being investigated @ UCL to extract the lumi spectrum • Beamstrahlung parametrisation fitting • Unfolding whole luminosity spectrum Log z scale, looks worse than is Stewart Boogert & David Miller (UCL)

  8. Fitting beamstrahlung parameters (Moenig) • Based on Circe • Initial (default) parameters (350 GeV Tesla) • a0=0.5461 • a1= normalisation condition • a2=20.3 • a3=-0.6275 • Shift parameters by ai=0.2, 0.5, 0.2 respectively • passed through BHWIDE, histogrammed (shown right; “fit basis”) • Compute spectrum at a given parameter point using Stewart Boogert & David Miller (UCL)

  9. Beamstrahlung fit results • Form usual 2 • Fit Bhabha results without beam spread: • Recovers original Circe parameters with high precision • Fit to 350 GeV TESLA Guinea-Pig sample • a0=0.612  0.001 (0.5461) • a2=19.39  0.17 (20.3) • a3= -0.594  0.003 (-0.6275) Stewart Boogert & David Miller (UCL)

  10. Fit including linac energy spread • Including beam spread • Convolute fit basis luminosity spectra with linac energy spread function fBS(x) • Fit results • Fit of Circe with 0.1% spread • a0,2,3 consistent within statistical error with the no-spread values • BS= 0.976 10-4 • Fit of Guinea-Pig with 0.1% spread • a0= 0.618 (0.6120.001) • a2= 17.83 (19.39 0.17) • a3= -0.609 (-0.594 0.003) but • BS= 1.004 10-4 Stewart Boogert & David Miller (UCL)

  11. Unfolding luminosity spectrum • Process of measurement • xm=Axt (A=response matrix) • Extracting xt from xm • Many different methods exist. • Inversion of A • xt=A-1xm • Problematic when A’s elements have statistical errors. • Regularisation term () to minimise bin-bin variation • Packages exist • GURU • Singular Value Decomposition A Stewart Boogert & David Miller (UCL)

  12. Unfolding given beam spread • Simple study (UG student @ UCL D. Turner) • 500 GeV TDR Tesla • Gaussian beam spread BS=0.1% • Data binned with variable bin width to minimise curvature of dL/dx • Careful choice of regularisation parameter () • Concentrate on peak region • Unfold consistent set of data (xm=Axt) • Try to recover xt measured true/unfolded Stewart Boogert & David Miller (UCL)

  13. Unfolding signed x • Avoid lack of data at xm>1 • Give sign to xm and xt based on sign of A • Avoids the problem of the cliff at x=1 • For further study • Signed x sensitive to asymmetry between beams • Expect more stable extraction of spectrum • Could also use signed x in fit true/unfolded measured Stewart Boogert & David Miller (UCL)

  14. Effect on the top threshold • Results from talk in Top and QCD session • Effect of ISR and beamstrahlung only gives a shift of ~50 MeV • Next step to include linac energy spread on top threshold based on methods described above Stewart Boogert & David Miller (UCL)

  15. Conclusions Fitting seems to work Recover beam spread for Circe and Guinea-Pig Problems with other Guinea-Pig parameters with BS Needs further study. Unfolding seems to work with beam spread Careful choice of binning and regularisation parameter Signed x promising Future direction and work Fitting Better luminosity spectrum interpolation Ready to implement luminosity spectrum parametrisation on top threshold Unfolding Must complete study by unfolding x with independent MC samples. Signed x studies Summary and conclusions Stewart Boogert & David Miller (UCL)

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