Getting the Lumispectrum from Bhabha events

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

2
Next 20 mins

• 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

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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

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Bhabha acollinearity

• Bhabha (ee-?ee-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 gt?s (xtgt1)
• But only measure xmlt1 as Bhabha acollinearity
  only sensitive to ?p.
• (but can sign x)
• Luminosity weighted

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Bhabha simulation

• Beam simulation
• Circe/Guinea-Pig (modified)
• Accelerator simulation (G. White) Beam
  collision simulation
• E0175 GeV, simple scaling of accelerator
  parameters.
• Guinea-Pig
• TESLA TDR parameters scaled appropriately by
  energy (500 ?350GeV)
• Bhabha scattering
• BHWIDE (350 GeV, ?gt7?)

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Reconstruction performance

• 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 x1.
• Mean shift ltxm-xtgt
• 16.05?10-4
• Large due to asymmetric tails in xm-xt

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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 _at_ UCL to extract
  the lumi spectrum
• Beamstrahlung parametrisation fitting
• Unfolding whole luminosity spectrum

Log z scale, looks worse than is
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Fitting beamstrahlung parameters (Moenig)

• Based on Circe
• Initial (default) parameters (350 GeV Tesla)
• a00.5461
• a1 normalisation condition
• a220.3
• a3-0.6275
• Shift parameters by ?ai0.2, 0.5, 0.2
  respectively
• passed through BHWIDE, histogrammed (shown right
  fit basis)
• Compute spectrum at a given parameter point using

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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
• a00.612 ? 0.001 (0.5461)
• a219.39 ? 0.17 (20.3)
• a3 -0.594 ? 0.003 (-0.6275)

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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

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Unfolding luminosity spectrum

• Process of measurement
• xmAxt (Aresponse matrix)
• Extracting xt from xm
• Many different methods exist.
• Inversion of A
• xtA-1xm
• Problematic when As elements have statistical
  errors.
• Regularisation term (?) to minimise bin-bin
  variation
• Packages exist
• GURU
• Singular Value Decomposition

A
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Unfolding given beam spread

• Simple study (UG student _at_ UCL D. Turner)
• 500 GeV TDR Tesla
• Gaussian beam spread ?BS0.1
• 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 (xmAxt)
• Try to recover xt

measured
true/unfolded
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Unfolding signed x

• Avoid lack of data at xmgt1
• Give sign to xm and xt based on sign of ?A
• Avoids the problem of the cliff at x1
• For further study
• Signed x sensitive to asymmetry between beams
• Expect more stable extraction of spectrum
• Could also use signed x in fit

measured
true/unfolded
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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

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Summary and conclusions

• 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