E¯ Energy Resolution
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e¯ Energy Resolution For e⁻ e⁺-> e⁻ e⁺ events. 50000 e⁻ e⁺-> e⁻ e⁺ (3 TeV ) generated with Whizard1 Pt > 5 GeV , 10 ⁰ < θ < 170⁰ , σ ( e⁻ e⁺-> e⁻ e⁺) 6250 fb Pt and θ cut to get rid of γγ -> background Simulation: Mokka :

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E energy resolution for e e e e events

  • 50000 e⁻ e⁺-> e⁻ e⁺ (3 TeV ) generated with Whizard1

  • Pt > 5 GeV, 10⁰ < θ < 170⁰ , σ (e⁻ e⁺-> e⁻ e⁺) 6250 fb

  • Pt and θ cut to get rid of γγ -> background

  • Simulation: Mokka:

  • Reconstruction: Marlin, no overlay (50000) and overlay (10000)

  • e± energy calculation from slepton analysis; use the energy of the

  • clusters, not the track momentum, apply energy correction when

  • γradiation.

  • Energy resolution ΔE/E².

  • √s measurement using the energy of the outgoing e±

  • √s’ measurement using the angles of the outgoing e±

  • Summary

WG6, J-J.Blaising, LAPP/IN2P3


E e without with
ΔE/E² without/with γγ

(left) ΔE/E² (no γγ) 2.4% overflow tail ; (right) ΔE/E²(with γγ) 7% overflow

Tails from events with bremsstrhalung. The γ E correction is based on the track momentum, it requires identifying the track before γ radiation and after γ radiation in order to add the photon E to the track P after radiation. The poor momentum resolution in the FW region=> bad Track_momentum and Cluster_energy matching

=> Remove bremstrahlung events (nb tracks > 2). Correction ok for FSR ( 2 tracks only)

WG6, J-J.Blaising, LAPP/IN2P3


E e without with 2 track events
ΔE/E² without/with γγ2 track events

2 track event selection => reduced tails (events with γγ, overflow ↘ from 7 to 1.4 %)

Energy resolution ΔE/E² = 2.3 10¯⁵, similar to the momentum resolution in barrel

=> Δ E/E = 3.5% and ΔE= 52 GeV for 1.5 TeV e±.

Similar resolution with γγ -> hadrons overlaid.

WG6, J-J.Blaising, LAPP/IN2P3


S s without with
Δ√s/s without/with γγ

Without γγ, Δ √s/s = = 8.6 10¯⁶ => Δ√s = 78 GeV for 1.5 TeV e±

With γγ , Δ √s/s = = 9.1 10¯⁶

WG6, J-J.Blaising, LAPP/IN2P3


S and s without
√s and √s’ without γγ

√s’ calculated from e± angles (true) assuming only one photon is radiated.

(left) dN/d√s’ no crossing angle boost correction and dN/d√s (true); very bad agreement already shown last meeting .

(right) dN/√s’ with boost correction; better agreement, but √s’ wrong when photon radiation on both beams

WG6, J-J.Blaising, LAPP/IN2P3


S and s without1
√s and √s’ without γγ

To show the effect, select events for which Ee- or Ee+ (true) > 1498 GeV => Events with photon radiation only on one beam. Much better agreement.

No measurement < 1.5 TeV

This constraint is not applicable in real data.

The √s’ measurement with multi photon radiation requires the fit method developed by Andre and Stephane.

It uses both the angles and the energies of the outgoing e±.

Estimate the √s’ resolution reachable with the fit method.

WG6, J-J.Blaising, LAPP/IN2P3


S and s without2
√s and √s’ without γγ

(left) √s’ from reconstructed angles, poor agreement with true √s

(right) √s’ from reconstructed angles, requiring √s’ and√s from energy of outgoing e± to be within 3 σ. It is an illustration to show that the measurement of the shape of the lumi spectrum can be measured accurately when the both the angles and the energies are taken into account. For the lower part of the spectrum, 2γrad, the energy resolution dominates.

WG6, J-J.Blaising, LAPP/IN2P3


E energy resolution for e e e e events
Δ√s’/s

To estimate the resolution, compute Δ√s’ =√s’-√s (true) /s (true) , left plot

Δ√s’/s = 1.4 10¯⁶ => Δ√s’= 13.0 GeV at peak energy

Right plot ΔE/E²vsΔθ, no strong ΔE/E², Δθ correlation

ΔE/E² = ~ 2.3 10¯⁵ andΔθ=6 10¯⁶ rad

WG6, J-J.Blaising, LAPP/IN2P3


Summary
Summary

  • The energy resolution for bhabha events is ΔE/E ²= 2.3 10¯⁵

  • (from energy of the clusters)

  • The angular resolution is Δθ= 6 10¯⁶ rad (from tracks)

  • The shape of the luminosity spectrum can be measured using the

  • angles and energies of the e± of bhabha events

  • Δ√s’/s = 1.4 10¯⁶ => Δ√s’= 13.0 GeV at peak energy

  • Guineapig fit can be performed at generator level using ΔE/E² and

  • Δθ from full reconstruction study.

  • The selection efficiency is 80% when removing the bremsstrahlung events and ~ 40% for √s’ > 1.5 teV.

  • Why is ΔE # 0.2/√E ~ 0.5% at 1.5 TeV

  • To measure the lower part of the √s spectrum may require to use

  • the Cluster_energy and/or the Track_momentum

  • WG6, J-J.Blaising, LAPP/IN2P3


    Backup s from energy
    Backup √s from Energy

    WG6, J-J.Blaising, LAPP/IN2P3


    Backup
    Backup

    WG6, J-J.Blaising, LAPP/IN2P3


    E energy resolution for e e e e events
    Δθ and Δφ

    WG6, J-J.Blaising, LAPP/IN2P3


    3 0 tev
    3.0 TeV

    (left) dN/dE distribution of outgoing e ± (true and reco from track)

    (right) dN/dE distribution of outgoing e ± (true and reco from cluster)

    Improved resolution

    WG6, J-J.Blaising, LAPP/IN2P3