Luminosity Measurement at the International Linear Collider

Iftach Sadeh

Tel Aviv University

( On behalf of the FCAL collaboration )

December 28th 2008http://alzt.tau.ac.il/~sadeh/

sadeh@alzt.tau.ac.il

Overview

1.The International Linear Collider (ILC).

2.Luminosity measurement at the ILC.

3.Design and performance of the luminosity calorimeter (LumiCal).

4.A clustering algorithm for LumiCal.

2

The ILC & The ILD detector3

LumiCal Performance requirements

1. Required precision is:

2. Measure luminosity by counting the number of Bhabha events (NB) in a well defined angular and energetic range:

3 9

3 6

3 6

10 , GigaZ (hadronic Z decays) 10 / year

~10 , 10 / year

~10 , 10 / year

L

LL

e e W WLL

e e q qL

3

1Bd

d

max

min

, rec genB B

B B gen

N NN NLL

L N N

RIGH LEFTTΔθ - θθLEFTθ

RIGHTθ

4

LumiCal Design parameters

3. Layers:

Number of layers - 30

Tungsten Thickness - 3.5 mm

Silicon Thickness - 0.3 mm

Elec. Space - 0.1 mm

Support Thickness - 0.6 mm

1. Placement:

2270 mm from the IP

Inner Radius - 80 mm

Outer Radius - 190 mm

2. Segmentation:

48 azimuthal & 64 radial divisions:

Azimuthal Cell Size - 131 mrad

Radial Cell Size - 0.8 mrad

5

ares

σ(θ)

Intrinsic parameters of LumiCal

Relative energy resolution:

Position reconstruction (polar angle):

6

4

min

21.5 10

L

L

Topology of Bhabha scattering Bhabha scattering with √s = 500 GeV

θ Φ

Energy

Separation between photons and leptons, as a function of the energy of the low-energy-particle.

7

Clustering Algorithm

Phase I:Near-neighbor clustering in a single layer.

Phase II:Cluster-merging in a single layer.

8

Phase III:Global (multi-layer) clustering.

Overlap of multiple showers

Profile of the energy of a single 250 GeV shower.

Profile of the energy of two showers (230 and 20 GeV) separated by one Moliere radius (indicated by the circles).

9

Clustering - Results (event-by-event)

Event-by-event comparison of the energy and position of showers (GEN) and clusters (REC) as a function of EGen.

10

(θGen - θRec)/ θGen(ΦGen - ΦRec)/ ΦGen

(EGen - ERec)/ EGen

Summary1. Intrinsic properties of LumiCal:

Energy resolution: ares ≈ 0.21 √GeV.

Relative error in the luminosity measurement:ΔL/L = e(rec) e(stat) = 1.5 · 10-4 4 · 10-5 (at 500 fb-1).

- The reconstruction error, e(rec), is due to the error in reconstruction of the polar angle.

- The statistical error, e(stat), is due to fluctuations in the expected number of Bhabha events, ΔNB/NB, for an integrated luminosity of 500 fb-1.

- The theoretical uncertainty is expected to be ~ 2 · 10-4.

2. Partial event reconstruction (counting of radiative photons):

Merging-cuts need to be made on the minimal energy of a cluster and on the separation between any pair of clusters.

The algorithm performs with high efficiency and purity. The number of radiative photons within a well defined phase-space may be counted with an acceptable uncertainty.

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AuxiliarySlides

The ILC & The LDC detector13

Physics Background Four-fermion processes are the main background, dominated by two-photon

events (bottom right diagram).

The cuts reduce the background to the level of 10-4

ffeeeeFour-fermion processes

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Selection of Bhabha events

Right side signal

Left

sid

e si

gnal

deg5

rad310

LRLR RERE ,min1.0

Simulation distribution

Distribution after acceptance and energy balance selection

15

RIGH LEFTTΔθ - θθLEFTθ

RIGHTθ

Detector signal

Distribution of the deposited energy spectrum of a MIP (using 250 GeV muons):MPV of distribution = 89 keV ~ 3.9 fC.

Distributions of the charge in a single cell for 250 GeV electron showers.

The influence of digitization on the energy resolution and on the polar bias.

16

ares

σ(θ)

ares

Digitization

σ(θ)

Δθ

Thickness of the tungsten layers (dlayer)

σ(θ)Δθ

ares

18

Number of radial divisions

σ(θ) Δθ

min

2

L

L

-1

5

500GeV

1.23nb

500 fb

4 10

s

L

N

N

Dependence of the polar resolution, bias and subsequent error in the luminosity measurement on the angular cell-size, lθ.

19

Inner and outer radii

Beamstrahlung spectrum on the face of LumiCal (14 mrad crossing angle): For the antiDID case Rmin must be larger than 7cm.

-1500 fbL

63.2 10 rad

20

MIP (muon) Detection in LumiCal Many physics studies demand the ability to detect muons (or the lack thereof) in

the Forward Region.

Example: Discrimination between super-symmetry (SUSY) and the universal extra dimensions (UED) theories may be done by measuring the smuon-pair production process. The observable in the figure, θμ, denotes the scattering angle of the two final state muons.

“Contrasting Supersymmetry and Universal Extra Dimensions at Colliders” – M. Battaglia et al. (http://arxiv.org/pdf/hep-ph/0507284)

1 1 1 1

2UED:

~ 1 coscos

e e

d

d

0 01 1

2SUSY:

~ 1 coscos

e e

d

d

21

MIP (muon) Detection in LumiCal

Multiple hits for the same radius (non-zero cell size).

After averaging and fitting, an extrapolation to the IP (z = 0) can be made.

22

1. High beam-beam field (~kT) results in energy loss in the form of synchrotron radiation (beamstrahlung).

2. Bunches are deformed by electromagnetic attraction: each beam acting as a focusing lens on the other.

Change in the final state polar angle due to deflection by the opposite bunch, as a function of the production polar angle.

Beam-Beam effects at the ILC

Since the beamstrahlung emissions occur asymmetrically between e+ and e-, the acolinearity is increased resulting in a bias in the counting rate.

“Impact of beam-beam effects on precision luminosity measurements at the ILC”

– C. Rimbault et al. (http://www.iop.org/EJ/abstract/1748-0221/2/09/P09001/)

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Effective layer-radius, reff(l) & Moliere Radius, RM

Dependence of the layer-radius, r(l), on the layer number, l.

RM

r(l)

24

Distribution of the Moliere radius, RM.

Clustering - Algorithm

Phase I:Near-neighbor clustering in a single layer.

Phase II:Cluster-merging in a single layer.

Longitudinal shower shape.

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Clustering Algorithm26

Phase III:Global (multi-layer) clustering.

Clustering - Energy density corrections

Event-by-event comparison of the energy of showers (GEN) and clusters (REC).

Before After

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Clustering - Results28

(2→1): Two showers were merged into one cluster.

(1→2): One shower was split into two clusters.

The Moliere radius is RM (= 14mm), dpair is the distance between a pair of showers, and Elow is the energy of the low-energy shower.

Clustering - Geometry dependence29

96 div

48 div

24 div

Clustering - Results (measurable distributions)

Energyhigh

θhigh θlow

Energylow

Δθhigh,low Energy and polar angle (θ) of high and low-energy clusters/showers.

Difference in θ between the high and low-energy clusters/showers.

Merging-cuts:Elow ≥ 20 GeV , dpair ≥ RM

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Clustering - Results (relative errors) Dependence on the merging-cuts of the errors in counting the number of

single showers which were reconstructed as two clusters (N1→2), and the number of showers pairs which were reconstructed as single clusters, (N2→1).

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