Luminosity determination at LHC J. Pek 1 1 Faculty of Nuclear - - PowerPoint PPT Presentation

Luminosity determination at LHC

• J. Půček1

1Faculty of Nuclear Sciences and Physical Engineering

Czech Technical University of Prague

Defence of research project, 26.09.2018

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Luminosity

Luminosity is proportional to interaction rate L = Rσ. For bunched beams the luminosity can be expressed as: L = KnbfN1N2 ∞

−∞

S1(x, y, z)S2(x, y, z)dV (1)

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Thesis overview

• Five chapters + introduction and conclusion
• 1. Luminosity
• 2. Van der Meer scan
• 3. Luminosity determination at the LHC
• 4. Simulation of luminosity
• 5. Simulation with a realistic vertex resolution

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Completed tasks

• Literature review on luminosity papers of the LHC experiments, creating

same structure for all the reviewed papers (experiment overview, luminosity detectors, luminosity measurement protocol, other methods of luminosity determination)

• Benchmark of simulation framework for single and double Gaussian

distribution, estimating simulation uncertainties

• Study of change in luminosity for correlated distributions, describing this

phenomenon analytically

• Examination of difference between generated and smeared vertices

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Remark to bachelor thesis

The bias of 2-4% was found in the RMS of generated 2D distributions.

Table 1 : Porovnání hodnot σrov vypočtených z rovnice (..) s hodnotami σfit získanými nafitováním jednorozměrné projekce 2D Gaussovy distribuce. Ukazuje se, že hodnoty jsou podhodnoceny o 2-4%.

ρ 0.27 0.53 0.80 σrov 0.963 0.848 0.6000 σfit 0.942± 0.007 0.816± 0.006 0.586± 0.004 The fault originated from low bin contents, which implied the need to fit with likelihood method. Afterwards the results agreed perfectly.

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Benchmarking

Comparing simulation output with analytical computation for several cases:

• Head-on collisions
• Offset collisions
• Collisions with a crossing angle
• Collisions with a crossing angle and an offset

First tested for single Gaussian bunches, later verified with double Gaussian bunches.

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Benchmarking

Head-on collisions

]

2

[cm

y

σ

x

σ 0.5 1 1.5 2 2.5 3

analytical

/Lumi

simulation

Lumi 0.985 0.99 0.995 1 1.005 1.01 1.015 1.02 1.025

/ ndf

2

χ 11.259 / 18 p0 0.001 ± 1.004 / ndf

2

χ 11.259 / 18 p0 0.001 ± 1.004

The average ratio between simulated and computed luminosity is

Ls La = (1.004 ± 0.001).

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Benchmarking

Offset collisions

Separation [cm] 0.2 − 0.15 − 0.1 − 0.05 − 0.05 0.1 0.15 0.2

HeadOn

/L

• ffset

L 0.2 0.4 0.6 0.8 1

Constant 0.00164 ± 0.99941 Mean 0.00004 ± 0.00012 Sigma 0.00003 ± 0.07066 Constant 0.00164 ± 0.99941 Mean 0.00004 ± 0.00012 Sigma 0.00003 ± 0.07066

Expected σa = 0.07071, obtained σfit = (0.07066 ± 0.00003), difference of 0.07%.

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Benchmarking

Collisions with a crossing angle

[rad] φ 0.01 − 0.005 − 0.005 0.01 Correction factor [-] 0.88 0.9 0.92 0.94 0.96 0.98 1

p0 0.00 ± 2500.00 p1 0.01 ± 1.00 p0 0.00 ± 2500.00 p1 0.01 ± 1.00

Luminosity angle correction factor

The overall uncertainty is 1%, although the errors are overestimated.

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Benchmarking

Collisions with a crossing angle and an offset

Separation [cm] 0.20 − 0.15 − 0.10 − 0.05 − 0.00 − 0.05 0.10 0.15 0.20

HeadOn

/L

• ff+angle

L 0.2 0.4 0.6 0.8 1.0

Constant 0.00164 ± 0.99874 Mean 0.00009 ± 0.00031 Sigma 0.00009 ± 0.10238 Constant 0.00164 ± 0.99874 Mean 0.00009 ± 0.00031 Sigma 0.00009 ± 0.10238

The difference here between the analytical prediction and the simulation is 0.4%, which is comparable to the head-on uncertainty.

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Benchmarking

Head-on collisions - Double Gaussian model

1A-x

σ 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

1A-y

σ 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.994 0.996 0.998 1 1.002 1.004

From standard formula the predicted uncertainty of two colliding Double Gaussians should be 0.25% and was measured to be 0.27%.

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Non-factorisation

If the bunch has an xy correlation the luminosity value changes.

ρ 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 [a.u.]

sim

L 20 21 22 23 24 25 26

9

10 ×

The other bunch had a correlation of 0.5, that is the reason why the minimum is shifted.

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Non-factorisation

Non-factorisation ratio

The value of delivered luminosity divided by the value obtained from vdM method is called non-factorisation ratio, noted R. R = S1(x, y)S2(x, y)dxdy

• S1(x)S2(x)dx
• S1(y)S2(y)dy

(2)

[-] ρ 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 R [-] 0.92 0.94 0.96 0.98 1 Půček J. (FNSPE) Luminosity determination at LHC RP defence 13 / 16

Simulation with a realistic primary vertex resolution

Can the detector’s effects change the measured vertices? Generated vertices are smeared by real-world data and the fits are compared.

0.01 − 0.008 − 0.006 − 0.004 − 0.002 − 0.002 0.004 0.006 0.008 0.01 0.01 − 0.008 − 0.006 − 0.004 − 0.002 − 0.002 0.004 0.006 0.008 0.01

/ ndf

2

χ 731.8 / 748 Constant 1.177 ± 72.24 Correlation 0.0122 ± 0.01597

x

µ 05 − 2.455e ± 06 − 6.384e

x

σ 05 − 2.035e ± 0.002236

y

µ 05 − 1.613e ± 05 − 2.344e −

y

σ 05 − 1.354e ± 0.001472

10 20 30 40 50 60 70 80 90

/ ndf

2

χ 731.8 / 748 Constant 1.177 ± 72.24 Correlation 0.0122 ± 0.01597

x

µ 05 − 2.455e ± 06 − 6.384e

x

σ 05 − 2.035e ± 0.002236

y

µ 05 − 1.613e ± 05 − 2.344e −

y

σ 05 − 1.354e ± 0.001472

Generated Vertices

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Simulation with a realistic primary vertex resolution

0.02 − 0.015 − 0.01 − 0.005 − 0.005 0.01 0.015 0.02 0.02 − 0.015 − 0.01 − 0.005 − 0.005 0.01 0.015 0.02 / ndf

2

χ 1004 / 838 Constant 1.334 ± 78.02 Correlation 0.0121 ± 0.06397

x

µ 05 − 3.991e ± 06 − 2.192e

x

σ 05 − 3.357e ± 0.003716

y

µ 05 − 3.397e ± 05 − 2.799e −

y

σ 05 − 2.934e ± 0.003181 10 20 30 40 50 60 70 80 90 100 / ndf

2

χ 1004 / 838 Constant 1.334 ± 78.02 Correlation 0.0121 ± 0.06397

x

µ 05 − 3.991e ± 06 − 2.192e

x

σ 05 − 3.357e ± 0.003716

y

µ 05 − 3.397e ± 05 − 2.799e −

y

σ 05 − 2.934e ± 0.003181

Smeared Vertices

A correlation emerged after smearing, generated (0.01 ± 0.01), smeared (0.06 ± 0.01).

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Outlook

• Further examination of smeared vertices by 3D fit
• To be able to take into account uncertainties, which is analytically possible
• nly for single Gaussian, while using more complicated fit models
• Study differences of using single Gaussian fits while generating double

Gaussian bunches

• Develop an "unfolding" method

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