Impact of transverse coupling on the ATLAS

luminosity calibration in the Gaussian beam limit

Lee TomlinsonThe University of Manchester

IOP Liverpool8 – 10 April 2013

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The van der Meer method

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Beam separation, h

Prop

ortio

nal t

o lu

min

osity

, R(h

)

The vdM method allows one to calibrate the absolute

luminosity scale by scanning the beams past one another.

S. van der Meer, Calibration of the effective beam height

in the ISR. oai:cds.cern.ch:296752, Tech.

Rep. CERN-ISR-PO-68-31, CERN, Geneva, 1968.Implicitly assumes factorisation of x and y components! How does

(linear) x-y correlation in the beam affect this method?

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The single-Gaussian model

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where and

The luminosity in this model is proportional to

This is the single-Gaussian bunch parameterisation

In the absence of explicit beam crossing angle

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Two illuminating examples

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Different beam sizes

x-y correlation

Beam 1 Beam 1

Beam 2Beam 2

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Scanning beams of different size

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Luminous region follows the bulk of the narrow beam as it scans the wider beam

Scan in horizonta

l direction

Beam 1 Beam 2

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Movements of luminous region is transverse to scan direction

Scanning x-y correlated beams

Beam 1 Beam 2

Scan in horizonta

l direction

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Movements of the luminous centroid

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July 2012 scan (6) data

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ATLAS work in progress

ATLAS work in progress

ATLAS work in progress

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July 2012 scan (6) data

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ATLAS work in progress

ATLAS work in progress

ATLAS work in progress

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Constraints(July 2012 scan 6)

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1ATLAS work in progress

ATLAS work in progress

ATLAS work in progressATLAS work in progress

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Constraints(July 2012 scan 6)

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1

1

ATLAS work in progress

ATLAS work in progress

ATLAS work in progressSimilarly for the y-width constraints

Widths are uncertainties on measured Σ values

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Constraints(July 2012 scan 6)

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1

1

2ATLAS work in progress

ATLAS work in progress

ATLAS work in progress

Similarly for the y position during x scan From direct measurement of luminous region

correlation

ATLAS work in progress

κ is correlation coefficient

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Constraints(July 2012 scan 6)

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1

1

2

Uncertainties from constraints in (1) are propagated to band

widths in (2)

ATLAS work in progress

ATLAS work in progress

ATLAS work in progress

Small allowed

region in correlation space,

consistent with zero

κ is correlation coefficient

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Explicit beam crossing angle

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“Significant” crossing angle

…vdM scan III (3) in April 2012

ATLAS work in progress

…has been included in the model, essentially functioning as an x-z and a y-z correlation.

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Conclusions• Permits a fully-analytic approach. Soluble with series solution about

small correlation.

• Systematic method for constraining all beam parameters without boot-strapping, iterating, etc.

• Arbitrary crossing-angle easily incorporated, retaining analyticity.

• Applied to vdM scans in Oct ’10, Mar ’11, May ’11, Apr ’12 and Jul ’12.

• Consistently suggests impact of (linear) transverse coupling on luminosity calibration is negligible.

• One of the systematic contributions that enters an unprecedented 1.8% luminosity error at ATLAS.

• On-going work: Further models have been explored in detail, which successfully account for many of the non-linear features observed in the data.

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BACKUP SLIDES

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Successes and limitations

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ATLAS work in progress

Non-linear tails cannot be described using single-

Gaussian model

ATLAS work in progress

Crossing angles are

easily implemented

in single-Gaussian

model

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Further models and work in progress

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Further models have been explored in detail, which successfully

account for many of the non-linear features observed in the data.

An analytical approach is not always possible, as with the single-Gaussian model. Work is based on

solving these as far as possible.

Double Gaussian Super Gaussian

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Scanning beams of different size

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Higher negative separation

Higher positive separation

Centred

Beam 1 Beam 2

Luminous region follows the bulk of the narrow beam as it scans the wider beam

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Movements of luminous region is transverse to scan direction

Higher negative separation

Higher positive separation

Centred

Scanning x-y correlated beams

Beam 1 Beam 2