impact of transverse coupling on the atlas luminosity calibration in the gaussian beam limit
DESCRIPTION
Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit. Lee Tomlinson The University of Manchester IOP Liverpool 8 – 10 April 2013. The van der Meer method. Proportional to luminosity, R ( h ). - PowerPoint PPT PresentationTRANSCRIPT
Impact of transverse coupling on the ATLAS
luminosity calibration in the Gaussian beam limit
Lee TomlinsonThe University of Manchester
IOP Liverpool8 – 10 April 2013
Lee Tomlinson 2
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