Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit
description
Transcript of Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit
![Page 1: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/1.jpg)
Impact of transverse coupling on the ATLAS
luminosity calibration in the Gaussian beam limit
Lee TomlinsonThe University of Manchester
IOP Liverpool8 – 10 April 2013
![Page 2: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/2.jpg)
Lee Tomlinson 2
The van der Meer method
8 - 10 April 2013
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?
![Page 3: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/3.jpg)
Lee Tomlinson 3
The single-Gaussian model
8 - 10 April 2013
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
![Page 4: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/4.jpg)
Lee Tomlinson 4
Two illuminating examples
8 - 10 April 2013
Different beam sizes
x-y correlation
Beam 1 Beam 1
Beam 2Beam 2
![Page 5: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/5.jpg)
Lee Tomlinson 5
Scanning beams of different size
8 - 10 April 2013
Luminous region follows the bulk of the narrow beam as it scans the wider beam
Scan in horizonta
l direction
Beam 1 Beam 2
![Page 6: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/6.jpg)
Lee Tomlinson 68 - 10 April 2013
Movements of luminous region is transverse to scan direction
Scanning x-y correlated beams
Beam 1 Beam 2
Scan in horizonta
l direction
![Page 7: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/7.jpg)
Lee Tomlinson 7
Movements of the luminous centroid
8 - 10 April 2013
![Page 8: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/8.jpg)
Lee Tomlinson 8
July 2012 scan (6) data
8 - 10 April 2013
ATLAS work in progress
ATLAS work in progress
ATLAS work in progress
![Page 9: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/9.jpg)
Lee Tomlinson 9
July 2012 scan (6) data
8 - 10 April 2013
ATLAS work in progress
ATLAS work in progress
ATLAS work in progress
![Page 10: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/10.jpg)
Lee Tomlinson 10
Constraints(July 2012 scan 6)
8 - 10 April 2013
1ATLAS work in progress
ATLAS work in progress
ATLAS work in progressATLAS work in progress
![Page 11: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/11.jpg)
Lee Tomlinson 11
Constraints(July 2012 scan 6)
8 - 10 April 2013
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
![Page 12: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/12.jpg)
Lee Tomlinson 12
Constraints(July 2012 scan 6)
8 - 10 April 2013
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
![Page 13: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/13.jpg)
Lee Tomlinson 13
Constraints(July 2012 scan 6)
8 - 10 April 2013
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
![Page 14: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/14.jpg)
Lee Tomlinson 14
Explicit beam crossing angle
8 - 10 April 2013
“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.
![Page 15: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/15.jpg)
Lee Tomlinson 15
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.
8 - 10 April 2013
![Page 16: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/16.jpg)
Lee Tomlinson 16
BACKUP SLIDES
8 - 10 April 2013
![Page 17: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/17.jpg)
Lee Tomlinson 17
Successes and limitations
8 - 10 April 2013
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
![Page 18: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/18.jpg)
Lee Tomlinson 18
Further models and work in progress
8 - 10 April 2013
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
![Page 19: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/19.jpg)
Lee Tomlinson 19
Scanning beams of different size
8 - 10 April 2013
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
![Page 20: Impact of transverse coupling on the ATLAS luminosity calibration in the Gaussian beam limit](https://reader036.fdocuments.net/reader036/viewer/2022062222/56816039550346895dcf5ad0/html5/thumbnails/20.jpg)
Lee Tomlinson 208 - 10 April 2013
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