WeνThe W->eν analysis is a phi uniformity calibration, and only yields relative calibration constants. This means that all of the α’s in a given eta ring will be shifted by a constant that must be determined in an “absolute” analysis like the Z or J/ψ methods.

W Methods

We have investigated two methods for extracting these constants. In the “ratio” method, we simply take the ratio of the Et in a phi bin to the Et in the ring that it belongs to:

The denominator on the left side cannot be determined from this method, but can be found in either the Z or J/ψ methods. Instead we define “relative” constants that are shifted so that they average to 0 in a ring.

It the “fit” method, we fit an ad hoc function to the Et distribution of the electron for an entire η ring. This is treated as a parent distribution for the bins in that ring. So we fit to the bin distributions, varying only the scale to recover the α’s. Again, this scale is relative to the ring scale, so these are relative α’s. Show below is our best fit to the Et distribution. It is a three region fit: gaussian:4th order polynomial: exponential. This is the more complicated of the two methods, and it needs additional work to match the precision of the ratio method, so the remaining plots shows are with the ratio method.

J/ψee We use methods identical to the Z methods to calibrate with the J/ψ. The low mass (~3.1 GeV) of the J/ψ allows us to compare the calibration constants between the roughly 40 GeV lepton scale and the few GeV scale. This is a good check on linearity of the detector response as well as a check on a possible offset of the form

The backgrounds for the J/ψ are much larger than those for the Z, but there will be nearly a factor of 10 more J/ψ after selection than Z’s.

Missing Et

EM Cluster e

Zee In the Z->ee and J/ψ->ee methods we use the reconstructed mass to extract the calibration constants. The leading order correction to the reconstructed mass is

The α’s are varied in a log likelihood fit of the reconstructed mass to a predicted line-shape for the Z mass.

Zee Methods

Three methods are used for the likelihood fits

I.The Standard Method. In this method all of the α’s are fit simultaneously. This method is the most computationally intensive of the methods.

II.The Beta-Alpha Method. In this method we define βij=αi+αj. for each pair of bins. The mass is then varied in the likelihood fit according to the leading order correction above in N2

bins/2 fits. Once the β’s are obtained the α’s are recovered in a least squares analysis. This is the fastest of the three methods. But for low statistics, pairs of bins often only contain two or three events, and this leads to a bias in the recovered α’s.

III.The Iterative Method. In this method the α in a single bin is fit, keeping all of the other α’s constant. All of the bins are run through several times (in these plots 10 times). This is the method that is used in the plots shown.

M rec M true 1 i j

2

Relative α Residuals

In order to compare the Z and W channels for the phi calibration we make relative α’s from the Z absolute α’s and the truth α’s. The difference between the truth and reconstructed constants is shown.

Relative α Residuals

In order to compare the Z and W channels for the phi calibration we make relative α’s from the Z absolute α’s and the truth α’s. The difference between the truth and reconstructed constants is shown.

RMS of Residuals vs NW

We have compared the combined Z and W relative α’s to each Z and W methods alone for statistics up to 200 pb-1. The W:Z ratio shown is 10:1.

RMS of Residuals vs NW

We have compared the combined Z and W relative α’s to each Z and W methods alone for statistics up to 200 pb-1. The W:Z ratio shown is 10:1.

E

E

ErecEtrue

1

Statistical Uncertainties

The statistical uncertainty for the truth and W ratio methods are calculated from the uncertainty in the mean of the distributions. The uncertainty in the Z iterative method is calculated from the shape of the likelihood curve. Systematic effects are currently under investigation.

Statistical Uncertainties

The statistical uncertainty for the truth and W ratio methods are calculated from the uncertainty in the mean of the distributions. The uncertainty in the Z iterative method is calculated from the shape of the likelihood curve. Systematic effects are currently under investigation.

Validation: Truth α’s

If we consider the α definition (see abstract) to be defined event by event then we have a distribution of α’s (shown above). To choose a single α to apply to all of the events in a bin we take the position of the peak of the distribution. Taking the peak instead of the mean of the distribution reduces the bias due to brehmstrahlung.

Validation: Truth α’s

If we consider the α definition (see abstract) to be defined event by event then we have a distribution of α’s (shown above). To choose a single α to apply to all of the events in a bin we take the position of the peak of the distribution. Taking the peak instead of the mean of the distribution reduces the bias due to brehmstrahlung.

Validation: Injected α’s

The Z methods are validated by injecting α’s from a gaussian distribution into each bin (shown is μ=0 and σ=2%).

Validation: Injected α’s

The Z methods are validated by injecting α’s from a gaussian distribution into each bin (shown is μ=0 and σ=2%).

Z Mass Distribution

We have used two different models for Z mass reference distribution. In the first we model the reconstructed Z lineshape as a relativistic breit-wigner smeared by the detector resolution. The distribution is also adjusted to model brehms, and includes a parton luminosity correction. In the second method we fit to a reconstructed distribution in the full GEANT simulation with ideal detector geometry.

Z Mass Distribution

We have used two different models for Z mass reference distribution. In the first we model the reconstructed Z lineshape as a relativistic breit-wigner smeared by the detector resolution. The distribution is also adjusted to model brehms, and includes a parton luminosity correction. In the second method we fit to a reconstructed distribution in the full GEANT simulation with ideal detector geometry.

J/ Mass Distribution

. The mass line-shape is a fit to the fully reconstructed J/ψ monte carlo events. This is done with a ROOT algorithm RooKeysPdf.

J/ Mass Distribution

. The mass line-shape is a fit to the fully reconstructed J/ψ monte carlo events. This is done with a ROOT algorithm RooKeysPdf.

Z->ee,100 pb-1

J/ψ->ee,20 pb-1

Validation

. Just as with the Z’s, the J/ψ analysis is validated by injecting α’s from a gaussian distribution and comparing to the recovered α’s. The plot to the left shows the injected and recovered α distributions The above plot shows the difference between injected and recovered α’s. The data shown is for 20 pb-1, which is enough to achieve 0.5% precision.

Validation

. Just as with the Z’s, the J/ψ analysis is validated by injecting α’s from a gaussian distribution and comparing to the recovered α’s. The plot to the left shows the injected and recovered α distributions The above plot shows the difference between injected and recovered α’s. The data shown is for 20 pb-1, which is enough to achieve 0.5% precision.

CLR vs Statistics

The desired 0.5% long-range constant term is achieved at roughly 140 pb-1, which corresponds to roughly 220K events in the plot. These are event numbers before selection.

CLR vs Statistics

The desired 0.5% long-range constant term is achieved at roughly 140 pb-1, which corresponds to roughly 220K events in the plot. These are event numbers before selection.

Corrected J/ψ Mass

. The blue curve shows the uncorrected reconstructed J/ψ mass, and the red after applying the α’s.

Corrected J/ψ Mass

. The blue curve shows the uncorrected reconstructed J/ψ mass, and the red after applying the α’s.

3.1 GeV

Inter-calibration of the LAr EM Calorimeter

J. Farley, A. Ahmad, J.Gray, K. Tschann-GrimmStony Brook University

New York

We have used three different physics signals for an inter-calibration of the LAr barrel and endcap. In the Z->ee and J/ψ->ee methods we use the reconstructed mass to estimate a linear scaling of the energy. The W->eν method gives relative calibration constants (calibrates only around phi), which can improve the constants from the other methods.

The uncertainty in the energy measurement has the form

To meet the Atlas physics goals the constant term C should be less than 0.7%. Clocal is determined from test-beam data to be about 0.5%. Therefore the long-range term should be less than 0.5%.

We divide the detector into regions in eta-phi coordinates (called “bins” here). The calibration constants αi, defined for each region i, are given in terms of the reconstructed and true energies by

The uncertainties on the α’s determine the long-range constant term.

Erec Etrue(1 i ).

(E)

EA

EB

EC,

C Clocal Clong range.

1bin

1bin ring

Et

bin events

Etring events

RMS of Residuals vs W:Z Ratio

We will investigate further the ratio of W:Z after selection that we will see in the experiment. We have shown the comparison of the combined W/Zα’s with each method alone for different values of this ratio. The combined analysis is an improvement over a wide range of ratios.

RMS of Residuals vs W:Z Ratio

We will investigate further the ratio of W:Z after selection that we will see in the experiment. We have shown the comparison of the combined W/Zα’s with each method alone for different values of this ratio. The combined analysis is an improvement over a wide range of ratios.

Combined Z and W α’s

. The Z channel is better than the W in the phi calibration, but the two can be used together for an improved phi calibration. The plot shows a weighted average of the Z and W “ratio” relative alpha residuals compared to each method alone.

Combined Z and W α’s

. The Z channel is better than the W in the phi calibration, but the two can be used together for an improved phi calibration. The plot shows a weighted average of the Z and W “ratio” relative alpha residuals compared to each method alone.

Erec Etrue(1 ) Eoffset .