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First Lo ok at Bhabha Energy Calibration with Beamstrahlung

· Wide angle Bhabha scattering is an essential pro cess for constraining new physics (contact interactions, extra-dimensions).

· Represents largest ( 1.0nb at 500 GeV, > 60mrad) interesting physics cross sections (requires greatest precision).

· Smaller angle Bhabha scattering will b e a key pro cess for understanding the luminosity sp ectrum (see Bo ogert and Miller (hepph/0211021), MЁ g (LC-PHSM-2000-60-TESLA) and LC talks by oni Jadach, Torrence and Cinabro).

· Will the techniques used for calorimeter energy calibration at lower energy e+e- machines still work at a Linear collider?
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David Strom ­ UO


Bhabha diagrams:

e-

+ Z, g e-

Z, g +

?

2

· t-channel photon term dominates at small angles · s-channel + new physics interference usually most interesting · "Luminosity" measurement will probably b e based on larger angles ( 100mrad) than at LEP ( 25mrad) due to pair background. · Interference among SM comp onents more imp ortant at an LC than at LEP Significant theoretical Monte Carlo work needed (See Jadach)
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David Strom ­ UO


Key ingredients in Bhabha analysis are
( see Eur. Phys. J. C.14(2000)373 for more details)

· Acollinearity ( 1 - 2) · Energy cuts: E1 + E2 > Etot E1 > Emin > Emin E2

E1 q1 q2 E2

· Acollinearity dep ends on reconstruction of showers in the calorimeter. The intrinsic resolution of the Si-W electromagnetic calorimeter for 500 GeV electrons should b e quite go o d, p erhaps 100µm. It can b e calibrated using tracks in physics events and from the test b eam. · Energy resp onse dep ends crucially on upstream material and leakage. It can usually only b e mapp ed in situ.
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-1

OPAL

Schemes to measure b eamstrahlung use acollinearity
(effectively assumes only one hard initial state or b eamstrahlung photon)

Prob. / 0.05 cm

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Exp erimentally and theoretically well understo o d at LEP for small angles

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4 6 Radius difference (cm)

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Presence of tracker in front of calorimeter will make understanding the p osition bias and resolution somewhat easier than at small angles at LEP.

How do es Si-W calorimeter pad geometry effect the spatial reconstruction resolution and bias?

Imp ortant to understand the effects of b eam parameters such as, longitudinal b eam size ( 100µm at NLC), b eam divergences ( 30µrad at NLC), b eam energy differences and b eam alignment.
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· Energy resp onse of the calorimeter can b e determined by requiring one "trigger electron" and a small acollinearity (> 0.4mrad) angle. · At LEP the rate of "double radiative" events was very small
The solid histogram is tree level BHLUMI, the green band is our mo del of calorimeter energy resolution and the black p oints are the data.

OPAL
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Almost no uncertainty in Bhabha energy calibration from double radiative events! Exp ect double radiative events to scale as ln(s/m2) (15%effect). e
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meas/Ebeam

1.2 1.1 1 0.9 0.8 0.7

OPAL
Mean Raw Energy Corrected Energy

· Can also correct for leakage and material in front of the calorimeter. · OPAL measurement used longitudinal shower shap e as well as distance from calorimeter edge. · Leakage and material effects should b e smaller at wide angles at an LC.

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(Emeas)/E

RMS of Mean Raw Energy RMS of Corrected Energy

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OPAL
Prob./0.01

Comparison of BHLUMI and observed energy sp ectrum with two different acollinearity cuts BHLUMI works for single radiative events. Requires one hard electron and then lo oks at "unbiased" side. Not sensitive to double radiative events!

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Will b eamstrahlung correlations sp oil this metho d?

Most b eamstrahlung calculations (e.g. Circe) ignore correlations b etween the p osition of the colliding electrons and p ositrons in the bunch.
P. Chen Phys. Rev. D. 46(1992)1186.

i.e., one assumes dL = f ( x1 ) f ( x 2 ) dx1dx2 where x1 and x2 are the energy fractions of the electron and p ositron. Since some parts of the bunches will see higher fields than other, we would exp ect correlations b etween b eamstrahlung for the electron and p ositron.
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At TESLA a first study by MЁ g found that the correlations changed oni the roughly 50% of events at the nominal b eam energy by ab out 2%. This could lead to an error as large as 2% in cross section measurements if these double radiative events are not treated the same way in the luminosity analysis and in the cross section numerator. Effect on average s / s is only 3 в 10-4 ­ will not cause a large error on contact interaction typ e new physics measurements.

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David Strom ­ UO


We need to use D. Schulte's program GuineaPig to explore p ossible effects at NLC in more detail:

· At NLC b eamstrahlung will b e somewhat rare but harder.

· Beam alignment is likely to b e imp ortant.

· Since correlated b eamstrahlung is not due to a well understo o d exp erimental configuration, we must develop a metho d which uses b oth energy and acollinearity to extract it from the data. This may put demands on the electromagnetic calorimeter which we haven't yet considered.

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Op en Questions Collab orate with the machine and calorimeter working groups for answers

1. How do es the calorimeter pad geometry effect p osition resolution?

2. How large is the correlated b eamstrahlung effect in an NLC typ e machine?

3. How do es correlated b eamstrahlung dep end on b eam alignment?

4. Can our LC electromagnetic calorimeter measure the correlated b eamstrahlung? i.e., how large are the tails in the calorimeter energy sp ectrum?
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David Strom ­ UO