Ivan Smiljanic

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Energy resolution and scale requirements for
luminosity measurement
Ivan Smiljanic Vinca Institute of Nuclear
Sciences, Belgrade, Serbia
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The aim of study

• The aim of this study is to optimize event
  selection taking into account following effects
• beam-beam deflection and
• physics background,
• as well as to minimize sensitivity on detector
  energy resolution and scale.

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Overview

• General information
• Event selection
• Luminosity vs. bias of the energy scale
• Luminosity vs. energy resolution using relative
  energy cut
• Luminosity vs. energy resolution using energy
  balance cut
• Conclusion

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General information
1. Geometry rmin 80 mm rmax 195
mm tungsten thickness 3mm silicon
thickness 0.3mm Segmentation 30 planes,
64 rings, 48 sectors z position 2270 mm 2.
Total cross section (from BHLUMI)
(from WHIZARD) 3. No crossing angle
GALUGA gives muon cross section of 0,3940,002nb
(phone meeting from 31st of January 2008, B.
Pawliks presentation), while with WHIZARD we
have 0,5440,008nb, which means that the
difference between two generators is about 38,
or that model/generator dependence is of order of
magnitude of 2,810-1.
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Event selection

• Asymmetric cuts
• Asymmetric theta cuts are proposed by C. Rimbault
  and P. Bambade in order to accommodate to
  beam-beam deflection effects. Due to beam-beam
  deflection effects, Bhabha events become more
  accolinear, which results in reduction of the
  effective Bhabha cross section. To compensate for
  it, asymmetric theta cuts are proposed. These
  cuts are applied subsequently to forward and
  backward sides of the detector, in order to
  reduce systematics for the IP position and
  relative position of forward and backward
  detector.
• LCAL angular acceptance for geometry used is
  35-87 mrad. Therefore, cuts are set as follows
• cut 1 39-80 mrad
• cut 2 35-87 mrad.
• Asymmetric cuts are applied in all results in
  this study!
• Relative energy cut
• Energy balance cut

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Relative energy cut
In following results, asymmetric cuts on theta
are applied in a way explained earlier, together
with the cut on relative energy (ERCUT), where
relative energy is defined as a sum of energies
of both particles belonging to a pair divided by
twice the energy of the beam This
practically mean that the Bhabha particle carries
Erel fraction of Ebeam.
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Relative energy cut
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Relative energy cut
This plot (thanks, Mila!) explains the sharp
drops in background between 0 and 40 GeV and
between 125 and 150 GeV. It seems that looser
cut on relative energy (60 instead of 80 of
relative energy, e. g. 150 GeV instead of 200
GeV) can be used together with asymmetric theta
cut!
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Bias of energy scale
This plot is trying to answer what if there is
some (known) bias in our energy measurement.
According to these results, if there is an
energy bias, it should be known with margin of
148 MeV, if one wants to know luminosity at
the 10-4 level.
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Energy resolution from the detector design
Energy of particles in LCAL is measured through
the calibration procedure, assuming both showers
fully contained in the LCAL. Measured particle
energy is, thus, affected by resolution effect.
Since the detector is being calibrated under
realistic beam conditions, the bias of energy
scale can also be present. According to results
presented at the phone conference on 31st of
January 2008 by I. Sadeh, energy resolution of
20?GeV is taken in this study as a resolution
that will be most probably achieved with the
current LCAL design.
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Luminosity vs. E resolution using relative energy
cut
As mentioned, we assume the energy resolution of
20?GeV with the current design. In order to
check how well we have to control the resolution
itself, a set of simulations has been done. In
following simulations, a random number generator
is used to smear, according to energy resolution,
the actual energy of particles that caused a
shower in the LCAL.
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Luminosity vs. E resolution using relative energy
cut
For ERCUT200 GeV, if one wants to achieve
luminosity uncertainty below 10-4, uncertainty of
energy resolution at 20 should be about 1,5.
This is consistent with the value calculated by
A. Stahl in his famous Note, though these two
results are not fully comparable due to presence
of additional asymmetric cuts on theta. But
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Luminosity vs. E resolution using relative energy
cut
In both cases (cuts _at_ 200 and 150 GeV), we are
dominated by the statistical dissipation (of
order 10-3) due to finite detector resolution.
For ERCUT150 GeV, polynomial fit is not needed,
a very simple linear fit looks quite fine. For
luminosity uncertainty of 10-4, we have to
control energy resolution at the level of 25,
practically independent of resolution itself.
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Energy balance cut
In following section, selection based on energy
balance cut value (EBCUT) is studied. Energy
balance is defined as the difference between
energies of two particles from the pair divided
by the energy of the particle with the lower
energy Asymmetric theta cuts are also
applied.
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Energy balance cut
With the nominal ILC luminosity, we are
practically insensitive to the statistical loss
of signal due to selection efficiency. If the
signal/background ratio can be controlled to the
level of 10-1, we can move from EBCUT0,1 (used
as default value so far) to EBCUT0,2 and still
to keep the uncertainty at the level of 10-4.
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Luminosity vs. E resolution using energy balance
cut
For luminosity uncertainty of 10-4, with this cut
we have a very small margin to control energy
resolution. For ?E20, we have to know it at the
level of 0,56! In comparison with the relative
energy cut at 150 GeV, where we are practically
insensitive to the level we control energy
resolution, this result indicates that energy
balance cut should not be used instead of cut on
relative energy.
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Conclusion

• Taking into account beam-beam deflection effects,
  presence of physics background from 4-fermion
  processes, energy resolution of the detector and
  possible biases of energy scale, we propose the
  following selection for luminosity measurement
• asymmetric theta cuts
• relative energy cut at 150 GeV (particles carry
  at least 60 of the beam energy).
• With such selection, systematics from all
  mentioned sources is kept below 10-3, if we
  assume that we can really control the beam-beam
  deflection effects at the level of 10-2 and
  physics background at the level of 10-1. Energy
  resolution of the detector should (and certainly
  will) be controlled better than 25 and the
  possible bias of energy scale has to be known to
  approximately 150 MeV, or at the level of 10-3.