Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 1 Measuring Mass Difference at LHC...
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Transcript of Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 1 Measuring Mass Difference at LHC...
Jan 17, 2007
Measuring Mass Difference using soft τ PT Slope 1
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Measuring Mass Difference
at LHC using soft τ PT Slope
11~ - ~
Alfredo Gurrolain collaboration with
Richard Arnowitt, Bhaskar Dutta, Teruki Kamon,
David Toback, Abram Krislock,
Nikolay Kolev (Regina, Canada)
Jan 17, 2007
Measuring Mass Difference using soft τ PT Slope 2
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Outline
SUSY Signature at the LHC
Analysis Methods in 2& 3 Papers
Gaugino Universality
Measuring M in a Non-Universal SUGRA model
Simultaneous measurement of model parameters to test Universality
Jan 17, 2007
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SUSY at LHC 1. , Production is dominant SUSY process at LHC ( )
2. Interested in events with or pairs
3. & Branching Ratios are ~ 97%
4. In Coannihilation Region of SUSY Parameter Space: GeV
g~ q~
Soft
Soft
p p p
g~
q~
01
~
02
~
~
q
q~q
q
~ 01
~
02
~
p
g~
q~
01
~
02
~
~
1
~
q
q~q
q
~ 01
~
Soft
Hard Hard
Hard
ggqqgqpp ~~ ,~~ ,~~02
02
021
02
01
~~ ,~~ ,~~
15 - 5 ~~~ 011
11102
~~ ~~
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Measuring Mass Difference using soft τ PT Slope 4
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Looking Back at 2 & 3 Papers 1. Use Hadronically Decaying ’s
2. Sort τ’s by ET (ET1 > ET2 > …) & use OS-LS
method to extract pairs from the decays
on a statistical basis
3. Use Counting Method (NOS-LS) & Ditau
Invariant Mass (M) to measure
mass difference
4.
5.
2~
2~
2~
2~
~
1
01
02
102
11
M
M
M
MMM end
),,( 02
~~ MMMfN gLSOS
),(
),(
0.8m~M & 2.8m~M
tyUniversali Gaugino Assume
~
~
1/2χ~1/2g~ 02
MMgM
MMfN
gend
gLSOS
hep-ph/0603128
hep-ph/0608193
02
~
Jan 17, 2007
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Non-Universal SUGRA
g~q~
02
~
01
~~
1
~
g~
g~
02
~
02
~
Non-Universal SUGRA
Methods used in 2 & 3 papers
depend on Gaugino Unification
Those methods can’t be used in
a Non-Universal SUGRA model
without using another observable!
How can we measure M?
SUSY Mass Hierarchy
M ~ 5 – 15 GeV
Jan 17, 2007
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PT STUDY
Slope of the soft PT distribution has a M dependence
hep-ph/0603128
01
~~
Slope of PT distribution contains ΔM Information.
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EVENTS WITH CORRECT FINAL STATE (2 OR 3) - 2 + 2j + ETmiss
APPLY CUTS TO REDUCE SM BACKGROUND (W+jets, …)
ETmiss > 180 GeV, ET
j1 > 100 GeV, ETj2 > 100 GeV, ET
miss + ETj1 + ET
j2 > 600 GeV
ORDER TAUS BY PT & APPLY CUTS ON TAUS: WE EXPECT A SOFT AND A HARD
PTall > 20 GeV, PT
1 > 40 GeV
LOOK AT PAIRS AND CATEGORIZE THEM AS OPPOSITE SIGN (OS) OR LIKE SIGN (LS)
OS: FILL LOW OS PT HISTOGRAM WITH PT OF SOFTER
FILL HIGH OS PT HISTOGRAM WITH PT OF HARDER
LS: FILL LOW LS PT HISTOGRAM WITH PT OF SOFTER
FILL HIGH LS PT HISTOGRAM WITH PT OF HARDER
LOW OS
HIGH OS
LOW LS
HIGH LS
LOW OS-LS
HIGH OS-LS
Extracting Pairs from Decays02
~
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PT STUDY ISAJET 7.64 to simulate our model of SUSY production
TAUOLA to re-decay the ’s
Run generated particles through detector simulator, PGS4 (author:
John Conway) using CMS parameter file
Used reconstructed jets
Used generator level ’s after being re-decayed by TAUOLA
- “visible” values of momentum and energy were used
Separate Monte Carlo routine in ROOT to simulate the effects of
identification efficiency and jet to fake rate
Jan 17, 2007
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OS
OS-LS
LS
GeVM
GeVM
g 831
6.10
~
ETmiss + 2j + 2Analysis: PT
soft
[1] ETmiss , at least 2 jets, at least 2 ’s with PT
vis > 20, 40 GeV
[2] = 50% , fake rate 1%
[3] Cuts: ETjet1 > 100 GeV, ET
jet2 > 100 GeV, ETmiss > 180 GeV
ETjet1 + ET
jet2 + ETmiss > 600 GeV
Jan 17, 2007
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Can we still see the dependence of the PT slope on M using OS-LS Method?
PT STUDY
GeVM
GeVM
GeVM
GeVM
GeVM g
0.15
6.10
7.5
286.260
831
02
~
~
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PT STUDY: ETmiss + 2j + 2
What is the dependence of PT slope on mass & mass?02
~g~
Luminosity = 40 fb-1
GeVM
GeVM
g 831
6.10
~
GeVM
GeVM
286.260
6.10
02
~
PT Slope is insensitive to mass & mass!!02
~g~
What is the dependence on M?
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Measuring M from the PT Slope
PT STUDY: ETmiss + 2j + 2
Luminosity = 40 fb-1
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How accurately can M be measured for our reference point?
Considering only the statistical uncertainty:
We can measure M to ~ 6% accuracy at 40 fb-1 & ~ 12% accuracy at 10 fb-1 for mass
of 831 GeV.
g~
PT STUDY: ETmiss + 2j + 2
Jan 17, 2007
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Can parameterize the our observables as functions of M, , &
NOS-LS , to first order, does not depend on mass. A large increase or decrease
in mass is needed to obtain a point that lies outside the error bars Cross-Section is dominated by the gluino mass
02
~02
~
Simultaneous Measurement of Model Parameters
gM ~ 02
~M
Jan 17, 2007
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Simultaneous Measurement of Model Parameters
2~
2~
2~
2~
~
1
01
02
102
11
M
M
M
MMM end
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Testing Gaugino Unification
CONTOURS OF CONSTANT VALUES ( L = 40 fb-1 )
• Intersection of the central contours
provides the measurement of M,
, &
• Auxilary lines determine the 1
region
• 1st order test on Universality
gM ~ 02
~M
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SUMMARY
Soft PT distribution is sensitive to M
PT slope is independent of gluino mass and neutralino mass
M can measured to ~ 12% accuracy at 10 fb-1 for our reference point
Methods used in 2 and 3 papers can’t be used in a Non-Universal
SUGRA model
We can combine counting method, ditau invariant mass measurement
and PT slope to test the idea of gaugino unification to first order
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PROBLEM: OS-LS method does NOT give the “true” slope
PT STUDY
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PT STUDY – Method I How accurately can we measure M with this method? Assuming the theoretical dependence (‘True’ Fit) of M on Slope:
We can measure M to ~ 8-9% accuracy at 40 fb-1 for mass of 831 GeV.g~
Slope does NOT change
with ~ 10% change in
gluino mass, but the
uncertainty changes due
to change in NOS-LS
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PT STUDY
BACKGROUND: SM, SUSY, soft ’sfrom the ’s from the is the dominant background!
How can the slope be corrected?
02
~
GeV 22002
~ M
02
~
What causes this difference?
GeV 26002
~ M
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Correcting the Slope: Method I Defining the measured PT slope by and the theoretical (“true” identification) PT slope by ,
the mean statistical uncertainty on the slope is with the mean
statistical uncertainty of . The shift S due to background effects is given by the mean difference
of the theoretical slope and the measured slope:
The root-mean-square uncertainty is
With these definitions, the CORRECTED measured Slope is
Mim T
im
N
iN 1
Mi
Mstat m
1m
Mim
Mim
N
iN 1
Mi
Ti )m(m
1S
N
iNS
1
2Mi
Ti S)m(m
1
)m( S)(m m Mi
Mi
correctedi S
Jan 17, 2007
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.003166
S .008900
.002032
Mstatm
S
A plot of the distribution of the
shift S between theoretical and
measured values. The shift S is
fairly close to being constant.
A summary of the calculated uncertainties
and shift in GeV.
Correcting the Slope: Method I
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Correcting the Slope: Method II Soft ’s from is the dominant background By increasing the second PT cut, this source of background can be reduced Other Background (SM & other SUSY Background) is reduced
02
~
GeV 40
GeV 201
T
allT
P
P
GeV 80
GeV 201
T
allT
P
P
GeV 22002
~ M
Jan 17, 2007
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Correcting the Slope: Method II
Jan 17, 2007
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Optimizing PT Cut
Optimized Cut would be ~ 70 – 80 GeV for M = 10.6 GeV