Title: The measurement of SUSY masses in cascade decays at the LHC
1The measurement of SUSY masses in cascade decays
at the LHC
D. J. Miller
 Based on
 B. K. Gjelsten, D. J. Miller, P. Osland
 ATLPHYS2004029
 hepph/0410303
 B.K. Gjelsten, E. Lytken, D.J. Miller, P. Osland,
G. Polesello,  LHC/LC Study Group Working Document.
 ATLPHYS2004007
2Contents
 Introduction
 How applicable is this method?
 The SPS 1a point(s) and slope
 Cascade decays at ATLAS
 Summary and conclusions
3Introduction
 Low energy supersymmetry presents an exciting and
plausible extension to the Standard Model.  It has many advantages
 Extends the Poincarré algebra of spacetime
 Solves the Hierarchy Problem
 More amenable to gauge unification
 Provides a natural mechanism for generating the
Higgs potential  Provides a good Dark Matter candidate (? )
 Supersymmetry may be discovered at the LHC
(switch on in 2007)
0 1
4Supersymmetry predicts many new
particles Scalars squarks sleptons Spin
½ gauginos higgsinos (neutralinos) Predicts
SUSY particles have same mass as SM partners
wrong!
SUSY must be broken, but how is not clear
MSSM break supersymmetry by hand by adding
masses for each SUSY particle
Supergravity break SUSY via gravity GMSB SUSY
is broken by new gauge interactions AMSB SUSY
is broken by anomalies
Which, if any, of these is true?
5SUSY breaking models predict masses at high
energy Evolved to EW scale using (logarithmic)
Renormalisation Group Equations
Uncertainties in masses at low energy magnified
by RGE running
Zerwas et al, hepph/0211076
Need very accurate measurements of SUSY masses
6 2 problems with measuring masses at the LHC
 Dont know centre of mass energy of collision vs
 Rparity conserved (to prevent proton decay)
SM particles have P 1
R
SUSY partners have P  1
R
Rparity ? Lightest SUSY Particle (LSP) does not
decay
All decays of SUSY particle have missing
energy/momentum This cannot be recovered by
using conservation of momentum
7Measure masses using endpoints of invariant mass
distributions
e.g. consider the decay
mll is maximised when leptons are backtoback in
slepton rest frame
angle between leptons
83 unknown masses, but only 1 observable, mll
extend chain further to include squark parent
now have mll, mql, mql, mqll 4 unknown
masses, but now have 4 observables
Hinchliffe et al, Phys. Rev D 55 (1997) 5520,
and many others
9How applicable is this method?
 To make this work we need
 The correct mass hierarchy to allow

 i.e.

 A large enough crosssection and branching ratio
Examine mSUGRA scenarios to see if this is
likely (if it isnt
we would have to study a different decay)
10In mSUGRA models have universal boundary
conditions at GUT scale (1016 GeV)
SUSY scalar mass m0 SUSY fermion mass
m1/2 Common triple coupling A0 Higgs vacuum
expectation values tan?, ?gt0
Also
11Snowmass benchmark model slope SPS 1a A0
m0, tan? 10, ?gt0
12(?gt0)
A0 m0, tan? 10
13Squark decay branching ratios
(¼ SU(2) singlet)
14bottom squarks are mixtures of left and right
handed states
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16Constraints from WMAP
2? exclusion
Ellis et al, hepph/0303043
A large part of interesting parameter space has
the decay
17The SPS 1a slope and point(s)
Snowmass points and slopes are benchmark
scenarios for SUSY studies
See Allanach et al, Eur.Phys.J.C25 (2002) 113,
hepph/0202233
Defined as low energy (TeV scale) parameters
(masses, couplings etc) as evolved by version
7.58 of the program ISAJET from the GUT scale
parameters
SPS 1a slope
18widths
masses
a
a
ß
ß
NB instabilities due to inaccuracy in ISAJET,
and thus inherent to definition
19Parent gluino/squark production crosssections in
pb
a
ß
not useful
These are not yet the relevant numbers for our
analysis it doesnt matter where the parent
squark comes from
20?20 branching ratios
21Some extra difficulties
Cannot normally distinguish the two leptons
Endpoints are not always linearly independent
? Four endpoints not always sufficient to find
the masses
It is the minimum of this distribution which is
interesting
22Spin correlations
PYTHIA does not include spin correlations
(HERWIG does!) OK for decays of scalars, but may
give wrong results for fermions
This could be a problem for mql
23Without spin correlations
With spin correlations
 Recall, cannot distinguish ql and ql

 must average over them
 Spin correlations cancel when we
 sum over lepton charges
 Pythia OK
Barr, Phys.Lett. B596 (2004) 205
24Cascade decays at ATLAS
25Generate simulated data using PYTHIA 6.2 (with
CTEQ 5L) Pass events through ATLFAST 2.53, a
fast simulation of ATLAS.
 ATLFAST has no lepton identification efficiency

include 90 efficiency per lepton by hand  ATLFAST has no pileup, or jets misidentified as
leptons 
not included here
26 Initial (untuned) cuts to remove backgrounds
 3 jets, with pT gt 150, 100, 50 GeV
 ET, miss gt max(100 GeV, 0.2 Meff) with
 2 isolated oppositesign sameflavour leptons
(e,?) with pT gt 20,10 GeV
 Split remaining background into two categories
 Correlated leptons (e.g. Z ? ee)
  processes where the
leptons are of the Same Flavour (SF)  Uncorrelated leptons (e.g. leptons from
different decay branches)   processes where the
leptons need not be SF
27Uncorrelated backgrounds have the same number of
events with SF leptons (a background to the
signal) as events with Different Flavour (DF)
leptons Can remove SF events by Different
Flavour (DF) subtraction
End result of DF subtraction
Theory curve
Z peak (correlated leptons)
28When distribution includes a quark have an extra
problem  which quark to pick?
This will give a combinotoric background
Estimate this background with mixed
events Combine the lepton pair with a jet from
a different event to mimic choosing the wrong
jet gives dashed curve
Here we have chosen the jet (from the two
highest pT jets) which minimises mqll
29Fit mll endpoint to Gaussian smeared
triangle Fit other distributions to a Gaussian
smeared straight line where indicated It is not
clear that this is the best thing to do!
30Theory curves
can we really trust a linear fit? something to
improve in the future?
 notice the foot here
 this can be easily
 hidden by backgrounds
31Point ß much more difficult due to lower
crosssections
32Energy scale error 1 for jets, 0.1 for leptons
33From endpoints to masses
 Can (in principle) extract the masses in two
ways  Analytically invert endpoint formulae for masses
 Endpoints in terms of masses are already
complicated,  with 9 different physical mass regions.
 mqll(?gt?/2) particularly complicated to invert
 Not very flexible
 Not all endpoints should be given the same
weight,  e.g. mll is much better measured.
see over
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352. Fit masses to these endpoints using method of
least squares
Use analytic expressions to find a starting point
for the fit
Problem the multiregion nature of the endpoint
formulae often lead to 2 consistent solutions
for the masses. Usually these are sufficiently
different that we can distinguish them from the
real masses by some other means and/or the
wrong mass spectrum has a much lower
likelihood.
36SPS 1a (a) results
37second solution
38SPS 1a (ß) results
39Conclusions and summary
It will be important to accurately measure SUSY
masses at the LHC Rparity conservation and
unknown CME makes measuring masses
difficult Can measure masses using endpoints of
invariant mass distributions in cascade
decays We have studied the decay
at ATLAS
for the Snowmass benchmark SPS 1a This decay is
applicable over much of the allowed parameter
space as long as m0 is not too large compared
with m1/2 We examined a second point on the SPS
1a line which has less optimistic crosssections
40Simulated data using PYTHIA and ATLFAST Remove
real and combinotoric backgrounds using DF
subtraction and mixed events Fit straight
lines to edges of distributions to find
endpoints it is not clear whether this is a
good idea Use method of least squares to fit for
the masses Often find multiple solution (though
correct solution is always favoured) This method
provides reasonable mass measurements, but even
better measurements of mass differences