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The measurement of SUSY masses in cascade decays at the LHC
Based on:
B. K. Gjelsten, D. J. Miller, P. OslandATL-PHYS-2004-029
hep-ph/0410303
B.K. Gjelsten, E. Lytken, D.J. Miller, P. Osland, G. Polesello, LHC/LC Study Group Working Document.
ATL-PHYS-2004-007
D. J. Miller
November 10, 2004 D.J. Miller 2
Contents
• Introduction
• How applicable is this method?
• The SPS 1a point(s) and slope
• Cascade decays at ATLAS
• Summary and conclusions
November 10, 2004 D.J. Miller 3
Introduction
Low energy supersymmetry presents an exciting and plausible extension to the Standard Model.
It has many advantages:
• Extends the Poincarré algebra of space-time• 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)
01
~
November 10, 2004 D.J. Miller 4
Supersymmetry 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 gravityGMSB: SUSY is broken by new gauge interactionsAMSB: SUSY is broken by anomalies
Which, if any, of these is true?
November 10, 2004 D.J. Miller 5
SUSY breaking models predict masses at high energy
Evolved to EW scale using (logarithmic) Renormalisation Group Equations
Need very accurate measurements of SUSY masses
[Zerwas et al, hep-ph/0211076]
Uncertainties in masses at low energy magnified by RGE running
November 10, 2004 D.J. Miller 6
2 problems with measuring masses at the LHC:
• Don’t know centre of mass energy of collision √s
• R-parity conserved (to prevent proton decay)
P = (-1)R
3B-3L+2s
SM particles have P = +1R
RSUSY partners have P = - 1
R-parity 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
November 10, 2004 D.J. Miller 7
Measure masses using endpoints of invariant mass distributions
e.g. consider the decay
mll is maximised when leptons are back-to-back in slepton rest frame
angle between leptons
November 10, 2004 D.J. Miller 8
3 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
) can(?) measure masses from endpoints
[Hinchliffe et al, Phys. Rev D 55 (1997) 5520, and many others…]
November 10, 2004 D.J. Miller 9
How applicable is this method?
To make this work we need
• The correct mass hierarchy to allow
i.e.
• A large enough cross-section and branching ratio
Examine mSUGRA scenarios to see if this is likely
(if it isn’t we would have to study a different decay)
November 10, 2004 D.J. Miller 10
In 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, >0
Run down from GUT scale:
• QCD interaction push up mass of squarks and gluino• unification at GUT scale pushes up masses compared to
Also
Quarks and gluons tend to be heavy
LSP is usually ‘B-like’:~
Consequently:
November 10, 2004 D.J. Miller 11
Snowmass benchmark model ‘slope’ SPS 1a: A0 = -m0, tan = 10, >0
lighter green is where
November 10, 2004 D.J. Miller 12
A0 = -m0, tan = 10
A0 = 0, tan = 10
A0 = 0, tan = 30
A0 = -1000GeV, tan = 5
0)
November 10, 2004 D.J. Miller 13
Squark decay branching ratios:
‘W-like’~ ‘B-like’
~
(¼ SU(2) singlet)
November 10, 2004 D.J. Miller 14
bottom squarks are mixtures of left and right handed states
both decay to
November 10, 2004 D.J. Miller 15
20 decay branching ratios~
20 - 1
0) independent of m0~ ~
November 10, 2004 D.J. Miller 16
A large part of ‘interesting’ parameter space has the decay
Constraints from WMAP:
A0 = 0
2 exclusion
[Ellis et al, hep-ph/0303043]
November 10, 2004 D.J. Miller 17
The SPS 1a slope and point(s)
SPS 1a slope:
SPS 1a point
Standard point
SPS 1a point
Extra point, with smaller cross-sections
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:
Snowmass ‘points and slopes’ are benchmark scenarios for SUSY studies
[See Allanach et al, Eur.Phys.J.C25 (2002) 113, hep-ph/0202233]
November 10, 2004 D.J. Miller 18
masses widths
NB: instabilities due to inaccuracy in ISAJET, and thus inherent to definition
αα β β
November 10, 2004 D.J. Miller 19
Parent gluino/squark production cross-sections in pb:
[not useful]
These are not yet the relevant numbers for our analysis; it
doesn’t matter where the parent squark comes from
α β
November 10, 2004 D.J. Miller 20
βα
20 branching ratios:~
Maybe we could use
or
at point β?
November 10, 2004 D.J. Miller 21
Cannot normally distinguish the two leptons
is Majorana particle:
Must instead define mql (high) and mql (low)
?Do we have
Endpoints are not always linearly independent
Four endpoints not always sufficient to find the masses
Introduce a new distribution mqll (>/2) identical to mqll except enforce the constraint > /2
It is the minimum of this distribution which is interesting
Some extra difficulties:
November 10, 2004 D.J. Miller 22
Spin correlations
PYTHIA does not include spin correlations (HERWIG does!)
OK for decays of scalars, but may give wrong results for fermions
PYTHIA ‘forgets’ spin
This could be a problem for mql
November 10, 2004 D.J. Miller 23
Without spin correlations:
With spin correlations:
[Barr, Phys.Lett. B596 (2004) 205]
Recall, cannot distinguish ql+ and ql-
must average over them
Spin correlations cancel when we sum over lepton charges
Pythia OK
November 10, 2004 D.J. Miller 24
Cascade decays at ATLAS
November 10, 2004 D.J. Miller 25
Generate simulated data using PYTHIA 6.2 (with CTEQ 5L)
Pass events through ATLFAST 2.53, a fast simulation of ATLAS.
• Acceptance requirements:
• ATLFAST has no lepton identification efficiency – include 90% efficiency per lepton by hand
• ATLFAST has no pile-up, or jets misidentified as leptons – not included here
November 10, 2004 D.J. Miller 26
Initial (untuned) cuts to remove backgrounds:
• ≥ 3 jets, with pT > 150, 100, 50 GeV
• ET, miss > max(100 GeV, 0.2 Meff) with
• 2 isolated opposite-sign same-flavour leptons (e,) with pT > 20,10 GeV
After these cuts, remaining background is mainly and other SUSY processes
Split remaining background into two categories:
• Correlated leptons (e.g. Z → e+e-) - 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
November 10, 2004 D.J. Miller 27
Uncorrelated 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’
‘Theory’ curve
End result of DF subtraction
Z peak (correlated leptons)
November 10, 2004 D.J. Miller 28
When 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
November 10, 2004 D.J. Miller 29
Fit 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!
November 10, 2004 D.J. Miller 30
Theory 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
November 10, 2004 D.J. Miller 31
Point β: much more difficult due to lower cross-sections
November 10, 2004 D.J. Miller 32
Energy scale error: 1% for jets, 0.1% for leptons
November 10, 2004 D.J. Miller 33
From endpoints to masses
Can (in principle) extract the masses in two ways:
1. Analytically invert endpoint formulae for masses
Endpoints in terms of masses are already complicated, with 9 different physical mass regions.
mqll(>/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
November 10, 2004 D.J. Miller 34
November 10, 2004 D.J. Miller 35
Consider 10,0000 ‘gedanken’ ATLAS experiments, with measured endpoints smeared from the nominal value by a Gaussian of width
given by the statistical & energy scale error
with Ai and Bi picked from Gaussian distribution
Use analytic expressions to find a starting point for the fit
2. Fit masses to these endpoints using method of least squares
Problem: the multi-region 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.
November 10, 2004 D.J. Miller 36
SPS 1a (α) results
second mass solutions- at α this is caused by
Note mass differences much better measured – could be exploited by measuring one of the masses at an e+e- linear collider
November 10, 2004 D.J. Miller 37
second solution
November 10, 2004 D.J. Miller 38
SPS 1a (β) results
much worse than SPS 1a (α)
additionally have extra solutions – at β caused by
November 10, 2004 D.J. Miller 39
Conclusions and summaryIt will be important to accurately measure SUSY masses at the LHC
R-parity 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 spaceas 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 cross-sections
November 10, 2004 D.J. Miller 40
Simulated 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
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