the measurement of susy masses in cascade decays at the lhc based on: b. k. gjelsten, d. j. miller,...

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


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

~


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?


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


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


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


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…]


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)


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:


Snowmass benchmark model ‘slope’ SPS 1a: A0 = -m0, tan = 10, >0

lighter green is where


A0 = -m0, tan = 10

A0 = 0, tan = 10

A0 = 0, tan = 30

A0 = -1000GeV, tan = 5

0)


Squark decay branching ratios:

‘W-like’~ ‘B-like’

~

(¼ SU(2) singlet)


bottom squarks are mixtures of left and right handed states

both decay to


20 decay branching ratios~

20 - 1

0) independent of m0~ ~


A large part of ‘interesting’ parameter space has the decay

Constraints from WMAP:

A0 = 0

2 exclusion

[Ellis et al, hep-ph/0303043]


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]


masses widths

NB: instabilities due to inaccuracy in ISAJET, and thus inherent to definition

αα β β


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


βα

20 branching ratios:~

Maybe we could use

or

at point β?


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:


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


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


Cascade decays at ATLAS


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


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


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)


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


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!


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


Point β: much more difficult due to lower cross-sections


Energy scale error: 1% for jets, 0.1% for leptons


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


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.


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


second solution


SPS 1a (β) results

much worse than SPS 1a (α)

additionally have extra solutions – at β caused by


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


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

the measurement of susy masses in cascade decays at the lhc based on: b. k. gjelsten, d. j. miller,...

Documents

miller slide

definition slide

different decay slide

measurement of susy

susy particles

hepph0303043 slide

hepph0202233 slide

susy studies