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Managing Multilepton Topologies:
the Tau Trouble
& a Concrete Proposal
Sunil Somalwar
with Sourabh Dube, Julian Glatzer, Richard Gray, Alex Sood
and Scott Thomas
(Rutgers)
Characterization of New Physics @LHC
Workshop
CERN Nov 5-6, 2010
Rutgers University, New Brunswick, NJ
Sunil Somalwar
1
Outline
• Multilepton complications & an attempt at
making CDF trilepton results model-independent
• An LHC proposal from the lessons learnt:
-- exclusive “theory” channels
• Practical realities from working experience
“Addressing the Multi-Channel Inverse Problem at High Energy Colliders:
A Model Independent Approach to the Search for New Physics with
Trileptons”
Sourabh Dube, Julian Glatzer, Sunil Somalwar, Alexander Sood, Scott Thomas
arXiv:0808.1605
(Scott Thomas yesterday)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
2
“Channels” : Theory vs Expt
•For experimentalists:
Number of leptons 3, 4 or more
Flavor of leptons  e or mu
Lepton Reconstruction
High Quality: Tight e or mu (could be from a tau)
Medium Quality: Loose e/m, 1-prong t as isolated track
Low Quality: 3-prong tau’s, possibly jumbled up tau’s
•For Theorists:
Number of leptons
Flavor of (parent) leptons (tau in particular)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
3
Expt. Channels Give Observed Signals
CDF 2fb-1 Trilepton PRL 101, 251801 (2008) Exclusive channels:
(t – tight lepton, l – loose lepton, T – isolated track)
Observed minus expected  Nobserved signal in each channel
•Limit or measurement – No distinction.
•No Model so far (although signal now “observed”.)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
4
Now Need A Model
Model for the “observed” signal (for PRL purposes…)
(mSUGRA)
PRL 101, 251801 (2008). t – tight lepton, l – loose lepton, T – (isolated) Track
Rutgers University, New Brunswick, NJ
Sunil Somalwar
5
Expt.Channels    PRL
(via a Rather Messy Scenario)
 sigma*BR vs Model Expectations Contours
(1st mSUGRA)
tan(beta) =3.
CDF 2fb-1 Trilepton PRL 101, 251801 (2008)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
6
Not a Pretty Scene
Tom Banks: “Nice work,
Sunil, but we already
know that mSUGRA
does not describe
Nature.”
Rutgers University, New Brunswick, NJ
Sunil Somalwar
7
The Question
• Regardless
of the motivation behind cuts, the analysis is done.
• N(observed signal) /Luminosity written in stone (in many expt channels).
• How to map the experimental result onto theory channels?
• Theory tau’s show up as e, mu, clean isolated tracks, or as
dirty pencil jets.
• Experimental acceptance is model dependent (specific topology).
• Clean acceptance: kinematics: pt, eta, phi, met, angles..
• Dirty acceptance: Isolation, resolution, tails, pileup…
“Just show sigma*BR. Why do you need models?”
Rutgers University, New Brunswick, NJ
Sunil Somalwar
8
What We Did After CDF Trileptons
Experimental [σB] is model-dependent because of acceptance.
N
[B] 
LA
N : Observed signal (excess over SM in several
experimental channels)
L: Luminosity
A: Total acceptance
= Clean A (kinematic) times Dirty A (isolation etc)
Stay in the topology but factorize: Factorize out the “theory” channels
0t:(e/m) (e/m) (e/m)
1t:(e/m)(e/m)t
2t:(e/m) tt
3t:ttt
Provide: [σB]0τ, [σB]1τ, [σB]2τ, and [σB]3τ, where,
[σB]0τ = N/LA0τ etc
• Same observed signal N is used four times. The topology under consideration is split
into four sub-topologies AT THE GENERATOR LEVEL.
• e/mu go together and are fine with the combined treatment.
• No approximations so far.
Rutgers University, New Brunswick, NJ
Sunil Somalwar
9
How does it help?
The signal is spread across four t channels, and not always in a simple way.
n
N   L  Bi Ai
i1
Rearrange:
1
n
L Ai
 (
)Bi
 i1 N
But, [σB]i = N/Lai, so
1
 XM
Rutgers University, New Brunswick, NJ
Bi

[B]i
i
Sunil Somalwar
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How does it help?
1
 XM
Bi

[B]i
i
1. Run a topology 4 times (with generator level cuts) through analysis,
calculate acceptances & publish [σB]0τ, [σB]1τ, [σB]2τ, & [σB]3τ.
2. A theorist has her own BR’s (=Bi) (Maybe it is a different tan(beta))

3. Use the equation to combine the experiment and theory to get XM
(Experimentally measured cross section for the theorist’s model.)
No approximations so far and we took care of the branching ratios.
Branching ratios just an example.
 We mapped the experimental result onto theory channels. (Basis or
eigen channels that can be recombined with weights.)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
11
An Example: Experimental Side
Luminosity = 0.1 fb-1, SM expectation=6, observed=9
 Observed signal = 3
 N/L = (3)/(0.1fb-1) = 30fb [=(σB)A ]
Pick the topology. It has four exclusive “theory” channels. Get acceptances,
selecting the channels at generator level.
0t:(e/m) (e/m) (e/m) (generator level) : Full acceptance A0=
1t:(e/m)(e/m)t
A1=
2t:(e/m) tt
A2=
3t:ttt
A3=
11%
5%
3%
1.4%
 [σB]0 = (N/L)/A0 = (30fb)/ (11%) = 0.27 pb
[σB]1 = (N/L)/A0 = (30fb)/ (5%) = 0.6 pb
[σB]2 = (N/L)/A0 = (30fb)/ (3%) = 1.0 pb
[σB]3 = (N/L)/A0 = (30fb)/(1.4%) = 2.1 pb
Publish [σB]0, [σB]1, [σB]2, and [σB]3 .
Rutgers University, New Brunswick, NJ
Sunil Somalwar
12
Example (contd): Theorist Side
Theorist 1: tan(beta) = 2 etc, has  = 1.25 pb
& BR’s B0=20%, B1=B2=B3=0
 XM
(1/XM) = (20%/0.27pb) + 0 + 0 + 0
 XM = 1.35 pb
1
Bi

[B]i
i
Compare to theory = 1.25 pb (Consistent)

Theorist 2: tan(beta) = 8 etc, has  = 5 pb
& BR’s B0=10%, B1=30%, B2=30%, B3=20%
(1/XM) = (10%/0.27pb) + (30%/0.6pb) + (30%/1.0pb) + (20%/2.1pb)
 XM = 0.8 pb
Compare to theory = 5 pb (Ruled out)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
13
Towards Model-independence
Part A : Exclusive theory channels
Define (experimental) channels, selection, SM expectations, N(Obs
Signal), full acceptance (clean and dirty) for theory channels, and publish
(for a given topology):
•
•
[σB]i’s for exclusive theory channels.
A spreadsheet utility for combining [σB]i‘s and theory BR’s.
Part B: Simplify/generalize topology
•
•
•
No general solution, approximations and scatter-shot at best.
Cover as many topologies as possible (We didn’t, but LHC can.)
[σB]i’s get extra mileage out of each topology.
The emphasis here is on Part A: [σB]i’s for exclusive theory channels.
Our topology efforts were rudimentary (but worked out alright.)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
14
mSUGRA  Simple Topology
1.
2.
3.
4.
Approximations begin
 Having a variety of topologies will be extremely useful.
Had to do some underhanded things at the Tevatron
 It is great that we are doing it in an organized/legal fashion @LHC
(Thank you, organizers!)
Here is the simplified model we used for CDF trileptons:
• Three mass parameters
• M (Lowest state mass)
• ΔM1 (Upper minus
intermediate mass)
• ΔM2: (Upper minus
lowest state mass)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
15
A Simple Topology Parameterization
(M = lowest, ΔM1 =upper – middle, ΔM2: upper – lowest)
• Dependence on M factors out: fi(M)
• No intermediate particle case:
[σB]i)-1 = fi(M) * gi(ΔM2)
• One intermediate particle case:
[σB]i)-1 = fi(M)*hi(ΔM1,ΔM2)
• Taylor expansions:
fi(M) = 1 + a1(M) + a2(M)2
gi(ΔM2) = b0 + b1(ΔM2) + b2(ΔM2)2
hi(ΔM1,ΔM2) = c0 + c1(ΔM2) + d1(ΔM1) + c2(ΔM2)2 + d2(ΔM1)2 +
e2(ΔM1*ΔM2)
Rutgers University, New Brunswick, NJ
Sunil Somalwar
16
A Simple Topology Parameterization
(M = lowest, ΔM1 = upper–middle, ΔM2: upper–lowest)
[σB]i)-1 = fi(M) * gi(ΔM2) or fi(M)*hi(ΔM1,ΔM2)
f0(M)
An Excel spreadsheet at:
http://www.physics.rutgers.edu/pubarchive/0901
Good to 20-30% in the validity range
Rutgers University, New Brunswick, NJ
Sunil Somalwar
17
CDF Published vs “Model-Independent”
 CDF
arXiv:0808.1605
1
 XM
Bi

[B]i
i
& parameterized simplified topology
Rutgers University, New Brunswick, NJ

Sunil Somalwar
18
Turning to LHC
Scott Thomas and
Richard Gray
Also, Sanjay Padhi
earlier.
More complicated, but
the exclusive theory
channel approach,
coupled with
(possibly parameterized)
simplified topology
approach, should work.
Rutgers University, New Brunswick, NJ
Sunil Somalwar
19
A Concrete Proposal for Disseminating Results
THEORISTS
Provide topologies (and sub-topologies). Identify exclusive channels
for each topology (start with Feynman diagrams for subtopologies, or
generator level jets, met, # leptons… exclusive signatures)
COMMON
SLHA files, possibly LHE.
Generation Level Kinematic (Clean) Acceptances (pt, eta, met, angles…)
EXPERIMENTALISTS
(experimental) channels, selection, SM expectations, N(Obs Signal),
full acceptances (clean and dirty) for theory channels, and publish
• Publish N(Obs Signal)/L = (BA) (very little effort) (Scott)
• [σB]i’s for exclusive theory channels.
• Generation-level clean acceptances (see Common above).
• A spreadsheet utility for combining [σB]i’s and theory BR’s.
Rutgers University, New Brunswick, NJ
Sunil Somalwar
20
How will a theorist use the results?
Back-of-the-envelope Theorists
Identify a published topology that is closest to your topology
Input BR’s into the spreadsheet utility
Compare theory and experimental cross section
Enterprising (Simulation-Savvy) Theorists
Run on published (simple) topologies
SLHA files  Events  Generator level cuts  Verify the
experimental values of Clean Acceptance
 Normalize to experiment: Conclude the dirty acceptance
(resolution, isolation etc) and use it as a correction factor
 Switch to topology of interest, not necessarily a simple one.
Rutgers University, New Brunswick, NJ
Sunil Somalwar
21
Exclusive Channels: an Ambitious Example
At the generator level, split the entire SUSY signal of a model
 5 or more leptons (e, mu and tau’s), then
 4 leptons (0,1,2,3,4 tau’s), then
 3 leptons (0,1,2,3 tau’s), then
 …
 Same-sign e/mu’s (additional leptons too soft to be above.), then
 …
1
Bi
 Monolepton

 Jets without leptons
 XM
[B]i
i
(Works short of interference effects)
MET, HT, # jets used along the way to build up signal/background
Also: Define sub-channels just for individual lepton/jet searches
Complicated color chains: Each chain a channel (no interference)


ATLAS and CMS (with theorists) can identify these channels and
then each generate channel-tagged MC (CTMC) samples. Multiple
analysis groups within both ATLAS and CMS can then produce
combinable results in form of exclusive (Bi)’s.
Rutgers University, New Brunswick, NJ
Sunil Somalwar
22
Conclusions
 Identify exclusive channels in a model at the generator level.
Channel-tagged MC (CTMC) will identify (simpler) constituent
topologies within a complicated model and track them all the
way through publication and follow-up pheno analyses.
 Get much more mileage out of a model/topology by providing
sigma*Br’ s for exclusive internal channels.
 Doing so makes it easy to combine pieces within and between
experiments.
 At the very least, easily factorize branching ratios from the
multidimensional parameter space for models.
 Experiments will always have to deal with the dirty acceptance,
but providing generator-level clean acceptance separately will
allow enterprising theorists to tune their simulation tools better.
 Unrelated: Organizing analyses within the experiment along
exclusive (experimental) channels is advantageous.
Rutgers University, New Brunswick, NJ
Sunil Somalwar
23