AI in HEP: Can “Evolvable Discriminate Function”

discern Neutral Pions and Higgs from background?

James Cunha WernerChristmas Meeting 2006 – University of Manchester

Neutral Pion ReconstructionNeutral Pions decays into 2 Gammas (in the same way Higgs does!), detected by BaBar’s Electromagnetic Calorimeter

222 ii PEM

How to DISCRIMINATE background from real neutral pions?

2 gammas from background can reconstruct a neutral pion

just by chance!

Previous papers using Genetic Programming for event selection in HEP:

Cranmer,K.; Bowman,R.S.; "PhysicsGP: A genetic programming approach to event selection" Computer Physics Communications 167 (2005) 165-176.

Focus Collaboration, "Application of genetic programming to high energy physics event selection" Nuclear instruments and methods in physics research

A 551 (2005) 504-527.

Focus Collaboration; "Search for L+c -> pK+p- and D+s -> K+K+p- using genetic programming event selection" Physics letters B 624 (2005) 166-172

Mjahed, M.; "Search for Higgs boson at LHC by using genetic algorithms" Submitted to Nuclear Instruments and Methods in Physics Research.

My approach is original because…it uses genetic programming to obtain a discriminate function to discern between neutral pions and

background.

Discriminate Functions

• Mathematical model obtained with GP maps the variables hyperspace to a real value through the discriminator function, an algebraic function of kinematics variables.

• Applying the discriminator to a given pair of gammas:– if the discriminate value is bigger than zero, the pair of

gammas is deemed to come from pion decay. – Otherwise, the pair is deemed to come from another

(background) source.

How Genetic Programming works…

• AI algorithm that mimics evolution:– Initial random population.– Each individual is one problem solution. Its chromosome codes the

solution using functions and variables.– Chromosome represents a mathematical model.– Fitness evaluates solution’s economic function.

• GP is underlined by Markov chain theory.

For more information see http://www.geocities.com/jamwer2002/public.html

Methodology

MC data

Training data

Test dataDiscriminate

function

Raw data

Select Real / background events

MC data

1. Obtaining Discriminate Function (DF):

2. Test DF accuracy:

3. Selecting events

for superposition:

GP

Criteria and Events Selection in this study

I will focus in neutral pion decaying from Rho(770) resonance.

Training Genetic Programming (GP) to obtain NPDF

• Monte Carlo (MC) generators integrates particle decays models with detector’s system transfer function.

• MC events contain all information from each track particle and gamma radiation, which allows select high purity training and test datasets (96%+).

• Events with real neutral pion were selected and marked as “1”.

• Events without real pions into MC truth and invariant mass reconstruction in the same region of real neutral pions where also selected and marked as “0”.

Energy cuts cases

• all gammas without energy cut (60,000 real and background records for training, and 60,000 real and 44527 background for test),

• more energetic than 30 MeV electronics’ noise threshold (32,000 real and background records for training and test),

• more energetic than 50 MeV (15,000 real and background records for training and test),

• more energetic than 30MeV, lateral moment between 0.0 and 0.8, and have hit more than one crystal in the electromagnetic calorimeter - the conventional cut for neutral pion(16,000 real and background records for training and test).

NPDF Final results for several energy cuts-α: Sensitivity or efficiency.

-β: specificity or purity.

-γ: accuracy.

Superposition of all NPDF

NPDF obtained from different selection conditions produce the same energy distributions.

Hadronic tau decays results:

ener1 pz1 Sinteta1 Sinteta131 ener2 25.0809ener1ener2 ener2Sinteta2Sinteta122ener2 2ener1ener2 ener22 ener2px2 3ener2pz1 ener2Costeta1 2ener2Sinfi1

Sinteta2 65.2024ener1ener2Sinteta2 ener2py1Sinteta2 ener2pz1Sinteta22•All gammas:

•30 MeV cut:Sinteta1 ener2ener2 2px2 ener1Sinteta1 Sinteta2 ener1ener1 ener2 py2 28.3513 Cosfi1 Costeta1 Sinfi1 2Sinteta1ener2 pz2 Costeta2 Sinteta11 Sinteta2px2px2 Sinteta1 ener2ener2 2px2 ener1Sinteta1 Sinteta2 ener1ener1 ener2 py228.3513 Cosfi1 Costeta1 Sinfi1 2Sinteta1ener2 pz2 Costeta2 Sinteta11 Sinteta2

•50 MeV cut:

2Sinteta1 Sinteta2Sinteta2ener1 Sinteta1 ener2ener1 ener2 15.198 Costeta1Sinteta1 Sinteta2 ener1Sinteta22 Sinteta1ener2 15.198Sinteta1 Sinteta2ener1 ener2 ener1Sinteta22Cosfi117.2482 ener2 pz2Sinteta2px2px2 2Sinteta1 Sinteta2 Sinteta2ener1 Sinteta1 ener2ener1 ener2 15.198 Costeta1Sinteta1

Sinteta2 ener1Sinteta22 Sinteta1ener2 15.198Sinteta1 Sinteta2ener1 ener2 ener1Sinteta22Cosfi117.2482 ener2 pz2Sinteta2•Conventional Cuts:

4.40996 2.40996ener1 2ener1px2 2ener1pz2 ener1ener210.8199 2ener1 4ener2 4Cosfi2Sinteta2ener12 83.2834ener2Sinteta22 Sinteta12 79.2834ener1ener2Sinteta2

Discriminate functions obtained by GP

Further development in LHC: Higgs to +0j, +1j and +2j

H+1jH+0j

ATLFAST/DC1

Signal: VBFSignal: gg Fusion

EW+DPS jjQCD jjjjj+jjjj

H+2jL = 10 fb-1

Conclusion

Genetic programming approach obtains neutral pion discriminate function to discern between background and real neutral pion particles with an average 80% accuracy, 87% sensitivity (efficiency), and 84% specificity (purity).

Further development: understand what NPDF model means. What is its relationship with physics laws and properties.

Merry Christmas and Happy New Year!!!