JET CHARGE AT LHCScott Lieberman

New Jersey Institute of Technology

TUNL REU 2013

Duke High Energy Physics Group

Working with:

Professor Ayana Arce

Dave Bjergaard

Outline• The detector• Jets and Jet Charge• Unfolding and Inverse Problems• Unfolding of Jet Charge

The ATLAS Detector

What is a Jet?

Jets are only meaningful once you have a “jet definition”

Jets are as close as we can get to a physical single hard quark or gluon (Salam)

Jet Definition/Algorithm• A jet definition is a systematic procedure that projects

away the multiparticle dynamics, so as to leave a simple picture of what happened in an event

Sequential Recombination

Next Eventually

Cones with Split Merge (SM)

Feynman Diagram

Jet

Jet, pions

p+p → W+ + q + x

μ+ + υ

Jet Charge

Put in words, it’s the sum of the charge of the constituent particles weighted by the particle's transverse momentum. (Bjergaard)

Krohn et al., “Jet Charge at the LHC”, June 2013,

Unfolding and Inverse Problems• Easy to take pdf or “ideal” data and add smearing and

probabilistic effects• Ex. A delta function becomes a Gaussian• Preferred Method – Unfolding should be avoided if possible• Compare models by smearing truth data and comparing to

measured data

A Simple Unfolding Method• y=Ax where x is the truth data and y is measured• A is the “response matrix” which shows the probability for

data to shift from each and to each bin• Obtained by Monte Carlo simulations of data and assumptions

about the smearing

• So A-1y=A-1Ax=x, the original distribution

The Problem with Inversion

But Unfolding (deconvolution) with the inverse transition is a complex mathematical operation (ill-posed problem, instability of solution) and requires a good understanding of the detector. Straightforward methods can result in solutions which look chaotic. Alternative home-made methods usually produce biased results. (Blobel)

Small eigenvalues don’t converge and cause oscillations in the solutions.

Matrix inversion only works with very symmetrical, simple problems.

Blobel (DESY)

Other Methods• Least Squares Regression

• Gauss-Markov theorem: least square estimate is unbiased and efficient• But result will often show large fluctuations inherent to the problem

• Diagonalization with eigenvalue truncation• Only sum over the larger, significant eigenvalues• Issue: truncation causes covariance matrix of result x to be singular

• Regularization Methods• Incorporate certain a-priori assumptions about the size and/or

smoothness of the solution!); control the norm of the residuals and, simultaneously, the norm of the solution x

D’Agostini: Iterative Bayesian Unfolding

Why Unfold Jet Charge• Bias in the jet charge equation that shifts results negative• Individual peaks of charge 1/3, 2/3 are obscured by

detector effects and uncertainty

• By Unfolding, we can:• Experimentally confirm the charge of quarks and bosons (which

produce quarks in certain interactions)• Utilize conservation of charge more effectively in particle collisions,

including the search for new particles (search for missing charge made simpler since neutrinos have no charge)