Characterizing the hadronization of parton showers using the HOMER method

We update the HOMER method, a technique to solve a restricted version of the inverse problem of hadronization – extracting the Lund string fragmentation function f(z) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> from data using only observable information. Here, we demonstrate its utility by extracting f(z) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> from synthetic Pythia simulations using high-level observables constructed on an event-by-event basis, such as multiplicities and shape variables. Four cases of increasing complexity are considered, corresponding to e^+e^- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow> </mml:math> collisions at a center-of-mass energy of 90≥v <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>90</mml:mn> <mml:mo>≥</mml:mo> <mml:mi>v</mml:mi> </mml:mrow> </mml:math> producing either a string stretched between a q <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>q</mml:mi> </mml:math> and \bar{q} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mover> <mml:mi>q</mml:mi> <mml:mo accent="true">‾</mml:mo> </mml:mover> </mml:math> containing no gluons; the same string containing one gluon g <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> </mml:math> with fixed kinematics; the same but the gluon has varying kinematics; and the most realistic case, strings with an unrestricted number of gluons that is the end-result of a parton shower. We demonstrate the extraction of f(z) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> in each case, with the result of only a relatively modest degradation in performance of the HOMER method with the increased complexity of the string system.