Rank Indistinguishability in String Fragmentation

Abstract

The aim of this thesis is to investigate whether quantum interference between indistinguishable hadronization histories, that is, different ways the string can break while resulting in the same final state, can lead to observable effects in the momentum distributions of particles produced in string fragmentation. In the standard picture, hadronization is treated as a probabilistic process in which each event follows a single fragmentation history. However, if different histories lead to the same final state and cannot be distinguished experimentally in principle, they should be combined at the amplitude level, which allows for interference effects. This is studied in a simplified toy model.

An analytic expression for the three-particle correlation function C3 is derived for the final states pi+ pi- pi0 and pi+ pi- eta. Here, the eta is treated as a neutral pseudoscalar state rather than the physical meson. The calculation is performed by summing amplitudes coherently over the three contributing hadronization histories for a fixed up–antiup string and averaging the production points over a Gaussian source. The two channels behave in opposite ways: the pi0 channel is suppressed at small relative momenta with C3(0) = 1/3, while the eta channel is enhanced with C3(0) = 3, both relative to an incoherent baseline. The analytic results are illustrated numerically using PYTHIA with a reweighting procedure.

The results show that rank indistinguishability can produce observable effects within the toy model that are absent in the standard probabilistic treatment of hadronization. In addition, the sign of the interference is found to depend on the produced hadron.

Popular Abstract

From Invisible Quarks to Visible Matter

Imagine smashing two tiny particles together at almost the speed of light. For a very short moment, something strange happens: the smallest building blocks of matter, quarks and gluons, are set free. But no one has ever seen a free quark. So where do they go?

Almost immediately, they transform into new particles, like pions and protons, which detectors can observe. This transformation is called hadronization. And yet physicists still do not fully understand it. We understand how quarks behave at short distances. But when they move apart, the force between them grows stronger and stronger, like a rubber band that refuses to break. Eventually, instead of snapping, it creates new particles.

Physicists describe this using the Lund string model. In this picture, quarks are connected by a string of energy. As they move apart after a collision, the string stretches until it breaks, again and again, creating new quark pairs that combine into the particles we finally detect. What looks like a simple spray of particles is actually the result of many tiny breaks in this invisible string.

If we look at the final particles, can we really tell how they were created? In many cases, there are several different ways the string could have broken to produce exactly the same outcome. It is like watching the final scene of a movie without knowing which path the story took to get there.

In quantum physics, when different possibilities cannot be distinguished, they interfere with
each other, like overlapping waves. This is the same idea behind the double-slit experiment, where a particle fired at a wall with two openings behaves as if it went through both at once. The same logic applies here: if the string can break in multiple indistinguishable ways, those histories interfere.

Instead of treating each possible history separately, I ask: what if nature does not choose just one? If different histories lead to the same final particles, they can overlap and affect each other. This suggests that the final particles carry traces of the interference, and those traces differ depending on which particles are produced. In one case they cluster together in momentum, in another they are pushed apart.

I chose this topic because it felt like a mystery rather than a solved problem. The process is
completely hidden from us, and yet that hiddenness has real consequences. That felt worth understanding. And the fact that it could be explored both through detailed calculations and computer simulations made it even more interesting.

Hadronization happens in every high-energy collision, including those at the Large Hadron Collider at CERN. The models used to describe it directly affect how experimental data is interpreted. If quantum interference plays a role that current models ignore, some of what we measure could be misread. And since hadronization connects theory to what detectors observe, understanding it matters.

• author: Soltani, Zahra
• supervisor: Christian Bierlich
• organization: Department of Physics; Particle and nuclear physics
• alternative title: Interference Effects in Three-Particle Hadronization Correlations
• course: FYSK04 20261
• year: 2026
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• language: English
• id: 9233121
• date added to LUP: 2026-06-09 10:44:31
• date last changed: 2026-06-09 10:44:31