A detailed quantum mechanical explanation of complex particle tracks in collider detectors?

Question

I would be interested in knowing whether anybody ever attempted to study, in consistent field-theoretic terms, the formation of complex particle tracks (including secondary vertices) in collider detectors.

As far as I know, tracks observed in real detectors are routinely analyzed with software that models them as if they were trajectories of classical point particles originated from the decays, applying geometrical considerations and classical conservation laws to identify the interaction vertices and decay products. This kind of analysis has allowed the successful experimental verification of the Standard Model, which is a quite remarkable feat.

However there seems to be a quite general consensus among theorists that fully localized point particles are not compatible with the QFT framework, so the emergence of such apparently point-like entities leaving traces, generating secondary vertices, being finally detected at specific locations etc. can at best be explained in terms of approximately localized interacting wave packets.

In this context, I suppose that if we could assume that the primary decay generates a set of approximately localized excitations originating at the primary interaction vertex position, the subsequent steps of the process could be described in terms of approximately point-like particles. In my understanding ,this would amount to assuming that the primary interaction generates quasi-asymptotic states in a scattering theory sense.

On the other hand, I know that, at least in one famous case (alpha particle decay, Mott 1929), it is possible to explain the formation of tracks in a detector even without invoking any (approximate) preliminary localization of a primary spherical wave originating from a decay event. In this case there would not even be a need for defining a primary vertex position: the primary tracks would originate at random positions and directions in the detector bulk. But then I wonder how this approach could be extended to cover complex decay processes involving multiple interactions, i.e. multiple tracks, and still reproduce the apparently classical observed trajectories.

More generally, has this problem ever been tackled in detail from a theoretical and/or simulation point of view?

Thank you,
Paolo

Comments

Can we retag this as "quantum mechanics", retitle to ask about a "quantum mechanical" explanation rather than a "quantum field theoretic" explanation, and remove the field theory tag? This is not about waves in physical space, but about wavefunction description of complex systems in configuration space.

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Ron,

My original intention was indeed to inquire the availability of quantum field theoretic explanations for particle tracks in detectors, since I was somewhat concerned by what seemed to me a fairly scant interest by QFT theorists in the very objects the QFT experimentalists are looking at to test their theories.

However I am available to retag the question in case you still think it is mistagged.

Thank you,
Paolo

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I can do the retitling and retagging, but I want your consent, that's all. The reason it is mistagged is because the question does not require the particular aspects of relativistic quantum field theory  to understand--- you don't need a formalism for creation and annihilation of particles, or relativistic paths, or a path-integral formalism, any of that stuff.

This question is about how you can turn the wave scattering in quantum mechanical description of particles (the wave description of particles is the same in quantum field theory) into a physical particle track. This is resolved in quantum mechanics, it is not the problems of field theory.

The quantum field theory formalism takes this resolution for granted, and moves on to new problems. There is a reformulation of the quantum mechanical formalism to talk about expectation values of operator products, instead of detailed wavefunctions, because detailed wavefunctions are inconvenient to calculate with in field theory. There is no overlap in the methods used to answering this question with those of quantum field theory.

The reason quantum field theorists ignore this question is because it is completely solved at a more fundamental level. Once you understand what is going on, you won't worry about it any more than they do.

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Ron,

I understand and agree with your observation.
Please go ahead with the retitling and retagging!

Thank you,
Paolo

Answer 1

Mott needs to use the decohering environment to produce the localization, and this is essential. The "secondary vertices" are inferred from the decohered tracks which are produced at the detector, or, in a bubble-chamber, they are produced after the initial ionization trails decohere the spherical wave.

The reconstruction of complex paths in the detector from a pure wave-mechanics is the main point of Everett's analysis leading up to the many-worlds interpretation, and this part of the analysis, without any philosophical commitments regarding the ontology, is the uncontroversial aspects of many-worlds. By including the environment, you can see that particle trajectories are compatible with the wave formalism of quantum mechanics, they are a prediction, once you apply the formalism to include a sufficiently large part of the environment, and apply measurement postulates only on a large scale.

The controversial step in many worlds is removing the measurement postulate altogether, and considering the alternate paths in a wavefunction description as physically real, but necessarily unobservable. But the analysis doesn't require you to take this philosophical step, philosophy, as always is up to you. But it resolves the technical issue of how to reproduce particle paths in a detector, you just include the environment in the quantum description. In this regard, it's just a more sophisticated version of the Heisenberg-Mott analysis of spherical wave symmetry breaking in bubble-chamber environmental interaction.

The best source for this is Everett's thesis, although there are more modern sources.

Comments

Hi Ron,

Thank you for your kind reply.

If I get it right, the idea is that the original spherical wave gets decohered by the interaction with the environment and ends up having a ray-like rather than sphere-like propagation.

At that point the symmetry has been broken irreversibly, and the geometry of following processes (secondary vertices etc) can be explained in terms of the direction of the decohered ray-like propagation of the wave.

Did I get it right?

And thank you for the suggestion: I will definitely look at Everett's thesis.

Paolo

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Yes, this is the content of Heisenberg-Mott. The extension to further processes, like the ray interacting with other things, and so on, up to macroscopic scales is implicit in Von-Neumann, and explicit in Everett. This stuff becomes taboo after the many-worlds interpretation comes out, but it is really now considered sort-of solved, that is, solved up to philosophical quibbles (which can never be solved because they don't make sense in positivism).

Answer 2

For a simulation study of secondary particle tracks (in water, but a modern wire detector is not so different in terms of the principles) see 

D. Emfietzoglou et al., An event-by-event computer simulation of interactions of energetic charged particles and all their secondary electrons in water, J. Phys. D: Appl. Phys. 33 (2000) 932–944.

Comments

This is not appropriate, as the simulation is not quantum, so it doesn't answer OP's question. He is asking the classic question "how do Schrodinger waves produce definite particle tracks?", and the answer, as always is because the waves are in configuration space, and entangle the particle with the environment in ways where the environment sees linear tracks.