Partial Wave Analysis for High Energy Physics Experiments

[Ps9]

Hi,

at first i want to apologize for my bad english.

I have to give a speech on some result of a high energy physics experiment and need some basic information about the concept of partial wave analysis (PWA) from the experimenter's point of view. My problem is that quantum mechanics textbooks are too theoretical - they explain the partial wave decomposition but not how to get get information about resonances practically. In contrast, papers are way too complicated to learn from them.

I'd like to learn about the process:
IN: detector data of final states
OUT: single partial waves with intensities and quantum numbers -> hidden resonance

a) It is said "42 partial waves are include in in the fit". Does this mean the existence of those certain waves was somehow extracted from the data ore were they assumed?

b) How does the fitting work in general? I could imagine one takes an expression for the total cross section and fits all waves at once so that the theoretical total cross section best fits the experimental one. Then i can examine single waves. Is this rudimental correct?

c) At first a mass-independend max-likelihood-fit is used and after that a mass-dependet chi-squared fit. What does mass-(in)dependend mean and what is the difference between both methods? Why are they done in this order?

d) Why does a certain resonance (that can be discovered by PWA) can not simply be seen in the invariant mass spectrum of the final state?

Thank you very much!

ps.: You may help me by highlighting my linguistic mistakes too ;)

 

[evilcman]

Hi,

at first i want to apologize for my bad english.

I have to give a speech on some result of a high energy physics experiment and need some basic information about the concept of partial wave analysis (PWA) from the experimenter's point of view. My problem is that quantum mechanics textbooks are too theoretical - they explain the partial wave decomposition but not how to get get information about resonances practically. In contrast, papers are way too complicated to learn from them.

I'd like to learn about the process:
IN: detector data of final states
OUT: single partial waves with intensities and quantum numbers -> hidden resonance

a) It is said "42 partial waves are include in in the fit". Does this mean the existence of those certain waves was somehow extracted from the data ore were they assumed?

b) How does the fitting work in general? I could imagine one takes an expression for the total cross section and fits all waves at once so that the theoretical total cross section best fits the experimental one. Then i can examine single waves. Is this rudimental correct?

c) At first a mass-independend max-likelihood-fit is used and after that a mass-dependet chi-squared fit. What does mass-(in)dependend mean and what is the difference between both methods? Why are they done in this order?

d) Why does a certain resonance (that can be discovered by PWA) can not simply be seen in the invariant mass spectrum of the final state?




Thank you very much!

ps.: You may help me by highlighting my linguistic mistakes too ;)

a) The partial wave analysis expansion is one of the commonly used orthogonal expansions in physics. This means that any function can be decomposed into infinity partial waves. If a fit includes 42 partial waves that means they truncated the expansion at 42 terms, which will supposedly give a really good approximate solution. The different partial waves correspond to different angular momenta(l) physically.

b) The measured quantity is usually a differential cross-section of some scattering reaction. But, the differential cross-section does not depend on the phase shifts in a nice way, meaning that a differential cross-section does not give you the phase shifts right away. What I believe usually happens in nuclear physics when doing such fits is that a potential model is developed for the fit. A potential form is assumed for the scattering which has quite a few free parameters, but satisfies properties we know about the system(for example we know that the Nucleon-Nucleon potential at large distances looks like a Yukawa potential). The potential model is than used to calculate the phase shift and from the phase shifts one gets the differential cross-section. Then the parameters of the potential model are changed until one achieves agreement with the measured cross-section. And the phase shifts will be what they calculated than. I imagine particle physics is similar.

c) Without knowing the problem itself, I don't know what mass dependent and mass independent fit means. Maybe the reaction involves a particle with poorly known mass, and they either use that as a fitted parameter too or use the current value? Or it may be something different...

d) A reason for resonances being hard to detect can be the existence of lots of overlapping resonances, which are superposed on the spectrum. An other can be a high non-resonant contribution and a small resonance peak. PWA helps because it is a selection, since a single phase shift only includes one l, and it is quite straightforward to see resonances in phase shifts, as it approximately manifests as a sudden rise in the phase shift from 0 to pi, so the appropriate phase shift looks somewhat similar to a Heaviside function.

Hope I cleared some things up...

 

[Ps9]

Thank you evilcman, that helped a lot.