Two easy questions for particle physicists

[metroplex021]

Hi folks -- I am a non-physicist writing a popular piece on particle physics and I have a couple of questions which I suspect will be very easy for you. Any answers would be massively appreciated!

(1) Am I right in thinking that the brunt of what particle physicists predict is the probability of getting certain particles out when we smash particles together? Can anyone give me some examples of what PPists predict beyond such probabilities?

(2) Am I right in thinking that the probability of getting certain particles out when we smash particles together can be deduced just from a knowledge of the symmetry of the interaction that kicks in when they're smashed together (through the Clebsch-Gordan coefficients)? If so, and relating I guess to the first question, what considerations apart from symmetry do we need in order to deduce the empirical predictions that PPists standardly make?

I appreciate there is no exhaustive answer to be given to these questions but thoughts from the initiated would be very gratefully received. Thanks a lot!

 

[mfb]

(1) Am I right in thinking that the brunt of what particle physicists predict is the probability of getting certain particles out when we smash particles together?

For some theoretical particle physics and writers of simulation software. Not just the probability of getting a particle is relevant - its momentum distribution (and correlation with other particles) can be interesting, too.

Can anyone give me some examples of what PPists predict beyond such probabilities?

The decays of particles and their relative probability, their lifetime, spin, charge and mass, the angular distribution of their decays, and some things I did not think about.

And that is just the particle physics part - you have to understand the detectors as well to measure anything.

(2) Am I right in thinking that the probability of getting certain particles out when we smash particles together can be deduced just from a knowledge of the symmetry of the interaction that kicks in when they're smashed together (through the Clebsch-Gordan coefficients)? If so, and relating I guess to the first question, what considerations apart from symmetry do we need in order to deduce the empirical predictions that PPists standardly make?

You need the particle types, the energy, parton structure functions (for protons and antiprotons) and a lot of quantum field theory calculations.

 

[metroplex021]

Thank you very much! That's really helpful. Can I ask further: can the momentum distribution be deduced from considerations of symmetry as well (I guess rotational symmetry)? But thanks already -- that's really useful.

 

[mfb]

Without polarization, the system is symmetric with respect to a rotation around the beam axes (in a frame with head-on collisions), of course, but momentum has 3 degrees of freedom. There is no symmetry to exploit to determine the remaining two-dimensional distribution.
In general, symmetries don't help much in the prediction of differential cross-sections ("probability" that a particle is created and flies in some specific direction with some specific energy).

 

[metroplex021]

Great. You get the impression from the popular literature (eg the popular writings of Weinberg) that symmetry is the be all and end all of modern particle physics. It is great to have some the qualifications on that idea pointed out. Thanks mate!

 

[mfb]

Symmetries are very important if you want to see which types of particles a model has. As an example, quantum chromodynamics has a SU(3)-symmetry, and this directly gives the number of gluon types (8). In a similar way, supersymmetry predicts a partner to every known particle (and some more for the Higgs). It does not tell you how often they would appear in the detector, however.

 

[metroplex021]

OK -- just so I understand you, do you mean that supersymmetry in particular can't predict for you how often you'll see particles of a given type in your accelerator, while the SU3 theory could indeed predict such things as e.g. how many times I'll see pions come out when I bash together some protons?

 

[mfb]

If you fix the free parameters of supersymmetry to some values, it is possible to calculate how often you should see the particles - but it is not easy, and does not simply follow from some symmetry.

while the SU3 theory could indeed predict such things as e.g. how many times I'll see pions come out when I bash together some protons?

Pions are a mess, they are so light that it is hard to predict their number at all. Simulations are just tuned to agree with experiments somehow.

Some values are easy to predict with symmetries. As an example, consider the following decays of a Z boson:
$Z \to e^- e^+$ (electron+positron)
$Z \to \mu^- \mu^+$ (muon+antimuon)
$Z \to \tau^- \tau^+$ (tau+antitau)
Those decay products are all leptons, and they are all light compared to the Z boson. By symmetry, all decays should have very similar probabilities. And they do: The probability of muons is 0.1% above the probability of electrons, and the probability for tau particles is 0.2% above that. Those small deviations correspond to the mass differences between the different leptons.

 

[metroplex021]

lovely. thank you very much indeed. :)

 

[humanino]

can the momentum distribution be deduced from considerations of symmetry as well (I guess rotational symmetry)?

Think of the formation of an interference pattern : if you would shine light on a pattern, the angular distribution would be related to the Fourier transform of the spatial pattern. If you "shine" an electron (point-like) elastically on a hadron (say a proton), the angular distribution of the outgoing electron would be related to the Fourier transform of the spatial distribution of charge inside the hadron. If you would scatter the electron deep inside a hadron (inelastic reaction), the outgoing electron angular distribution would be more complex, related to the spatial and momentum distribution of quarks inside the hadron. If you scatter two hadrons on one another, the resulting angular distribution are obtained from convolutions the internal distributions of quarks in both hadrons. As mfb said, symmetries in the initial state can provide some constraints on the final state distributions. But in general, the angular distributions contain a great deal of information.

 

[Crazymechanic]

i haven't seen anyone adding that what you get out in particle physics is a lot to do not only what you put in like smashing two protons in the LHC but also at what energies you accelerate them that directly corresponds to the outcome and the particles formed their energies and so on.

 

[metroplex021]

Thanks people -- point from Humanino in particular made things particularly graphic. Your help time & expertise is much appreciated guys.