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When discussing events at the quantum level, we deal in probabilities and not absolutes. Articles I've read on particle physics state that a particle has a probability of being created in a collision. What determines this probability?

Assuming we have the energy and other criteria met, which would allow us to create range of particles (please feel free to expand what particles would make sense for an example), why do certain particles have a higher probability of being created than others?

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This is actually an open question.

So far what we are able to state from theoretical considerations are restrictions in terms of the conservation laws that we have observed. These tells you for example that the whole momentum in a reaction is conserved, an the mass-energy, or some quantum numbers. And this already constraints much of what can come out from certain reaction: for example a photon interacting with charged matter can originate a positron-electron pair, and while you cannot say how probable is this without measuring experimentally, you can already say that measuring the probability for electrons you will have the one for positrons because they only can come in pair and due to charge and momentum conservation.

But when it comes to predicting ratios of outgoing particles, theoretically this would need as well the full knowledge of the coupling constants among all particles, or in other words, the exact form of the interactions, and this cannot be provided so far without experimental values.

We are more or less able to state the form of our fundamental Lagrangian, writing terms for all kinds of interactions, but we are unable to give values to the constants without experimental evidence.

So what we do so far is: we elaborate constraints from theory based on our current understanding, this helps processing the experimental information and deducing unknown yields based on the known ones, and find relative yields between particles which gives these probabilities.

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Once one specifies a quantum field theory, typically in the form of a Lagrangian density, one can calculate the probabilities of various outcomes in collisions.

A quantum field theory is a theory based on fields that obeys quantum mechanics and special relativity. The so-called Standard Model is perhaps the most famous quantum field theory, and certainly the most successful in reproducing experimental observations.

The probability of a particular outcome is related to the number of ways that that outcome could happen. Indeed, as in famous double-slit experiments, possible intermediate states could interfere constructively or destructively. Some ways that an outcome could happen are more probable than others. This typically happens because one outcome proceeds by an interaction with a bigger coupling constant $g$, or with particles that are lighter.

The full details of these calculations are rather involved. You can make rough guesses for which outcomes are most probable by considering the power of the coupling constant that the probability is proportional to, i.e. $g^n$. If an outcome requires lots of interactions, and so high powers of $n$, it will be improbable, because $g<1$. You must also consider "phase-space" - if there are few ways in which a final state could satisfy energy-momentum conservation, the total probability for that final-state will be small.

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