Why is this decay allowed and another not?

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Discussion Overview

The discussion revolves around the allowed and forbidden decay processes in particle physics, specifically examining the decay of the \(\Sigma^0\) particle into a \(\Lambda\) and a \(\pi^0\), and the proton-proton collision resulting in additional particles. The focus is on the conservation laws that govern these interactions.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that the decay \(\Sigma^0 \rightarrow \Lambda + \pi^0\) is not allowed due to conservation of energy, questioning the reasoning behind this restriction.
  • Others propose analyzing the total energy of the initial \(\Sigma^0\) particle and the minimum energy required for the final state containing a \(\Lambda\) and a \(\pi^0\) to understand the decay's feasibility.
  • One participant argues that the process \(p + p \rightarrow p + p + p + \bar{p}\) is allowed because the proton-proton system is not bound and can have significant kinetic energy in the center of mass frame, which is necessary for the creation of additional particles.
  • Another participant clarifies that a diagram presented for the proton-proton interaction is incorrect, as it suggests a single proton decaying into multiple particles, which is also forbidden by energy conservation and color conservation laws.
  • Some participants summarize the distinction between the forbidden decay and the allowed collision, indicating that the former is a decay process while the latter is a collision event.

Areas of Agreement / Disagreement

Participants express differing views on the reasons behind the allowed and forbidden processes, with no consensus reached on the interpretations of conservation laws in these contexts.

Contextual Notes

There are unresolved questions regarding the specific energy thresholds and conservation laws that apply to the discussed decay and collision processes, which may depend on additional assumptions or definitions not fully explored in the discussion.

unscientific
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Consider ##\Sigma^0 \rightarrow \Lambda + \pi^0##. (Not Allowed)

vertex1.png


According to griffiths, this strong interaction is not allowed by 'Conservation of Energy'. I'm not sure why, as this simply shows an up and anti-up quark coming together, producing a gluon, where mass of gluon is mass of up and anti-up quark combined.

Consider ##p + p \rightarrow p + p + p + \bar p##. (Allowed)

Why is this possible by the strong interaction then?

vertex2.png
 
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unscientific said:
Consider ##\Sigma^0 \rightarrow \Lambda + \pi^0##. (Not Allowed)

According to griffiths, this strong interaction is not allowed by 'Conservation of Energy'. I'm not sure why

Consider this process in the rest from of the initial ##\Sigma^0## particle. What is the total energy of the initial ##\Sigma^0## particle? What is the minimum possible total energy of a final state containing a ##\Lambda^0## particle and a ##\pi^0## particle?

unscientific said:
Consider ##p + p \rightarrow p + p + p + \bar p##. (Allowed)

Why is this possible by the strong interaction then?

vertex2.png

This is not a diagram that contributes to ##p + p \to p + p + p + \bar p##. In your diagram, one of the protons is unaffected and might as well not be there. So effectively the process you have drawn is ##p \to p + p + \bar p##, which like your first example is not allowed because of energy conservation. (Also there is a more technical reason why this diagram is not allowed, which is that a single gluon cannot produce a proton-antiproton pair because of color conservation. You need at least two gluons).

Here is a possible diagram for ##p + p \to p + p + p + \bar p##:
pp_to_pppp.png
 
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Also, the reason a proton-proton collision can create an additional proton-antiproton pair is that the pp system is not a bound system and the protons can have a significant kinetic energy in the CoM frame (if they do not have enough, the process is forbidden).
 
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Put simply, the first one is a (forbidden) decay, whereas the second one is a collision
 
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dukwon said:
Put simply, the first one is a (forbidden) decay, whereas the second one is a collision
That totally clears it up. Thanks!
 

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