Suppose a particle reaction $A+B\to C+D$ is allowed in nature. Then, the reactions, \begin{align} A&\to \bar{B}+C+D,\\ \bar{C}+\bar{D}&\to \bar{A}+\bar{B},\\ B&\to\bar{A}+C+D,\\& \ldots\text{ etc.} \end{align} are also allowed in nature (but maybe they occur at different rates). Can we claim that if $A+B\to C+D$ is governed by strong interactions (or anything else), the others will also be governed by strong interactions?
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asked Jul 24, 2023 at 16:04
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$\begingroup$ 1. What, exactly, do you mean by "governed"? 2. It is certainly not true that all these reactions are "allowed": For one some of these reactions may be trivially forbidden by kinematic constraints. $\endgroup$– ACuriousMind ♦Commented Jul 24, 2023 at 16:08
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$\begingroup$ Yes, you're right. I should have been careful. For example, $n\to p+e^-+\bar{\nu}_e$ is governed by weak interactions. If kinematic constraints are satisfied, $e^+ +n\to p+\ne_e$ is also mediated by weak interactions. By governed, I mean, mediated. $\endgroup$– SolidificationCommented Jul 24, 2023 at 16:11
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1$\begingroup$ Your title has an alarming consonant transposition. If allowed kinematically, basically yes. Note the middle reaction you wrote could go backwards, too... $\endgroup$– Cosmas ZachosCommented Jul 24, 2023 at 16:12
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1$\begingroup$ @CosmasZachos Not anymore, it doesn't. $\endgroup$– rob ♦Commented Jul 24, 2023 at 16:13
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1$\begingroup$ I don't really understand what the question is. Do you understand how to draw Feynman diagrams corresponding to the "mediations"? If yes, what specific problem do you have in figuring out the answer here? $\endgroup$– ACuriousMind ♦Commented Jul 24, 2023 at 16:15
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1 Answer
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Partial answer (to be updated)
Let me try my own answer to this question. Let the process $$A+B\to C+D$$ occurs/is allowed in nature. This means that all the quantum numbers, $L, B, Q,...$ are conserved. Let me collectively denote them by $x=(L, B,Q,...)$. Then, $$x_A+x_B=x_C+x_D$$ which also means, trivially, $x_A=x_C+x_D+(-x_B).$, Since the antiparticles carry flipped values of the quantum numbers $x$, if $x$ is conserved in $A+B\to C+D$, it will also be conserved in the reactions \begin{align} A&\to \bar{B}+C+D,\\ \bar{C}+\bar{D}&\to \bar{A}+\bar{B},\\ B&\to\bar{A}+C+D,\\& \ldots\text{ etc.} \end{align} and hence, they will also be allowed, provided kinematic constraints are satisfied.
In addition, if it is found that strangeness (S), isospin (I), etc are violated in $A+B\to C+D$, then this process must be mediated by weak interactions, and so does the other processes associated with it listed above.
However, if $S, I_3$ all are conserved, but a neutrino is involved, the process is still governed by weak interactions, and if $\gamma$ is involved, the process must be mediated by electromagnetic interactions.
Please feel free to comment on this/correct any error.
answered Jul 24, 2023 at 16:45