So we have a particle a and a particle b. Is there any meaning to say that a interacts more with the higgs field than particle b ? (Note that both particles have mass)
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2 Answers
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Yes. We would say that the Higgs field interacts more with particle $a$ if the coupling constant between the Higgs and $a$ is greater than the one between the Higgs and $b$.
The interactions with the Higgs $h$ are schematically of the form: $g_a h a^2 + g_b h b^2$ so the condition would be $g_a>g_b$. The masses of the particles are proportional to their couplings to the Higgs, so this implies that $a$ is heavier than $b$ (if all their mass comes from the Higgs mechanism, of course).
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$\begingroup$ Why did you add the two interactions? $\endgroup$ Commented Feb 26, 2017 at 9:12
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$\begingroup$ @MockingBird Just to show explicitly where do they appear $\endgroup$– coconutCommented Feb 26, 2017 at 9:17
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$\begingroup$ Actually I don't understand Higgs interaction. But I think OP's question was to compare A&B particle's interaction separately. But when you add them I don't understand why! $\endgroup$ Commented Feb 26, 2017 at 10:15
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1$\begingroup$ @Mockingbird Usually, the lagrangian is a polynomial on the fields. This means that it is a sum of terms that are products of fields. Each term corresponds to a vertex in Feynman diagrams, an interaction between the fields that appear in the product $\endgroup$– coconutCommented Feb 26, 2017 at 10:50
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Yes, since a particles mass depends on how much it interacts with the higgs field. When a particle interacts with the higgs field it spin keeps flipping. The rate at which a particle spins due to the higgs field determines it's mass.
