CP violation and allowed interactions

[Safinaz]

Hi,

My question about CP- violation, but it has many parts, so I appreciate any help about..

First: I know that, any complex coupling leads to CP - violation, so if for example A is a complex scalar, and H is a real scalar, interaction as: A HH will be forbidden if we considered CP conservation, but what about H A A, will it be allowed ?

Second: I read that $^{(1)}$ there is no coupling as : Z A A, because CP–invariance im-
plies that the two Higgs bosons must have an opposite parity. I don't understand why cp -invariance implies that ?

And what about a coupling to a gluon as: G S S ( consider S is a coloured cp- odd or cp- even scalar), will it be allowed ? I mean is there in the strong interactions CP - invariance or violation (since CP- violation observed only in the EW interactions )

Bests,
s

(1) " arXiv:hep-ph/0503173v2 ", Sec. 1.2.3,

 

[Sleuth]

Hi!

Before trying to answer (I am also not an expert but I am trying to learn this stuff my self), I am confused by your question.

You say that any complex coupling generates CP violation. What do you mean? A complex coupling constant, say 'g'? Or a vertex which contains a complex field? The you say that AHH would be forbidden for this reason (because there is one complex field?), and you ask whether HAA would be forbidden. You mean HA*A I guess...

Second, you say " Z A A, because CP–invariance implies that the two Higgs bosons must have an opposite parity"

Where is the Higgs boson here? Are you assuming a CP odd Higgs boson?