Unparticle Physics and Higgs Sector

[Tack]

Hi!

That's my first thread and I apologize for my bad English, but there's a question in my mind that makes me crazy...

At the moment I'm working on Unparticle Physics especially on the coupling between the SM Higgs sector and the unparticle sector.

There is a paper by Fox, Rajaraman and Shirman called "Bounds on Unparticles from the Higgs Sector" (arXiv:0705.3092), where they say that once the Higgs acquires a vev, the Higgs Operator introduces a scale into the Conformal Theory and the theory will become non-conformal at a certain scale.

That kind of makes sense to me, but I can't figure out a strikt mathematically statement for that phenomenon.
Maybe someone can help me out with a Idea, how to show this breaking of scale invariance exactly.

I thank you!

Tack

 

[Haelfix]

Mmm, what are you looking for exactly?

You have a coupling HHO that relates the standard model to the unparticle sector via the Higgs, that we are interested in studying in the infrared. Once you turn on a vev, you introduce a mass scale into the theory and will deform the conformal diagram by exactly the contributions of this 'relevant' operator (in principle there could be many operators that also break conformal invariance, but here they are studying a simple toy model where O is unique).

So are you asking about the renormalization group aspects (eg why you flow away from the fixed point in this case) or why a scale is introduced when you turn on the vacuum expectation value? Or maybe you want to show something more explicitly, like noninvariance under scale transformations?

Either way the necessary (but probably not sufficient) material can be found in a textbook on conformal field theory, like Di Francesco. But as far as I can see, the answer is more or less manifest.

 

[Tack]

Ok, what I'm looking for is, why I introduce a mass scale when I turn on a vev.

So are you asking about the renormalization group aspects (eg why you flow away from the fixed point in this case)

Isn't that the same? I thought, when I introduce a mass scale, the coupling gets energy dependent and it flows away from the fixed point...

Hmmm... I think tomorrow I will look for a textbook...

Thanks a lot!

 

[Haelfix]

"Ok, what I'm looking for is, why I introduce a mass scale when I turn on a vev."

The Higgs mechanism gets turned on, and you will now have mass term(s) present. This mechanism spontaneously breaks the conformal symmetry and the rest follows.

"Isn't that the same? I thought, when I introduce a mass scale, the coupling gets energy dependent and it flows away from the fixed point..."

Correct!

 

[Demystifier]

This paper
http://lanl.arxiv.org/abs/0707.0893
may (or may not) be relevant.

 

[Tack]

Thank you!

The Higgs mechanism gets turned on, and you will now have mass term(s) present.

Ok, I understand what happens, when I turn on the vev, but not exactly why. When I have a SM Lagrangian I know what happens. I introduce a Higgs potential, decompose it and see immediately the mass dependence. But now, I have this operator coupling HHO and I don't know how to show the mass dependence mathematically. My problem is to handle these Operators mathematically...

This paper
http://lanl.arxiv.org/abs/0707.0893
may (or may not) be relevant.

Thanks, but I've read all these Unparticle/Higgs papers and they all just say, "when the Higgsfield gets a vev, the conformal symmetry is broken"...