Yukawa Term in Langrangian

[sgurruti]

Hello,
I'm trying to understand how SARAH's conventions works. In the SM, there is a Yukawa term with the form

Y_u \overline{q} i \sigma_2 \phi* u

in order to give mass to up-type quarks. Looking the SM version provided by SARAH, I found the term

Yu H.u.q

What happened with the i \sigma_2 term and the bar over one spinor?

Best regards,
Sebastian

[FStaub]

Hi,

SARAH contracts the indices automatically to get the terms into a gauge-invariant form. See also: http://stauby.de/sarah_wiki/index.php?t ... ontraction

Cheers
Florian

[sgurruti]

Thank you very much!
I read that section, but I did not fully understand. How do I apply automatic index contraction to Pauli matrices?

Best,
Sebastian

[FStaub]

I'm not sure, if I got your question:
if you refer to the i sigma_2 in the term you have written down: that's nothing else than epsilon tensor (the anti-symmetric tensor) which SARAH uses to contract two fundamental representations of SU(2). See the second example on the wiki page.

Cheers
Florian

[sgurruti]

That's exactly what I wanted to know!

Thank you so much, and Happy New Year,
Sebastian