Recent content by Ramtin123

I am trying to renormalise the following loop diagram in the Standard Model: Using the Feynman rules, we can write the amplitude as follows: $$ \Gamma_f \sim - tr \int \frac{i}{\displaystyle{\not}\ell -m_f} \frac{i^2}{(\displaystyle{\not}\ell+ \displaystyle{\not}k -m_f)^2} \frac{d^4 \ell}{(2...

That paper discusses kinetic mixing of an Abelian U(1) gauge field with the electroweak isospin fields as shown in equations (1.1) and (1.3). The Abelian field strength tensor ##X_{\mu\nu}## is gauge invariant. This is not true for non-Abelian field strength tensor ##F^a_{\mu\nu}##. But the...

Consider two non-Abelian gauge fields ##A_\mu^a## and ##A_\mu^{'a}## belonging to the same symmetry group. An example could be the SM electroweak isospin fields and another exotic SU(2) hidden sector where ##a=1, \dots 3##. Is the kinetic mixing of the following form gauge-invariant? $$...

PS: I was told that after a transformation of the form ##\Phi \to U \Phi## and similarly ##\Psi \to u \Psi##, we get: $$\Phi ^\dagger T^a \Phi \to \Phi ^\dagger U^{-1} T^a U \Phi = ad(U)_b^a \ \Phi ^\dagger T^b \Phi$$ and similarly, for the term involving ##\Psi##. where ##ad(U)## is the adjoint...

Consider two arbitrary scalar multiplets ##\Phi## and ##\Psi## invariant under ##SU(2)\times U(1)##. When writing the potential for this model, in addition to the usual terms like ##\Phi^\dagger \Phi + (\Phi^\dagger \Phi)^2##, I often see in the literature, less usual terms like: $$\Phi^\dagger...

My first question is how to do this integral? I have Peskin & Schroeder at hand.

I am trying to compute the cross-section for the diagram below with a divergent triangle loop: where ##X^0## and ##X^-## are some fermions with zero and negative charge respectively. I am interested in low energy limits, so you can consider W-propagator as ##\frac {i\eta_{\mu\nu}} {M_w^2}##...

I am adding a triplet to electro-weak sector of the Standard Model. The triplet is in real non-chiral representation of ##SU(2)_L \times U(1)_Y##, and has vanishing hyper charge ##Y=0##. The model is discussed in details in section 3.1 of this paper.

##L^+##, ##L^0## and ##L^-## are independent fields. Let's call them ##\psi^+##, ##\phi^0## and ##\chi^-##. So I am wondering why ##\psi^{+†}=\chi^-## or ##\chi^{-†}=\psi^+## ?

Thanks Orodruin . So, in this case mass term should read: $$ -\frac m 2 \bar L L = -\frac m 2 \left( L^{+†} L^+ + L^{0†} L^0 + L^{-†} L^- \right)$$ So, why should this expression be the same as the expression above in eqn (4) of arXiv:0710.1668v2 [hep-ph] ?

Consider a three dimensional representation of ##U(1)\times SU(2)## with zero hypercharge ##Y=0##: $$ L= \begin{pmatrix} L^+ \\ L^0 \\ L^- \end{pmatrix} $$ Then the mass term is given by [1]: $$ \mathcal{L} \supset -\frac m 2 \left( 2 L^+ L^- +L^0 L^0 \right) $$ I am wondering where the...

Thanks... really great notes.

Thanks Abdul Aziz, Fermion masses problem seems really interesting. I also went through your nice PhD thesis about this problem in GUT’s. But I’m not sure about your idea of connecting Neutrino masses to cosmology brother… Do you mean one can find a cosmological mechanism during inflation or due...

Very interesting theory...

100% agree :)