Glashow resonance (UHE neutrinos)

[ChrisVer]

I'm obviously studying about neutrinos lately...

So, I wanted to ask about the Glashow resonance. I don't understand what they mean when saying:

Ultra-high energy electron anti-neutrinos allow the resonant formation of W− in their interactions with electrons, at 6.3 PeV. This process, known as the Glashow resonance

http://arxiv.org/pdf/1108.3163v2.pdf (sec.2)

Unfortunately I don't have access in the refs.

If I understand this correctly, it says that the intermediate W-boson is a real particle, right? But if that's true, I don't understand why this appears at PeV energies and not energies ~$M_W$. Thanks...

 

[mfb]

You have to consider energy and momentum conservation at the same time. An 80 GeV neutrino with an electron at rest has a CMS energy way lower than 80 GeV.

 

[ChrisVer]

So I should say that the initial 4-momentum is:
$P_{in} = \begin{pmatrix} E_\nu + m_e \\ \vec{p}_\nu \end{pmatrix}$ and that its square =$M_W^2$?

 

[mfb]

Right.

 

[ChrisVer]

Yes, that works fine :) I think I need to regain my form...

 

[Orodruin]

So I should say that the initial 4-momentum is:
$P_{in} = \begin{pmatrix} E_\nu + m_e \\ \vec{p}_\nu \end{pmatrix}$ and that its square =$M_W^2$?

Or even simpler:
$$
M_W^2=
(p_e + p_\nu)^2 = m_e^2 + m_\nu^2 + 2p_e\cdot p_\nu \simeq 2m_e E_\nu
$$
Actually summing it first is just extra work.