Glashow resonance (UHE neutrinos)

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Discussion Overview

The discussion revolves around the Glashow resonance, specifically focusing on the interactions of ultra-high energy electron anti-neutrinos with electrons and the conditions under which a W− boson can be formed. Participants explore the implications of energy and momentum conservation in this context, as well as the energy thresholds involved.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the statement that ultra-high energy electron anti-neutrinos can lead to the resonant formation of W− bosons at 6.3 PeV, questioning why this occurs at such high energies rather than around the W boson mass scale.
  • Another participant emphasizes the importance of considering both energy and momentum conservation when analyzing the interaction of neutrinos with electrons.
  • A participant proposes a formulation for the initial 4-momentum of the system, suggesting that its square equals the mass of the W boson.
  • There is an agreement among participants on the proposed formulation of the initial 4-momentum, with one participant affirming that it works fine.
  • Another participant suggests a simplified approach to calculating the mass of the W boson in the context of the interaction, indicating that summing the momenta first may be unnecessary.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical formulations presented, but there remains uncertainty regarding the underlying physics of the Glashow resonance and the energy conditions required for W boson formation.

Contextual Notes

The discussion includes assumptions about energy and momentum conservation that are not fully resolved, as well as dependencies on the definitions of the particles involved. The implications of the energy threshold for the Glashow resonance are also not conclusively established.

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

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