Recent content by ryanwilk

Hi, this is probably pretty simple but it's puzzling me... In neutrino oscillation, you produce and detect neutrinos with a specific flavour (e,μ,τ) but they travel as mass eigenstates (1,2,3). The flavour eigenstates are just linear superpositions of mass eigenstates: nu_e = U_e1 nu_1 +...

Does this seem correct? =/

So, for (2), F[a,b,g] = \int d^4x \left[ A(\partial_{\mu} g(x))a(x)b(x) + Bg^3(x) \right]\>. \implies \frac{\delta F[a,b,g]}{\delta g(y)} = \lim_{\epsilon \to 0} \frac{1}{\epsilon} \left[ \int d^4x\>[A(\partial_{\mu}(g(x)+\epsilon \delta(x-y)))a(x)b(x) - A(\partial_{\mu}g(x))a(x)b(x) +...

Oh. Yes, I did assume that. I'll have another go.

Homework Statement Hey, can I just check these functional derivatives?: 1) \frac{\delta F[g]}{\delta g(y)} where F[g] = \int dx \left[ \frac{1}{\sqrt{1+(g'(x))^2}} - 2g(x) + 5 \right]\>. 2) \frac{\delta F[a,b,g]}{\delta g(y)} where F[a,b,g] = \int d^4x \left[ A(\partial_{\mu}...

Hi, Quick question. In the SM, why can't we have loop-level interactions that give neutrinos their small masses? (It seems like we must also have Majorana neutrinos)Thanks.

Hi, quick question. "In electroweak theory, the neutrino belongs to an SU(2) doublet" So, does the neutrino belong to an SU(2)xU(1) (electroweak) doublet or just SU(2)? Thanks!

Hi, this is probably very simple. 1) What is the product of two singlets? 2) What is the product of two singlets and a doublet? It looks like (2) breaks SU(2) symmetry and (1) doesn't, but I don't really understand why =/. Any help would be appreciated, Thanks!

So, I've attempted to do the calculation. Does this look correct? (there are lots of steps I'm unsure about):

Thank you!

Hi, this is probably very simple but what is the difference between these two Feynman propagators: \frac{i}{q^2-m^2} \frac{i(p/+m)}{p^2-m^2} E.g. Is one used for the invariant amplitude and the other for loop integrals? Or is one for a fermion and the other for a boson? =s Thanks!

Homework Statement Hi. I'm trying to calculate the cross section for this process: where \phi is a massive neutral scalar, N is a massive Majorana neutrino and \nuL is the normal SM neutrino. Homework Equations N/A The Attempt at a Solution Apparently the answer should be something like...

Awesome, thanks a lot! =D

Ok, so something like?: m_{\nu_L} = m_N\>\bigg[\frac{m^2(1+x)}{m_N^2 - m^2(1+x)}\>\mathrm{ln} \bigg(\frac{m_N^2}{m^2(1+x)} \bigg) - \frac{m^2(1-x)}{m_N^2 - m^2(1-x)}\>\mathrm{ln} \bigg(\frac{m_N^2}{m^2(1-x)} \bigg) \bigg] \simeq m_N\>\bigg[\frac{m^2(1+x)}{m_N^2 - m^2(1+x)}\>\bigg[...

Ah ok thanks, so would this be correct?: X = m_N\>\bigg[\frac{m^2(1+x)}{m_N^2 - m^2(1+x)}\>\mathrm{ln} \bigg(\frac{m_N^2}{m^2(1+x)} \bigg) - \frac{m^2(1-x)}{m_N^2 - m^2(1-x)}\>\mathrm{ln} \bigg(\frac{m_N^2}{m^2(1-x)} \bigg) \bigg] Expanding the logs, \simeq...