Hello everyone,
I am stuck in deriving the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is
$$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$
I have rewritten this term using the...
Because massive gauge bosons have a finite half life, are they excluded from the (infinitely, asymptotically remote?) in and out states of QFT? Or, to put it another way, are they restricted to the internal legs of Feynman diagrams, i.e. to being virtual only? We can see W and Z tracks in...
Is there anyone on here who could help me fill in my gaps in quantum field theory up to renormalization? I know how to canonically quantize a theory and how to use scalars (spin 0), vectors (spin 1) and spinors (spin 1/2) but lack more advanced knowledge like renormalization which I could...
Attempting to understand the following: Compton scattering can happen either
(a) an electron could absorb a photon and later emit a photon, or
(b) an electron could emit a photon and later absorb a photon.
OK, the maths works out, but I am trying to get intuition on track. These two are...
First, is it suitable to solve a Green's function by one-order self-energy, since it only consider partial high order perturbation, so it's unclear that this calculation corresponding to which order perturbation. In other word, if one wants to use self-energy to get Green's function, he should...
1. Homework Statement
2. Homework Equations
3. The Attempt at a Solution
I worked out that the baryon number of X is 0 and the lepton number is +1 which means x is a lepton.
However, when I work out the charge of X, do I add W+ to the left hand side or right hand side of the equation?
1. Homework Statement
Consider four real massive scalar fields, \phi_1,\phi_2,\phi_3, and \phi_4, with masses M_1,M_2,M_3,M_4.
Let these fields be coupled by the interaction lagrangian \mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}.
Find the scattering...
In the first diagram above, if I understand it correctly, the photon turns into an electron positron pair and then back again to a photon. However, what exactly is happening in the second diagram at the bottom left hand corner? Is the electron being converted to an electron photon pair?
Griffith's Introduction to Elementary Particles, if I understand it correctly, states that in QED, the fine structure constant contributes less and less to the strength of the EM interaction as we add more and more vertices since the constant is so small (1/137). However, in QCD, since the...
In the following Møller scattering process, two electrons enter, exchange a photon and then leave (and if I understand this correctly, we say that both of the electrons emitted a photon).
However, in this case:
We have an electron scattering off a photon, but the interaction happens by an...
Hello everyone,
I am currently trying to understand how we can use feynman diagrams to estimate the matrix element of a process to be used in fermi's golden rule so that we can estimate decay rates. I am trying to learn by going through solved examples, but I am struggling to follow the logic...
I was reading Feynman Diagrams and stumbled upon this query: If the electrons and protons interact by exchange of photons, does the electron inside an atoms also interact with the nucleus with a similar kind of exchange?
Question:
Draw the lowest-order Feynman diagrams for the e+e- --> W+W-process
The answer gives three diagrams. I understand the first two, but the third makes no sense to me. Here it is:
So this is a t-channel Feynman diagram. As far as I can tell regarding how these types of Feynman...
Hi all,
I'd like to calculate the self energy amplitude of the following sunset diagram (take the middle for instance )
can any one help me in distributing the momentum on the internal propagators ?
Best
I'm reading these lecture notes but there is something I don't understand. In page 15, it starts to consider vacuum diagrams of various orders and tries to associated a factor to them according to the rule:
## diagram \sim (\frac \lambda N)^p(\frac N \lambda)^v N^l=\lambda^{p-v} N^{l+v-p}##...
I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. Link to the book:
The path integral for the phi-cubed theory is equation 9.11 in the book. Please read that.
I get the...
I am trying to calculate box diagram of Kaon mixing by follow the "CP Violation" book.
Now, I arrived at equation (B.8) and I have problem with getting equation (B.12).
F(x_\alpha,x_\beta)=\dfrac{1}{(1-x_\alpha)(1-x_\beta)}(\dfrac{7x_\alpha...
For quartic scalar field theory these are some of the lowest order diagrams (taken from the solutions to 9.2 srednicki). I'm wondering if someone can give me an intuition of how to actually calculate them.
What I'm thinking is that vertices are $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and for the...
Could someone please tell me the difference between tree diagrams and loop diagrams? If I'm thinking correctly tree diagrams are before contracting? Also how do vacuum diagrams fit into the picture?
Thanks!
On page 60 of srednicki (72 for online version) for the $$\phi^{3}$$ interaction for scalar fields he defines
$$Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta J})^{3}\right]Z_0(J)$$
Where does this come from? I.e for the quartic interaction does this...
Consider a ##j## point all massive leg one loop polygonal Feynman diagram ##P## representing some scattering process cut on a particular mass channel ##s_i##. Invoking the relevant Feynman rules and proceeding with the integration via dimensional regularisation for example gives me an expression...
Hello all,
If I am having the the effective lagrangian which is actually free + interaction lagrangian (obtained from the minimal substitution for pseudoscalar and vector mesons). then how to compute the vertices of the interaction ?
I have taken into consideration of all symmetry breaking...
Hi there, my question is the following.
If an electron and positron annihilate, how can they result in ZZ?
The issue i'm having is that due to charge conservation, the exhange particle can't be W- or W+.
It also can't be a photon since the Z's don't have electrical charge to couple to.
It also...
Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent...
Hi. Do you know any book/paper/lecture notes where I can find complete derivation of Feynman rules for both scalar and pseudo-scalar Yukawa theory, and maybe an example of application to decay of fermion?
I was studying my notes and specifically for the ##e^+e^- \rightarrow \mu^+ \mu^-## process, cross section is given by
\sigma = \frac{4\pi}{3} \left( \frac{\alpha \hbar c}{W} \right)^2
where ##\alpha = \frac{g_{EM}^2}{4\pi}## and ##W## is the centre of mass energy.
Is this the same for...
As I understand it, the fundamental unit of interaction in QED is a term with a pair of (spinor) electron factors and a (vector) photon factor, represented in a Feynman diagram as two (anti-)electron lines and one photon line meeting at a vertex.
I get the case where the photon and electron...
1. Homework Statement
(a) What is a meson?
(b) State what these mesons are made up of and explain their quantum numbers and interactions.
(c) Find the lifetimes of rho meson and kaon.
(d) Find the dominant decay mode and explain why.
(e) Why is decay to 2 neutral pions forbidden?
(f) Explain...
1. Homework Statement
(a) Explain lepton universality.
(b) Explain why decay mode is forbidden and find hadronic branching ratios.
(c) Find the lifetime of tau lepton.
(d) What tau decay mode would be suitable?
(e) Find the precision.
(f) How do you improve the results?
(g) Why is it much...