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0
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2answers
74 views

Quantum field theory why is it a trace?

So in perskin when computing the amplitude of $e^+e^-\rightarrow\mu^+\mu^-$ summing up over spin they say \begin{align}\sum_{s,s'}\bar{v}^{s'}_a(p_2)\gamma^\mu_{ab}u^s_b(p_1)\bar{u}^{s}_c(p_1)\gamma^...
6
votes
0answers
90 views

In QED/Yang Mills, why do fermions contribute 4 times as much as scalars to vacuum polarization?

Consider a Yang-Mills theory in $4D$ over a gauge group $G$ $$ \mathcal{L} = - \frac{1}{4} F^{a\mu\nu}F_{\mu\nu}^a + \bar \psi i D_\mu \gamma^\mu \psi + (D_\mu \phi)^\dagger D^\mu \phi $$ where $\...
10
votes
2answers
314 views

How to count the number of cubic tree-level Feynman diagrams at $n$ points?

I'm following this paper: arXiv:0805.3993 [hep-ph] where it's said that the total number of distinct tree-level diagrams at $n$-points with cubic vertices only is $(2n-5)!!$ I want to know where this ...
3
votes
1answer
57 views

Physical interpretations of the generating functions $Z[J]$ and $W[J]$ (or $E[J]$)

In quantum field theory, the generator of all Green's functions $Z[J]$ and that of the connected Green's functions $E[J]$ are related as $$Z[J]=\exp[-iE[J]]=\int D\phi\exp[i\int d^4x(\mathcal{L}(\phi)+...
0
votes
0answers
34 views

Two Loop QED Feynman Diagram

I'm trying to find the momentum space integral representation of the below Feynman Diagram, but am having troubles with the fact that there are two loops within the system. The main question I have ...
1
vote
2answers
60 views

Where does $W$ boson mass come from in neutron decay?

Here's a diagram of neutron decay. Up and down quarks have rest masses of 2-4 MeV. The $W$ boson has a rest mass of 80 GeV. Where has this extra mass come from?
0
votes
0answers
27 views

color structure of a QCD Feynman diagram

I am trying to find a color structure of a Feynman diagram in QCD. I understand that for the diagram shown (left) we read from the double line notation diagram (right) , that the color structure is $ \...
0
votes
0answers
23 views

Elementary particles interaction time (in LHC, for example)

Feynman description of an interaction contains diagrams with different total time steps (that contribute only a little to the amplitude, I guess). Is there a calculation, for a given interaction, what ...
2
votes
3answers
308 views

Is Bohmian Mechanics incompatible with loop corrections?

For those who continue to be unsatisfied with Quantum Mechanics (QM), Bohmian Mechanics (BM) is an alternative worth considering. It is sometimes claimed that BM is equivalent to QM, but Lubos Motl ...
0
votes
0answers
41 views

Feynman graph, proportional charge of a vertex

It is defined that the contribution of a vertex in a Feynman Graph towards the probability amplitude $ M_{fi} $ is proportional to a charge $Q_f$. Yet I seem to cannot find any precise explanation how ...
0
votes
2answers
81 views

What particles do these Feynman diagram lines represent?

What particles could be represented by A and B (labels I have added myself - this is not a homework question)? For A, it looks like it's supposed to be a photon, but I was under the impression that ...
0
votes
0answers
33 views

Feynman Diagram of $\nu_\mu + p \rightarrow \nu_\mu + p + \pi^0$

According to my class notes, the following interaction is possible $$\nu_\mu + p \rightarrow \nu_\mu + p + \pi^0$$ I tried drawing a Feynman diagram and got the below, but don't know what happens ...
-1
votes
1answer
30 views

For processes with multiple Feynman diagrams is the cross section increased?

For example in electron, positron annihilation $e^- + e^+ \rightarrow 2\gamma$ has 2 diagrams, whereas, $e^- + e^+ \rightarrow 3\gamma$ has 6 possible diagrams. This suggests, $\frac{\sigma_{2\gamma}}...
0
votes
0answers
49 views

How to draw Feynman diagram for K^- + p -> Sigma^0 + pi^0 — superposition in diagram

I'm trying to draw the Feynman diagram for the reaction $$K^- +p \rightarrow \Sigma^0 + \pi^0$$ I have two problems: How to draw the $\pi^0 = (u\bar u + d\bar d)/\sqrt 2$, a superposition of ...
0
votes
0answers
31 views

Superficial degree of divergence for scalar theories

I have a few questions regarding the derivation of the degree of divergence for feynman diagrams. The result is $$D = [g_E] - \sum_{n=3}^{\infty} V_n [g_n]$$ (following notation in Srednicki, $P118$) ...
0
votes
0answers
34 views

Wick contraction in proton-pion production

Proton-pion production $\gamma + p \rightarrow \pi^0 + p$ occurs through the interaction hamiltonian $$\mathcal H_{int} = ig \bar \psi^{(p)} \gamma_5 \psi^{(p)} \phi + e \bar \psi^{(p)} \gamma_{\mu} \...
3
votes
1answer
55 views

Feynman graph of induced current

I'm self studying QFT from Peskin and Schroeder. In chapter 19 of this book, page 653 (Perturbation theory anomalies) the expectation value of the induced current is calculated. I'm confused with the ...
1
vote
0answers
49 views

Conventions for propagators in Feynman diagrams [closed]

So far, I picked up the following rules for the propagators: Scalars: Dashed Fermions: Solid Abelian gauge boson: Wavy Non-abelian boson: springy Ghost: Dotted This made much sense to me until I ...
0
votes
0answers
54 views

Pion-pion scattering amplitude with an effective Lagrangian

I have to compute the scattering amplitude at tree level for the process $$ \pi^{a}\pi^{b} \rightarrow \pi^{c}\pi^{d} $$ with an interaction given by what is written in the square brackets of the ...
2
votes
1answer
37 views

Computation of theta-term from triangle diagram

The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
0
votes
0answers
49 views

Coherent Addition of Feynman Diagrams

I've performed a scattering cross section calculation for a tree level Feynman diagram. My adviser wants me to perform the second order calculation which involves a loop in the Feynman diagram. His ...
0
votes
0answers
23 views

1-loop integration for self-energy

I am trying to calculate the following integral that corresponds to 1-loop contribution to electron self-energy for a specific component of the momentum: $$ \Delta_i(q) = \int \frac{dp_1 dp_2 \ldots ...
3
votes
1answer
88 views

Interpreting the Cross Section Ratio R

Below is experimental data for the ratio $$R=\frac{\sigma(e^+e^-\rightarrow hadrons)}{\sigma(e^+e^-\rightarrow\mu^+\mu^-)}$$ as a function of the centre of mass energy $\sqrt s$. I am interested in ...
0
votes
0answers
36 views

Divergent diagrams in QED

I was reading about how to choose divergent diagrams in QED by using the concept of Superficial degree of divergence. We have an empirical relation $$ D= 4-E_b -\frac{3}{2}E_f $$ where $E_b$ is number ...
3
votes
2answers
68 views

How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
1
vote
1answer
102 views

How does Bremsstrahlung occur in a vacuumized particle accelerator?

In our electrodynamics course we have learned that accelerating a charged particle will lead to a loss of energy in the particle due to Bremsstrahlung. The exact amount of power radiated away is given ...
1
vote
1answer
98 views

Does massive particle really move at speed of light? [closed]

According to this answer I understood that particles with mass also move at speed of light but interaction with higgs field make this movement zigzag. So average speed is below speed of light. But I ...
0
votes
1answer
31 views

How to determine the direction of arrow on Feynman diagram for $W$ boson line?

I am somewhat confused. Looking through these slides (especially the 11th), which show Feynman diagrams involving $W$-bosons, I can't figure out which way to draw the arrow near the $W$ boson? How do ...
1
vote
1answer
71 views

Tree Level Feynman Diagrams of Electron Positron Interaction

Consider the interaction $$e^-+e^- \rightarrow e^-+e^-$$ The following is a tree level Feynman diagram for this: We can also make the paths of the two electrons on the right hand side cross over and ...
1
vote
1answer
67 views

Cutoff-dependent “inverse propagator” for renormalization

In Zee's QFT in a Nutshell, when introducing mass renormalization, he calculates the "inverse propagator" for a $\phi^4$ scalar field theory to order $\lambda^2$ by considering the two diagrams shown: ...
2
votes
0answers
76 views

Feynman rules from interaction Lagrangian with electromagnetic tensor (vertex)

I am currently studying for my QFT exam and in particular learning the methods of reading the Feynman rules directly off the Lagrangian. However, I'm still a bit uncertain how to deal with ...
0
votes
0answers
33 views

Obtaining the $s,t,u$ Feynman diagrams by Wick contraction

Consider a real scalar field described through the following lagrangian $$\mathcal L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi - \frac{1}{2}m^2 \phi^2 - \frac{g}{3!}\phi^3$$ The second ...
8
votes
2answers
221 views

How do derivative couplings affect canonical quantization?

Consider a Lagrangian for a scalar field $\phi$ with an interaction term $$\mathcal{L}_{int} = (\partial^2 \phi)^2 \phi.$$ Here I'm suppressing all indices for brevity. Now, this is just a three-...
0
votes
1answer
45 views

What interaction shown in this Feynman diagram and is it possible?

I saw the following Feynman diagram in my textbook, not sure if a typo or something I don't know: Just to clarify, the "e" on the upper left does not have any superscript. I am not sure if such a ...
2
votes
0answers
48 views

A box loop-integral [closed]

I am trying to evaluate the integrate $$ \int\frac{d^Dk}{(2 \pi)^D} \frac{1}{(k^2)^2(k^2-m^2)} $$ using dimensional regularisation ($D=4-2\epsilon$). From various references it appears that it should ...
1
vote
0answers
18 views

Magnetic susceptibility in the spin triplet channel

In the literature and articles I sometimes see the phrase magnetic/electric susceptibility(or other kinds of correlation functions) in the triplet channel. I don't know what does it exactly mean. ...
0
votes
1answer
96 views

What is a Parton Level Feynman Diagram?

I am studying elementary particle physics and I am wondering what a parton level Feynman diagram is? My understanding is that partons are representations of the quark and gluon substructure of hadrons,...
11
votes
5answers
358 views

Can Feynman diagrams be used to represent any perturbation theory?

In Quantum Field Theory and Particle Physics we use Feynman diagrams. But e.g. in Schwartz's textbook and here it is shown that it applies to more general cases like general perturbation theory for ...
1
vote
0answers
26 views

relative minus sign in radiation of gluon jets

I am trying to calculate the cross-section for electron-positron annihilation into a quark-antiquark pair and a gluon. I find that I need a relative minus sign between the two contributing diagrams in ...
1
vote
1answer
54 views

Simple feynman parameters question

I have the following integral $$\int d^D l \frac{1}{p^2 (p-l)^2 l^2}$$ which I want to rexpress using feynman parameters. I can write as a first step, $$2 \int_0^1 dx \int_o^{1-x} dy \int d^D l \frac{...
2
votes
1answer
125 views

On shell and off shell simultaneously?

I am considering the following one loop virtual correction in the DIS process: where I have a quark of momentum $p$ coming in, emitting a gluon before interacting with a photon of momentum $q$ to ...
0
votes
1answer
39 views

Gluon to quark scattering

I am trying to calculate the $g g\to q \bar q$ amplitude but am finding it intractably complex. I have determined that there are only two independent polarizations that contribute non-zero ...
0
votes
0answers
23 views

Nonequilibrium Green's functions weakly interacting two-component Bose gas

I am planing to describe time evolution of two-component BEC. I was thinking about non-equilibrium Green's functions, but I don't if the method can be applied to the problem describe below. I know ...
0
votes
0answers
23 views

IBP application in feynman box diagram

I'm trying to calculate the box diagram also mentioned in this question, but with the Integration by Parts (IBP) identities. At first, if I neglect all the external momenta for a moment, I get $$\int ...
1
vote
1answer
67 views

Betti number of Feynman graph

Let $\mathcal{L}$ be a Lagrangian, which contains polynomials of bosonic fields $\phi$. After Wick's rotation we obtain a perturbation expansion od Green's function. In this expansion there are terms ...
1
vote
0answers
65 views

In a $\phi^4$ theory, does the single vertex Feynman diagram (with no internal propagators) contribute to the scattering amplitudes? [closed]

If I have an interaction term in the Lagrangian of the form: $$ L_{int}=g\frac{1}{4}\phi^4 + g'\phi^3\chi + \dots $$ How does the trivial diagram (i.e. just a cross with a vertex at the center) ...
1
vote
0answers
122 views

Feynman diagram; $\pi^0+\pi^0\rightarrow \pi^++\pi^-$

For the reaction below draw three Feynman diagrams, one that proceeds through exchange of a gluon, one through a photon and one exchanging a weak W-Boson. $\pi^0+\pi^0\rightarrow \pi^++\pi^-$ Which ...
3
votes
0answers
42 views

how to construct self-energie diagrams

I am working on self-energie and feynmann diagrams. they are not very easy to get but i think i am starting to understand how it works but of course i am not realy sure.and before going any further i ...
4
votes
1answer
90 views

Superficial degree of divergence on Weinberg

Reading volume 1 of Weinberg's QFT book, chapter 12, page 505 he says that if you consider a diagram with degree of divergence $D\geq{}0$, its contribution can written as a polynomial of order $D$ in ...