Questions tagged [feynman-diagrams]

A diagrammatic technique introduced by Richard Feynman to describe the quantum behaviour of subatomic particles and their interactions. Do not use for general questions on diagrams that are not of the Feynman kind.

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$\log{(4 \pi)}$ in dimensional regularization integral for vacuum polarization

I have been reading through Peskin's chapter 7 and I have arrived at this expression for the first order correction to the photon propagator. Peskin uses dimensional regularization and even though I ...
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Non-Abelian vertex 3-gauge-boson

I am trying to understand how the vertices depicted in page 507 of Peskin and Schroeder come about. I understand that vertex where we have 1 gauge boson and two fermions but I'm confused on the ...
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What is the mathematical expression for the Higgs boson coupling constant?

I have been searching around and cannot get an expression for the Higg's coupling constant. By 'coupling constant', I mean for the strong force $$\alpha_S=\frac{{g_S}^2}{4 \pi \hbar c}\approx 0.1\tag{...
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Are these two Feynman diagrams different?

I am a little confused about the symmetry of Feynman diagrams. As far as I understand, Feynman diagrams are not symmetric with respect to exchange of external points or momentums if the diagrams are ...
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Renormalized Fermi velocity due to Fock term of interacting electron gas

My task is to calculate the renormalized Fermi velocity of an interacting electron gas. That is, I need to evaluate the following diagram in momentum space to obtain the self-energy contribution $\...
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Deriving the momentum Feynman rule for a vertex with a derivative of the field

Consider the following modification of the klein gordon lagrangian: $$S = \int\left(\frac{1}{2}(\partial \phi)^2 - \frac{m^2}{2}\phi^2 + \frac{\delta Z}{2}(\partial \phi)^2 - \frac{\delta m^2}{2}\phi^...
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Logarithmically divergent Feynman diagrams in $\phi^4$ theory

I am going through the lecture notes for my class and I can't seem to follow the logic. Maybe this is considered a homework problem, but I could not find anything that directly answers my question on ...
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Tadpole VEV from a fermion loop?

We have one extra complex scalar $\Phi$ beyond the Standard Model (BSM) protected by an $U(1)$ global symmetry, which is broken by an Yukawa coupling $ y_\Phi \Phi \overline{\chi} \chi$, where $\chi$ ...
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How can a flavour changing neutral current be drawn for the higgs decay to two down-type quarks?

I am trying to draw a Feynman diagram for the decay $ h \rightarrow d+\bar{s} $, but I'm struggling to create one which makes sense. So far I have this diagram: . Please could someone explain what is ...
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NLO and NLL difference [duplicate]

The next-to-leading order (NLO) Feynman diagram is the next leading process having more vertices than the tree-level diagram, but what is next-to-leading-logarithm (NLL)?
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How do you deal with particle interaction amplitudes which contain projection operators?

From a Feynman diagram I have written down the matrix element. It is for a decay: $$ P_{L}[u(k)] \rightarrow \bar{u}(p_{1}) + Z^{*} \rightarrow \bar{u}(p_{1}) + \bar{u}(p_{2}) + P_{L}[v(p_{3})] $$ ...
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Symmetry Factors in $n$-point one-loop function for QCD

I am calculating (the divergent part) of the gluon 3-point function and gluon 4-point function in the QCD Lagrangian. So I have found here what I believe to be all the 1PI Feynman diagrams at one-loop....
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Does every fermion loop have two contributions?

Suppose I have a Feynman Diagram with a closed fermion loop. This introduces a negative sign, and a trace over the product of the propagators. Is the same Feynman diagram, but with the arrows in the ...
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What are all the 1PI gluon 3-point function Feynman diagrams at 1-loop?

As an exercise in renormalization, I want to calculate the divergent part of the gluon 3-point function and gluon 4-point function matrix element. What are all the 1PI one-loop Feynman diagrams?
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Why does this particular Diagram in Third Order $\Phi^4$ theory not contribute?

In this question Moeman asked a question about third order Feynman diagrams in $\phi^4$ theory. I am also working on this problem now on my own and encountered the diagram illustrated below, which ...
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Loop Integrals and Dimensional Regularization

I want to calculate the divergent part of a Feynman diagram using the Feynman parameters: $$\frac{1}{A_1 A_2 \ldots A_n} = \int_0^1 dx_1 ... dx_n \delta (\Sigma x_i -1) \frac{(n-1)!}{[x_1 A_1 + x_2 ...
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How to diagrammatically show this Green's function from a tridiagonal Hamiltonian?

Consider the following electronic Hamiltonian $$ \begin{bmatrix} \ddots & \ddots & & & \\ \ddots & H_{n-1} & V^- & & \\ & V^+ & H_n & V^- & \\ &...
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Charged current $e^-e^+$ weak interaction Feynman diagram

I am new to the weak interactions and in particular to the interactions given by charged current interaction lagrangian $$ \mathcal{L}_{int}^{CC} = \frac{g}{2\sqrt{2}}\left[J^{\mu}W^{+}_{\mu}+J^{\mu \...
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Exact propagator - 1pI diagrams

Above diagram can be written in terms of series: $$i\Delta = -\frac{i}{p^2 + m^2} + \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{i}{p^2 + m^2}\Big)+ \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{...
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Confusion with the definition of propagator in canonical quantization and path integral formalism

Imagine the following $1$-loop diagram with two vertices in interacting $\lambda \phi^4$ theory: In momentum space the way to write down the correlator is: Drawing incoming and outgoing legs, ...
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Symmetry factors in two interacting fields

Red and blue colored lines represent the two different fields. At 1st order, by the exchange of the blue legs and red legs we get $\frac{1}{4}$ factor and in one of the 2nd order term drawn above, ...
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Electron Muon scattering in the CM frame, question about the energy

I calculated the spin-averaged amplitude for the $e^{-}\mu^{-} \rightarrow e^{-}\mu^{-}$ scattering in the CM frame in the high energy regime($m_{e}$,$m_{\mu} \rightarrow 0$) following the hints ...
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How to evaluate effective Feynman diagrams in the standard model?

I was reading the "Weak Hamiltonian, CP Violation and Rare Decays" by Andrzej J. Buras and, in the page 57 I don't understood how he calculate the effective Feynman diagrams for to get the ...
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The conditions for a shift in a loop momentum to be allowed

When we evaluate the Feynman diagram containing a loop, we commonly use the identity: \begin{align} \frac{1}{A_{1}^{m_{1}} A_{2}^{m_{2}} \cdots A_{n}^{m_{n}}}= \int_{0}^{1} d x_{1} \cdots d x_{n} \...
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Why does the LSZ reduction formula only give the connected part of the $S$ matrix?

As an example, using the LSZ reduction formula, the $S$ matrix element for $2\rightarrow 2$ scattering is found in Peskin and Schroeder to be $$\langle \boldsymbol{p}_1 \boldsymbol{p}_2\rvert S \lvert ...
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Disconnected Feynman Diagram Combinatorics Factor

Many sources, e.g. these questions (Proof of Connected Diagrams, Most general Feynman diagram) say that the amplitude for a disconnected Feynman diagram is given by $$D = \prod_{i}\frac{1}{n_i!}{C_i}^{...
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Doubly-charged scalar decay and spinors

In the minimal type-II seesaw, in addition to the SM Higgs doublet $\phi (\phi^+,\phi^0)^\top$, one introduces a complex $SU(2)_L$ scalar triplet that can be written as $$\Delta_{L}=\left(\begin{array}...
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Implication and proof of conserved charge due to coupling of spin-1(massless) to spin-0 or spin-1/2

I'm following Schwartz's QFT book and problem 11.3 asks to prove that the coupling of massless spin-1 to spin-0 or spin-1/2 implies a conserved charge. It asks to refer to result from section 9.5, ...
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Feynman rules in Grassmann variables [duplicate]

I'm given the following integral $$ Z[w] = \frac{1}{ (2 \pi)^{n/2}} \int d^n x \prod_{i=1}^n d \overline{\theta}_i d \theta_i \exp \left( - \overline{\theta}_i \partial_j w_i (x) \theta_j - \frac{1}{2}...
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Peskin and Schroeder Exercise 10.2 - Yukawa Theory Renormalization

I am having some trouble with exercise 10.2 in Peskin and Schroeder, on the renormalization of Yukawa theory. Part a) of the exercise says show that the theory contains a superficially divergent 4$\...
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Schwartz's derivation of the Feynman rules for scalar fields

In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions ...
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Feynman vertex of an effective operator $\frac{\phi}{\Lambda}F_{\mu\nu}F^ {\mu\nu}$

Could anyone give some advice on how to calculate Feynman rule for vertex (Feynman rule of $\bar{\phi} \phi F_{\mu \nu}F^{\mu \nu}$ and its corresponding 4-photon scattering amplitude) of an effective ...
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Generating functional in $\phi^4$ theory calculation upto 1st order

This question is based on section $1.2$ of Gauge Theory of Elementary Particle Physics by Ta-Pei Cheng and Ling-Fong Li. In $\phi^4$ or $-\frac{\lambda}{4!}\phi^4$ theory let $W[J]$ be the vacuum-to-...
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Why is there an upper mass limit of $300$ GeV of the Higgs boson for $W/Z$ associated production and t$\bar{\mathrm{t}}$H associated production modes?

I am currently trying to understand this graph for the cross-section versus Higgs mass: As you can see from the above graph, there is an abrupt cut-off at $M_H=300$ GeV where I have put a green box ...
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Does anyone know or knows how I can find papers with loop diagrams (one and more) that involve the Standard Model and $Z'$ only?

I have tried to search for them on arXiv and the Web of Science, but without having a specific reference I was not successful, even though invested some hours. What I am trying to find could well be ...
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Computation of functional determinant using Feynman diagram

The above equation is from chapter 9.5 "Functional Quantization of the Spinor Field" of Peskin's and Schroeder's book $($page $305)$. I understand that the initial determinant equal to the ...
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Regarding mass insertion and helicity (?) flip

I am reading Grozin's book "Lectures on QED and QCD: Practical Calculation and Renormalization of One- and Multi-loop Feynman Diagrams" and specifically, I want to understand a paragraph on ...
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Drawing Feynman diagram for positronium decay into 2 photons

I am studying the annihilation processes and read that electron-positron annihilation releases 2 photons. I know that releasing 1 photon is not possible because it violates the conservation of $E$. ...
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1 answer
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Resummation of single class of diagrams vs all 1PI diagrams

In the book A Modern Introduction to Quantum Field Theory, Maggiore considers the resummation of tadpole diagrams as its own individual geometric series to give $$\frac{i}{p^2-m^2-B}\tag{1}\label{1}$$ ...
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What is the physical interpretation of the two tree-level Feynman diagrams for $e^-e^- \to e^-e^-$ scattering?

In the tree level, the $e^-e^- \to e^-e^-$ scattering has two Feynman diagrams, the first one is indicative that one electron emitted a photon which was later absorbed by the other electron: However,...
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Evaluation of the OPE coefficients in Peskin&Schroeder's book

I was reading the book by Peskin&Schroeder and at page 616 the authors write the operator product expansion of the quarks electromagnetic current $J^{\mu} (x) J^{\nu} (0)$ as: $ J^{\mu} (x) J^{\nu}...
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Scattering amplitude of $e^-\mu^-\to e^-\mu^-$ in terms of matrix elements of $j_\mu$

Using Feynman rules for QED, we can write the Feynman amplitude of a typical electromagnetic scattering process, for example, $$e^-(k)\mu^-(p)\to e^-(k')\mu^-(p'),$$ at the lowest order, in terms of ...
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4 votes
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QFT: Normal Ordering Interaction Hamiltonian Before Using Wick's Theorem

It has recently come to my attention, though reading the notes of a course on QFT that I've started, that there seems to be an "ambiguity" in, or at least two distinct ways of, calculating ...
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Feynman rule with complex coupling

Suppose I have 3 complex scalar fields and an interaction term $$ \mathcal{L}\supset -g \chi \phi_1 \phi_2 + {\rm h.c.} $$ where $g$ is a complex constant whose phase I cannot get rid of by field ...
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2 votes
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What does 't Hooft mean by "integrating symmetrically"?

I always wanted to understand what re-normalization in particle physics really means. Having a background in statistical physics I do understand it in there but as far as I know re-normalization in ...
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Four-point correlation function path integral for free scalars

In An Introduction to Quantum Field Theory by Peskin and Schroeder, section 9.2, they calculate the four-point correlation function for a free real scalar field $\phi(x)$ using the path integral ...
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Definition and proof of Symmetry Factor of Feynman Diagram

Studying QFT, I was told that symmetry factor is defined by: if there are $m$ ways of arranging vertices and propagators to give identical parts of a diagram (keeping the outer ends of external lines ...
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Symmetry Factor for Feynman diagram of complex field

When studying Feynman diagram I have been told that when treating a complex scalar field we use pertubation which is normalize with factor $1/n$ (where $n$ is the number of terms in the perturbation) ...
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How to derive the Clausius–Mossotti relation using Feynman diagrams?

The Clausius–Mossotti relation is usually derived by assuming that a molecular in a crystal is surrounded by a spherical hole, or by the $- \frac{1}{3k^2} \delta(\boldsymbol{R})$ term in the dyadic ...
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Why the Feynman diagrams contributing to the effective action $\Gamma[\phi_{\rm cl}]$ are stripped/amputated/have no external lines?

I am reading P&S Chapter 11 and specifically I am trying to understand the derivation of $\Gamma[\phi_{\rm cl}]$. All the algebra is okay, but I am failing to understand the connection to Feynman ...
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