Questions tagged [effective-field-theory]

An effective field theory is a systematic approximation for an underlying quantum field theory or a statistical model that includes the appropriate degrees of freedom of phenomena occurring at a chosen length scale (or energy scale), while ignoring substructure and degrees of freedom at shorter distances (or higher energies), summarizing those in its parameters.

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EFT's $\hbar$ counting at loop level

In the Saclay Lectures on EFT, the author Falkowski claims under eq. (2.29) on p. 22: Note that $\hbar$ counting still works at the loop-level. To see this, one should take into account that, when $\...
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EFT matching: using tree-level to perform 1-loop-level

I'm reading the Saclay Lectures on EFT, and I don't understand how it uses the tree-level matching to compute the 1-loop-level matching. To simplify, in this post I'll put its $C_6,\lambda_1=0$ since ...
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Does the neutrino interact with the photon?

I know that the straight answer is no, but in my EFT course, where we're interested in nonrenormalizable operators of the Lagrangian, things aren't so straightforward. The non-minimal QED Lagrangian ...
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Most general 4-fermion EFT

In order to understand EFTs, I'm trying to work with an example: namely, the UV Yukawa theory that reduces to 4-fermion theory in the IR: $$\mathcal{L}^\text{UV}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}...
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How to understand crystal momentum, its relation to translational symmetry, Noether theorem, and to symmetry breaking/Landau-Ginzburg theory?

This question continues from my another question How to understand critical points of the Brillouin zone, (in)direct bands of transition-metal dichalcogenides?, and is related to Is crystal momentum ...
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Unfamiliar notations about $\pi\pi\rightarrow\pi\pi$ scattering amplitudes in Weinberg’s QFT?

I’m reading section 19.5 of Weinberg’s second volume of QFT, and confused about some notations. In that chapter, he introduce the non linear sigma model as an low energy effective theory of 2-flavor ...
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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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What does the Spontaneous Symmetry Breaking with Higgs Mechanism imply effectively?

Suppose it is understood how the Spontaneous Symmetry Breaking work mathematically to give masses to Fermions through Yukawa Interactions and to Gauge Bosons via Higgs Mechanism. In this case, my ...
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Bosonic closed string effective action

Neil Lambert in his lecture notes https://nms.kcl.ac.uk/neil.lambert/SBQG.pdf in section 3.9 states that imposing conformal invariance at one-loop imposes the following equations on the spacetime ...
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Relation between perturbative renormalization and RG group flow

I have been trying to understand renormalization for a few days. I have consulted many sources and physics.stackexhange posts but I have unresolved issues, so I am hoping someone can help me! I think ...
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Doesn't minimal subtraction alone solve the large log problem?

Assume we have an amplitude regularized through Dimensional Regularization, of a theory with a scale hierarchy $m \ll M$. If we renormalize the amplitude with an on-shell renormalization scheme, ...
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EFT unitarity violation

Standard Model Effective Field Theory is said to not be a complete model because the presence of nonzero anomalous, say, Quartic Gauge Couplings would violate tree-level unitarity at sufficiently high ...
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Effective Lagrangian for integer quantum Hall state

Non-relativistic Lagrangian of electrons in a magnetic field is written as \begin{equation} L=i\psi^{\dagger}\partial_{t}\psi + \frac{1}{2m}\psi^{\dagger}\big(\partial_{i}-ieA_{i}\big)\psi \end{...
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Coset construction for space-time symmetry breaking: how is the covariant derivative built?

I am currently learning how to build effective field theories for Nambu-Goldstone modes (NG modes) by using the coset construction formalism. I essentially follow 2 reviews: For the breaking of ...
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What are "effective" operators and what is meant by effective operators "at the LHC"?

My research supervisor told me to read about this topic but is currently on leave for the next two weeks. I believe it is related to effective field theory but please could someone elaborate on what ...
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Term violating diff invariance for Wess-Zumino action in higher loops while maintaining conformal symmetry

Conventional quantization for 2-D requires either maintaining diff invariance and sacrificing conformal invariance outlined in the paper:(https://arxiv.org/abs/2010.06771v2) Diffeomorphisms demand ...
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Does renormalization in QFT mean averaging the field over spacetime?

I found this post about renormalization very helpful, since I don't really know QFT. Now I'm curious, is this fundamentally all renormalization means in QFT as well, or is it just an analogy? That ...
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Charge term in the chiral Lagrangian with dynamical photons

When constructing the effective Lagrangian, we parametrize the Goldstone bosons (such as the pions $\pi_a$) by $U = \exp(i \pi_a \tau_a/2 f)$, where $\tau_a$ are the Pauli matrices. (See e.g. here). ...
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Propagator in Large Momentum Shell - Renormalization Group

I am reading P&S, specifically Chapter 12. I have trouble understanding why the propagator in momentum space (if the following is indeed the propagator in momentum space) in a $\phi^4$ theory in ...
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Locality of interactions and their high energy behavior

In a classic Georgi review of EFT, I have read the following quote The result of eliminating heavy particles is inevitably a nonrenormalizable theory, in which the nontrivial effects of the heavy ...
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What are the Higgsless Theories that can explain the Higgs boson detection at the LHC?

As many know, in 2012 the Higgs Boson was "detected" at the LHC. I have read that the Higgs boson was not actually directly observed, but the existence of the Higgs boson in the standard ...
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Derivative interactions in Wilsonian $\phi^4$

In chapter 12.1 from Peskin & Schroeder we see how we can integrate out the high momenta of our theory. Here we consider a $\phi^4$ theory for which we can seperate high and low momenta modes as ...
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What does it mean for a loop to be shrunk?

I am trying to follow the proof of the Appelquist-Carazzone decoupling theorem (PhysRevD.11.2856) and am having a hard time at it. One of the things that confuses me is what is meant by 'shrinking a ...
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Propagator in $\phi^4$ theory

In chapter 12.1 of Peskin and Schroeder we derive the propagator of a high momenta shell of a $\phi^4$ theory. Following the derivation, we ignore quartic terms as well as mass terms. The original ...
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What is meant by GR being nonrenormalisable, given that "scale" is the very thing being quantised?

TL;DR Usually, RG flow involves scaling the metric $g_{\mu\nu}\to\lambda^2 g_{\mu\nu}$ and seeing how couplings change. But if we're quantising $g_{\mu\nu}$ itself, I don't see how this process can be ...
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Is there an analogue of string landscape in condensed matter physics?

Possibly not every quantum field theory can be viewed as an effective theory of string theory, and possible effective theories are called the landscape. It's natural to guess that something similar ...
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Higher-order derivatives than second-order differential equations

From https://doi.org/10.1063/1.2155755 he limited himself to second-order differential equations. Our experience in elementary-particle physics has taught us that any term in the field equations of ...
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3 votes
1 answer
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Does every Renormalization Group fixed point correspond to a phase of the system?

(Sorry if this has been asked before but I can't find a similar question on here) My bachelors thesis had some connections to renormalization group theory. I covered some theory briefly and used the ...
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Non-abelian Chern-Simons from fermion effective action

(1) Starting from the fermion effective action $$S_\text{eff}[A,m] = \log \det(i\gamma^\mu{\partial_\mu} + \gamma^\mu A_\mu + m)\tag{223}$$ once can do a loop expansion following https://arxiv.org/abs/...
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How to understand Schwartz chapter19 equation (19.85)?

I am reading Schwartz's QFT books, chapter 19. In section 19.5, he claims,in equation 19.85/19.86, that there is a simpler way to prove that $Z_1=Z_2$ in all orders of perturbation theory. He first ...
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Does the Euler-Heisenberg Lagrangian lead to attractive or repulsive interaction between photons?

Photon - photon scattering in QED at low energies can be accurately described by the Euler-Heisenberg effective Lagrangian. This only involves the photons (naturally) because the electron has been ...
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Standard Model Effective Field Theory: when studying SMEFT, are we looking for deviations?

The Standard Model consists of renormalizable interactions (dimension 4) between the known fermions and bosons. The Standard Model Effective Field Theory (SMEFT) includes additional higher dimension ...
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How does the electromagnetic dipole operator appear in the decay $b \rightarrow s \gamma$?

I was analyzing the effective theory of the process $b \rightarrow s \gamma$ and and I was in doubt about the emergence of the effective operator of photon dipole $$O_7 = e m_b \bar{s}_L \sigma_{\mu\...
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6 votes
2 answers
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Proof that Wilsonian renormalization only generates terms consistent with the symmetry of the action

In the Wilsonian approach to renormalization it's easy to see that integrating out high momentum dofs in the path integral generates an infinite number of terms in the renormalized action. It's often ...
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2 votes
1 answer
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Deriving an action from a metric

I try to find out how in this paper https://arxiv.org/abs/hep-ph/9905221 the authors derived an effective action from the metric. The paper I study is related to string theory and modified gravity ...
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Are orbifolded 10d E8 GUTs valid low-energy EQFTs of string theory? Or swampland?

AdAMP recently proposed a string-reminiscent E8 GUT (digest, full) where 6 extra dimensions are compactified on a $\mathbb T^6/(\mathbb Z_3\times\mathbb Z_3)$ orbifold to yield the 4d Standard Model. ...
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Can lattice field theory be used with $1$-loop effective actions?

It's all in the title. If I have, say, a $1$-loop effective action, is it possible to perform reliable lattice computations? I am asking because I heard lattice is not that accurate if the coupling is ...
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Proof of Weinberg effective field theorem?

In the book Effective field theory at page 6 there is this Weinberg's theorem To any given order in perturbation theory, and for a given set of asymptotic states, the most general possible ...
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Two-point correlation function for metric perturbation

Can anyone explain how to calculate this two-point correlation function for metric perturbation? \begin{equation} \langle h_{\mu\nu}(x) h_{\alpha\beta}(y)\rangle \end{equation}
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RG flow of coupled two scalar fields

Considering an action in $1\le d<4$ dimensions that including deformation of a Gaussian action: $$S=S_0+\int d^dx[g_1 \mu^{\epsilon_1}\cdot\phi_1^4(x)+g_2 \mu^{\epsilon_2}\cdot\phi_2^4(x)+g_3\mu^{\...
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1 answer
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Which quantities are expandable in $1/M$ in effective (quantum) field theories?

According to this Wikipedia article on Effective field theory, the effective field theories used in QFT can be seen as an expansion in $1/M$, where $M$ is a characteristic mass scale of a certain ...
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Effective Hamiltonian of the Hubbard model

In Girvin and Yang's appendix that deals with effective Hamiltonian (p. 677) they discuss the example of a two sites Hubbard model of spin-$\frac{1}{2}$ fermions. The Hamiltonian is $$ H = T + V \\ T =...
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Are Coset Effective Field Theories CFTs?

The coset construction of the low energy effective action is a powerful way of understanding how theories with spontaneously broken symmetry behave at low energy, as it tells us what the essential ...
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Effective field theory relevant to $B \rightarrow X_s l^+ l^-$ decay

In effective field theory, the local operators of dimesion $ \le 6 $ built out of the light fields relevant to the $ B \rightarrow X_s l^+l^- $ decay are \begin{align} O_1^u&=\left( \overline{s}...
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5d nonabelian gauge theory or 5d QCD explicit $\beta$-function

Question: Are there some derived $\beta$-function formula $$ \beta(g) = \frac{\partial g}{\partial \log(\mu)} $$ for nonabelian gauge theory in the 5-dimensional spacetime at some energy scale $\mu$ ...
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Equivalence between wilsonian and non-wilsonian RGE on QFT

My current way of viewing Wilsonian RGE applied to QFT: (1) We start with a lagrangian that accurately models dynamics up to a scale $\Lambda_0$. (2) We fix $\Lambda_0$ as a cutoff to regulate the ...
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1 vote
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Wilsonian renormalization group effective interactions

My current way of viewing wilsonian RGE applied to QFT: (1) We start with a lagrangian that accurately models dynamics up to a scale $\Lambda_0$. (2) We fix $\Lambda_0$ as a cutoff to regulate the ...
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How to integrate out linear terms in Lagrangian?

Consider, for example, the Higgs Lagrangian for leptons $$L = Y_{yukawa} \bar{L} H e_R + h.c.$$ If I want to integrate out the Higgs field, what should I do? As it is linear, if I solve the Euler-...
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Similarity between 1PI effective action and Wilsonian effective action

A similar question about the difference between 1PI and Wilsonian effective actions was asked and answered here. Now I ask, when are they the same? Particularly, Seiberg says here (Pg 6, Sec 2.3) that ...
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Do we have to fix parameters by experiment when using the renormalization group?

In traditional renormalization, renormalized masses have to be fixed by experiment before going on to make other predictions. Do renormalization group methods, like Wilson's, require fixing parameters ...
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