Here is a response from Xiaojun Yao, who is a former student of EFTx and, at the time of writing, is a postdoc studying EFTs at MIT:
So far, there is no single EFT that can describe every observable in heavy ion collisions. But for some observables, EFTs have been constructed and have achieved phenomenological success. For example, for light particle production spectrum at low pT, (pion, kaon and proton with pT smaller than a few GeV), hydrodynamics and simple hadronization models can describe the data.
Softer observables:
For softer observables, hydrodynamics itself is an effective theory. The modern construction of hydrodynamics is as follows
- First, write down the most general form of the stress energy tensor, that is consistent with the symmetry of the system. The building blocks include the metric and flow velocity fields.
- The construction then is organized by the order of the derivatives on the flow velocity fields. So the power counting here is the order of the derivatives. Lowest order terms have no derivatives. In this sense, the construction is similar to the two-nucleon EFT, covered in Chapter 10 of this course.
For a review along this philosophy of EFT construction, see https://arxiv.org/abs/1712.05815. When thinking in terms of the quantum fields, we are really expanding out short wavelength fields and keeping the long wavelength modes. So hydrodynamics is a EFT of long wavelength modes. For discussion along this perspective, see https://arxiv.org/abs/1805.09331 and references in the list of course projects (PFL, RSE, VHY).
5) Is it possible to apply EFT to String Theory?
Sure, the general ideas apply to string theory too. For example, in the classical limit, string theory reproduces general relativity, so you can think of string theory as a mother theory that can be used to systematically match onto a theory that is general relativity plus higher order corrections. The suggested video project "Quantum Gravity in Perturbation Theory" (QGP) explores the resulting EFT in detail, but from a bottom up perspective.
Hard Observables
For hard observables (by hard, I mean jets and heavy flavor particles), different EFTs have been used. When jets travel through the quark-gluon plasma described by hydrodynamics, their transverse momentum with respect to the jet axis will change constantly due to interactions with the plasma. This phenomenon, [known as momentum broadening -SA], has been studied by using SCET with the Glauber exchange in the forward scattering regime. For SCET in the forward scattering, you can find references in the list of course projects (SMX). For its application in the jets in the plasma, see https://arxiv.org/abs/1211.1922 and https://arxiv.org/abs/2004.11403. For quarkonium production in heavy ion collisions (at low pT), potential NRQCD has been applied. Again, you can find relevant papers of pNRQCD in the list of course projects (PNR). A recent development is to use pNRQCD to derive the Boltzmann equation for quarkonium in the plasma in a systematic expansion. One can clearly see the connection between the validity of the semiclassical transport approach and the EFT power counting. See https://arxiv.org/abs/1811.07027 for details. For other developments using pNRQCD in plasma, see https://arxiv.org/abs/1711.04515.
5) Iain mentioned that EFT is particularly useful in understanding logarithmic divergences. Why logarithmic divergences in particular rather than, say, power divergences?
The logarithmic UV divergences in the EFT are related to what would have been logarithms involving two widely separated scales in the full theory (mother theory) of a particular EFT. We will discuss this in quite a bit of detail in Chapter 4.
6) Once we have derived a tree level effective action which includes loop effects in a full theory, why do we still account for loop level effects (in the effective theory) in our calculations?
The EFT is replacing the full theory at low energies. So the leading Lagrangian in the EFT is quantized in the usual fashion, and once you have a QFT you have no choice but to consider the loops that that QFT yields. Indeed, unitarity of the EFT connects the loop diagrams to tree diagrams [(e.g. through the optical theorem) --SA], so in order to have a unitary calculational framework you must include the loops.
This question is a common one that people asked in the early days of Chiral Perturbation theory once it was understood to come from QCD. For example, it is reasonable to ask "Do loops of pions in ChPT make sense, versus loops of quarks in the full theory of QCD?" They do, and we can see that the logarithms of the quark masses that the ChPT loops yield are precisely those found in lattice QCD calculations of full QCD. All the information of the full theory is contained in the EFT for low energy observables, just organized in a different fashion.