Loop Corrections: A Layman's Explanation

[physics_domme]

TL;DR Summary

I am looking for a Layman's terms explanation of loop corrections, EFT, and dijets, please and thank you!

I am currently a senior physics major working on my undergrad, and I just began a new research position at my school, and am teaching myself particle physics because the group I am working with is looking to expand the SM, and my project specifically is to implement Monte Carlo simulations of particle collisions in hopes of finding answers that bring us closer to solving the whole dark matter issue. My question is: can someone please, in Layman's terms, explain what a loop correction is? I would be very appreciative! I actually would also like the same type of explanation for EFT, and dijets (I am assuming this is the result of particle collisions, in which there are two jets for particles and anti-particles, or according to their charge, etc.), if possible. Thank you so much for your help!

 

[Dr.AbeNikIanEdL]

the group I am working with

So what did the professor leading this group and the more experienced members of it say to that? What literature are you working with? These things (apart from maybe EFTs) should be covered in introductory book on particle physics like e.g. Griffith’s book. I suggest coming back with more specific questions after reading on those topics in those, because at the moment you are basically asking us to write such a book.

my project specifically is to implement Monte Carlo simulations of particle collisions

What particles specifically are we talking about, at what energies? Sounds quite ambitious for an undergrad project to me!

 

[ohwilleke]

can someone please, in Layman's terms, explain what a loop correction is?

The dynamics of a quantum particle are summarized by a path integral of a propagator function that basically describes every possible way that a particle could go from point A to point B and then assigns a probability to that which the integral sums up to get the combined probability for all possible paths which shows the probability that the particle will go from point A to point B. Similar approaches are used for decays because there is a probability that a particle will emit, for example, a W+ boson that then has probabilities to decay in particular way, for which empirical data are often used but which can be calculated from first principles.

The possible paths can be categorized as corresponding to particular Feynman diagrams that each can be calculated. The first set of paths are called the "tree level" path and make the biggest contribution to the final result. The next set of paths involve creation and destruction of a particle at an intermediate step that doesn't end up in the final outcome, and forms a "loop". The more loops you consider, the more of the possible outcomes you are taking into account, and the closer you get to an accurate solution up to the limits of what we are able to calculate on a practical basis. Each additional number of loops involves many more calculations than the previous number, because there are more possible permutations of Feynman diagrams when you consider more possible loops.

Two or three loop calculations are common, and some calculations have been done up to six or more loops. It is possible to meaningfully estimate the uncertainty caused by truncating your calculation at a certain number of loops. A loop correction is the modification to the bottom line prediction due to considering more than tree level outcomes.

A good example of this is in the theoretical prediction the magnetic moment of the muon. which is exactly 2 at tree level. Muon g-2 is the amount of the loop corrections to the tree level value. This calculation is customarily broken up into Feynman diagrams that have only photons and the muon (the EM part), diagrams that also have W and Z bosons (the electroweak or EW part) and diagrams that also have quarks (the hadronic part, which is further broken up into heavy and light hadronic parts). The EM part is very close to the truth for the overall value, but the loop corrections do impact the final result and most of the theoretical uncertainty in the final result actually comes from the tiny hadronic contribution to the overall loop correction.

The infinite series involving all possible loops is actually not convergent, but it doesn't start to diverge until you do more loops than we are able to do on a practical basis so far, so physicists don't worry too much about that.

There is a powerpoint presentation hitting the high points (and possibly correcting any subtle flaws in my terminology) http://www.physics.indiana.edu/~dermisek/QFT_08/qft-II-2-1p.pdf. "QED" by Richard Feynman is a good introductory book to explain the concepts involved in a breezy easy to understand, yet still very accurate manner, without undue mathematical elaboration.

I actually would also like the same type of explanation for EFT

I am assuming that you mean an effective field theory. An EFT is a model of how physics works within a domain of applicability that doesn't presume that it is actually the true and complete fundamental law of nature and instead makes the humble claim that is a phenomenological description of how nature behaves (generally at low energies and in non-extreme conditions) which is good enough for government work in the kind of interaction you are dealing with, that is merely inspired by what people think that the fundamental laws of nature look like. Of course, it refers not just to any other model, but in particular to a field theory, either classical or quantum.

Field theory usually refers to a construction of the dynamics of a field, i.e. a specification of how a field changes with time or with respect to other independent physical variables on which the field depends. Usually this is done by writing a Lagrangian or a Hamiltonian of the field, and treating it as a classical or quantum mechanical system with an infinite number of degrees of freedom. The resulting field theories are referred to as classical or quantum field theories. The dynamics of a classical field are usually specified by the Lagrangian density in terms of the field components; the dynamics can be obtained by using the action principle. It is possible to construct simple fields without any prior knowledge of physics using only mathematics from several variable calculus, potential theory and partial differential equations (PDEs).

One way to classify a field theory is by the spin that a carrier boson of a field of that type would have to have scalar (spin-0), vector (spin-1), tensor (spin-2), or a spinor field: spinor fields (such as the Dirac spinor) arise in quantum field theory to describe particles with spin which transform like vectors except for the one of their component; in other words, when one rotates a vector field 360 degrees around a specific axis, the vector field turns to itself; however, spinors would turn to their negatives in the same case. There are also classical equivalents to these (in which case the classification refers to how many data points are needed to describe the field at any given point in space-time). Another way to classify a field theories are also defined by the quantum numbers that they preserve (e.g. color charge, EM charge, baryon and lepton number, etc.). It turns out that both of the concepts above the define the broad framework of a field theory can be expressed as symmetries.

dijets (I am assuming this is the result of particle collisions, in which there are two jets for particles and anti-particles, or according to their charge, etc.), if possible.

Close, a dijet is when, as a result of particle collisions to quite heavy or energetic particles decay into a jet of many decay products, sometimes, but not necessarily, one for particles and one for anti-particles. Particle and antiparticle jet pairs are common but the term dijet isn't restricted to such jets and unlike Higgs bosons and Z bosons which usually have symmetrical decays, W+ and W- boson decays are asymmetrical.