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Posts Tagged ‘QCD Corrections’

All those super low energy jets that the LHC cannot see? LHC can still see them.

Hi Folks,

Particle colliders like the Large Hadron Collider (LHC) are, in a sense, very powerful microscopes. The higher the collision energy, the smaller distances we can study. Using less than 0.01% of the total LHC energy (13 TeV), we see that the proton is really just a bag of smaller objects called quarks and gluons.

myproton_profmattstrassler

This means that when two protons collide things are sprayed about and get very messy.

atlas2009-collision-vp1-142308-482137-web

One of the most important processes that occurs in proton collisions is the Drell-Yan process. When a quark, e.g., a down quark d, from one proton and an antiquark, e.g., an down antiquark d, from an oncoming proton collide, they can annihilate into a virtual photon (γ) or Z boson if the net electric charge is zero (or a W boson if the net electric charge is one). After briefly propagating, the photon/Z can split into a lepton and its antiparticle partner, for example into a muon and antimuon or electronpositron pair! In pictures, quark-antiquark annihilation into a lepton-antilepton pair (Drell-Yan process) looks like this

feynmanDiagram_DrellYan_Simple

By the conservation of momentum, the sum of the muon and antimuon momenta will add up to the photon/Z boson  momentum. In experiments like ATLAS and CMS, this gives a very cool-looking distribution

cms_DY_7TeV

Plotted is the invariant mass distribution for any muon-antimuon pair produced in proton collisions at the 7 TeV LHC. The rightmost peak at about 90 GeV (about 90 times the proton’s mass!) is a peak corresponding to the production Z boson particles. The other peaks represent the production of similarly well-known particles in the particle zoo that have decayed into a muon-antimuon pair. The clarity of each peak and the fact that this plot uses only about 0.2% of the total data collected during the first LHC data collection period (Run I) means that the Drell-Yan process is a very useful for calibrating the experiments. If the experiments are able to see the Z boson, the rho meson, etc., at their correct energies, then we have confidence that the experiments are working well enough to study nature at energies never before explored in a laboratory.

However, in real life, the Drell-Yan process is not as simple as drawn above. Real collisions include the remnants of the scattered protons. Remember: the proton is bag filled with lots of quarks and gluons.

feynmanDiagram_DrellYan_wRad

Gluons are what holds quarks together to make protons; they mediate the strong nuclear force, also known as quantum chromodynamics (QCD). The strong force is accordingly named because it requires a lot of energy and effort to overcome. Before annihilating, the quark and antiquark pair that participate in the Drell-Yan process will have radiated lots of gluons. It is very easy for objects that experience the strong force to radiate gluons. In fact, the antiquark in the Drell-Yan process originates from an energetic gluon that split into a quark-antiquark pair. Though less common, every once in a while two or even three energetic quarks or gluons (collectively called jets) will be produced alongside a Z boson.

feynmanDiagram_DrellYan_3j

Here is a real life Drell-Yan (Z boson) event with three very energetic jets. The blue lines are the muons. The red, orange and green “sprays” of particles are jets.

atlas_158466_4174272_Zmumu3jets

 

As likely or unlikely it may be for a Drell-Yan process or occur with additional energetic jets, the frequency at which they do occur appear to match very well with our theoretical predictions. The plot below show the likelihood (“Production cross section“) of a W or Z boson with at least 0, 1, 2, 3, or 4(!) very energetic jets. The blue bars are the theoretical predictions and the red circles are data. Producing a W or Z boson with more energetic jets is less likely than having fewer jets. The more jets identified, the smaller the production rate (“cross section”).

cms_StairwayHeaven_2014

How about low energy jets? These are difficult to observe because experiments have high thresholds for any part of a collision to be recorded. The ATLAS and CMS experiments, for example, are insensitive to very low energy objects, so not every piece of an LHC proton collision will be recorded. In short: sometimes a jet or a photon is too “dim” for us to detect it. But unlike high energy jets, it is very, very easy for Drell-Yan processes to be accompanied with low energy jets.

feynmanDiagram_DrellYan_wRadx6

There is a subtlety here. Our standard tools and tricks for calculating the probability of something happening in a proton collision (perturbation theory) assumes that we are studying objects with much higher energies than the proton at rest. Radiation of very low energy gluons is a special situation where our usual calculation methods do not work. The solution is rather cool.

As we said, the Z boson produced in the quark-antiquark annihilation has much more energy than any of the low energy gluons that are radiated, so emitting a low energy gluon should not affect the system much. This is like massive freight train pulling coal and dropping one or two pieces of coal. The train carries so much momentum and the coal is so light that dropping even a dozen pieces of coal will have only a negligible effect on the train’s motion. (Dropping all the coal, on the other hand, would not only drastically change the train’s motion but likely also be a terrible environmental hazard.) We can now make certain approximations in our calculation of a radiating a low energy gluon called “soft gluon factorization“. The result is remarkably simple, so simple we can generalize it to an arbitrary number of gluon emissions. This process is called “soft gluon resummation” and was formulated in 1985 by Collins, Soper, and Sterman.

Low energy gluons, even if they cannot be individually identified, still have an affect. They carry away energy, and by momentum conservation this will slightly push and kick the system in different directions.

feynmanDiagram_DrellYan_wRadx6_Text

 

If we look at Z bosons with low momentum from the CDF and DZero experiments, we see that the data and theory agree very well! In fact, in the DZero (lower) plot, the “pQCD” (perturbative QCD) prediction curve, which does not include resummation, disagrees with data. Thus, soft gluon resummation, which accounts for the emission of an arbitrary number of low energy radiations, is important and observable.

cdf_pTZ dzero_pTZ

In summary, Drell-Yan processes are a very important at high energy proton colliders like the Large Hadron Collider. They serve as a standard candle for experiments as well as a test of high precision predictions. The LHC Run II program has just begun and you can count on lots of rich physics in need of studying.

Happy Colliding,

Richard (@bravelittlemuon)

 

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