How much top quark is in the proton?

We know that protons are made up of two up quarks and a down quark. Each only weigh a few MeV—the rest of the proton mass comes from the strong force binding energy coming from gluon exchange. When we collider protons at high energies, these partons interact with each other to produce other particles. In fact, the LHC is essentially a gluon collider. Recently, however, physicists have been asking, “How much top quark is there in the proton?

Presenting: Top-Quark Initiated Processes at High-Energy Hadron Colliders
Authors: Tao Han, Joshua Sayre, Susanne Westhoff (Pittsburgh U.)
Reference: 1411.2588JHEP 1504 (2015) 145

In fact, at first glance, this is a ridiculous question. The top quark is 175 times heavier than the proton! How does it make sense that there are top quarks “in” the proton?

The proton (1 GeV mass) doesn't seem to have room for any top quark component (175 GeV mass).
The proton (1 GeV mass) doesn’t seem to have room for any top quark component (175 GeV mass).

The discussion is based on preliminary plans to build a 100 TeV collider, though there’s a similar story for b quarks (5 times the mass of the proton) at the LHC.

Before we define what we mean by treating the top as a parton, we should define what we mean by proton! We can describe the proton constituents by a series of parton distribution functions (pdf): these tell us the probability of that you’ll interact with a particular piece of the proton. These pdfs are energy-dependent: at high energies, it turns out that you’re more likely to interact with a gluon than any of the “valence quarks.” At sufficiently high energies, these gluons can also produce pairs of heavier objects, like charm, bottom, and—at 100 TeV—even top quarks.

But there’s an even deeper sense in which these heavy quarks have a non-zero parton distribution function (i.e. “fraction of the proton”): it turns out that perturbation theory breaks down for certain kinematic regions when a gluon splits into quarks. That is to say, the small parameters we usually expand in become large.

Theoretically, a technique to keep the expansion parameter small leads to an interpretation of this “high-energy gluon splitting into heavy quarks inside the proton” process as the proton having some intrinsic heavy quark content. This is called perturbative QCD, the key equation known as DGLAP.

High energy gluon splittings can yield top quarks (lines with arrows). When one of these top quarks is collinear with the beam (pink, dashed), the calculation becomes non-perturbative.
High energy gluon splittings can yield top quarks (lines with arrows). When one of these top quarks is collinear with the beam (pink, dashed), the calculation becomes non-perturbative. Maintaining the perturbation expansion parameter leads on to treat the top quark as a constituent of the proton. Solid blue lines are not-collinear and are well-behaved.

In the cartoon above: physically what’s happening is that a gluon in the proton splits into a top and anti-top. When one of these is collinear (i.e. goes down the collider beamline), the expansion parameter blows up and the calculation misbehaves. In order to maintain a well behaved perturbation theory, DGLAP tells us to pretend that instead of a top/anti-top pair coming from a gluon splitting, one can treat these as a top that lives inside the high-energy proton.

A gluon splitting that gives a non-perturvative top can be treated as a top inside the proton.
A gluon splitting that gives a non-perturvative top can be treated as a top inside the proton.

This is the sense in which the top quark can be considered as a parton. It doesn’t have to do with whether the top “fits” inside a proton and whether this makes sense given the mass—it boils down to a trick to preserve perturbativity.

One can recast this as the statement that the proton (or even fundamental particles like the electron) look different when you probe them at different energy scales. One can compare this story to this explanation for why the electron doesn’t have infinite electromagnetic energy.

The authors of 1411.2588 a study of the sensitivity a 100 TeV collider to processes that are produced from fusion of top quarks “in” each proton. With any luck, such a collider may even be on the horizon for future generations.

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Flip Tanedo

Assistant Professor at University of California, Riverside
Flip is an assistant professor in theoretical physics at the University of California, Riverside. He previousy completed a Bachelors of Science at Stanford, Masters degrees at Cambridge and the IPPP in Durham, and a Ph.D at Cornell. He has been supported by a Goldwater scholarship, a Marshall scholarship, an NSF Gradaute Research Fellowship, a Paul & Daisy Soros fellowship, and a UCI Chancellor's ADVANCE fellowship. He was a participant in the original Communicating Science 2013 workshop which led to the creation of ParticleBites. His research focuses on models and signatures of physics beyond the Standard Model, including dark matter, supersymmetry, and extra dimensions. Much of his creative thinking is done while swimming or driving along Southern California's freeways.

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One Reply to “How much top quark is in the proton?”

  1. Dear Dr.Tanedo
    That is very small for detect a pair t-t bar production at p-p interaction at TeV energy. Of course We determined this portion when BGF is dominance at e-p interaction at LHeC.Phys.Lett. B744 (2015) 142-145; Phys.Lett. B741 (2014) 197-201.
    Regards
    G.R.Boroun

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