{"id":3063,"date":"2015-05-23T03:27:46","date_gmt":"2015-05-23T03:27:46","guid":{"rendered":"http:\/\/www.particlebites.com\/?p=3063"},"modified":"2017-02-19T01:26:18","modified_gmt":"2017-02-19T01:26:18","slug":"how-much-top-quark-is-in-the-proton","status":"publish","type":"post","link":"https:\/\/www.particlebites.com\/?p=3063","title":{"rendered":"How much top quark is in the proton?"},"content":{"rendered":"

We know that protons are made up of two up quarks<\/strong>\u00a0and a down quark<\/strong>. Each\u00a0only weigh a few\u00a0MeV—the rest of the proton mass comes from the\u00a0strong force binding energy coming from gluon<\/strong> exchange.\u00a0When we collider protons at high energies,\u00a0these\u00a0partons<\/strong> interact with each other to produce other particles. In fact, the\u00a0LHC is essentially a gluon collider.\u00a0Recently, however, physicists have been\u00a0asking, “How much top quark is there in the proton?<\/em>”<\/p>\n

Presenting:\u00a0<\/strong>Top-Quark Initiated Processes at High-Energy Hadron Colliders
\n<\/strong>Authors: <\/strong>Tao Han, Joshua Sayre, Susanne Westhoff (Pittsburgh U.)
\nReference<\/strong>: 1411.2588<\/a>,\u00a0JHEP 1504 (2015) 145<\/a><\/div>\n

In fact, at first glance, this is a ridiculous question. The\u00a0top quark\u00a0is 175 times<\/em>\u00a0heavier than the proton! How does it make sense that there are top quarks “in” the proton?<\/p>\n

\"The<\/a>
The proton (1 GeV mass) doesn’t seem to have room for any top quark component (175 GeV mass).<\/figcaption><\/figure>\n

The discussion is based on preliminary plans\u00a0to build a 100 TeV collider, though there’s a similar story for\u00a0b<\/em> quarks (5 times the mass of the proton) at the LHC<\/a>.<\/p>\n

Before we define what we mean by\u00a0treating the top as a parton, we should define what we mean by\u00a0proton<\/em>! We can describe the proton constituents\u00a0by a series of parton distribution functions <\/strong>(pdf<\/strong>):\u00a0these tell\u00a0us\u00a0the probability of\u00a0that 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\u00a0interact with a gluon than any of the “valence quarks.”\u00a0At sufficiently high energies, these gluons can also produce pairs of heavier objects, like charm, bottom, and—at 100 TeV—even top quarks.<\/p>\n

But there’s an even deeper sense in which these heavy quarks have\u00a0a non-zero parton distribution function (i.e. “fraction of the proton”): it turns out that\u00a0perturbation theory breaks\u00a0down\u00a0for certain kinematic regions when a gluon splits into quarks. That is to say,\u00a0the small parameters we usually expand in become large.<\/p>\n

Theoretically, a\u00a0technique\u00a0to keep\u00a0the\u00a0expansion\u00a0parameter small leads to an interpretation of this “high-energy\u00a0gluon splitting into heavy quarks inside the proton” process\u00a0as the proton having some intrinsic heavy quark content. This is called perturbative QCD<\/a>,\u00a0the key equation known as DGLAP<\/a>.<\/p>\n

\"High<\/a>
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\u00a0leads on to treat the\u00a0top quark as\u00a0a constituent of the proton. Solid blue lines are not-collinear and are well-behaved.<\/figcaption><\/figure>\n

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\u00a0is collinear (i.e. goes down the collider beamline), the\u00a0expansion parameter blows up and the calculation misbehaves. In order to maintain\u00a0a well\u00a0behaved perturbation\u00a0theory,\u00a0DGLAP\u00a0tells us\u00a0to pretend that\u00a0instead of a top\/anti-top pair coming\u00a0from a gluon splitting,\u00a0one can treat these as\u00a0a top that lives inside the high-energy proton.<\/p>\n

\"A<\/a>
A gluon splitting that gives a non-perturvative top can be treated as a top inside the proton.<\/figcaption><\/figure>\n

This is the sense in which the top quark can be considered as\u00a0a parton. It doesn’t have to do with whether the top “fits” inside a\u00a0proton and whether this makes sense given the mass—it boils\u00a0down to a trick to preserve perturbativity.<\/p>\n

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.\u00a0One can compare this story to\u00a0this explanation<\/a> for why the electron doesn’t have infinite electromagnetic energy.<\/p>\n

The authors of\u00a01411.2588<\/a>\u00a0a study of the sensitivity\u00a0a 100 TeV collider to processes that\u00a0are produced from fusion of top quarks “in”\u00a0each proton.\u00a0With any luck, such a collider may even be on the horizon for future generations.<\/p>\n","protected":false},"excerpt":{"rendered":"

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?”<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[42,39,40,41],"class_list":["post-3063","post","type-post","status-publish","format-standard","hentry","category-particlebites-summary","tag-100-tev","tag-parton","tag-perturbative-qcd","tag-top-quark"],"_links":{"self":[{"href":"https:\/\/www.particlebites.com\/index.php?rest_route=\/wp\/v2\/posts\/3063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.particlebites.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.particlebites.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.particlebites.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.particlebites.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3063"}],"version-history":[{"count":11,"href":"https:\/\/www.particlebites.com\/index.php?rest_route=\/wp\/v2\/posts\/3063\/revisions"}],"predecessor-version":[{"id":4658,"href":"https:\/\/www.particlebites.com\/index.php?rest_route=\/wp\/v2\/posts\/3063\/revisions\/4658"}],"wp:attachment":[{"href":"https:\/\/www.particlebites.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.particlebites.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.particlebites.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}