# What is $p_T$? (transverse momentum?)

I've been looking at a few papers in experimental physics (from the ATLAS collaboration, for example) and I've often run across phrases such as "high-$p_T$ electron." What exactly is $p_T$? Is it simply momentum, but with the component parallel to the main beam projected off?

Also, why is $p_T$, as opposed to $p$, an important characteristic of a particle in a collision process?

The component of momentum transverse (i.e. perpendicular) to the beam line.

It's importance arises because momentum along the beamline may just be left over from the beam particles, while the transverse momentum is always associated with whatever physics happened at the vertex.

That is, when two protons collide, they each come with three valence quarks and a indeterminate number of sea quarks and gluons. All of those that don't interact keep speeding down the pipe (modulo Fermi motion and final state interaction).

But the partons that react do so on average{*} at rest in the lab frame, and so will on average spray the resulting junk evenly in every direction. By looking at the transverse momentum you get a fairly clean sample of "stuff resulting from interacting partons" and not "stuff resulting from non-interacting partons".

There are also advantages related to the engineering of the detector.

{*} Only on average. Indivudual events may involve high Bjorken $x$ particles and be a long way from at rest in the lab frame.

• Thanks for the explanation! Could you perhaps expand on why the partons interact, on average, at rest when the protons are speeding towards each other (in the lab frame)? – Nilay Kumar Jan 11 '12 at 3:26
• @NilayKumar In a collider with equal momentum projectiles coming in, the lab frame is the rest frame. That is fine in e+e- colliders because the electrons do not have substructure. For proton colliders, even though the collision of the protons happens at rest in the lab frame, the partons which will interact are each moving within the nucleons with some momenta. To know the exact scatter of two quarks is not possible,but the transverse components are not affected by the Lorenz transformation that would take the quark projectiles to their center of mass system. – anna v Jan 11 '12 at 8:10

The collisions of protons are complicated, because the proton has a big mess inside. In order to see simple collisions, you want to find those cases where a single quark or gluon, a single parton scattered off another parton in a nearly direct collision. Such collisions are relatively rare, most proton proton collisions are diffractive collective motions of the whole proton, but every once in a while, you see a hard collision.

The characteristic of a hard collision is that you get particles whose momentum is very far off the beam line direction. This is a "high P_T" event. A high P_T electron usually means that an electrically charged parton (a quark) collided with some other parton, and emitted a hard photon or a Z which then produced an electron and a positron. Alternatively, it could mean that a W boson was emitted by the quark, and this produced an electron and a neutrino. Alternatively, it could be a higher order process in the strong interaction, where two gluons produced a quark-antiquark, and one of the quark lines then emitted an electroweak boson, which decayed leptonically.

The point is that any way it happened, the event indicates that a clean hard collision happened between two partons, and this is a useful indication that the event was an interesting one, which will give useful clues about new physics if similar events are isolated and counted.

The reason P_T is important is because when the actual collision event is a short distance collision dominated by perturbative QCD, the outgoing particles are almost always away from the beam-line by a significant amount. Even in interesting events, when the outgoing particles are near the direction of the beam, it is hard to distinguish this from the much more common case of a near glancing collision, which lead to diffractive scattering.

Diffractive scattering is the dominant mechanism of proton proton scattering (or proton antiproton scattering) at high energies. The cross section for diffractive events are calculated by Regge theory, using the Pomeron trajectory. This type of physics has not been so interesting to physicists since the mid 70s, but more for political reasons. It is difficult to calculate, and has little connection with the field theory you are trying to find. But Regge theory is mathematically intimately related to string theory, and perhaps it will be back in fasion again.

• Thanks for the detailed response! Just to make sure I have things straight - diffractive collisions, where hard collisions don't occur, tend not to yield high p_T particles because the protons don't stray too far from the beam line? Is this because the energy in such diffractive scattering processes is relatively low? – Nilay Kumar Jan 11 '12 at 3:48
• @NilayKumar your "because the protons don't stray too far from the beam line" needs the qualification "the scattered protons" make a small angle to the beam line. The incoming protons are on the beam line by construction. If they were billiard balls they might graze or hit head on. As nuclei their scatter is described as "diffractive" (wave/particle duality) – anna v Jan 11 '12 at 8:30
• @QuantumDot: I just mean that Regge theory was killed off in the 1970s, by field theorists who hated Regge theory (it was S-matrix theory). This is a great tragedy, it means that nobody knows Regge theory anymore, and it is one of the most beautiful and important of discoveries in physics. You can learn in in Gribov's "The Theory of Complex Angular Momentum". Regge theory is what developed into string theory in the 1960s and early 1970s, so in some sense it never really died, but it is also phenomenological QCD, so that the Pomeron/Odderon discoveries in the 1990s were not properly recognized. – Ron Maimon Nov 29 '12 at 0:20
• Thanks. But, your language sounds quite harsh. Is it an accurate reflection of the atmosphere felt by the physics community in the 1970s (if so, where can I read more about it?), or is it just your personal attitude about its disappearance? Also, I'm proud to say that I devoted the last 3 years of my personal study time (independent of my research) to the subject of S-matrix theory, Regge theory and dual resonance theories if it makes you feel any better. – QuantumDot Nov 29 '12 at 4:42
• @QuantumDot: It's harshness is accurate, the field theorists didn't understand S-matrix, and drove all the practitioners out of physics (including many early string giants). The theory was too sophisticated for the 1960s stoners, it's not baby-boom physics. Ask anna v for 1st hand experience. This stuff is now actually back in fasion, even Pomeron physics, so it is hard to remember the rejection. The hostility was everywhere (you can see it in Streater's "lost causes", Woit's "not even wrong", Gross personally told me when I asked him about N/D equations, his thesis! that it was tautology). – Ron Maimon Nov 29 '12 at 5:35