# High $p_T$ and high $Q^2$ in deep inelastic hadronic collisions

When reading about high energy collisions (for example proton-proton collisions at LHC), I always find the relation $Q\sim p_T$, which, for me, is hard to demonstrate. Moreover, I found statements about the interaction time $\tau$, which is related to $Q$ and $p_T$ in this way: $\tau\sim \frac{1}{Q} \sim \frac{1}{p_T}$, where again $Q\sim p_T$ is assumed. To understand, I would really like someone to define $Q$ for a proton-proton (parton-parton) interaction. Is this $Q$ the same if I take an $s$ channel or a $t$ channel process? Thanks!

• Hi Marco, and welcome to Physics Stack Exchange! It sounds like you're asking several different things here. Could you try to narrow down your question to ask one specific thing? You can post other questions separately. In your case, I'd suggest removing the first question about the relation between DIS and $p_T$ and posting that separately. – David Z Jun 14 '16 at 23:36
• Hi @David, thank you for the suggestion, I just edited my question. – Don Jun 15 '16 at 1:04

Q^2 is the Mandelstam variable t, i.e. the four momentum transfer squared where the s channel is the x axis in the feynman diagram.

where p1 p2 are incoming.

In the same link it is seen that at the relativistic limit :

The dot product for t (Q^2) is p transverse to the incoming beam direction of p1 , p2 are incoming.

etc.

Is this Q the same if I take an s channel or a t channel process

No, Q is only defined in the t channel, with incoming p1 p2.

• Hi @anna, thanks for your answer. What I don't understand is why all people say: "At LHC we look at high $p_T$ events, as these events are due to deep inelastic scattering processes". This statement works for a process with a photon exchanged in the $t$ channel. But take a Drell-Yan process: $q\bar{q}\rightarrow \gamma^*\rightarrow q\bar{q}$, which happens in the $s$ channel. In this case the two out-coming quarks (which I'll see as two jets) won't have a preferred direction (i.e. they won't be necessarily at high $p_T$). Am I wrong? – Don Jun 15 '16 at 10:55
• One chases high ptransverse events because they are the true picture of the center of mass interaction, the transverse component does not change with the Lorenz transformation. It is sufficient for an interesting event to have a high pt because it shows high break up at the cms. Identifying the pt with Q2 is a mathematical definition which in terms of Feynman diagrams may be useful or not. – anna v Jun 15 '16 at 11:49