1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proton-Antiproton colliding to produce top-antitop pair

  1. Nov 16, 2015 #1
    1. The problem statement, all variables and given/known data

    Suppose a proton and an antiproton collide producing a pair of top-antitop quarks.

    What would be the minimum required momenta of both proton and antiproton in order for this pair creation to occur?

    [tex]p + \bar{p} \rightarrow t + \bar{t} [/tex]

    (Answer: [itex]173 \frac{GeV}{c^2}, 59.9 \frac{TeV}{c^2} [/itex])


    2. Relevant equations

    I. Energy-momentum relation
    [tex]E^2 = (pc)^2 + (m_0 c^2)^2 [/tex]

    II. Relativistic kinetic energy equation
    [tex]E_{ki} = m_i c^2 \left(\frac{1}{\sqrt{1-\frac{v_i^2}{c^2}}} -1 \right) [/tex]

    III. Relativistic momentum equation
    [tex]p_i = \frac{m_i v_i}{\sqrt{1-\frac{v_i^2}{c^2}}} [/tex]

    IV. Rest masses of proton and top quark

    [tex] m_p = 938 \frac{MeV}{c^2}, m_t = 173 \frac{GeV}{c^2}[/tex]


    3. The attempt at a solution

    1. Conservation of energy:
    [tex]E_i = E_f \Rightarrow E_{p} + E_{\bar{p}} = E_{t} + E_{\bar{t}} [/tex]

    [tex]\sqrt{ (p_{p}c)^2 + (m_p c^2)^2 } + \sqrt{ (p_{\bar{p}}c)^2 + (m_{\bar{p}} c^2)^2 } = \sqrt{ (p_{t}c)^2 + (m_t c^2)^2 } + \sqrt{ (p_{\bar{t}}c)^2 + (m_{\bar{t}} c^2)^2 } [/tex]

    2. Conservation of momentum:
    [tex]p_i = p_f \Rightarrow p_{p} + p_{\bar{p}} = p_{t} + p_{\bar{t}} [/tex]

    I'm really stuck here because I feel like there isn't enough information and I'm missing something, one thing that occurred to me is that since I'm trying to find the minimum momenta of the proton-antiproton, I could argue that the momenta of the quarks are zero, i.e. they're created at rest, but then on a second thought, I'm not certain about this because it would provide an equal momentum in magnitude for the proton-antiproton, which isn't the case.

    Can anyone point me in the right direction here, please?
     
  2. jcsd
  3. Nov 17, 2015 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello MyNameIs,

    Your book answer surprises me: why does it consist of two numbers ?

    Are there two questions, perhaps? Like: one in a colliding beam machine and one in a stationary target machine (in which case one of the momenta is 0) ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted