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What is this mystery particle - LHC?

  1. May 4, 2015 #1
    1. The problem statement, all variables and given/known data

    (a) Draw the feynman diagram for ##p \bar p \rightarrow## reaction.
    (b) Find an expression for mass of the particle.
    (c) Find an expression for number of ##\mu^{+} \mu^{-}## produced.
    (d) Find an expression of ##n_{jj}## in terms of ##m_{inv}## and its spin.
    (e) Deduce the crosssection and lifetime.
    (f) What is its baryon number?

    2011_B4_Q7.png

    2. Relevant equations


    3. The attempt at a solution

    Part(a)
    2011_B4_Q7_2.png

    Part(b)

    In rest frame, ##m_X^2 = (P + \bar P)^2 = P^2 + \bar P^2 + 2P_u \cdot \bar P_{\bar u}##
    We assume kinetic energy is much more than rest mass energy, so
    [tex]m_X^2 \approx 2 x_1 x_2 P_p \cdot \bar P_{\bar p}[/tex]
    [tex]m_X^2 = x_1 x_2 E_{cm}^2 = x_1 x_2 s [/tex]

    I have no idea how to start part (c). I know this particle couples equally to all fermions?
     
  2. jcsd
  3. May 6, 2015 #2

    mfb

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    The LHC is a proton-proton collider. No antiprotons.

    The muons/jet branching ratio is similar to how you calculated branching fractions for the J/Psi a while ago.

    Does the problem statement come from a theorist? At least certainly someone not familiar with high-energy experiments. Or someone ignoring how they work on purpose.
     
  4. May 7, 2015 #3

    So for part (c) it is essentially ##\frac{\Gamma_{\mu^{+}\mu^{-}}}{\Gamma_{jj}} = \frac{1}{(3 \times 3) + 3 + 3} = \frac{1}{15}##? There are ##3 \times 3## states for hadrons, ##3## states for lepton-antilepton and ##3## for neutrino-antineutrino. Is the particle the higgs boson?
     
    Last edited: May 7, 2015
  5. May 7, 2015 #4

    mfb

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    Your new particle is heavier than a J/Psi.
    It is not a Higgs-like boson, otherwise the coupling would depend on the masses of the fermions.
     
  6. May 10, 2015 #5
    Is my ratio ##\frac{1}{15}## right?
     
  7. May 10, 2015 #6

    mfb

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    You are missing some quark decay modes there.
     
  8. May 10, 2015 #7
    Are all 6 quarks possible? If so then the ratio becomes ##\frac{1}{3 \times 6 + 3 +3} = \frac{1}{24}##.
     
  9. May 10, 2015 #8

    mfb

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    Are 2000 GeV sufficient to produce all types of quark pairs?

    Right.
     
  10. May 10, 2015 #9
    That makes sense.

    I don't understand the part where they want us to "compare the shape of normalization for ##\mu^+\mu^-## to the graph above". I found the ratio to be ##\frac{1}{24}## which implies about ##7## out of ## 170 ## events.
     
  11. May 10, 2015 #10

    mfb

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    Right.
    And I don't see a reason to expect a different shape as the problem statement is ignoring all experimental issues anyway.
     
  12. May 10, 2015 #11
    Ok, then for part (d): How is the number of events related to its spin? I thought the number of events is simply related to the cross section ##\sigma##?
     
  13. May 10, 2015 #12

    mfb

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    Hmm... looks like Breit-Wigner can depend on spin somehow, but I don't know details.
     
  14. May 10, 2015 #13
    Would appreciate it anyone else could contribute
     
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