What is this mystery particle - LHC?

[unscientific]

Homework Statement

(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?[/B]

Homework Equations

The Attempt at a Solution

Part(a)

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
$$m_X^2 \approx 2 x_1 x_2 P_p \cdot \bar P_{\bar p}$$
$$m_X^2 = x_1 x_2 E_{cm}^2 = x_1 x_2 s$$

I have no idea how to start part (c). I know this particle couples equally to all fermions?

 

[mfb]

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.

 

[unscientific]

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.

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?

 

[mfb]

Your new particle is heavier than a J/Psi.

Is the particle the higgs boson?

It is not a Higgs-like boson, otherwise the coupling would depend on the masses of the fermions.

 

[unscientific]

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.

Is my ratio $\frac{1}{15}$ right?

 

[mfb]

You are missing some quark decay modes there.

 

[unscientific]

You are missing some quark decay modes there.

Are all 6 quarks possible? If so then the ratio becomes $\frac{1}{3 \times 6 + 3 +3} = \frac{1}{24}$.

 

[mfb]

Are all 6 quarks possible?

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

Right.

 

[unscientific]

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

Right.

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.

 

[mfb]

Right.
And I don't see a reason to expect a different shape as the problem statement is ignoring all experimental issues anyway.

 

[unscientific]

Right.
And I don't see a reason to expect a different shape as the problem statement is ignoring all experimental issues anyway.

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 $\sigma$?

 

[mfb]

Hmm... looks like Breit-Wigner can depend on spin somehow, but I don't know details.

 

[unscientific]

Would appreciate it anyone else could contribute