# What kinds of particles can decay to Lambda hyperons?

## Main Question or Discussion Point

Such as ##\Sigma^0 \to \bar{\Lambda}\gamma\gamma##.

I want to make a complete collection of all these decay modes, i.e.

##X \to \Lambda / \bar{\Lambda} + \cdots##.

At least some major channels.

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ChrisVer
Gold Member

Ok, it's easy to find the ##\Lambda## decay mode in PDG, but not so easy to do it inversely I think.

If there isn't a ready-made collection, I'll try to search one by one in PDG.

Thanks all the same.

Staff Emeritus
2019 Award
Any baryon weighing more than 1115 MeV.
Any other particle weighing more than 2230 MeV.

Any baryon weighing more than 1115 MeV.
Any other particle weighing more than 2230 MeV. Really?

mfb
Mentor Really?
Those numbers are not exact, but yes. As long as conservation laws can be conserved, a decay is possible. Many of them are very unlikely, however.

I guess you look for particles that frequently produce Lambdas? Then look for baryons with two light quarks (up/down) and one heavier quark (especially strange and charm, but also bottom). In addition, some B-mesons can decay to lambda+X.

Z and W can produce lambdas as well, but those are quite rare. For very high-energetic lambdas, they might be relevant.

Where/how do you want to use such a collection?

Staff Emeritus
2019 Award
Z and W can produce lambdas as well, but those are quite rare.
Not as much as you think. The mean number of lambdas in a Z-decay is about 0.4.

The mean number of lambdas in a Z-decay is about 0.4.
What did you mean by 0.4?
##\frac{\sum Z \to {\Lambda}/\bar{\Lambda} + X}{\sum Z \to X}## = 40% ?

Staff Emeritus
2019 Award
No, I mean that in a sample of a million Z decays there are 400,000 Lambdas. It's a statistical statement, not event by event.

Hepth
Gold Member
If you are looking for things beside short-distance production and the Z production just look at any heavier baryonic resonance and see what can give you the most Lambdas. Your end goal is a [uds]. So you can have some

##[uds]^* \to [uds] + (f \bar{f},\pi \pi, \gamma)## Resonant decays ##[\Lambda^*]##
##[udc] \to [uds] + \left(f \bar{\nu}_f, \pi^{+}, \rho^{+}, etc\right) ## electroweak decays ##[\Lambda_c, \Sigma_c, \Xi_c]##
##[udb]-> [uds] + f \bar{f}## (FCNC, highly suppressed) ##[\Lambda_b, \Sigma_b, \Xi_b]##

mfb
Mentor
Not as much as you think. The mean number of lambdas in a Z-decay is about 0.4.
I meant Z and W are rare. Even with a branching fraction of 100% they would be a small contribution.

At the LHC, the cross-sections are 100nb for the W and 30nb for the Z (ATLAS result at 7 TeV).

I didn't find a proper cross-section measurement of the lambda at the LHC, but an approximate number of 100µb given here (note: those lines are "100 events"), and I think this is restricted to the LHCb acceptance - that means the total cross-section is significantly higher. For the total number of lambdas, W and Z contribute less than .1%. That number could be larger for large transverse momentum.

For all other accelerators, the energy is lower, and the W/Z cross-section goes down faster than the other production modes, so there the contribution is even smaller (unless you run an electron-positron collider at the Z peak, of course).

I found a master thesis with a collection of (predicted) mother particles for Lambdas at LHCb.