# Probability of forming mesons vs baryons

When a heavy quark hadronizes it has some probability of forming a meson vs forming a baryon. I suspect there is a well known branching ratio for each type of hadron. Does anyone know what the probability is or, even better, a reference that discusses this? An ideal answer (though not necessary) would further give a crude approximation of this probability (though I don't know if this is even possible).

• Isn't this something people studying jet physics at colliders do? Feb 11, 2014 at 14:57
• When running Monte Carlo simulations in colliders, people studying jet physics run programs like Pythia and Herwig that calculate such probabilities for any initial conditions. I would think that in the limit that the mass of heavy quark goes to infinity the answer should be quite simple, though I don't know how to find it. Feb 11, 2014 at 15:38
• The answer can't be simple as one needs a lot of inputs (decay rates, form factors, etc.) to carry out the computation. I think the papers of Field and Feynman (FF) from the late 70's on hadronization of quarks might be a good starting point. See here arxiv.org/abs/0809.0281 to get an idea on more modern literature as well as the reference to the FF papers. Feb 12, 2014 at 0:20
• Thanks for the reference. I will look into it. However, the reason I believe the result should be simple is because in the heavy quark limit, the quark acts as a single color source. This tends to simplify many calculations using heavy quark effective theory, though I don't understand the details. I do of course need to assume that the quark has a large enough lifetime such that hadronization has enough time to occur. Feb 12, 2014 at 3:41
• Let me know if and when you find some answers. Feb 12, 2014 at 5:23

Well, you could do worse than skim the classic Lund model:B. Andersson, G. Gustafson, G. Ingelman and T. Sjöstrand, PhysRep 97 (1983) 31 prototype for these things... it is dated, but, hey! you are asking for color flux string basics, not quarz-sharp theory, there.

The diquark to quark pair production ratio for light quarks is, according to their section 3.4, eqn (3.38) about 0.7, so not too far from the Chliapnikov ratio of 0.10 you quote in your supplemental comment. I am only a theorist, but the seasoned combatant experimentalists at the LHC go by the "10 mesons to 1 baryon" rule in their daily routines. (Even more so, the rule of thumb in bottom production is that your b quark is 10 times more likely to end up in a meson than in a baryon.)

But there is an enormous phenomenological cottage industry for this type of prediction, with far too many mechanisms and considerations (spin, flavor, ...) to account for it conceptually.

An easy-to-understand reference with the asymptotic 1/10 ratio in the first figure is Andronic, Braun-Munzinger, Redlich, & Stachel (2011). "The thermal model on the verge of the ultimate test: particle production in Pb–Pb collisions at the LHC", Jou Phys G: Nuclear and Particle Physics, 38 (12) 124081. As a lark, you might consider combinatoric schemes from quark-gluon plasma stretches of the waterfront: E Cuautle and A Ayala, JouPhys: Conf Ser 509 (2014) 012092.