This should be an easy general question to someone out there. My "quarks and Leptons" book by Halzen and Martin introduces the term "phase space" 50 pages before the index reference, and never seems to define it.

Just a fancy term for energy-momentum conservation. In a nutshell, either the rest mass of the products is larger than the rest mass of the initial particle, or the difference is extremely small. Most likely the formerl.

Roughly speaking, it's a jargon term for the amount of momentum available to the decaying particle. If the sum of the rest mass of the product particles is very close to the rest mass of the initial particle, one says that there is little phase space available, meaning that that the produced particles are created with almost no three-momenta (in the rest frame of the decaying particle). However, if the mass of the produced particles is much smaller than the mass of the decaying particle, there's plenty of momentum to share among the produced particles and this enhanced the decay rate.

By the way, H&M *do* define the explicit expressions for phase space in the case of a decaying particle. Unfortunately, I don't have it with me but I'll give you the equation number later if you want.

Phase space for a system is the set of possible momentum/energy points for which momentum and energy are conserved. If, for example, A -> B + C, then in A's center of momentum frame, pB + pC = 0 (3D vector equation), and eB+eC = mA. In this case, the available phase space is a spherical surface whose radius depends on the masses.

Also, sometimes people will refer to integration over 3- or 4- momentum space as integration over phase space.