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Phase space functions

There is a special set of phase space functions which may be used to construct cuts and distributions in the framework of CompHEP. The general notation looks like
(Key Character)(momentum set).
A set of momenta is represented as a set of digits. Any digit corresponds to a momentum number. For example, C13 means a cosine of the angle between momenta ${\bf p_1}$ and ${\bf p_3}$. The momenta are assigned to particles according to their sequence in the process name.

Below we list the available key characters and explain the meaning of the corresponding physical functions.

A

- angle in degree units.

C

- cosine of angle.

J

- jet cone angle. The jet cone angle ${\it J_{ij}}$ is defined as $\sqrt{\Delta y^2+\Delta\varphi^2}$, where $\Delta y$ is the pseudo-rapidity difference and $\Delta \varphi$ is the azimuth angle difference for momenta ${\bf p_i}$ and ${\bf p_j}$.

E

- energy of the particle set.

M

- mass of the particle set.

P

- cosine in the rest frame of pair. ${\it Pij}$ is defined as follows: we imply a boost in the direction of ${\bf p_i + p_j}$ to get the rest frame of the pair. Then P is a cosine of angle between the transformed ${\bf p_i}$ and the direction of boost.

T

- transverse momentum of the particle set.

S

- squared invariant mass of the particle set.

Y

- rapidity of the particle set.

U

- user's implemented function. The character string following U is passed on to the user Fortran/C  function usrfun(str) which, as it is assumed, calculates a corresponding value. See Section for further explanations.

Zero components of all momenta are positive, and the conservation law means that the sum of momenta of incoming particles is equal to that of outgoing particles. Relative momenta signs for the S function are substituted automatically.

There are some natural requirements on the momentum set, namely: a) the momentum sets following A, C, J, P must consist of two elements; b) the momenta following M, P, T must belong to outgoing particles only; c) any momentum can appear only once in one set.