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Masses

Quark masses are not particularly well defined. In the program it is necessary to make use of three kinds of masses, kinematical, running current algebra ones and constituent ones. The first ones are relevant for the kinematics in hard processes, e.g. in $\mathrm{g}\mathrm{g}\to \c\overline{\mathrm{c}}$, and are partly fixed by such considerations [Nor98]. The second define couplings to Higgs particles, and also other mass-related couplings in models for physics beyond the Standard Model. Both these kinds directly affect cross sections in processes. Constituent masses, finally, are used to derive the masses of hadrons, for some not yet found ones, and e.g. to gauge the remainder-mass below which the final two hadrons are to be produced in string fragmentation.

The first set of values are the ones stored in the standard mass array PMAS. The starting values of the running masses are stored in PARF(91) - PARF(96), with the running calculated in the PYMRUN function. Constituent masses are also stored in the PARF array, above position 101. We maintain this distinction for the five first flavours, and partly for top, using the following values by default:
quark kinematical current algebra mass constituent mass
d 0.33 GeV 0.0099 GeV 0.325 GeV
u 0.33 GeV 0.0056 GeV 0.325 GeV
s 0.5 GeV 0.199 GeV 0.5 GeV
c 1.5 GeV 1.23 GeV 1.6 GeV
b 4.8 GeV 4.17 GeV 5.0 GeV
t 175 GeV 165 GeV --

For top no constituent mass is defined, since it does not form hadrons. For hypothetical fourth generation quarks only one set of mass values is used, namely the one in PMAS. Constituent masses for diquarks are defined as the sum of the respective quark masses. The gluon is always assumed massless.

Particle masses, when known, are taken from ref. [PDG96]. Hypothesized particles, such as fourth generation fermions and Higgs bosons, are assigned some not unreasonable set of default values, in the sense of where you want to search for them in the not-too-distant future. Here it is understood that you will go in and change the default values according to your own opinions at the beginning of a run.

The total number of hadrons in the program is very large, whereof some are not yet discovered (like charm and bottom baryons). There the masses are built up, when needed, from the constituent masses. For this purpose one uses formulae of the type [DeR75]

\begin{displaymath}
m = m_0 + \sum_i m_i + k \, m_{\d }^2 \sum_{i<j} \frac{\lang...
...a$}_i \cdot
\mbox{\boldmath$\sigma$}_j \rangle}{m_i \, m_j} ~,
\end{displaymath} (266)

i.e. one constant term, a sum over constituent masses and a spin-spin interaction term for each quark pair in the hadron. The constants $m_0$ and $k$ are fitted from known masses, treating mesons and baryons separately. For mesons with orbital angular momentum $L = 1$ the spin-spin coupling is assumed vanishing, and only $m_0$ is fitted. One may also define `constituent diquarks masses' using the formula above, with a $k$ value $2/3$ that of baryons. The default values are:
multiplet $m_0$ $k$
pseudoscalars and vectors 0. 0.16 GeV
axial vectors ($S = 0$) 0.50 GeV 0.
scalars 0.45 GeV 0.
axial vectors ($S = 1$) 0.55 GeV 0.
tensors 0.60 GeV 0.
baryons 0.11 GeV 0.048 GeV
diquarks 0.077 GeV 0.048 GeV.

Unlike earlier versions of the program, the actual hadron values are hardcoded, i.e. are unaffected by any change of the charm or bottom quark masses.


next up previous contents
Next: Widths Up: Masses, Widths and Lifetimes Previous: Masses, Widths and Lifetimes   Contents
Stephen Mrenna 2007-10-30