Counting Quarks

Characteristic | Definition |

the total number of Z-type quarks | $N^{\sf{Z}} \equiv n^{\sf{\bar{z}}} + n^{\sf{z}}$ |

the net number of Z-type quarks | ${\Delta}n^{\sf{Z}} \equiv n^{\sf{\bar{z}}} - n^{\sf{z}}$ |

the total number of all types of quarks | $\begin{align} N = \sum_{\zeta =1}^{16} n^{ \bar{\zeta}} + n^{\zeta} \end{align}$ |

*always*report a positive integer or zero,

*never*fractions or negative numbers. If all seeds are paired in quarks, then P can also be represented as a set of quarks and mathematically described by counting quarks. We note the results of such an inventory using the letter

*n*. For example, if P contains three southern quarks, we write $n^{\sf{a}}=3$. These numbers are called

**quark coefficients**because they can be interpreted as factors in a nuclear reaction that yields P. For example if $\sf{s}+2\sf{c} \to \sf{P}$ then the quark coefficients of P are $n^{\sf{s}} = 1$ and $n^{\sf{c}} = 2$. Quark coefficients are always integers because quarks are defined by pairs of perfectly distinct seeds. In general, we use the symbols $n^{\sf{z}}$ or $n^{\zeta}$ to note the coefficients of ordinary quarks. Recall that the Roman letter Z or the Greek letter $\zeta$ are used to indicate quark-type. Coefficients of anti-quarks are written with an overline as $n^{\bar{\sf{z}}}$ or $n^{\bar{\zeta}}$. A few other numbers used for describing particles are defined in the accompanying table. The letter $\Sigma$ indicates the use of summation notation. Theorem: The net number of quarks in particle P and its anti-particle P are related as

$\rm{\Delta} \it{n} ^{\sf{Z}} \left( \sf{P} \right)= - \rm{\Delta} \it{n}^{\sf{Z}} \left(\overline{\sf{P}} \right)$

Summary |

Adjectives | Definition | |

Quark Coefficients | $n \; \; {\sf{\text{and}}} \; \; N \; \; \sf{\text{count the number of quarks in a particle}}$ | 4-3 |