Quarks - Maple Help

Quarks

Main Concept

The elementary particles of the Standard Model of particle physics are divided into two main groups, the elementary fermions, which have half-integral spin, and the elementary bosons, whose spins are whole integers. Elementary bosons include gauge bosons (such as photons, gluons, and theoretically gravitons) which transmit the forces between particles, and the scalar Higgs boson, an excitation of the Higgs field which gives all the particles their masses.

The elementary fermions are divided into matter particles and anti-matter particles. For each matter particle there is an equivalent anti-matter particle of the same mass but for which certain other properties (such as electric charge, lepton number, and baryon number) are equal in magnitude but reversed in sign. The matter particles themselves consist of leptons (examples include the electron, muon, and neutrino) and quarks.

Unlike leptons, quarks cannot exist independently; they can only combine together using the strong nuclear force to form larger particles called hadrons. Hadrons come in two main groups: baryons and mesons. Baryons, such as protons and neutrons, consist of three quarks. Mesons, including the pion and the kaon, are unstable particles consisting of a quark and an antiquark.

Quarks have a property called flavor; the six flavors are: up, down, charm, strange, top and bottom. Quark flavor is denoted with lowercase letter u, d, c, s, t, b and the corresponding antiquark is the same letter with an overbar as in $\stackrel{‾}{u},\stackrel{‾}{d},$$\stackrel{‾}{c},\stackrel{‾}{s},\stackrel{‾}{t},$$\stackrel{‾}{b}$.  Protons consist of two up quarks and a down quark; neutrons consist of two down quarks and an up quark. The other flavors of quarks are harder to find in nature. Both quarks and leptons are divided into three generations; interactions generally occur between quarks and leptons of the same generation. The first generation, and the most common, includes the up and down quarks that make up protons and neutrons, and the electron and electron neutrino.

All quarks have spin 1/2. The up, charge and top quarks have electric charge + (where e is the charge of a proton), while the down, strange, and bottom quarks have electric charge  . The masses of the quarks range from about 2 to 173000 $\mathrm{MeV}/{\mathrm{c}}^{2}$, as shown in the table below.

Another intrinsic property of quarks is color charge. The color charge of a quark can be either red, blue, or green (and the color of an antiquark can be either antired, antiblue, or antigreen). Color charge is not an actual color since it is impossible to see quarks, but rather just another type of charge similar to electric charge. In composite particles, color charges add as if they were actual colors. In particular, the three quarks making up a proton or neutron must all have separate color charges (one each of red, blue, and green) for the composite particle to have zero net color charge. Similarly, the quark and antiquark making up a meson must have opposite color charges (for example red and antired).

 Generation Flavor Symbol Charge $\left(e\right)$ Mass $\left(\frac{\mathrm{MeV}}{{c}^{2}}\right)$ First Up $u$ $+\frac{2}{3}$ Down $d$ $-\frac{1}{3}$ $4.1-5.7$ Second Charm $c$ $+\frac{2}{3}$ $1290$ Strange $s$ $-\frac{1}{3}$ $100$ Third Top $t$ $+\frac{2}{3}$ $173000$ Bottom $b$ $-\frac{1}{3}$ $4190$

Building Mesons

Select two quarks to see which meson they create.

 Quark Antiquark Meson udsc u'd's'c' $\mathbf{+}$ $\mathbf{=}$

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