The Model of Quarks

The panorama of the physics in the years 1950-1960 offered many challenges. Was a favorable land to creation. The central preoccupation of the physicists was to understand the origin and the constitution of the particles; and to find a scheme to classify, in terms of the most elementary constituents.

Based on symmetry arguments, Gell-Mann and others, separately, proposed the existence of the quarks. With this scheme of things, they can classify all known particles. The quarks are the constituents of all hadrons. The idea is no new. Other authors had tried to classify the particles taking others as the elementary blocks -for example the proton.

The leptons, up to where physicists have experimented, are structureless particles. As we have said before.

The original proposition of Gell-Mann consisted of three quarks. In these days it is required 6 of these to classify all known particles. These are: $u(up)$, $d(dawn)$, $s(strange)$, $c(charm)$, $b(bottom)$, $t(top)$. The Table 1 and 2 illustrate all known properties of the quarks. The Figure 6 illustrates the elementary particles. The quarks, the leptons, and the carriers of fundamental forces. We will comment some about the elementary particles in the Section 4.

Table 6: Family of 20 particles. Baryons.

	$\Omega^{++}_{ccc}(ccc)$
$\Xi^+_{cc}(dcc)$	$\Xi^{++}_{cc}(ucc)$
	$\Omega^{+}_{cc}(scc)$
$\Xi^0_c(ddc)$	$\Sigma^+_c(udc)$          $\Sigma^{++}_c(uuc)$
$\Xi ^0_c(dsc)$	$\Xi ^+_c (usc)$
	$\Omega^{0}_{c}(ssc)$
$\Delta^-(ddd)$         $\Delta^0(udd)$	$\Delta^+(uud)$          $\Delta^{++}(uuu)$
$\Sigma^-(dds)$	$\Sigma^0(uds)$         $\Sigma^+(uus)$
$\Xi^-(dss)$	$\Xi^0(uss)$
	$\Omega^{-}(sss)$

Table 7: Lepton physical properties.

	Leptons
	Flavor		Mass$(GeV/c^2$)	Charge (e)	L. number	Spin
	$\nu_{e}$	e neutrino	$< 7\times10^{-9}$	0	$+1$	$\frac{1}{2}$
	$e^-$	electron	0.000511	$-1$	$+1$	$\frac{1}{2}$
	$\nu_{\mu}$	$\nu$ neutrino	$< 0.0003$	0	$+1$	$\frac{1}{2}$
	$\mu^-$	muon	0.106	-1	$+1$	$\frac{1}{2}$
	$\nu_{\tau}$	$\tau$ neutrino	$< 0.03$	0	$+1$	$\frac{1}{2}$
	$\tau$	tau	1.7771	-1	$+1$	$\frac{1}{2}$

Table 8: Fundamental force carriers.

	Carrier	Force	Mass (GeV)	Electric charge (e)
	$\gamma$, Photon	(electromagnetic)	0	0
	$G$, graviton	(gravitational)	0	0
	$Z^0$, $W^{\pm}$	(electroweak)	91.187,80.41	0,$\pm1$
	$g$, gluon	(strong)	0	0

Table 9: High energy physics conserved quantities.

	Conserved quantities
	1	energy-mass
	2	momentum
	3	angular momentum, and spin
	4	electric charge
	5	charge color
	6	quark number
	7	electron number
	8	muon number
	9	tau number
	7-8-9	number of leptons

If the particles have three quarks, they are known as baryons; if they have two quarks, they are known as mesons. $\Lambda^0 \{uds \}$, $p\{uud\}$, $n\{udd\}$, are baryons; $\pi^+ \{u\bar d\}$, $K^+ \{u \bar s\}$, are mesons.

All the above particles interact via strong interaction; they are known generically as hadrons. If the particles interact via weak interaction they are known as leptons; these are not composed of quarks. Example of leptons: The electron, the muon, the tau, the neutrino associated to the electron, the neutrino associated to the muon, and the neutrino associated to the tau. These are all the leptons that exist. Of course each of them has their corresponding antiparticle. They are atoms, in the strict sense of the word. For they are not composed of any other particle.

The $\Lambda^0$ decays into $p \pi^{-}$ via weak interaction. The mean life is $\sim 7.5 \times 10^{-8}$ seconds. Also the $\mu$ decays via weak interaction into a $e\nu _e \nu_{\mu}$. The $\Sigma^*(1385)$ decays via strong interaction into a $\Lambda^0\pi$ in $\sim 10^{-23}$ seconds. These last states are known as resonances. The $\Sigma^0$ decays in $\Lambda^0\gamma$ via electromagnetic interaction in $\sim 10^{-19}$ seconds.

The actual idea of the structure of matter that we have is shown in the Figure 6. It is possible to speak of the generation I. The members are: $(u,d)~ and ~(e^-,\nu_e)$; they are all the constituents required to construct the world of every day life. It is possible to speak of the generation II. The members are:

$(s,c)~ and ~(\mu, \nu_{\mu})$. Occasionally they appear in the daily life; for instance in the cosmic rays; they are also created in the big accelerators of the world like Fermilab, BNL, or CERN. It is possible to speak about the generation III. The integrants are: $(b,t)~ and ~(\tau, \nu_{\tau})$. All of them, except $\nu_{\tau}$ that has not been detected directly, were detected in the big accelerators of high energy physics -like Fermi National Accelerator Laboratory, USA; Brookhaven National Laboratory, USA; CERN, Europe; SLAC, USA; etc.-. It is possible that there are other families; there are no reasons in pro nor in con.

The Figure 7 shows the different levels in the organization of the elementary particles. From the cells, up to the quarks and leptons. Historically there are no reasons to doubt about the existence of structures for the quarks and the leptons. Maybe it is a matter of energy and of method to reach that structure.

It is worthwhile to say it again.

Besides the leptons and the baryons, there are the carriers of the interactions: The photons $(\gamma)$ for the electromagnetic interactions, the gluons $(g)$ for the strong interactions, the $(W^{\pm},Z^0)$ for the weak interactions, and the gravitons $(G)$ -not yet detected- for the gravitational interactions.

For each one of those particles, of elementary particles, of the carriers, etc. there exists the corresponding antiparticle. The photon, for example, is its own antiparticle. The student can conclude on the cosmological consequences of this. The neutral particles, like the neutron, are not their own antiparticles. The student can verify it checking the products of disintegration of the neutron and of the antineutron. The antimatter is accurately established by experiment. In these days there is an experiment at Fermilab that studies the production of atoms of antihydrogen. The second step will be study the spectrum of emission of the atom of antihydrogen. Maybe we can have surprises. And the antimatter does not behave exactly like the matter.