Quark Combinations

As mentioned earlier, quarks bind together in groups of two or three to form hadrons. Baryons are formed from three quarks. Sample baryons, including quark content and properties, are given in Table. Interestingly, the delta plus ((Delta^+)) baryon is formed from the same three quarks as the proton, but the total spin of the particle is 3/2 rather than 1/2. Similarly, the mass of (Delta^+) with spin 3/2 is 1.3 times the mass of the proton, and the delta zero ((Delta^0)) baryon with a spin 3/2 is 1.3 times the neutron mass. Evidently, the energy associated with the spin (or angular momentum) of the particle contributes to its mass energy. It is also interesting that no baryons are believed to exist with top quarks, because top quarks decay too quickly to bind to the other quarks in their production.

Table (PageIndex{2}): Baryon Quarks Name Symbol Quarks Charge (unit of e) Spin (s) Mass ((GeV/c^2)) Proton p u u d 1 1/2 0.938 Neutron n u d d 0 1/2 0.940 Delta plus plus (Delta^{++}) u u u 2 3/2 1.232 Delta plus (Delta^+) u u d 1 3/2 1.232 Delta zero (Delta^0) u d d 0 3/2 1.232 Delta minus (Delta^-) d d d -1 3/2 1.232 Lambda zero (Lambda^0) u d s 0 1/2 1.116 Positive sigma (Sigma^+) u u s 1 1/2 1.189 Neutral sigma (Sigma^0) u d s 0 1/2 1.192 Negative xi (Xi^-) s d s -1 1/2 1.321 Neutral xi (Xi_0) s u s 0 1/2 1.315 Omega minus (Omega^-) s s s -1 3/2 1.672 Charmed lambda (Lambda_{C+}) u d c 1 1/2 2.281 Charmed bottom (Lambda_{b0}) u d b 0 1/2 5.612

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Mesons are formed by two quarks—a quark-antiquark pair. Sample mesons, including quark content and properties, are given in Table (PageIndex{3}). Consider the formation of the pion ((pi^+ = uoverline{d})). Based on its quark content, the charge of the pion is

[dfrac{2}{3}e + dfrac{1}{3}e = e. nonumber ]

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Both quarks are spin-half ((s = dfrac{1}{2})), so the resultant spin is either 0 or 1. The spin of the ((pi^+)) meson is 0. The same quark-antiquark combination gives the rho ((rho)) meson with spin 1. This meson has a mass approximately 5.5 times that of the (pi^+) meson.

Table (PageIndex{3}): Meson Quarks Name Symbol Quarks Charge (e) Spin Mass ((GeV/c^2)) Positive pion (pi^+) (uoverline{d}) 1 0 0.140 Positive rho (rho^+) (uoverline{d}) 1 1 0.768 Negative pion (pi^-) (overline{u}d) -1 0 0.140 Negative rho (rho^-) (overline{u}d) -1 1 0.768 Neutral Pion (pi^0) (overline{u}u) or (overline{d}d) 0 0 0.135 Neutral eta (eta^0) (overline{u}u, , overline{d}d) or (overline{s}s) 0 0 0.547 Positive kaon (K^+) (uoverline{s}) 1 0 0.494 Neutral kaon (K^0) (doverline{s}) 0 0 0.498 Negative kaon (K^-) (overline{u}s) -1 0 0.494 J/Psi (J/psi) (overline{c}c) 0 1 3.10 Charmed eta (eta_0) (coverline{c}) 0 0 2.98 Neutral D (D^0) (overline{u}c) 0 0 1.86 Neutral D (D^{*0}) (overline{u}c) 0 1 2.01 Positive D (D^+) (overline{d}c) 1 0 1.87 Neutral B (B^0) (overline{d}b) 0 0 5.26 Upsilon (Upsilon) (boverline{b}) 0 1 9.46

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