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33.5 Quarks: is that all there is?  (Page 2/20)

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n → p + β − + v - e size 12{n rightarrow p+β rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } } {}   becomes  udd → uud + β − + v - e size 12{ ital "udd" rightarrow ital "uud"+β rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } } {} .

We see that this is equivalent to a down quark changing flavor to become an up quark:

d → u + β − + v - e size 12{d rightarrow u+β rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } } {}

Quarks and antiquarks The lower of the ± size 12{ +- {}} {} symbols are the values for antiquarks.
Name Symbol Antiparticle Spin Charge B size 12{B} {} B size 12{B} {} is baryon number, S is strangeness, c size 12{c} {} is charm, b size 12{b} {} is bottomness, t size 12{t} {} is topness. S size 12{S} {} c size 12{c} {} b size 12{b} {} t size 12{t} {} Mass ( GeV / c 2 ) Values are approximate, are not directly observable, and vary with model.
Up u size 12{u} {} u - size 12{ { bar {u}}} {} 1/2 ± 2 3 q e size 12{ +- { {2} over {3} } q rSub { size 8{e} } } {} ± 1 3 size 12{ +- { {1} over {3} } } {} 0 0 0 0 0.005
Down d size 12{d} {} d - size 12{ { bar {d}}} {} 1/2 ∓ 1 3 q e size 12{ -+ { {1} over {3} } q rSub { size 8{e} } } {} ± 1 3 size 12{ +- { {1} over {3} } } {} 0 0 0 0 0.008
Strange s size 12{s} {} s - size 12{ { bar {s}}} {} 1/2 ∓ 1 3 q e size 12{ -+ { {1} over {3} } q rSub { size 8{e} } } {} ± 1 3 size 12{ +- { {1} over {3} } } {} ∓ 1 size 12{ -+ 1} {} 0 0 0 0.50
Charmed c size 12{c} {} c - size 12{ { bar {c}}} {} 1/2 ± 2 3 q e size 12{ +- { {2} over {3} } q rSub { size 8{e} } } {} ± 1 3 size 12{ +- { {1} over {3} } } {} 0 ± 1 size 12{ +- 1} {} 0 0 1.6
Bottom b size 12{b} {} b - size 12{ { bar {b}}} {} 1/2 ∓ 1 3 q e size 12{ -+ { {1} over {3} } q rSub { size 8{e} } } {} ± 1 3 size 12{ +- { {1} over {3} } } {} 0 0 ∓ 1 size 12{ -+ 1} {} 0 5
Top t size 12{t} {} t - size 12{ { bar {t}}} {} 1/2 ± 2 3 q e size 12{ +- { {2} over {3} } q rSub { size 8{e} } } {} ± 1 3 size 12{ +- { {1} over {3} } } {} 0 0 0 ± 1 size 12{ +- 1} {} 173
Quark composition of selected hadrons These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
Particle Quark Composition
Mesons
π + size 12{π rSup { size 8{+{}} } } {} u d - size 12{u { bar {d}}} {}
π − size 12{π rSup { size 8{ - {}} } } {} u - d size 12{ { bar {u}}d} {}
π 0 size 12{π rSup { size 8{0} } } {} u u - size 12{u { bar {u}}} {} , d d - size 12{d { bar {d}}} {} mixture These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
η 0 size 12{η rSup { size 8{0} } } {} u u - size 12{u { bar {u}}} {} , d d - size 12{d { bar {d}}} {} mixture These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
K 0 size 12{K rSup { size 8{0} } } {} d s - size 12{d { bar {s}}} {}
K - 0 size 12{ { bar {K}} rSup { size 8{0} } } {} d - s size 12{ { bar {d}}s} {}
K + size 12{K rSup { size 8{+{}} } } {} u s - size 12{u { bar {s}}} {}
K − size 12{K rSup { size 8{ - {}} } } {} u - s size 12{ { bar {u}}s} {}
J / ψ size 12{J/ψ} {} c c - size 12{c { bar {c}}} {}
ϒ b b - size 12{b { bar {b}}} {}
Baryons Antibaryons have the antiquarks of their counterparts. The antiproton p - size 12{ { bar {p}}} {} is u - u - d - size 12{ { bar {u}} { bar {u}} { bar {d}}} {} , for example. , Baryons composed of the same quarks are different states of the same particle. For example, the Δ + size 12{Δ rSup { size 8{+{}} } } {} is an excited state of the proton.
p size 12{p} {} uud size 12{ ital "uud"} {}
n size 12{n} {} udd size 12{ ital "uud"} {}
Δ 0 size 12{Δ rSup { size 8{0} } } {} udd size 12{ ital "uud"} {}
Δ + size 12{Δ rSup { size 8{+{}} } } {} uud size 12{ ital "uud"} {}
Δ − size 12{Δ rSup { size 8{ - {}} } } {} ddd size 12{ ital "ddd"} {}
Δ ++ size 12{Δ rSup { size 8{"++"} } } {} uuu size 12{ ital "uuu"} {}
Λ 0 size 12{Λ rSup { size 8{0} } } {} uds size 12{ ital "uds"} {}
Σ 0 size 12{Σ rSup { size 8{0} } } {} uds size 12{ ital "uds"} {}
Σ + size 12{Σ rSup { size 8{+{}} } } {} uus size 12{ ital "uus"} {}
Σ − size 12{Σ rSup { size 8{ - {}} } } {} dds size 12{ ital "dds"} {}
Ξ 0 size 12{Ξ rSup { size 8{0} } } {} uss size 12{ ital "uss"} {}
Ξ − size 12{Ξ rSup { size 8{ - {}} } } {} dss size 12{ ital "dss"} {}
Ω − size 12{ %OMEGA rSup { size 8{ - {}} } } {} sss size 12{ ital "sss"} {}

This is an example of the general fact that the weak nuclear force can change the flavor of a quark . By general, we mean that any quark can be converted to any other (change flavor) by the weak nuclear force. Not only can we get d → u size 12{d rightarrow u} {} , we can also get u → d size 12{u rightarrow d} {} . Furthermore, the strange quark can be changed by the weak force, too, making s → u size 12{s rightarrow u} {} and s → d size 12{s rightarrow d} {} possible. This explains the violation of the conservation of strangeness by the weak force noted in the preceding section. Another general fact is that the strong nuclear force cannot change the flavor of a quark.

Again, from [link] , we see that the π + size 12{π rSup { size 8{+{}} } } {} meson (one of the three pions) is composed of an up quark plus an antidown quark, or u d - size 12{u { bar {d}}} {} . Its total charge is thus + 2 3 q e + 1 3 q e = q e size 12{+ left ( { {2} over {3} } right )q rSub { size 8{e} } + left ( { {1} over {3} } right )q rSub { size 8{e} } =q rSub { size 8{e} } } {} , as expected. Its baryon number is 0, since it has a quark and an antiquark with baryon numbers + 1 3 − 1 3 = 0 size 12{+ left ( { {1} over {3} } right ) - left ( { {1} over {3} } right )=0} {} . The π + size 12{π rSup { size 8{+{}} } } {} half-life is relatively long since, although it is composed of matter and antimatter, the quarks are different flavors and the weak force should cause the decay by changing the flavor of one into that of the other. The spins of the u size 12{u} {} and d - size 12{ { bar {d}}} {} quarks are antiparallel, enabling the pion to have spin zero, as observed experimentally. Finally, the π − size 12{π rSup { size 8{ - {}} } } {} meson shown in [link] is the antiparticle of the π + size 12{π rSup { size 8{+{}} } } {} meson, and it is composed of the corresponding quark antiparticles. That is, the π + size 12{π rSup { size 8{+{}} } } {} meson is u d - size 12{u { bar {d}}} {} , while the π − size 12{π rSup { size 8{ - {}} } } {} meson is u - d size 12{ { bar {u}}d} {} . These two pions annihilate each other quickly, because their constituent quarks are each other’s antiparticles.

Two general rules for combining quarks to form hadrons are:

  1. Baryons are composed of three quarks, and antibaryons are composed of three antiquarks.
  2. Mesons are combinations of a quark and an antiquark.

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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