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== 11.3#h(0.6em)Quarks


  In the 1960s, particle physicists began to realize that hadrons are not elementary particles but are made of particles called #emph[quarks]. (The name ‘quark’ was coined by the physicist Murray #strong[Gell-Mann], from a phrase in the James Joyce novel #emph[Finnegans Wake].) Initially, it was believed there were only three types of quarks, called #emph[up] (#emph[u]), #emph[down] (#emph[d]), and #emph[strange] (#emph[s]). However, this number soon grew to six—interestingly, the same as the number of leptons—to include #emph[charmed] (#emph[c]), #emph[bottom] (#emph[b]), and #emph[top] (#emph[t]).


  All quarks are spin-half fermions #math.equation(block: false, alt: "open parenthesis s equals 1 / 2 close parenthesis ,")[$( s = 1 "/" 2 ) ,$] have a fractional charge #math.equation(block: false, alt: "open parenthesis 1 / 3 or 2 / 3 e close parenthesis")[$( 1 "/" 3 #h(0.2em) "or" #h(0.2em) 2 "/" 3 e )$], and have baryon number #math.equation(block: false, alt: "B equals 1 / 3 .")[$B = 1 "/" 3 .$] Each quark has an antiquark with the same mass but opposite charge and baryon number. The names and properties of the six quarks are listed in .


  #figure(table(
  columns: 5, align: left, inset: 6pt,
  table.header([Quark], [Charge (units of #emph[e])], [Spin (#emph[s])], [Baryon number], [Strangeness number]),
  [Down (#emph[d])], [#math.equation(block: false, alt: "−1 / 3")[$−1 "/" 3$]], [1/2], [1/3], [0],
  [Up (#emph[u])], [#math.equation(block: false, alt: "plus 2 / 3")[$+ 2 "/" 3$]], [1/2], [1/3], [0],
  [Strange (#emph[s])], [#math.equation(block: false, alt: "−1 / 3")[$−1 "/" 3$]], [1/2], [1/3], [#math.equation(block: false, alt: "−1")[$−1$]],
  [Charm (#emph[c])], [#math.equation(block: false, alt: "plus 2 / 3")[$+ 2 "/" 3$]], [1/2], [1/3], [0],
  [Bottom (#emph[b])], [#math.equation(block: false, alt: "−1 / 3")[$−1 "/" 3$]], [1/2], [1/3], [0],
  [Top (#emph[t])], [#math.equation(block: false, alt: "plus 2 / 3")[$+ 2 "/" 3$]], [1/2], [1/3], [0],
))


  
    
=== 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 . Interestingly, the delta plus (#math.equation(block: false, alt: "Δ to the power plus")[$"Δ"^(+)$]) 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 #math.equation(block: false, alt: "Δ to the power plus")[$"Δ"^(+)$] with spin 3/2 is 1.3 times the mass of the proton, and the delta zero (#math.equation(block: false, alt: "Δ to the power 0")[$"Δ"^(0)$]) 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.


    #figure(table(
  columns: 6, align: left, inset: 6pt,
  table.header([Name], [Symbol], [Quarks], [Charge (unit of #emph[e])], [Spin (#emph[s])], [Mass (#math.equation(block: false, alt: "GeV/ c squared")[$"GeV/" c^(2)$])]),
  [Proton], [p], [#emph[u u d]], [1], [1/2], [0.938],
  [Neutron], [n], [#emph[u d d]], [0], [1/2], [0.940],
  [Delta plus plus], [∆#super[++]], [#emph[u u u]], [2], [3/2], [1.232],
  [Delta plus], [∆#super[+]], [#emph[u u d]], [1], [3/2], [1.232],
  [Delta zero], [∆#super[0]], [#emph[u d d]], [0], [3/2], [1.232],
  [Delta minus], [∆#super[−]], [#emph[d d d]], [#math.equation(block: false, alt: "– 1")[$"–" 1$]], [3/2], [1.232],
  [Lambda zero], [#math.equation(block: false, alt: "Λ to the power 0")[$"Λ"^(0)$]], [#emph[u d s]], [0], [1/2], [1.116],
  [Positive sigma], [#math.equation(block: false, alt: "Σ to the power plus")[$"Σ"^(+)$]], [#emph[u u s]], [1], [1/2], [1.189],
  [Neutral sigma], [#math.equation(block: false, alt: "Σ to the power 0")[$"Σ"^(0)$]], [#emph[u d s]], [0], [1/2], [1.192],
  [Negative xi], [#math.equation(block: false, alt: "Ξ to the power −")[$"Ξ"^("−")$]], [#emph[s d s]], [#math.equation(block: false, alt: "−1")[$−1$]], [1/2], [1.321],
  [Neutral xi], [#math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$]], [#emph[s u s]], [0], [1/2], [1.315],
  [Omega minus], [#math.equation(block: false, alt: "Ω to the power −")[$"Ω"^("−")$]], [#emph[s s s]], [#math.equation(block: false, alt: "−1")[$−1$]], [3/2], [1.672],
  [Charmed lambda], [#math.equation(block: false, alt: "Λ C plus")[$"Λ"_(C)^(+)$]], [#emph[u d c]], [1], [1/2], [2.281],
  [Bottom lambda], [#math.equation(block: false, alt: "Λ b 0")[$"Λ"_(b)^(0)$]], [#emph[u d b]], [0], [1/2], [5.619],
))


    Mesons are formed by two quarks—a quark-antiquark pair. Sample mesons, including quark content and properties, are given in . Consider the formation of the pion (#math.equation(block: false, alt: "π to the power plus equals u d −")[$π^(+) = u limits(d)^("−")$]). Based on its quark content, the charge of the pion is


    #math.equation(block: true, alt: "the fraction 2 over 3 e plus the fraction 1 over 3 e equals e .")[$frac(2, 3) e + frac(1, 3) e = e .$]
    Both quarks are spin-half (#math.equation(block: false, alt: "s equals ½")[$s = ½$]), so the resultant spin is either 0 or 1. The spin of the #math.equation(block: false, alt: "π to the power plus")[$π^(+)$] meson is 0. The same quark-antiquark combination gives the rho (#math.equation(block: false, alt: "ρ")[$ρ$]) meson with spin 1. This meson has a mass approximately 5.5 times that of the #math.equation(block: false, alt: "π to the power plus")[$π^(+)$] meson.


    #examplebox("Example 1")[Quark Structure][
Show that the quark composition given in  for #math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$] is consistent with the known charge, spin, and strangeness of this baryon.


      Strategy
#math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$] is composed of two strange quarks and an up quark (#emph[s u s]). We can add together the properties of quarks to predict the resulting properties of the #math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$] baryon.


      Solution
The charge of the #emph[s] quark is #math.equation(block: false, alt: "− e / 3")[$"−" e "/" 3$] and the charge of the #emph[u] quark is 2#emph[e]/3. Thus, the combination (#emph[s u s]) has no net charge, in agreement with the known charge of #math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$]. Since three spin #math.equation(block: false, alt: "− 1 / 2")[$"−" 1 "/" 2$] quarks can combine to produce a particle with spin of either 1/2 or 3/2, the quark composition is consistent with the known spin (#math.equation(block: false, alt: "s equals 1 / 2")[$s = 1 "/" 2$]) of #math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$]. Finally, the net strangeness of the (#emph[s u s]) combination is #math.equation(block: false, alt: "open parenthesis − 1 close parenthesis plus 0 plus open parenthesis − 1 close parenthesis equals − 2 ,")[$( "−" 1 ) + 0 + ( "−" 1 ) = "−" 2 ,$] which also agrees with experiment.


      Significance
The charge, spin, and strangeness of the #math.equation(block: false, alt: "Ξ to the power 0")[$"Ξ"^(0)$] particle can be determined from the properties of its constituent quarks. The great diversity of baryons and mesons can be traced to the properties of just six quarks: up, down, charge, strange, top, and bottom.
]


    #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[
What is the baryon number of a pion?


      
      #solutionbox[
0
]
]


    #figure(table(
  columns: 6, align: left, inset: 6pt,
  table.header([Name], [Symbol], [Quarks], [Charge (#emph[e])], [Spin], [Mass #math.equation(block: false, alt: "open parenthesis GeV/ c squared close parenthesis")[$( "GeV/" c^(2) )$]]),
  [Positive pion], [#math.equation(block: false, alt: "π to the power plus")[$π^(+)$]], [#math.equation(block: false, alt: "u d −")[$u limits(d)^("−")$]], [1], [0], [0.140],
  [Positive rho], [#math.equation(block: false, alt: "ρ to the power plus")[$ρ^(+)$]], [#math.equation(block: false, alt: "u d −")[$u limits(d)^("−")$]], [1], [1], [0.768],
  [Negative pion], [#math.equation(block: false, alt: "π to the power −")[$π^("−")$]], [#math.equation(block: false, alt: "u − d")[$limits(u)^("−") d$]], [#math.equation(block: false, alt: "−1")[$−1$]], [0], [0.140],
  [Negative rho], [#math.equation(block: false, alt: "ρ to the power −")[$ρ^("−")$]], [#math.equation(block: false, alt: "u − d")[$limits(u)^("−") d$]], [#math.equation(block: false, alt: "−1")[$−1$]], [1], [0.768],
  [Neutral Pion], [#math.equation(block: false, alt: "π to the power 0")[$π^(0)$]], [#math.equation(block: false, alt: "u − u")[$limits(u)^("−") u$] or #math.equation(block: false, alt: "d − d")[$limits(d)^("−") d$]], [0], [0], [0.135],
  [Neutral eta], [#math.equation(block: false, alt: "η to the power 0")[$η^(0)$]], [#math.equation(block: false, alt: "u − u")[$limits(u)^("−") u$], #math.equation(block: false, alt: "d − d")[$limits(d)^("−") d$] or #math.equation(block: false, alt: "s − s")[$limits(s)^("−") s$]], [0], [0], [0.547],
  [Positive kaon], [#math.equation(block: false, alt: "K to the power plus")[$"K"^(+)$]], [#math.equation(block: false, alt: "u s −")[$u limits(s)^("−")$]], [1], [0], [0.494],
  [Neutral kaon], [#math.equation(block: false, alt: "K to the power 0")[$"K"^(0)$]], [#math.equation(block: false, alt: "d s −")[$d limits(s)^("−")$]], [0], [0], [0.498],
  [Negative kaon], [#math.equation(block: false, alt: "K to the power −")[$"K"^("−")$]], [#math.equation(block: false, alt: "u − s")[$limits(u)^("−") s$]], [#math.equation(block: false, alt: "−1")[$−1$]], [0], [0.494],
  [J/Psi], [#math.equation(block: false, alt: "J/ψ")[$"J/ψ"$]], [#math.equation(block: false, alt: "c − c")[$limits(c)^("−") c$]], [0], [1], [3.10],
  [Charmed eta], [#math.equation(block: false, alt: "η sub to the power 0")[$η_(0)$]], [#math.equation(block: false, alt: "c c −")[$c limits(c)^("−")$]], [0], [0], [2.98],
  [Neutral D], [#math.equation(block: false, alt: "D to the power 0")[$"D"^(0)$]], [#math.equation(block: false, alt: "u − c")[$limits(u)^("−") c$]], [0], [0], [1.86],
  [Neutral D], [#math.equation(block: false, alt: "D to the power *0")[$"D"^("*0")$]], [#math.equation(block: false, alt: "u − c")[$limits(u)^("−") c$]], [0], [1], [2.01],
  [Positive D], [#math.equation(block: false, alt: "D to the power plus")[$"D"^(+)$]], [#math.equation(block: false, alt: "d − c")[$limits(d)^("−") c$]], [1], [0], [1.87],
  [Neutral B], [#math.equation(block: false, alt: "B to the power 0")[$"B"^(0)$]], [#math.equation(block: false, alt: "d − b")[$limits(d)^("−") b$]], [0], [0], [5.26],
  [Upsilon], [#math.equation(block: false, alt: "ϒ")[$ϒ$]], [#math.equation(block: false, alt: "b b −")[$b limits(b)^("−")$]], [0], [1], [9.46],
))


  
  
    
=== Color


    Quarks are fermions that obey Pauli’s exclusion principle, so it might be surprising to learn that three quarks can bind together within a nucleus. For example, how can two up quarks exist in the same small region of space within a proton? The solution is to invent a third new property to distinguish them. This property is called #strong[color], and it plays the same role in the strong nuclear interaction as charge does in electromagnetic interactions. For this reason, quark color is sometimes called “strong charge.”


    Quarks come in three colors: red, green, and blue. (These are just labels—quarks are not actually colored.) Each type of quark #math.equation(block: false, alt: "open parenthesis u , d , c , s , b , t close parenthesis")[$( u , d , c , s , b , t )$] can possess any other colors. For example, three strange quarks exist: a red strange quark, a green strange quark, and a blue strange quark. Antiquarks have anticolor. Quarks that bind together to form hadrons (baryons and mesons) must be color neutral, colorless, or “white.” Thus, a baryon must contain a red, blue, and green quark. Likewise, a meson contains either a red-antired, blue-antiblue, or green-antigreen quark pair. Thus, two quarks can be found in the same spin state in a hadron, without violating Pauli’s exclusion principle, because their colors are different.


  
  
    
=== Quark Confinement


    The first strong evidence for the existence of quarks came from a series of experiments performed at the Stanford Linear Accelerator Center (SLAC) and at CERN around 1970. This experiment was designed to probe the structure of the proton, much like Rutherford studied structure inside the atom with his #math.equation(block: false, alt: "α")[$"α"$]-particle scattering experiments. Electrons were collided with protons with energy in excess of 20 GeV. At this energy, #math.equation(block: false, alt: "E approximately equals p c")[$E ≈ p c$], so the de Broglie wavelength of an electron is


    #math.equation(block: true, alt: "λ equals the fraction h over p equals the fraction h c over E approximately equals 6 times 10 to the power −17 m .")[$λ = frac(h, p) = frac(h c, E) ≈ 6 #h(0.2em) × #h(0.2em) 10^(−17) #h(0.2em) "m" .$]
    The wavelength of the electron is much smaller than the diameter of the proton (about #math.equation(block: false, alt: "10 to the power −15 m close parenthesis .")[$10^(−15) #h(0.2em) "m" \) "."$] Thus, like an automobile traveling through a rocky mountain range, electrons can be used to probe the structure of the nucleus.


    The SLAC experiments found that some electrons were deflected at very large angles, indicating small scattering centers within the proton. The scattering distribution was consistent with electrons being scattered from sites with spin 1/2, the spin of quarks. The experiments at CERN used neutrinos instead of electrons. This experiment also found evidence for the tiny scattering centers. In both experiments, the results suggested that the charges of the scattering particles were either #math.equation(block: false, alt: "plus 2 / 3 e")[$+ 2 "/" 3 e$] or #math.equation(block: false, alt: "− 1 / 3 e")[$"−" 1 "/" 3 e$], in agreement with the quark model.


    #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[
Watch this #link("https://openstax.org/l/21quarks")[video] to learn more about quarks.
]


    The quark model has been extremely successful in organizing the complex world of subatomic particles. Interestingly, however, no experiment has ever produced an isolated quark. All quarks have fractional charge and should therefore be easily distinguishable from the known elementary particles, whose charges are all an integer multiple of #emph[e]. Why are isolated quarks not observed? In current models of particle interactions, the answer is expressed in terms of quark confinement. Quark confinement refers to the confinement of quarks in groups of two or three in a small region of space. The quarks are completely free to move about in this space, and send and receive gluons (the carriers of the strong force). However, if these quarks stray too far from one another, the strong force pulls them back it. This action is likened to a bola, a weapon used for hunting . The stones are tied to a central point by a string, so none of the rocks can move too far from the others. The bola corresponds to a baryon, the stones correspond to quarks, and the string corresponds to the gluons that hold the system together.


    #figure(figph[Three strings are tied together at one end. A weight is attached to the other end of each. The strings are labeled quark confinement. The weights are labeled quarks.], alt: "Three strings are tied together at one end. A weight is attached to the other end of each. The strings are labeled quark confinement. The weights are labeled quarks.", caption: [A baryon is analogous to a bola, a weapon used for hunting. The rocks in this image correspond to the baryon quarks. The quarks are free to move about but must remain close to the other quarks.])


  
  
    
=== Summary


    - Six known quarks exist: up (#emph[u]), down (#emph[d]), charm (#emph[c]), strange (#emph[s]), top (#emph[t]), and bottom (#emph[b]). These particles are fermions with half-integral spin and fractional charge.
- Baryons consist of three quarks, and mesons consist of a quark-antiquark pair. Due to the strong force, quarks cannot exist in isolation.
- Evidence for quarks is found in scattering experiments.


  
  
    
=== Conceptual Questions


    
      What are the six known quarks? Summarize their properties.


    
    
      What is the general quark composition of a baryon? Of a meson?


    
    #solutionbox[
3 quarks, 2 quarks (a quark-antiquark pair)
]


    
      What evidence exists for the existence of quarks?


    
    
      Why do baryons with the same quark composition sometimes differ in their rest mass energies?


    
    #solutionbox[
Baryons with the same quark composition differ in rest energy because this energy depends on the internal energy of the quarks #math.equation(block: false, alt: "open parenthesis m equals E / c squared close parenthesis")[$( m = E "/" c^(2) )$]. So, a baryon that contains a quark with a large angular momentum is expected to be more massive than the same baryon with less angular momentum.
]


  
  
    
=== Problems


    
      Based on quark composition of a proton, show that its charge is #math.equation(block: false, alt: "plus 1")[$+ 1$].


    
    #solutionbox[
A proton consists of two up quarks and one down quark. The total charge of a proton is therefore #math.equation(block: false, alt: "plus the fraction 2 over 3 plus the fraction 2 over 3 plus − the fraction 1 over 3 equals plus 1 .")[$+ frac(2, 3) + frac(2, 3) + "−" frac(1, 3) = + 1 .$]
]


    
      Based on the quark composition of a neutron, show that is charge is 0.


    
    
      Argue that the quark composition given in  for the positive kaon is consistent with the known charge, spin, and strangeness of this baryon.


    
    #solutionbox[
The #math.equation(block: false, alt: "K to the power plus")[$"K"^(+)$] meson is composed of an up quark and a strange antiquark (#math.equation(block: false, alt: "u s −")[$u limits(s)^("−")$]). Since the changes of this quark and antiquark are 2#emph[e]/3 and #emph[e]/3, respectively, the net charge of the #math.equation(block: false, alt: "K to the power plus")[$"K"^(+)$] meson is #emph[e], in agreement with its known value. Two spin #math.equation(block: false, alt: "−1 / 2")[$−1 "/" 2$] particles can combine to produce a particle with spin of either 0 or 1, consistent with the #math.equation(block: false, alt: "K to the power plus")[$"K"^(+)$] meson’s spin of 0. The net strangeness of the up quark and strange antiquark is #math.equation(block: false, alt: "0 plus 1 equals 1")[$0 + 1 = 1$], in agreement with the measured strangeness of the #math.equation(block: false, alt: "K to the power plus")[$"K"^(+)$] meson.
]


    
      Mesons are formed from the following combinations of quarks (subscripts indicate color and #math.equation(block: false, alt: "A R equals antired")[$A R = "antired"$]): #math.equation(block: false, alt: "open parenthesis d sub R , d − sub AR close parenthesis")[$( d_("R") , limits(d)^("−")_("AR") )$], (#math.equation(block: false, alt: "s sub G , u − sub AG")[$s_("G") , limits(u)^("−")_("AG")$]), and (#math.equation(block: false, alt: "s sub R , s − sub AR")[$s_("R") , limits(s)^("−")_("AR")$]).


      (a) Determine the charge and strangeness of each combination. (#emph[b]) Identify one or more mesons formed by each quark-antiquark combination.


    
    
      Why can’t either set of quarks shown below form a hadron?


      #figure(figph[Figure a has three red circles, each labeled u subscript R. Figure b has a blue circle labeled d subscript B and a purple circle labeled u subscript G.], alt: "Figure a has three red circles, each labeled u subscript R. Figure b has a blue circle labeled d subscript B and a purple circle labeled u subscript G.", caption: none)


    
    #solutionbox[
a. color; b. quark-antiquark
]


    
      Experimental results indicate an isolate particle with charge #math.equation(block: false, alt: "plus 2 / 3")[$+ 2 "/" 3$]—an isolated quark. What quark could this be? Why would this discovery be important?


    
    
      Express the #math.equation(block: false, alt: "β")[$β$] decays #math.equation(block: false, alt: "n → p plus e to the power − plus ν −")[$n → p + e^("−") + limits(ν)^("−")$] and #math.equation(block: false, alt: "p → n plus e to the power plus plus ν")[$p → n + e^(+) + ν$] in terms of #math.equation(block: false, alt: "β")[$β$] decays of quarks. Check to see that the conservation laws for charge, lepton number, and baryon number are satisfied by the quark #math.equation(block: false, alt: "β")[$β$] decays.


    
    #solutionbox[
#math.equation(block: true, alt: "d → u plus e to the power − plus v − sub e ; u → d plus e to the power plus plus v sub e")[$d → u + e^("−") + limits(v)^("−")_(e) ; u → d + e^(+) + v_(e)$]
]