Problem#1
Nine of the spin -3/2 baryons are four ∆ particles, each with 1232 MeV/c2, mass strangeness 0, and charges +2e, +e, 0, and –e; three ∑* particles, each with mass 1385 MeV/c2, strangeness –1, and charges +e, 0, and –e ; and two Ξ* particles, each with mass 1530 MeV/c2, strangeness –2 and charges 0 and –e. (a) Place these particles on a plot of S versus Q. Deduce the Q and S values of the tenth spin -3/2 baryon, the Ω– particle, and place it on your diagram. Also label the particles with their masses. The mass of the Ω– is 1672 MeV/c2; is this value consistent with your diagram? (b) Deduce the three-quark combinations (of u, d and s) that make up each of these ten particles. Redraw the plot of S versus Q from part (a) with each particle labeled by its quark content. What regularities do you see?Answer:
Construct the diagram as specified in the problem. In part (b), use quark charges
u = +2/3, d = –1/3 and s = –1/3 as a guide.
(a) The diagram is given in Figure 1. The Ω– particle has Q = –1(as its label suggests) and S = –3. Its appears as a “hole” in an otherwise regular lattice in the S – Q plane.
(b) The quark composition of each particle is shown in the figure.
Problem#2
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations: (a) uds; (b) cu̅; (c) ddd and (d) dc̅. Explain your reasoning.
Answer:
Each value for the combination is the sum of the values for each quark. Use Table 1.
(a) uds
Q = 2e/3 – e/3 – e/3 = 0
B = 1/3 + 1/3 + 1/3 = 1
S = 0 + 0 – 1 = –1
C = 0 + 0 + 0 = 0
(b) cu̅
The values for ū are the negative for those for u.
Q = 2e/3 – e/3 = 0
B = 1/3 – 1/3 = 1
S = 0 + 0 = –1
C = +1 + 0 = +1
(c) ddd
Q = –e/3 – e/3 – e/3 = –e
B = 1/3 + 1/3 + 1/3 = 1
S = 0 + 0 + 0 = 0
C = 0 + 0 + 0 = 0
(d) dc̅.
Q = –e/3 – 2e/3 = –e
B = 1/3 – 1/3 = 0
S = 0 + 0 + 0 = 0
C = 0 – 1 = –1
The charge, baryon number, strangeness and charm quantum numbers of a particle are determined by the particle’s quark composition
Problem#3
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations: (a) uus, (b) cs̅, (c) d̅d̅u̅, and (d) c̅b.
Answer:
The properties of the quarks are given in Table 2. An antiquark has charge and quantum numbers of opposite sign from the corresponding quark.
(a) uus,
Q/e = 2/3 + 2/3 – 1/3 = +1
B = 1/3 + 1/3 + 1/3 = 1
S = 0 + 0 – 1 = –1
C = 0 + 0 + 0 = 0
(b) cs̅,
Q/e = 2/3 + 1/3 = +1
B = 1/3 – 1/3 = 0
S = 0 + 1 = +1
C = 1 + 0 = +1
(c) d̅d̅u̅,
Q/e = 1/3 + 1/3 – 2/3 = 0
B = –1/3 – 1/3 – 1/3 = –1
S = 0 + 0 + 0 = 0
C = 0 + 0 + 0 = 0
(d) c̅b.
Q/e = –2/3 – 1/3 = –1
B = –1/3 + 1/3 = 0
S = 0 + 0 = 0
C = –1 + 0 = –1
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