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7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α γ ] β δ (7.b) U (detu = ) U SU() SU() U U = e i σ θ (7.) ( D ) SU()( ) SU() SU() * ) (charge independence) SU() z K / π Σ * )

7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ± = π ± iπ, π 0 = π (7.7) [ ] [ π π iπ π 0 ] π + τ π = = π + iπ π π π 0 L int = g ( ) N τn π = g [ p nπ + n pπ + + (p p n n)π 0] (7.9) (7.8) L int = g pn p nπ + + g np n pπ + + g pp p pπ 0 + g nn n nπ 0 (7.0) g pn : g np : g pp : g nn = : : : V pp = V nn = V pn 7.: V pp = V nn = V pn 7. π * ) N N = [ p n ] π gnγ 5 τn π

7 π 0 : V pp π 0 : V nn π 0 : V pn pn π ± : V pn np ( g g [() ()] = ) 7.(a) 4 ( g g [( ) ( )] = ) : 7.(b) 4 ( g g [() ( )] = ) : 7.(c) 4 ( g g [( ) ( )] = ) : 7.(d) V {pn} V pn pn +V pn np = V pp = V nn = g V (r) (7.) 4 V (r) π µ e µr r V {pn} n (pn) V [pn] V pn pn V pn np = 4 g V (r) (7.) ( =) ( =0) π π π π π < N,N,0 T [L INT L INT ] N,N,0 > < τ τ > V (r) (7.) 0 π < τ τ > / I (,0) I < τ τ > I I = [ (I + I ) I I ] = [I(I + ) I (I + ) I (I + )] = ( + ) ( + ) = 4 I= (7.4) 0 (0 + ) 4 = 4 I=0 I = 0 ( ) I = V (r) > 0 l = 0 l = I = 0 I=0 S=0 A + B(τ τ ) ( ρ ) [A + B(τ τ )][C + D(σ σ )] D

7 4 QCD p = uud,n = udd, π + = ud,π 0 = ( uu + dd)/, π = du) pn π 0,π ± π 7.: p n p n ( ) 7. SU() 7.. u d (s- ) S ( ) (a) π + P K + + Σ S 0 0 + - K + π + π 0 Σ π + n + 0 0-0 0 (c) K + P Ω + K + + K 0 S - 0 - + + Ω Ξ 0 + +π - - 0 Ξ 0 Λ 0 + π 0 - - 0 Λ 0 π P π 0 γ + γ - 0 0 0 0 0

7 5 Q B ( ) Q = I + B + S = I + Y (7.5) Y (hypercharge) ((u,d) πn () ) (u,d,s) SU() % 0% SU() SU(n) n = 4,5 s (.4GeV) SU(4) (flavor) (u,d,s) SU() SU() QCD SU() SU(N) U detu = N N ( U = exp i N θ i F i ), Tr[F i ] = 0, (7.6a) i= [F i, F j ] = i f i jk F k (7.6b) ( A ) F i N N θ i N F i SU(N) f i jk f i jk SU() F i = σ i SU() F i = { λ i ; i = 8} 7.. SU() (q i = u,d,s) SU() SU() (u,d,s)

7 6 u ψ = d = s q q q ψ ψ = Uψ = exp 0 0 = q i e i, e = 0, e =, e = 0 [ i i ] λ i θ i ψ 0 0 (7.7a) (7.7b) q i q i = U i jq j, q i (q i ) q i = q j U j i (7.7c) λ i [ ] 0 0 0 0 i τ i 0 λ i (i =,,) =, λ 4 = 0 0 0, λ 5 = 0 0 0, 0 0 0 0 i 0 0 (7.8a) 0 0 0 0 0 λ 6 = 0 0, λ 7 = 0 0 i, λ 8 = 0 0 0 0 0 0 0 i 0 0 0 (7.8b) [ λi, λ ] j { λi, λ j = i f i jk λ k } = δ i j + id i jk λ k (7.9a) (7.9b) Tr[λ i ] = 0, Tr[λ i λ j ] = δ i j (7.9c) f i jk SU() SU() f i jk,d i jk i jk 7. 7.: SU() f = f 47 = f 46 = f 57 = f 45 = f 56 = f 67 = / f 458 = f 678 = / d 8 = d 8 = d 8 = d 888 = / d 46 = d 57 = d 56 = d 44 = / d 47 = d 66 = d 77 = / d 448 = d 558 = d 668 = d 778 = /( ) 7.: I I Y Q B u + d s 0 0 SU() λ i Y Y Q B S Q = I + Y, Y = B + S (7.0) (u,d,s) (I,I ) Y Q B

7 7 7.. q i q j / q i q j q k ψψ = q i q i = q i q i SU() η (uu + dd + ss) (7.) SU() * ) / Φ i j = q i q j P i j = q i q j (uu dd ss) du su δi jtr[φ i j] ud (dd ss uu) sd us ds (ss uu dd) (7.) SU() (octet) = 8 (7.) I,I,Y 0 * 4) 7.: (a) J P = 0 (b) J P = π 0 P i + η 6 π + K + j = π π0 + η 6 K 0 K K 0 η (7.4a) π = ud, π + = du, π 0 uu dd =, K = us, K + = su, K 0 = sd, K 0 = ds, (7.4b) η = uu + dd ss 6 (7.4c) 7. * ) * 4) )

7 8 7..4 / q i q j q k T i j = q i q j T i j = (qi q j + q j q i ) + (qi q j q j q i ) = S i j + A i j (7.5) ( 7..) = 6 (7.6) (I,Y ) 7.4: 7.5: 7.. (7.5) q j (7.6) = 8 (7.7) A i j q k 8 (7.6) 6 = 8 0 (7.8) = A 8 MA 8 MS 0 S (7.9) (A) 0 (S) 8 I Y (MA) (MS) - / + 8 / + 0 ( 7.47.5)

7 9 I Y ( 7.6) ud (I = I ( u) + I(d),Y = (Y (u) +Y (d)) I Y ( 7.6(c)) q i,q j 7.7 I = Y = 0 ( 7.7 ) 7.6: u,d,s (I, Y ) = (/,/), ( /, /), (0, /) (a) (b) (u,d,s) (c) u d ud 7.7: 8,0 7. 0 ++ = uuu,ω = sss / l = 0 * 5) SU() xx () * 5)

7 0 ()π 0 γγ () - (Drell-Yan) (P + P ll + X) ()() qq (4)W eν, µ ν, τν, ud, cs (W tb m W = 8GeV,m top = 75Gev ) BR(W eν) = /5 = 0% BR(W eν) = /9 % 7.8: R = σ(ee ) σ(ee µµ) (5)R = σ(e e + hadron) σ(e e + µ µ + ) e + e + q i + q i (7.0) ee - Q i R = σ(ee ) σ(ee µµ) = σ(ee q iq i ) σ(ee µµ) = Q i (7.) i [ ( Q ) ( ) ] + = 5 s GeV i = 5 + ( ) = 7 s 0GeV (7.a) R (S GeV ) b (S 0GeV)

7 7.4 SU(6) 7.4. S * 6) SU(6) SU(6) (u, u, d, d, s, s ) (7.) 6 6 (,/) SU() 6 6 = 5 = (,0) (,) (8,0) (8,) (7.4) (0, ) ( ) 6 6 6 = 0 A 70 M A 70 M S 56 S (7.5) A= MA= MS= S= 56 * 7) 56 = (8,/) (0,/) (7.6) / / (/) + SU() / 8 SU(6) 7.4. SU(6) 8 L=0 p > uud uu, >=,,0 >= ( + ),, >= (7.7) / /, = ( + ) = [ ( + ) ] (7.8) 6 * 6) P D * 7) 0,70 P,D

7 p > uud[ ( + ) ] + cyclic 8 [uud( ) + udu( ) + duu( )] (7.9) < p p >= 7.4. (ud du)u( ) (7.40) 7.4. SU(6) (7.9) ud p >= uud { ( + ) } (7.4) 6 ) ( = 6 µ p = µ u + µ u µ d (7.4) ) ( = 6 µ p = µ u µ u + µ d (7.4) µ p = (µ u µ d ) + µ d = (4µ u µ d ) (7.44) µ n = (4µ d µ u ) (7.45) SU(6) m u = m d µ d = µ u / µ n /µ p = / (-0.685) SU(6) (7.44) / / m u,m d,m s 7.4. 7. µ i = q i e/m i m u = 8MeV, m d = MeV, m s = 50MeV (7.46) m u m d m p /, m s m u m Λ m p

7 7.: SU(6) p (4µ u µ d )/ INPUT.7984786 ± (6) n ( µ u + 4µ d )/ INPUT.90475 ± (45) Λ 0 µ s INPUT 0.6 ± 0.004 Σ + (4µ u µ s )/.67.49 ± 0.0 Σ 0 [(µ u + µ d ) µ s ]/ 0.79? Σ 0 Λ 0 (µ u µ d )/ -.6.6 ± 0.08 Σ (4µ d µ s )/ -.09.56 ± 0.04 Ξ 0 ( µ u + 4µ s )/ -.4.5 ± 0.04 Ξ ( µ d + 4µ s )/ -0.49 0.675 ± 0.0 Ω µ s -.84.08 ± 0.5 e/m p

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