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V II V 1 4 mnk A = x FmnkF 2 3! 1 1 4 = x (kAmn) kAmn - (mAmk) nAnk, 4 2 Fmnk = mAnk +kAmn +nAkm Tmn 1 4 mn mk A = x (kTmn) kT - (mT ) nTnk, 4 t mn Tmn t afab = m0Ab, aAb - bAa = m0fab, Am Amn 1 1 4 a A = x Aa mnpqFpq + (Aa )2, mn m 4 2 nmab 0123 = a +1 Fpq = pAa - qAa + fa AbAc a, b c q p bc p q G fa bc a a Aa = mn - nm, Aa = 0, mn m a a c mn = mn + fa Ab n bc m Aa mn Aa m a Fmn = mAa - nAa + fa Ab Ac = 0. n m bc m n g G Am = g-1mg, Am Am = i Aa Ta/2 Ta m TaTb = 2 ab mAa = 0 mn a a Cm Cm a Cn = (mAa ) mn a mCm = 0 a a Cab d = N = 1 d = 10 SO(32) E8 E8 ...m1...n ...m1...n j = (m+n)/2 (m/2, n/2) (n/2, m/2) m n (, ) 4 2 2 11 mm 1 n Aj = p ...m1...np...p p...p n...m1...n, p = pm(m) p = pm(m) T (m) = (C-1mC) C 11 mm 1 n p...p p 1...p n...m1...n = 0 ...m1...n (1, 0) (0, 1) 4 A(1,0) = p p . p 1 Tmn i = abmn(abC)Tmn. 4 A(1,0) = p Tab(p)p2abmn(p)Tmn(p), abmn(p) = [am(p)bn(p) - an(p)bm(p)] mn(p) = gmn - 2pmpn/p2 Ai = T0i Bi = 1/2 ijkTjk (1, 1) 2 (3/2, 1/2) (1/2, 3/2) (2, 0) (0, 2) Va[mn] [ab][mn] 1 Va[mn] [ab][mn] Rabmn Cabmn (1, 1/2) (1/2, 1) (3/2, 0) (0, 3/2) (1, 1/2) (1/2, 1) (3/2, 0) (0, 3/2) (1, 1/2) (1/2, 1) (3/2, 0) (0, 3/2) 1/2 p j 1 (1 5) (1 5) 0 GT qq LT = - (1 + 5) (1 - 5) eff 2 qGT qq = - [ - 5 5]. 2 q R B JP C 1-- 1+- R B R = , B = i 5, = / -2 B 1+- a1 b1 h1(1170) h1(1380) 1+- u d s R a1 I = 0 (782) (1020) (1420) (1680) m2 + m2 = m2 + m2. b1 a 1-- 1+- 1++ SU(6) O(3) b1 1-- 1+2m2 - m m + 2m R = 1. 3mb I = 1 RI=1 = 0.960.03 I = (782) (1420) h1(1170) RI=0 = 1.02 0.07 (1020) (1680) h1(s s) 1+- 2m2 - m m + 2m mh (ss) = = 1409 20. 1440 60 1380 20 0|qq|V (p, ) = mV fV e(p) T 0|qq|V (p, ) = ifV e(p)p - e(p)p, m m T f = , f = ; 2 gV 2 gR m m T f = - , f = ., 2 gV 2 gR gR = 2 gV T f = 0.707, f T f = -. f (2)L U(1)Y Am Bm Li = (L e )i L (e )i R Qi = (u d )i (u )i (d )i L L R R i (2)L (1)Y 0 - + H1 = (H1H1 ) H2 = (H2 H2) Umn = (Umn - + Umn) Tmn = (TmnTmn) Y (H1) = Y (U) = -1 Y (H2) = Y (T ) = +1 Dm = m - ig/2 T Am - ig/2 Y Bm g g T Y (2)L (1)Y 2/3 -1/3 (2)L (1)Y L = hu Qi(u )j H1 + hd Qi(d )j + he Li(e )j H2 +, ij R ij R ij R hu hd he L = tu Qimn(u )j Umn + td Qimn(d )j + te Limn(e )j Tmn ij R ij R ij R + Tmn Umn - + T (T T ) 0 T (T U+) P(q) = + T (U-T ) 0 T (U-U+) 4i (q2 - m2)-(q) 21=, 21+ (q2 - M2)+(q) q q = (q2 - m2)(q2 - M2) - 4 m M M/m = v1/v2 Tmn Umn v1 v2 + T U- T U+ 1 = mnab 1/2 (1mnab i/2 mnab) = 1 klab mnab mnkl 4qmqn Le = - 2 GF fT LmlR RnleL +, q qm 2 tfT = > 0, GF (1 - )M 4qmqn Lqe = - 2 GF fT mld RnlL +, q d = Vijdj i Lud = - 2 GF fT Lmld d nluL + Lmld d nluR R R R L 4qmqn +Rmld d nluL + Rmld d nluR. L R L L q V - A m m 0 V - A m i 0|5d| = meF 3.8 103 meF (md + mu)me V - A 0|d|(p) p e - e- fT 10-2 E > 50 Ee < 50 fT 10-2 a GF qm PT PT V -A MU 509, MU 719, MT 0 1017, MT 1137, g + LC = dR + eR U + 3 T+ Y + + g dL U - T+ + h.c. g R LN = dd + T Y g I + i d5d + 5 T R + g u U, I + i g 5u U, U = ( 3 U + T )/2 T = ( 3 T - U )/2 0 T U I 0 I CP T = 2ImT U = 2ImU R CP T = 2ReT R U = 2ReU CP B(U ) 2.1% B(W ) 8.3% B(T ) 6.3% W MV = MU 509 Tev W B(W ) 0.82 pb, T Uev B(U ) 0.26 pb. W dNW 16 (1 cos )2, = 1, = d sin2 , = 0, 8 U dNU 8 sin2 , = 1, = d cos2 , = 0, 4 d W -1 (1 + cos )2 cos2 pT = /2 sin = (pd + p)2 pT cos pT - d cos 2 2 4pT = - = - 1 - dp2 cos T p2 = T /4 W p2 = /4 T W U pT pT MV /2 Z T T W Z V II - e- K+ 0e+ t KL - KS Vud
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