introduction-weak-interaction-volume-one

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helicities, it is unnecessary to distinguish between them. Setting -V/„r,( x ) = r,,(x) _.r(x) - (4 .5 .9 ) we obtai n ~vr (x) +( 1 — Y 5 ) 2Jf (x) , (4 .5 .10 ) Ova (x) = +(1 + )(5)"141',(x) . (4 .5 .11 ) Thus the muon decay Hamiltonian becomes where = ( G/12) ( t, ( x ) Yr(1 - Y 5)v (x)) (1re(x) v ! r (1 + Y 5) 7,(x) ) } Herm . conj ., (4 .5 .12) 'let, denotes the complex conjugate of the muon field . This Hamiltonian is invariant under two gauge transformations : the lepton gauge e(x) -~i e6A e(x) , (4 .5 .13 ) r( x ) e jA }^( x ) . (4 .5 .14 ) v(x) -> e°A v(x) , (4 .5 .15) the symbol for the particles standing for their wave functions ; and th e so-called 'second gauge group' : e(x)--> e jB e(x) , (4 .5 .16 ) p,(x) e jB }n (x) , (4 .5 .17 ) > e°B1s v(x) v(x) . (4 .5 .18) Thus we have two conserved quantum numbers in our new formulation, and these , in fact, are equivalent to our original quantum numbers e and fA • At this point, we briefly consider the status of the muon with respect to the electron . These two particles appear to be identical, excep t for their large mass difference . Ross suggests (25) the possibility that th e muon consists of an electron with a zero mass particle, which he calls th e 'wavon',in orbit around it . He points out that if the 'wavon' has neutrino-like properties, then it would be unaffected by strong or electromagnetic force s from the central electron, and the weak interaction between the two particle s would be negligablo, since they would be spatially separated . Thus the onl y significant force within the Ross model of the muon would be gravitation . Using special relativity, Ross claims to be able to justify the comparative stability of the muon, and to predict a muon-electron mass ratio of 206 .55, which is close to the measured value of 206 .77 . Further, he suggests tha t the wavon, which must have a spin of one or zero to justify the muon spin ,
might be composed of a bound state v e — vr , which is attractive, since it would explain the muon decay. However, Ross' model fails to explain the existence of the mu—neutrino, and could only be verified by very high—energy electron—muon scattering experiments .
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INTRODUCTION TO THE WEAK INTERACTIO
Page 4:
D R A F T O N E B COPY TWO . Summer
Page 7 and 8:
Chapter Four : Weak Leptonic Reacti
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E = gf (1 .1 .5 ) which Planck had
Page 11 and 12:
1 .3 The Schrddinmer Equation . (21
Page 13 and 14:
IN, we have 1 )(e, t} (e°t , aE =
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(r~ t) _ f(r) ejEtm (1 .5 .5 ) We n
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.2+ V Thus H = (1/2m) p 2 -{- V and
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e and c = m . 0 (1 .7 .15 ) (1 .7 .
Page 21 and 22:
and thus, from (1 .7 .10) and (1 .7
Page 23 and 24:
CHAPTER TbO : FIELD THEORY . 2 .1 T
Page 25 and 26:
In 1939, Wigner introduced the time
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conjugate of the ket . We operate o
Page 29 and 30:
matrix is one such that Wt = u tU =
Page 31 and 32:
and under time reversal T (T( T ( x
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antiparticle's is always aligned pa
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and from (2 .6 .13) and (2 .6 .14 )
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an d CPT ( '(x)) --TA-2,:) 5 (2 .7
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energies, then it we difficult to s
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in timing or by a pulse from a furt
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less rigorous but still physically
Page 45 and 46:
constants . Noninvariance of the we
Page 47 and 48: B i rather than of the C . and C .
Page 49 and 50: universal electromagnetic coupling
Page 51 and 52: occured, but the observation of the
Page 53 and 54: u = e 3 P 'r 1 + r + (J p'r)2 . . .
Page 55 and 56: where X = 121, N . ue(+)(9.e) Fi uv
Page 57 and 58: = i Re (C S CV + cS caw ) vF,1 2 +
Page 59 and 60: 1g-t = z (1 + '( 5 )y , (3 .6 .8b )
Page 61 and 62: We find that any wave function 14r(
Page 63 and 64: - Ja/(Ja t 1) J b = Ja + 1 , J b =
Page 65 and 66: where C . = C! = G . /f 2 (3 .7 .7f
Page 67 and 68: wher e _1(1) = C(2) _O (3 .7 .15b )
Page 69 and 70: multiple scattering, which can simu
Page 71 and 72: The annihilation of free helical po
Page 73 and 74: of the decay gamma ray will be prop
Page 75 and 76: We are thus forced to conclude that
Page 77 and 78: ((Jg - E) w j )r qr u = = 0 , (3 .8
Page 79 and 80: REFERENCES . 1 . H . Becquerel : Co
Page 81 and 82: 37. See e .g . M . A . Preston : Ph
Page 83 and 84: CHAPTER FOUR : WEAK LIPTONIC REACTI
Page 85 and 86: (~ w/ St) (d3Pe)/(2n )5 J J d 3p v
Page 87 and 88: _ (-3a ' - 4b' + 14c')/(a t 4b + 6c
Page 89 and 90: necessary to have a high flux of hi
Page 91 and 92: 4 .4 Currents in Leptonic Reactions
Page 93 and 94: e t e > )-k- + , (4 .4 .22 ) which
Page 95 and 96: K(36) = (1/Y) (T/108 ) 8 (4 .4 .41
Page 97: neutrinos is 10 22 .5 * 2 .5 (22) .
Page 101 and 102: of T 3 the Pauli spin matrix (1 .7
Page 103 and 104: isospin—formulated fields, but th
Page 105 and 106: We see that the first term in (5 .2
Page 107 and 108: changing semileptonic reactions occ
Page 109 and 110: vanishes, the n e jn I 2 JH(o) e O"
Page 111 and 112: A(q 2) + B (q 2 ) tan g (O /2) (5 .
Page 113 and 114: where A and B are the initial and f
Page 115 and 116: magnetic effects in these decays wo
Page 117 and 118: values for the constants in (5 .5 .
Page 119 and 120: 5 .6 The Current-Current Approach .
Page 121 and 122: includes also neutral hadron curren
Page 123: in good agreement with the theoreti
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