u

d

e

e

_uu

dd

eepn

W

W links members of the same weak isodoublet

within a single generation

The decay conserves charge,but does NOT conserve iso-spin

(upness/downness)

u

d

e

e

_uu

dd

eepn

W

However, we even observe some strangeness-changing weak decays!

d uu

du

s

p

du

Ku ds

ss

s

su_

_

→ + ν 63.43% of all kaon decays

→ 0 + 21.13%

_

→ e + νe

_0.0000155%

u sK

νe

W

u sK

u u

W

u

d

_

u

d

e

e

_uu

dd

eepn

W

d uu

du

s

p

du

Ku ds

ss

s

su_

W

_

W

Cabibbo (1963)

Glashow, Illiopoulous, Maiani [GIM] (1970)

Kobayashi & Maskawa [KM] (1973)

Suggested the eigenstates of the weak interaction operators(which couple to Ws)

are not exactly the same as the “mass” eigenstatesparticipating in the STRONG interactions

(free space states)

The weak eigenstates are QUANTUM MECHANICAL admixtures

of the mass eigenstates

dweak = c1d + c2s where, of course c12 + c2

2 = 1

= sinθcd + cosθcs

To explain strangeness-changing decays, Cabibbo (1963) introduced the redefined weak iso-doublet

udc

=u Intended to couple to the

Jweak current in the Lagrangian

u

d

W

cosc

u

s

W

sinc

“suppressed”

sinc 0.225cosc 0.974

dcosc + ssinc

θc 13.1o

The relevant term, JweakW , then comes from:

iWigBigi iL

22 21

Y0)( Ldu† †

Ld

u

Bigi R

21Y0Ru †

Ru

i0Rd †

Rd ig1 BYR

2

Lcg

du )(22 † †

Ld

u

W3 W1iW2

W1iW2 W3

Lcg

du )(22 † †

Ld

u

W3 0

0 W3

0 W1iW2

W1iW2 0+

From which follows a NEUTRAL COUPLING to

c

c d

udu

g

10

01

22 = uu - dcdc

_ _

))(cos(sinsincos 22 dssdssdduucccc

d sK

0

Z 0

a coupling to astrangeness changing

neutral current!

u sK+

u d+

Z 0

BUT we do NOT observe processes like:

u sK+

u d Though we do see the very similar processes:+

Z 0

u sK+

u u0

W

d sK

0

u

W

W

d sK

0

Z 0

These are suppressed,but allowed (observed).

Compare to 0e+e

0

Also e+e

Glashow, Illiopoulous, Maiani [GIM] (1970)

even before charmed particles were discovered (1974) and the new quark identified,

proposed there could be a 2nd weak doublet that followed and complemented the Cabibbo pattern:

ccc

csscc

s

csc

g

10

01)(

22

So that the meaured Cabibbo “angle” actually represented a mixing/rotation!

s

d

s

d

cc

cc

cossin

sincos

so that:

ccsd

u

d

u

sincos

ccsd

c

s

c

cossin

orthogonal!

then together these doublets produce interactions of:

uu – dcdc + cc scsc

_ _ __

= uu + cc – (dcdc + scsc)

= uu + cc – (ddcos2θc + sinθccosθc (ds + sd) + sssin2θc

_ _ __

ccsdd sincos

ccsds cossin

ddsin2θc sinθccosθc (ds + sd) + sscos2θc)

= uu + cc – dd – ss_ _ __

_ _ _ _

_ _ _ _

absolutely NO flavor-changing neutral current terms!

1965 Gellmann & PaisNoticed the Cabibbo mechanism, where was the weak eigenstate,

allowed a 2nd order (~rare) weak interaction that could potentially induce the strangeness-violating transition of

cc sds cossin

K o K

o

a particle becoming its own antiparticle!

u u

s

d s

d

Ko

Ko

W

u

u

s

d s

d

Ko

Ko

W W