Lecture 11: Weak Interactions Cross-Section and the W Coupling The Cabibbo Angle and the CKM Matrix Parity Violation Kaons and Mixing CP Violation Sections.

Lecture 11: Weak Interactions

• Cross-Section and the W Coupling

• The Cabibbo Angle and the CKM Matrix

• Parity Violation

• Kaons and Mixing

• CP Violation

Sections 4.51, 8.1, Chapter 10

Useful Sections in Martin & Shaw:

(from ''Telephone Poles and Other Poems," 1963)

Neutrinos, they are very small. They have no charge, they have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass...

John Updyke

in fact, point-like in the Standard Model

and little(< 2eV)

hardly

true

should not be takento indicate a sensitive detection technique

interaction cross-sectionmuch higher than for typical neutrino energies

obvious foreshadowingof electroweak theory

Cosmic Gall

+e (Pauli)

Beta Decay

n p + e

(Pauli)

''Inverse" Beta Decay

e + p n + e+

~ 2 /c

''cross-sectional area" of wave packet

time spent by wave packet in presence of the proton

typical timescale for weak interaction to occur

e + p n + e+Inverse -decay:

(Pontecorvo)

From standard -decay, the lifetime of the free neutron is ~ 1000 s and the energies of the e and

e are ~ 1 MeV

= h/p ≃ 1200fm = 1.2x1010cm

thus, ~ (1.2x10-10cm)3/[(3x1010 cm/s)(1000s)] ~ 1043cm2

Note E3t1 and, from previous discussion, t1 E5

~ 1043 (EMeV

)2 cm2 Almost exactly right!(and very, very small!!!)

Interaction Length for a 1 MeV Neutrino in Lead

~ 10-43 cm2 (per proton)

= (11.4 g/cm3) x [1/(207 g/mole)]x (6.02x1023 atoms/mole)

x (82 protons/atom)

= 2.7x1024 protons/cm3

= 1/(2.7x10-19) cm

= 3.7 x 1018 cm = 4 light-years !!

n p + e- + e

ep n +

e+

Reines and Cowan, 1956

(Nobel Prize – 1995 !!)

Parity Violation in Weak InteractionsFirst suggested in 1956 by Lee & Yang based on review of kaon decay modes

60Co

e

60Co

e

Pnuclear spins aligned by cooling to 0.01 oKin a magnetic field

Should be the same under parity transformation, but fewer electrons are actually seen going forward !

Directly observed by Wu et al. in 1957 from the decay 60Co 60 Ni* + e +

e

(1.173 MeV) + (1.332 MeV)

(degree of polarisation determined from the anisotropy of -rays)

Garwin, Lederman & Weinrich (1957)

e+

e

+

+

precesspolarised muons(polarised)

Also, in 1958, Goldhaber et al. measured the helicity of the neutrino:

e + 152Eu(J=0) 152Sm*(J=1) + e

152Sm(J=0) +

events were chosen with the final states collinear and

e travel in opposite directions, so helicity

of the neutrino is found from that of the gamma

all neutrinos are left-handed !

Leon Lederman, Melvin Schwartz and Jack Steinberger, 1962

Neutrinos of the ''Second Kind"(not as popular as the Spielberg sequel)

Assume some Yukawa-like exchange process is at work.

Weak interactions obey a simple symmetry :

So, for example, for the process + (pion decay):

but, unfortunately, it is foundexperimentally that the couplingsare not the same!

W

ud ≃ 0.95 W

d

u

W

W

It can change ud (like -decay) sc tb

and, for leptons, ee

-decay (np+e+e) tells us the exchange particle must

be charged

s

u

W

Another hitch:

shouldn’t occur, but does ! (albeit infrequently)

We can explain all this (or, at least, parameterize our ignorance)by adopting the somewhat bizarre notion that the weak interactionactually couples to mixtures of quarks.

So, initially just considering the first twogenerations, the relevant quark doublets are:

ud

cs( ) and ( )

where d d cosC + s sin

C

s d sin

C + s cos

C

C ''Cabibbo angle"

or, alternatively d s sinC + d cos

C

s s cos

C + d sin

C

W

ud = W

cos2C

W

us = W

sin2C

~ 1/20 C = 12.7 + 0.1 degrees )

= tan2

C

(The factor of 1/20 delineates ''Cabibbo-suppressed" and ''Cabibbo-allowed" processes)

Generalizing to 3 generations and all possible mixings between quarks:

dsb

Vud

Vus

Vub

Vud

Vus

Vub

Vud

Vus

Vub

dsb( ) [ ] ( )=

(Cabibbo, Kobayashi and Maskawa)

CKM matrix

W

us

W

ud

=

Kaons: Ko = ds Ko = sd (S = +1) (S = 1)

But S is not conserved in weak interactions so Ko-Ko mixing can occur:

u

u

d

s

s

d

W+ WKo Ko

We can thus define two orthogonal mixtures:

K1

o = 1/2 ( Ko + Ko )

K2

o = 1/2 ( Ko Ko )

Note: C P K1

oK1

oand C P K2

oK2

o

K1

o + ; o o

K2

o + o ; o o o

Allowed

K1

o + o ; o o o

K2

o + ; o o

Forbidden

Experimentally, 2 kaon states are observed with different lifetimes:

KS

o ; o o ≃ 9x1011s

So we associate KS

o K1

o and KL

o K2

o

However, in 1964, Christenson, Cronin, Fitch & Turlay discovered

KL

o +

(branching ratio ~ 2x103)

KL

o ; o o o ; lepton () ≃ 5x10s

30 GeVprotons

steeltarget

beamcollimator

magnets sweeps out charged particles

lead-glass cutsout photons

KS+K

L KL

18 m

KL beam

direction

CM of + pair

KS

o = 1/ ( K1

o K2

o )

KL

o = 1/ ( K1

o + K2

o )

where small complex number parameterizing the size of the CP violation

(experimentally, ≃ 2.3x103 )

What does this mean??

Reason for antimatter assymmetry ??

Perhaps we can learn more from studyingCP violation in other particle systems...

Basically comparethe rates for

B0 = + KS

0

(+ mode)

B0 = + KS

0

versus

(+ mode)

dsb

Vud

Vus

Vub

Vud

Vus

Vub

Vud

Vus

Vub

dsb( ) [ ] ( )= ??

CP violation could be parameterized as partof the mixing angles in the CKM matrix

Unitarity of the matrix is needed to allow for local gauge symmetry

Which imposes constraints on the angles:

''Unitarity Triangle"

Matter-Antimatter Asymmetry Revisited:

Sakarov Conditions (1967)

1) Baryon Number Violationallows baryons and anti-baryons to appearand disappear independently of each other

2) CP Violationso the rate of appearance/disappearance of baryons is different from anti-baryons

EstablishesAsymmetry

3) Non-Equilibrium Conditionssince equilibrium would then tend to''average-out" any asymmetry

Locks InAsymmetry

!!!(GUTs)