Particle Physics II

Chris Parkes

Heavy Flavour Physics

• Weak decays – flavour changing

• Mass states & flavour states

• GIM mechanism & discovery of charm

• CKM matrix

3rd Handout

2

Weak decays• Weak decays are mediated by:

– W bosons charged current interactions

– Z bosons neutral current interactions

• Weak interaction does not respect conservation of flavour flavour changing interactions are possible

• Will discuss how this happens and difference between flavour changing charged (W±) currents, and neutral (Z0) currents

3

Weak Decays: Charged currents

ee

s

c

d

u

e e

W

Wc s

W

u d

W

gW

gWgW

gW

ud vertex: allowed us vertex: not-allowed but observed!

Have vertices:

Assume quarkshave similar vertices:

ud - us K

Consider observed reactions:

d

u W

-

-

s

u W

-

K-

4

Mass States & Flavour states• ‘flavour’ state is a superposition of the ‘mass’ states

– Flavour states = states that couple to W– Mass states = states of definite mass, ‘free’ quark states

b

s

d

b

s

d

'

'

'

Flavour massd

d’

ss’

θC

θC is known as Cabibbo angle

5

Quark mixing: udsc quarks

cc

cWuscWud

cc

sududu

gggg

sdd

sincos'

sin cos

sincos'

2.08.12

004.0277.0tan 22

2

c

cud

us

g

gK

u d’

W

gW

u s

W

gus

u d

W

gud= +

Flavour states as mixture of mass states:

cc

cwcscwcd

cc

scdcsc

gggg

sds

cos sin'

cos sin

cossin'

udW preferred to usW

6

Cabibbo-allowed/suppressed decays(2 generations)

20

1tan2 c

cs

cd

ud

us

g

g

g

g

gus and gcd are Cabibbo suppressed with respect to gud and gcs

e.g. consider Cabibbo-allowed decays of charm quarks, D+:cs+l+ and cs+u+dbar

Charmed meson decays most commonly include strange mesons

Also explains c decays to Kbars (cs+u+dbar) preferred to c decays to K (cd+u+sbar)

Example of: (p270 Bettini) )(

)(0

0

KD

KKD

7

Weak decays: neutral currents

• But measure strangeness changing

1S cossin

0S sincos

''

0

2020

0

cc

cc

sdsdZ

ssZddZ

ddZ

Z

u u

Zd’ d’

Z

l l

Z

gZ

gz gZ

gZ

82

10

010

100.5

105.1

K

K

Why no flavour changing neutral currents (FCNC)?

p261 BettiniCharged current W

neutral current Z

8

GIM Mechanism: Add in charm

ssZddZssZddZ

sdsdZ

ddZssZ

ssZ

sdsdZ

ssZddZ

ddZ

dssd

u

cc

cc

cc

cc

cccc

0000

0

2020

0

0

2020

0

''''

cancel components changingFlavour

1S cossin

0S sincos

''

1S cossin

0S sincos

''

sincos

c

sincos

charm...th doublet wiquark another Introduce

u u

Zd’

Z

gZ

gZ

c c

Zs’

Z

gZ

gZ

d’ s’

No flavour changing neutralCurrents (FCNC)

Glasgow, Iliopoulos, Maiani 1970, used this to suggest another quark was needed

(at tree level in SM)

9

Discovery of charm• Introduction of charm solved FCNC problem• Cancellation of FCNC predicted mass of charm to be ~1.5-2GeV

• Charm observed as J/ψ=cc in 1974

Ψ: R-measurement in e+e-

J: Hadron production p+BeJ+X

10

Charmonium – charm width• p+N: Experimental resolution hides small width

in mass reconstruction• e+e-: Extract width from line shape of resonance

– 91 keV, small width, large lifetime– Strong decay - Why so small width ?

• 1 gluon – 2* mass D > m ψ• 2 gluon – ψ C=-1, g C=-1

• 3 gluon allowed but s3

g

c

c

u

u

c

c

D0

D0

Not possible energetically for ψΨ’’ allowed 24MeV width

gc

c

d

d

u

u

Allowed

d

dπ-

π+

π0

11

Generalise mixing to 3 Families: CKM Matrix

• Generalise cabibbo matrix

• To three generations

s

d

s

d

cc

cc

cossin

sincos

'

'

KobayashiMaskawa

2008 Nobeldecays-bat look

100

0cossin

0sincos

'

'

'

b'b

Vgg

b

s

d

VVV

VVV

VVV

b

s

d

cc

cc

abWab

tbtstd

cbcscd

ubusud

12

Measuring Elements

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

Vud -decay (ud)

Vus K-decays (su)

Vub B-decays (bu) rare difficult to measure, B-factories have improved this

Vcd production of charm of valence quarks in -DIS

Vcs Semi-leptonic D-decays (cs)

Vcb B-decays (bc)

Vtd top-decay limits

Vts top-decay limits

Vtb top-decays tWb

See Bettini p265 et seq

13

Example: W decays revisitedu d

W

Vud

u s

W

Vud

u b

W

Vud

c d

W

Vud

c s

W

Vud

c b

W

Vud

In branching fraction calculation we assumed Vud=Vcs=1, and neglected othersQ) Why did we get answer right ?

2

abV

14

CKM Unitary

1

1

1

1

100

010

001

222

222

222

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

VV

And six equations of off-diagonal elements=0, e.g. 1st row * 3rd column:

For probability elements need only be real, but for CP violation (see next) need to be complex

Q) If the measurements of these were to add to < 1, how would you interpret this?

0*** tbtdcbcdubud VVVVVV