1 intro. to elementary particle physics y. kwon 11/24/2003 universality of weak interactions? n do...

Intro. to elementary particle physics Y. Kwon 11/24/2003

1

Universality of weak interactions?

Do all leptons and quarks carry the same unit of weak charge?– Yes, for leptons and no for quarks

for quarks, the couplings to the weak gauge bosons depend on the quark flavors, due to “quark-mixing” CKM mechanism

W e

eeg


2

Weak decays of quarks

Consider the (semileptonic) weak decay

een

eeus eepn

eeud 1S 0S

20

1

)(

)(

e

e

pen

ne

Assuming universality of weak decays of quarks,

we expect both decays would happen in similar rate, but...


3

Weak decays of quarks (2)

s u

W e

e

dd

dd

p

usg d u

W e

e

ud

n ud

p

udg

)1(20

1

)(

)(2

Og

g

ued

ues

ud

us

e

e


4

Weak decays of quarks (3)

So, what are we going to do?Discard the universality of weak interaction?

It was also noticed that the value of the Fermi constant GF deduced from nuclear -decay was slightly less than that obtained from muon decay.

d u

W e

e

ud

n ud

p

udg

2

4

2

2/ 2

2

22

2

F

WW

G

m

g

qm

g

eeM

W e

e


5

Cabibbo theory

Try to keep the universality, but modify the quark doublet structure…

Assume that the charged current (W) couples the “rotated” quark states

where d’, s’ (weak interaction eigenstates) are linear combinations of mass eigenstates d, s

'du

'sc

sd

sd

cc

cc

cossinsincos

''

angle Cabibbo"" angle mixingquark the:c


6

Cabibbo theory (2)

What we have done is to change our mind about the charged current: “Cabibbo-favored” vs. “-suppressed”

effective weak coupling for S=0 (duW) is cos c

effective weak coupling for S=1 (suW) is sin c

)1(20

1

cos

sin

)(

)(22

Og

g

ued

ues

c

c

ud

us

e

e

o12 c

Wu

d

Wu

sccos csin

q'q

c


7

Cabibbo theory (3)

(Ex) What is the relationship between the weak couplings for muon decay (G=GF) and nuclear -decay (G) ?

d u

W e

e

ud

n ud

p

W e

e

ccos

cGG cos25

25

GeV 10)003.0136.1(

GeV 10)00001.016639.1(

G

G


8

Suppression of flavor-changing neutral currents

a very stringent suppression of flavor-changing neutral current reactions

)%08.017.3()(

10)5.1()(0

104.32.1

KBF

KBF

(Ex) Draw the decay diagrams for the above two reactions!

Is it easy to understand this stringent suppression?


9

Flavor-changing neutral currents (FCNC)

Neutral-current reactions for (u,d’) quarks

cccc sddsssdduu cossin)()sincos( 22

0S 1S

In this picture, FCNC is perfectly allowed by theory ???

0Z

u

u

0Z

CC sdd sincos'

CC sdd sincos'


10

GIM mechanism for FCNC suppression

In 1970, Glashow, Iliopoulos & Maiani (GIM) proposed the introduction of a new quark of Q=+2/3, with label c for ‘charm’.

With this new quark, a second quark doublet is also introduced.

, sincos'

cc sdu

du

cc dsc

sc

sincos'

Then we have additional terms for the neutral current reactions.


11

GIM mechanism (2)

cccc

cccc

sddsssddcc

sddsssdduu

cossin)( )cossin(

cossin)( )sincos(22

22

ccssdduu FCNC has disappeared!

0Z

u

u

0Z

CC sdd sincos'

CC sdd sincos'

0Z

c

c

0Z

CC dss sincos'

CC dss sincos'


12

GIM mechanism (3)

At the price of a new quark ‘charm’ and another quark doublet, the (experimentally) unwanted FCNC has been removed!

Later, in 1974, the bound state of charmanti-charm was discovered: J/

Indeed, just before this discovery, it had been possible to estimate the mass of the new quark!!

by considering mixing00KK


13

Extension of Cabibbo theory to 3 quark generations

Leptons are not involved in the strong interactions Quarks & Leptons do not change its flavor when i

nteracting with neutral gauge bosons– quarks do not change flavor under strong int.

– leptons & quarks do not change flavor when interacting with or Z0

– leptons & quarks change flavor only when interacting with W, and only within its family

LLLb

t

s

c

d

u

'''

W

t b'

W+


14

Decays of b quark

Then how does b decay at all?Note: b Wt but m(t) >> m(b)

For quarks,– mass eigenstates weak interaction eigenstates

– flavor mixing through CKM matrix

weak interactioneigenstates

masseigenstates

bsd

bsd

tbtstd

cbcscd

ubusud

VVVVVVVVV

'''

very importantfor CP study

responsible formost b decays


15

CKM matrix

tbtstd

cbcscd

ubusud

VVVVVVVVV

CKMV CKM is 3x3 and unitary

– only 3 generations in the SM CKM is almost 1, but not exactly

Vii 1, Vij 0 for i j

)( phase 1 and ),,( parameters real 3

)1.0(

1)1(2/1

)(2/1

23

22

32

CKM

A

O

AiAA

iA

V

How do we determine the CKM matrix elements?


16

Expt’l determination of CKM elements

Vud

– from nuclear -decay 0008.09735.0 udV

Vus

– from– results of K+ and K0 decays agree

eeK 0023.02196.0 usV

Vcd

– from charm meson production via neutrino scattering

cd 016.0224.0 cdV


17

Vcs

– from semileptonic decay of D meson– unitarity constraint assuming only 3 generations gives a much tighter bound

11122s 1054.1)0( csDe VfeKD

16.004.1 csV



18


Vcb: from and HQETeeDB *0

0019.00402.0 cbV


19


Vub: from eeB 0

025.0090.0/ cbub VV


20


Vtb: from t-quark decay, assuming only 3 generations

• at the Tevatron collider at Fermi Lab, top quarks are produced mainly in pairs• Assuming one could obtain a pure sample of tt

b

b

NN

N

WqtBR

WbtBRR

/events taggedevents untagged

/events tagged

CL %90 80.015.099.0 29.099.0 3gen tbVR

(Ref. hep-ex/9707026)


21

Vtd and Vts

(1)

(2)

2

*/*

ts

tdK V

V

KBBR

BBRR

Vtd

Vtd

(s) (s)



22

Exp. determination of CKM elements & phase (7)

0VVVVVV *** tbtdcbcdubud

tbtstd

cbcscd

ubusud

VVVVVVVVV

CKMV

*VV ubud*VV tbtd

*VV cbcd

1

2

3

1 intro. to elementary particle physics y. kwon 11/24/2003 universality of weak interactions? n do...

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