Weak Interactions Kihyeon Cho. 2 입자의 표준모형 (The Standard Model)

Weak Interactions

Kihyeon Cho

2

입자의 표준모형 (The Standard Model)

3

기본상호작용

HEP Journal Club

표준모형 (Standard Model)• What does world made of?

– 6 quarks• u, d, c, s, t, b

• Meson (q qbar)

• Baryon (qqq)

– 6 leptons• e, muon, tau e, ,

bsd

bsd

tbtstd

cbcscd

ubusud

VVVVVVVVV

'''

C:\Documents and Settings\cho\My Documents\spring2004\collo\jiggle_animation.gif

What holds it together?(The four interactions)

Weak InteractionsSome Weak Interaction basicsWeak force is responsible for decay e.g. n → pev (1930’s)interaction involves both quarks and leptonsnot all quantum numbers are conserved in weak interaction:

parity, charge conjugation, CPisospinflavor (strangeness, bottomness, charm)

Weak (+EM) are “completely” described by the Standard Model

Weak interactions has a very rich history1930’s: Fermi’s theory described decay.

1950’s: V-A (vector-axial vector) Theory: Yang & Lee describe parity violation Feynman and Gell-Mann describe muon decay and decay of strange mesons

1960’s: Cabibbo TheoryN. Cabibbo proposes “quark mixing” (1963)"explains" why rates for decays with S =0 > S =1

%9.99)(%5.63)( BRKBR

Quarks in strong interaction are not the same as the ones in the weak interaction: weak interaction basis different than strong interaction basis previous example: ),(),( Ls

oo KKKK

Chapter 8 M&S

Chapter 8.2.3 M&S

Weak InteractionsWeinberg-Salam-Glashow (Standard Model 1970’s-today)

unify Weak and EM forces

predict neutral current (Z) reactions

gives relationship between mass of W and Z

predict/explain lots of other stuff!..e.g. no flavor changing neutral currents

existence of Higgs (“generates”mass in Standard Model)

Renormalizable Gauge Theory

But the picture is still incomplete:

must input lots of parameters into the Standard Model (e.g. masses)

where’s the Higgs and how many are there ?

how many generations of quarks and leptons are there ?

mass pattern of quarks and leptons ?

neutrinos have mass!

CP violation observed with quarks!

is there CP violation with leptons?

Weak InteractionsClassification of Weak InteractionsType Comment Examples

Leptonic involves only leptons muon decay ( evv)ee- ee-

Semileptonic leptons and quarks neutron decay (s=0)K+ + (s=1) (b=1)

Non-Leptonic involves only quarks -p & K+ +o

Some details of Weak Interactionsquarks and leptons are grouped into doublets (SU(2))

(sometimes called families or generations)For every quark doublet there is a lepton doublet

B Do

u

d

c

s

t

b

Q2 / 3|e|

Q 1/ 3|e|

e

e

Q |e|

Q 0

Charged Current Interactions (exchange of a W boson)W’s couple to leptons in the same doubletThe W coupling to leptons/quarks is a combination of vector and axial vector terms:

Ju = ugu(1- g5 )u (parity violating charged current)

e

e-

W-

-

W-

-

W-

,

e-

W-

e,

-

W-

e,

-

W-

AllowedNOT Allowed

9

CKM MatrixCKM Matrix

Original 2X2 Cabibbo angleCKM 3X3 Matrix

10

11

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

Universality of weak interactions?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


Weak decays of quarksWeak 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...


Weak decays of quarks Weak decays of quarks (2)(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


Weak decays of quarks Weak decays of quarks (3)(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


Cabibbo theoryCabibbo 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

• 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

Cabibbo theory (2)Cabibbo theory (2)

Cabibbo theory Cabibbo theory (3)(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


Suppression of flavor-changing Suppression of flavor-changing neutral currentsneutral 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?

The GIM MechanismIn 1969-70 Glashow, Iliopoulos, and Maiani (GIM) proposed a solution to theto the K0 + - rate puzzle. 8

90

1064.0

107

)(

)(

KBR

KBR

The branching fraction for K0 + - was expected to be small as the first order diagram is forbidden (no allowed W coupling).

+

u

W+

s

+

d

??0

s

-

K+

allowed

K0

forbidden

The 2nd order diagram (“box”) was calculated & was found to give a rate higher than the experimental measurement!

amplitude sinccosc

GIM proposed that a 4th quark existed and its coupling to the s and d quark was:

s’ = scos - dsinThe new quark would produce a second “box” diagram with

amplitude sinccoscThese two diagrams almost cancel each other out. The amount of cancellation depends on the mass of the new quark A quark mass of 1.5GeV is necessary to get good agreement with the exp. data.

First “evidence” for Charm quark!

Flavor-changing neutral currents Flavor-changing neutral currents (FCNC)(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'

Perkins 7.11

For all neutral current process

0S

GIM mechanism GIM mechanism for FCNC suppressionfor 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.

Perkins 7.11

GIM mechanism GIM mechanism (2)(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'


GIM mechanism GIM mechanism (3)(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

25

quark anti quark quark anti quark …… decay

Time

We are all the children of Broken symmetry

Just tiny deviation from perfect symmetry seems to have been enough

26

27

노벨 물리학상 2008

Citation: 5483

28

Cabibbo AngleCabibbo Angle

29

cossin

sincos

'

'

s

d

s

d

cc

cc

30

bsd

bsd

tbtstd

cbcscd

ubusud

VVVVVVVVV

'''

Vub

31

32

The CKM MatrixThe CKM Matrix

Unitary with 9*2 numbers 4 independent parameters Many ways to write down matrix in terms of these parameters

ud us ub

cd cs cC b

td ts tb

KM

V V V

= V V V

V V V

V


d'

s'

b'

=

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

d

s

b

The CKM matrix can be written in many forms:1) In terms of three angles and phase:

b

s

d

ccescsscesccss

csesssccessccs

escscc

b

s

d

ii

ii

i

132313231223121323122312

132313231223121323122312

1313121312

1313

1313

13

The four real parameters are , 12, 23, and 13.Here s=sin, c=cos, and the numbers refer to the quark generations, e.g. s12=sin12.

This matrix is not unique,many other 3X3 forms inthe literature. This one is from PDG2000.

2) In terms of coupling to charge 2/3 quarks (best for illustrating physics!)

3) In terms of the sine of the Cabibbo angle (12). This representation uses the fact that s12>>s23>>s13.

b

s

d

AiA

A

iA

b

s

d

1)1(

2/1

)(2/1

23

22

32

“Wolfenstein” representaton

Here =sin12, and A, , are all real and approximately one.This representation is very good for relating CP violation to specific decay rates.


9993.09990.010)3.45.3(10)4.14.0(

10)3.47.3(9749.09734.0225.0219.0

10)52(226.0219.09757.09742.0

22

2

3

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

The magnitudes of the CKM elements, from experiment are (PDG2000):

There are several interesting patterns here:1) The CKM matrix is almost diagonal (off diagonal elements are small).2) The further away from a family, the smaller the matrix element (e.g. Vub<<Vud).3) Using 1) and 2), we see that certain decay chains are preferred:

c s over c d D0 K-+ over D0 -+ (exp. find 3.8% vs 0.15%)b c over b u B0 D-+ over B0 -+ (exp. find 3x10-3 vs 1x10-5)

4) Since the matrix is supposed to be unitary there are lots of constraints among the matrix elements:

0

1***

***

tdtbcdcbudub

tdtdcdcdudud

VVVVVV

VVVVVV

So far experimental results are consistent with expectations from a Unitary matrix.But as precision of experiments increases, we might see deviations from Unitarity.

35

Heavy Flavor PhysicsHeavy Flavor Physics

정밀측정으로 표준모형의 검증 => 새로운 물리 현상

Foundation New Physics

Decays of Decays of b b quarkquark

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

For quarks,mass eigenstates weak interaction eigenstatesflavor mixing through CKM matrix

weak interaction

eigenstates

mass

eigenstates

bsd

bsd

tbtstd

cbcscd

ubusud

VVVVVVVVV

'''

very important

for CP study

responsible for

most b decays

CKM matrixCKM matrix

tbtstd

cbcscd

ubusud

VVVVVVVVV

CKMV CKM is 3x3 and unitary

– only 3 generations in the SM

CKM is almost 1, but not exactlyVii 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?

38F. Di Lodovico, ICHEP 2008

Measuring the CKM MatrixMeasuring the CKM MatrixNo one knows how to calculate the values of the CKM matrix.Experimentally, the cleanest way to measure the CKM elements is by usinginteractions or decays involving leptons.

CKM factors are only present at one vertex in decays with leptons.Vud: neutron decay: npev duevVus: kaon decay: K0 +e-ve suevVbu: B-meson decay: B- ( or +)e-ve buevVbc: B-meson decay: B- D0e-ve bcevVcs: charm decay: D0 K-e+ve csevVcd: neutrino interactions: d -c dc

“Spectator” Model decay of D0 K-e+ve

c

u

s

u

e,

e,W

K-D0 Vcs

Amplitude Vcs

Decay rate Vcs

For massless neutrinos the lepton “CKM” matrixis diagonal

Called a “spectator” diagram because only one quark participatesin the decay, the other “stands around and watches”.

Extension of Cabibbo theory Extension of Cabibbo theory to 3 quark generationsto 3 quark generations

Leptons are not involved in the strong interactions

Quarks & Leptons do not change its flavor when interacting 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+

Expt’l determination of CKM elements

Vud

- from nuclear b-decay0008.09735.0 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


• 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



• Vcb: from and HQETeeDB *0

0019.00402.0 cbV


• Vub: from eeB 0

025.0090.0/ cbub VV


• 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)


• Vtd and Vts

(1)

(2)

2

*/*

ts

tdK V

V

KBBR

BBRR

Vtd

Vtd

(s) (s)

Exp. determination of CKM elements & phase (7)

0VVVVVV *** tbtdcbcdubud

tbtstd

cbcscd

ubusud

VVVVVVVVV

CKMV

*VV ubud*VV tbtd

*VV cbcd

1

2

3

References

48

• I.S.Cho’s talk (2008)

• Class P720.02 by Richard Kass (2003)

• B.G Cheon’s Summer School (2002)

• S.H Yang’s Colloquium (2001)

• Class by Jungil Lee (2004)

• PDG home page

(http://pdg.lbl.gov)

• Newton (2009.1)

• Youngjoon Kwon’s Lecture (2003)

Thank you.