Particle Physics II

Chris Parkes

CP Violation

•Parity & Charge conjugation

•Helicity of the neutrino

•Particle anti-particle oscillations

•CP violation measurement in Kaons

•CP violation theory in CKM matrix

•Predicting b-quark

•Distinguishing Matter & Anti-matter

•Sakharov conditions

4th Handout

2

Matter and anti-matter asymmetry: CP-violation

• CP-violation is violation of charge conjugation and parity– distinguishes between matter and antimatter

• Not just a naming convention

– Responsible for matter-antimatter asymmetry in Universe• Equal amounts of matter & anti-matter in the big bang

• Elements– Parity violation– Charge conjugation and parity violation in muon decay, CP

conservation– Mixing in the K0 system– CP violation in the K0 system

3

Parity and charge conjugationParity is spatial inversion and reverses vectors r-r; p-pP operator acts on a state |(r, t)>

),(),(

),(),(

2 ttP

ttP P

rr

rr

Hence for eigenstates P=±1

(r, t)>= cos x has P=+1, even

(r, t)>= sin x has P=-1, odd

(r, t)>= cos x + sin x, no eigenvalue

Charge conjugation (C) particles anti-particlesreverses: charge, magnetic moments,

baryon number, strangenessOnly particles that are their own anti-particles are eigenstates of C (e.g. photon, π0, J/ψ…)

Revision

4

Parity Violation in weak interactions

The “ -” puzzle (1950s)• Two particles +, (21%) P =+1 ++-, (6%) P=-1• found to have same lifetime and mass

same particle? BUT opposite parity• Actually K+ weak decay• Led Lee and Yang to propose that parity may

not be conserved in weak interactions

Revision

5

Observation of parity violation

B field

e- (E,-p)

Co60Nuclei

spin aligned

Beta decay to Ni*60

e- (E,p)

Parity

JJ

Search for parity violation in -decayNeed to observe parameter that is sensitive to parity

•scalars aa •Vectors p-p•Pseudo-scalar pa.pbpa.pb

•Axial-vector L.p-L.p combination of momentum and spin• Measure <J>.pe = angular distribution of electrons with respect to nuclear spin

Rate ≠ Rate

60Co60Ni*+e-+e

Use from Ni*Ni to monitor spin alignment

Revision

JprJP

prJ

)()()(Spin parity:

6

Operating with P on this reverses p, not spin, produces a right-handed neutrino.Do not observe:

Helicity and the neutrinoIn angular momentum we choose the axis of quantisation to be the z axis.Lets choose this axis along the particle momentum direction.Helicity is the component of the spin along the momentum direction.•A spin ½ particle can thus have helicity +1 (ms=+ ½) or –1 (ms=- ½ ) E

pσ ˆˆ

Not so interesting for a massive particle, as not Lorentz invariant, but consider the neutrino.

p

s+1 -1

p

sRight-handed Left-handed

1) Only left-handed neutrinos exist and right-handed anti-2) Helicity is a pseudo-scalar

Operating with C on this produces a left-handed anti-neutrino.Do not observe: LLC ˆ

RLP ˆ

RRC ˆ

LRP ˆ

Operating with C and P on this produces a right-handed anti-neutrino.Do observe! RRL CPC )(ˆ)ˆ(ˆ

Weak force violates Parity, but CP OK?

7

Measuring Helicity of the Neutrino

152 152 * 152Eu Sm Sm (960 KeV)

J=0 1 1/2 0 1

ee

152 * 152Sm Sm

J= 1 0 1

Goldhaber et. al. 1958

Electron captureK shell, l=0

photon emission

Consider the following decay:Consider the following decay:

Eu at restSelect photons in Sm* dirn

Neutrino, SmIn opposite dirns

e-

•Momenta, p

•spin

OR

S=+ ½

S=- ½Left-handed

S=+ 1

S=- 1

right-handed

Left-handed

right-handed

•Helicities of forward photon and neutrino same•Measure photon helicity, find neutrino helicity

Bettini p252

8

Neutrino Helicity Experiment• Tricky bit: identify forward γ • Use resonant scattering!

• Measure γ polarisation with different B-field orientations

152 152 * 152Sm Sm Sm

magnetic field

Pb

NaI

PMT

152Sm152Sm

152Eu

γγ

Fe

Similar experiment with Hg carried out for anti-neutrinos

Vary magnetic field to vary photon absorbtion.Photons absorbed by e- in iron only if spins of photon and electronopposite.

)2

1()

2

1()1(

)2

1()

2

1()1(

'

ee SSS

Forward photons,(opposite p to neutrino),Have slightly higher p than backwardand cause resonant scattering

Only left-handed neutrinos exist

9

C P

CPParity InversionSpatialmirror

Charge InversionParticle-antiparticlemirror

10

Particle anti-particle oscillations• Neutral Mesons can oscillate into

Anti-particles: K0↔ K0, (also B0, B0s, D0)

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K0-mixingmixing 00 KK

Strangeness is violated in weak decaysK0 and K0 can mix via diagrams

-1CP and

1CP and

-1CP 2

1

1CP 2

1

000002

0001

0002

0001

ππππππK

ππππK

KKK

KKK

)1( );1( 00 SsdKSsdK

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CP-violation• Observed states are:– Ks

0 Essentially K10 CP=+1

• short lifetime 89ps– KL

0 Essentially K20 CP=-1

• long lifetime 51ns (due to available energy)• BUT

– KL0 (CP=-1) (CP=+1)

• is observed CP is violated in weak decays

02

012

0

02

012

0

1

1

1

1

KKK

KKK

L

S

Observed states are now mixtures

of CP=+1 and CP=-1 states

Experimentally ||=2.3x10-3, so CP violation small effect

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C P

CPParity InversionSpatialmirror

Charge InversionParticle-antiparticlemirror

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CPT theorem

• T is time reversal transformationt-t

• A general theorem states that in any relativistic quantum theory in which signals cannot travel faster than the speed of light, CPT must be an invariant

• CP is violated T must also be violated

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CPLEAR- some parameters•Beam – 106 anti-protons /s into Hydrogen target•Fast online trigger selection of events ~ 103/s•Ability to separate charged pions / kaons using Cherenkov, dE/dx, Time of flight

discriminate in momentum range 350-700 MeV/c•Can detect and reconstruct Ks vertex to ~ 60 lifetimes c~2.6 cm•Observe events over ~ 4•Magnetic field (0.4T) and tracking leads to particle momentum determination• (~5% accuracy)

Kaon OscillationKaon Oscillation

Rate difference Ko Ko Ko Ko is T violation

d

su, c, t W

W_

s

d_u, c, t

ds

u, c, tW W

_ sd_

u, c, t___

K0K0

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1) Identify Ko / Ko at production:produced in association with K+/K-

2) Identify Ko / Ko at decay from charge of lepton:

CPLEAR T invariance test

KK

KKpp

0

0

(S = 0)

)su(K

)su(K

Get positron: Or electron:

fKfK

fKfKf RR

RRA

00

00measure

(S = 0)

s

d

Ko

u

d

e-

ν

W-

s

d

Ko

u

d

e+

ν

W+

π+π -

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Experiment at LEAR ring

at CERN 1990-1996

Pions from kaon decay

18

Discovery of T violation• Currently the only direct observation of T violation

– Measure asymmetry in rates

3106.16.6 TA

CPLEAR,1998

)()(

)()(0000

0000

KKRKKR

KKRKKRAT

Number of lifetimes

•T, or equivalently CP, violated by this tiny amount

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CP violation in SM• How do we include CP violation CKM matrix ?

**

tstdcscdVVVVM fi

d

sc W

W_

s

d_t K0

K0

d

s

cWW

_s

d

_

t K0

K0

One diagram only for simplicity

***' fifi MVVVVMtstdcscd

Hence difference in rates:

)(2)()( *0000fififi MMMKKKK

CP violation introduced by making CKM matrix terms complex

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Number of Parameters in CKM• n x n complex matrix,

– 2n2 parameters

• Unitarity n2 constraints– n2 parameters

• Phases of quark fields can be rotated freely – (n-1)2 parameters (remove one per row)

• Real parameters, rotation (Euler) angles – n(n-1)/2 real

• Phases– (n-1)(n-2)/2 phases

ikjkj

ijVV *

n=2, 1 real, 0 phasen=3, 3 real, 1 phase

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K&M Predict 3 famillies (Prog. Theor. Phys. 49, 652(1973) )

• Only 3 quarks discovered– Charm predicted by GIM mechanism – CP violation discovered

• Hence predict three (or more) famillies!

Discovery of b quarkp+(Cu,Pt)Υ(upsilon) +X Similar to J/ψ discovery. At Fermilab 1977

Precision measurements in e+e-

Again narrow resonancesΥ (1s), Υ (2s), Υ (3s),

b bbar3S1 states of bottom ‘atom’

Cornell

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CKM – Unitarity Triangle

*cbcdVV

0*** tbtdcbcdubud VVVVVV

*

*

cbcd

ubud

VV

VV

•Three complex numbers, which sum to zero•Divide by so that the middle element is 1 (and real)•Plot as vectors on an Argand diagram•If all numbers real – triangle has no area – No CP violation

Real

Imag

inar

y

•Hence, get a triangle‘Unitarity’ or ‘CKM triangle’•Triangle if SM is correct.

Otherwise triangle will not close,Angles won’t add to 180o

*

*

1cbcd

cbcd

VV

VV

*

*

cbcd

tbtd

VV

VV

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Unitarity conditions ikjkj

ijVV *

hence 6 triangles in complex plane

123

1

i

ijV j=1,3

No phase info.

3

1

* 0i

ikijVV j,k =1,3 jk

0

0

0

0

0

0

***

***

***

***

***

***

cbubcsuscdud

tbcbtscstdcd

tbubtsustdud

tstdcscdusud

tbtscbcsubus

tbtdcbcdubud

VVVVVV

VVVVVV

VVVVVV

VVVVVV

VVVVVV

VVVVVVdb:

sb:

ds:

ut:

ct:

uc:

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CKM Triangle - Experiment• Find particle decays that are sensitive to

measuring the angles (phase difference) and sides (probabilities) of the triangles

•Measurements constrain the apex of the triangle•Measurements are consistent

•CKM model works, 2008 Nobel prize

25

B-mixing• Mixing also possible in the neutral B/D-systems

– B0d

– B0s (discovered 2006)

– D0 (discovered 2007)

• B-system is best laboratory forCP violation studies

– heavy system allows calculations– ‘long lifetime’

• CP violation observed in B-system– Babar/Belle (2000)– LHCb: New physics in loops

b s

-

u,c,t

Rate depends on top quark mass

C. Parkes, P.Soler

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CP Violation:Why is it interesting ?

• Fundamental: The Martian test– C violation does not distinguish between matter/anti-

matter. LH/RH are conventions– CP distinguishes matter from anti-matter

– CP says preferred decay KLe+ve-

• Least Understood: CP Violation is ‘add-on’ in SM– Parity violation naturally imbedded in coupling structure– CP requires a complex phase in 3 generation CKM

matrix, allowed but not natural

27

CP: Why ? cont.• Powerful: delicately broken symmetry

– Very sensitive to New Physics models– Historical: Predicted 3rd generation !

• Baryogenesis: there is more matter !• N(antibaryon) << N(baryon) << N(photons)

– Fortunately! 1 : 109

• Sakharov (1968) Conditions– Baryon number violation– CP violation– Not in thermal equilibrium

• Problem– Not enough CP violation in CKM !

Assuming not initial conditions,

but dynamic.Cannot allow all inverse reactions to have happened

28

backup

29

Muon decay

0

invariance-P coscos

invariance-C

invariance-C

cos3

121

e

e

e

e

By C-invariance cannot distinguish between particle and anti-particle

• identical lifetimes• identical decay distributions

P-invariance the rate should be the same for and –

Results show both C and P invariance are violatedBUTLifetimes are the same C respected for this

P

± ±e±

e±

Consider muon decay

04.000.1

Experimental results

30

Muon decayResults show both C and P invariance are violatedBUTLifetimes are the same C respected for this

Solution:CP is conserved (almost!) in weak interactions

Under C + -

Under P -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

cos(theta)

Muo

n de

cay

rate

invariance-CP

invariance-CP

coscos