particle physics ii
DESCRIPTION
Particle Physics II. 4th Handout. 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. - PowerPoint PPT PresentationTRANSCRIPT
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)
11
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
12
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
13
C P
CPParity InversionSpatialmirror
Charge InversionParticle-antiparticlemirror
14
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
15
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
16
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 -
17
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
19
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
20
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
21
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
22
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
23
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:
24
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
26
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