Symmetry and Symmetry Violation in Particle Physics
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Transcript of Symmetry and Symmetry Violation in Particle Physics
Summary Lecture 3• CP is violated in Weak-Interactions
– Neutral Kaon mass-matrix induced; scale 2x10-3
– Direct CPV in KL; scale = ’ = 1.6 x 10-3 • Observing CPV requires:
– Two interfering amplitudes– One with a CP-violating weak phase – Another “common” or “strong” phase
• In the W.I., the d and s quark mix d’ & s’– d’ =coscd +sin s; s’ =-sincd +coscs– c 120 is the “Cabibbo angle
• If all quarks are in pairs, FCNC = 0 by Unitarity – (GIM Mechanism)
CP: matter
W
gCP( ) =
For CPV: g g* (charge has to be complex)
CP operator:“charge”
antimatter
W†qg* q’
mirrorsome basic process
CP violating asymmetries in QM
• Even if CP is violated, generating matter-antimatter differences is hard– need a CP-violating phase ()– need 2 (or more) interfering
amplitudes– + a non-zero “common” phase () (often called a “strong” phase)
Common and weak phases“Common” (strong) phase (): same sign for
matter & antimatter CP conserving Weak phase (): opposite sign for matter
& antimatter CP violating
BA+B
A
BA+B
|B|eii B = |B|ei-i
How does CPV fit into the Standard model?
Clue: CPV is seen in strangeness-changing weak decays.
It must have something to do with flavor-changing Weak Interactions
how about a complex mixing matrix?
-
incorporate CPV by making complex?
(i.e. ≠*?)
not so simple: a 2x2 matrix has 8 parameters
unitarity: 4 conditions
4 quark fields: 3 free phases
# of irreducible parameters: 1
Cabibboangle
suGF
W
controls |S|-1where we see CPV
1001
*
*
2-generation flavor-mixing
-Only 1 free parameter: the Cabibbo angle
C120
not enough degrees of freedom to
incorporate a CPV complex phase d
s d’s’
cosCsinC
sinC cosC
Enter Kobayashi Maskawa a 3x3 matrix has 18 parameters
unitarity: 9 conditions
6 quark fields: 5 free phases
# of irreducible parameters: 4
3 Euler angles +1 complexphase
100010001
UU t
Original KM paper (1973)
From: Prog. of Theor. Phys. Vol. 49 Feb. 2, 1973
CP-violating phase3 Euler angles
3 quarks:
31
32
d
uq=2/3
q=1/3
1964-1974
3x3 matrix 3 generations, i.e. 6 quarks
s1/3
KM paper was in 1973, the 3-quark age
31
32
s
c
Predicted by Glashowbut not discovereduntil Nov.1974
31
32
b
t
These were not evenin our 1973 dreams.4 quarks:
6 quarks:
A little history
• 1963 CP violation seen in K0 system• 1973 KM 6-quark model proposed• 1974 charm (4th ) quark discovered• 1978 beauty/bottom (5th) quark discovered• 1995 truth/top (6th) quark discovered
CKM matrix (in 2008)
bsd
VVVVVVVVV
bsd
tbtstd
cbcscd
ubusud
'''
CPV phases are in the corners
t
d
W+
Vtd
bVub
W+
* u
• What are B mesons?– B0 = d b B0 = b d
– B = u b B = b u– JPC = 0
– = 1.5 x 10-12 s (cm)• How do they decay?
– usually to charm: |bc|2 |bu|2 100• How are they produced?
– ee (4S) B B is the cleanest process
Lesson 1: Basic properties
u-2/3b+1//3u+2/3 b-1/3
d+1/3b-1/3
b+1//3d-1/3
Lesson 2: “flavor-specific” B decays
In >95% of B0 decays: B0 and B0 are distinguishable by their decay products
X l
X lB0 B0
semileptonic decays:
D X
D XB0 B0
hadronic decays: qC+2/3
D
qC+2/3
D
Lesson 3: B CP eigenstate decaysIn ~1% of B0 decays: final state is equally accessible from B0 and B0
J/KS
J/KL
…
B0 B0
charmonium decays:
K+K
…
B0 B0
charmless decays:
C-2/3C+2/3
J/
JPC=1--
CP=+
Lesson 4: The (4S) resonance
(ee BB) 1nb• B0B0B+B• good S/N: (~1/3)• BB and nothing else• coherent 1-- P-wave
3S bb bound states
(e
e )
had
rons
BBthreshold
e+eqq continuum (u, d, s &c)
10.58GeV
Lesson 5: B0 B0 mixing
V*td
V*td
These have a weak phase: 1
A B0 can become a B0 (and vice versa)
_
u,c,t
u,c,t
b
d
d
b
tb
tb
(only short-distance terms are important)
b u dVub Vud
b c dVcb Vcd
b t dVtb Vtd
* * *bd:
Ά =VubVud f(mu) + VcbVcd f(mc) + VtbVtd f(mt)* * *
GIM: VubVud + VcbVcd + VtbVtd = 0* * *
Ά = 0 if: mu = mc = mt
Large mt overides GIMbut, mt >> mc & mu: GIM cancellation
is ineffective
B0 B0 mixing transition is strong(and this allows us to accesses Vtd)
V*td
V*td
t-quarkdominat
es
Y.H. Zheng, PhD ThesisAlso Y.H. Zheng et al., Phys Rev. D 67 092004 (2003)
N(B
) –
N(B
) N
(B)
+ N
(B)
Neutral meson mixing phenomenology
Neutral B mesons are producedas flavor eigenstates: B0 or B0
B0(t)
B0(t)B0(t)
B0(t)
B1 & B2
|B1> = p |B0> + q |B0>
|B2> = p |B0> - q |B0>
If CPV is small: q ≈ p ≈1/2
Time dependence of B0 (B0) mesons
( pq1/√2 )
|B0 (t)> = ( |B0> (1+eimt)+ |B0>(1-
eimt))e-t
|B0 (t)> = (|B0>(1+eimt)+ |B0>(1-eimt))e-t
common phase
m = m2-m1
B0
Interfere BfCP with BBfCP
td
td
B0
Vtb
V*
Vcb
KS
J/
J/
KS
V*2
Vtb
V*td
td
Vcb
B0B0
Sanda, Bigi & Carter:
+sin21
eimt
What do we measure?
t z/cβγ
Flavor-tag decay(B0 or B0 ?)
J/
KS
B - B B + B
e
e
more B tagsmore B tags
zt=0
fCP
(tags)
sin21
This is for CP=-1; for CP=+1, the asymmetry is opposite
Asymmetric energies
Requirements for CPV• Many B mesons
– “B-factory” & the ϒ(4S) resonance
• Reconstruct+isolate CP eigenstate decays– Kinematic variables for signal +(cont. bkg suppr+PID).
• “Tag” flavor of the other B
• Measure decay-time difference– Asymmetric beam energies, high precision
vertexing(Δz)– Likelihood fit to the t distributions
The PEPII Collider (magnetic separation)
9 x 3.0 GeV; L=(6.5 x 1033)/cm2/sec
On resonance:113 fb-1
Int(L dt)=131 fb-1
Cherenkov Detector (DIRC)[144 quartz bars, 11000 PMTs]
Silicon Vertex Tracker (SVT)[5 layers]
Instrumented Flux Return (IFR) [Iron interleaved with RPCs].
CsI(Tl) Calorimeter (EMC)[6580 crystals].
Superconducting Coil (1.5T)
Drift Chamber [40 stereo lyrs](DCH)
e- (9 GeV)
e+ (3 GeV)
The BaBar Detector
•Two ringse+ : 3.5 GeV 1.5Ae : 8.0 GeV 1.1A
•ECM : 10.58 GeV•Luminosity:
•target: 1034 cm-2 s-1
•ach’ved: 1034 cm-2 s-1 •(~20 B’s/s
KEKB
Drift chamber cell
+
-
-
- -
-
--
E-field
Charged particle track
-
-
---
--
Drift speed 50m/nsecPosition resolution 150 m
16m
m
17mm
Kinematic variables for the ϒ(4S)
invariant mass:
2/
2 )()2(SKJCMbc ppEm
2/ CMKJB EEEES
e+ e-
in CM:
e+ e-B0
B0
E=Ecm/2
E=Ecm/2
Beam-constrained mass:
J/KS
2/
2/ )()(
SS KJKJB ppEEm
Kinematic variables for the Υ(4S)
Energy difference:
Beam-constrained mass:
2/
2 )()2(SKJCMbc ppEm
2/ CMKJ EEEES
10MeV
2.5 MeV
B0 ψ KL signal event
pB* (cms)
[2332 events with a purity of 0.60]
Event display
J/ KL1399±67 signal
KL “crash”
Flavor-tagging the other B
Inclusive Leptons:high-p l b c l intermed-p l+ s l
Inclusive Hadrons:high-p - B0D(*)+ -, D(*)+ -, etc.intermed-p K- K- X,
low-p + D0 +
Belle: effective efficiency = 30 %
Figure of merit(Q) =ε(1-2 w)2 a.k.a effective tagging efficiency
Distinguishing different particle types (Cherenkov)
When (=v/c) > 1/n , “cherenkov” light is produced Only particles
with b>0.99count in these
Distinguishing different particle types (time-of-
flight)
Time =
L/v
x
x
ScintillationCounter barrel
A K- tag event means the other meson is (probably) a B0
(not a B0)
K-
Identify the other tracks in the event
DK- not K+
DK+ not K-
BD >> BD
Silicon detectors measure Δz
(typically ~200 m)
Beam spot: 110 μm x 5 μm x 0.35 cm
Step 4. Find decay time difference
Event-by-event Likelihood
background frac
Sidebands & MC
resolution functionB-lifetime studies
f= ±1 for CP=1
PDG
wrong-tag frac.lone free parameter
b-flavor tag
sin2sin211 measurement by Belle measurement by Belle (2003)(2003)
“Raw” asymmetry
BELLE-CONF-0353
5417 evts
Poor tags
Good tags
The “Unitary Triangle”
100010001
****
***
***
tbtstd
cbcscd
ubusud
tbcbub
tscsus
tdcdudt
VVVVVVVVV
VVVVVVVVV
UU
0*** tbtdcbcdubud VVVVVV
ubudVV *
cbcdVV *
tbtdVV *
Unitary triangle:
ubudVV *
cbcdVV *
tbtdVV *
~1~1
|Vtd| measuredby B0-B0 mixing
|Vub| measured inbuℓ- decay
|Vcb| measured inbcℓ- decay
|Vcd|=sinC
**tdcbcdub VVVV
luckily:
otherwise, the triangle would be flat
Overconstrained!!
CP is violated in B decays• ~70% effect in BJ/ KS decays
– compared to ~0.2% effect in K0 decays• Kobayashi-Maskawa mechanism
verified.
• After 35 years, 3 new quarks &, happily,**
tdcbcdub VVVV
Next Step
Check the Unitary Triangle with Penguins
bs FCNC decayt-quark is
the dominant contributor
Why is heso happy?
SM FCNC:
)( of effectsExpect 2,
2
YX
top
MM
O
i.e.> ~10% for MX,Y accessible @ LHC
t
at leastV
New heavy Particles?2nd-order weak process with t & W
in the loop
New Physics?:X
Y
sin21 with bs penguins (SM)Example:
no CP phase
SM: sin21 sin21 from BJ/ KS (bc c s)eff
Vtd
Vtd
+
1
B B, ’,
1
, ’,
_
*
*
B0 'K0
(bkg subtracted)B0 mass B0 momentum
535MBB
hep-ex/0608039
K0KS K0KL
1421 ± 46 signal evts
454±39 signal evts
B0 K0
B0 massB0 momentum
(bkg subtracted)
hep-ex/0608039
535MBB
K0KS
K0KL
307 ± 21 signal evts
114±17 signal evts
1 with b s Penguins
Naïve average of all b s modessin2eff = 0.52 ± 0.05
SM: 0.681 ± 0.025
~2.6difference
Hint, but not strong evidence for new physics.
Need more precision (data)
MX,Y > Mtop
• Space time symmetries conservation laws– Space translation symm Conser. of momentum– Rotational symm Conserv of angular momentum– Time translation symm Conserv. of Energy
E. Noether
•CP is violated in neutral K decay– Small effects:– (KL)/(KS)
= 2 4x10-6
– (KLe+)/(KLe-)
= 2x10-3
M(+-)<M(KL)
M(+-)>M(KL)
M(+-)=M(KL)
cosK0
K0
)(tA
3102)( tA
• Kobayashi Maskawa (1973) 6-quark model– Needs 3 more quarks than are known at the time– Predicts large CP violation in B-meson decays.
• 3 more quarks discovered– c (1974)– b(1978)– t(1995)
bsd
VVVVVVVVV
bsd
tbtstd
cbcscd
ubusud
'''
CP phases go here
• Large CP violation found in B meson decays
– ~70% effect
• KM predictions validated
sin21 = 0.681 ± 0.025
•CP measurements for Penguin (loop) processes can search for new particles at high mass scales
– Even higher than the LHC
New heavy Particles?
XY