How well do we know the
Unitarity Triangle?
An experimental overview
Gabriella Sciolla (MIT)
1988
Now
G. Sciolla – M.I.T.Kaon
How well
do we know the
Unitarity
2007
- Frascati
- May
21Triangle?
- 25, 2007
1
Outline

The beauty of the Unitarity Triangle



The players


B factories, Tevatron and kaon experiments
The measurements




Its role in understanding CP violation in the Standard Model
Sensitivity to New Physics
CP violation in K0: the “εK band”
CP violation in B0: the angles of the Triangle
B0 mixing and semileptonic B decays: the sides of the Triangle
… and more!
What have we learned?

Summary and conclusion
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
2
It all started with kaons…
In 1964 Cronin and Fitch discovered CP violation in the
decays of KL mesons: KLπ+π-
KL
V. Fitch
J.Cronin
G. Sciolla – M.I.T.
π+π−π0
π0π0π0
π+π−
π0π0
1980 NOBEL
PRIZE
How well do we know the Unitarity Triangle?
!
" CP= -1
#
!
" CP= +1
#
3
CP violation in the Standard Model


Explained in Standard Model in 1973 by Kobayashi and Maskawa
In KM mechanism, CP violation originates from a complex phase in the
quark mixing matrix (CKM matrix)
! Vud
V = # Vcd
#
" Vtd
Vus
Vcs
Vts
Vub $
Vcb &
&
Vtb %
Vcb Wb
G. Sciolla – M.I.T.
c
1
!
1 ' (2
(
#
2
#
1 2
#
=
'(
1' (
#
2
# A( 3 (1 ' ) ' i* ) 'A( 2
#
"
$
A( 3 ( ) ' i* )
&
&
& + O(( 4 )
A( 2
&
&
1
&
%
A,λ (Cabibbo angle): very well measured
ρ,η: poorly known until recently
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Going beyond CKM
The (many) strengths of CKM



Simple explanation of CPV in SM
It is very predictive: only one CPV phase
It accommodates all experimental results


CP violation in Kππ and KLπlν
CP violation in the B system
CKM
New Physics models have many sources of CP violation

e.g.: MSSM has 43 new CP violating phases!
 Exploit CKM prediction power: use CPV as probe for New Physics
Measure CP violation in channels theoretically well understood
.
and look for deviations w.r.t. SM expectations
G. Sciolla – M.I.T.
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The Unitarity Triangle
Unitarity of CKM implies: V†V = 1  6 unitarity conditions
*
*
Of particular interest: Vud Vub
+ Vcd Vcb
+ Vtd Vtb* = 0
! Vud Vus Vub $
V = # Vcd Vcs Vcb &
#
&
" Vtd Vts Vtb %
All sides are ~ O(1)  possible to measure both sides and angles!



CP asymmetries in B meson decays measure α, β and γ
Sides from semileptonic B decays, B mixing, rare B decays
Complementary constraints from CP violation in KL (εK)
G. Sciolla – M.I.T.
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6
The Unitarity Triangle
Unitarity of CKM implies: V†V = 1  6 unitarity conditions
*
*
Of particular interest: Vud Vub
+ Vcd Vcb
+ Vtd Vtb* = 0
!
VtdVtb!
VcdVcb!
!
VudVub!
VcdVcb!
!
0
!
!
1
All sides are ~ O(1)  possible to measure both sides and angles!



CP asymmetries in B meson decays measure α, β and γ
Sides from semileptonic B decays, B mixing, rare B decays
Complementary constraints from CP violation in KL (εK)
G. Sciolla – M.I.T.
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Going beyond the Standard Model
(ρ,η)
VudVub*
α
VcdVcb*
(0,0)
γ
VtdVtb*
VcdVcb*
β
(1,0)
 Two measurements fully define the apex
 This triangle has a base normalized to 1
 All additional measurements probe Physics Beyond SM
 All pieces of the puzzle must fit in the Standard Model
 Inconsistencies can be explained only by New Physics
G. Sciolla – M.I.T.
Precision
and redundancy are essential!
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The experiments:
B meson experiments

Asymmetric B factories:
BaBar (SLAC) and Belle (KEK)



.e + e - ! "(4s) ! BB
Very clean environment
Very high luminosity
1 billion BB pairs (BaBar/Belle)

Tevatron experiments:
CDF and D0 at Fermilab

.pp collisions at

Challenges: high multiplicity and bb trigger

s ~ 2 TeV
Complementarity: all b hadrons are produced
 B , Λ , B ,…
S
b
C
G. Sciolla – M.I.T.
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The experiments:
Kaon Experiments


Many experiments: 43 years of history!
Just some examples:
Add plots of … as a collage + some keywords …
 KTeV
KTeV  NA31???
 Daphne
NA48
 CPLear
KLOE
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CPLear
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The measurements: εK
CP violation in KL: εΚ
α
VudVub*
VcdVcb*
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Vtd Vtb*
Vcd Vcb*
γ
How well do we know the Unitarity Triangle?
β
11
CP violation in KL

Constraints on Unitarity Triangle come from indirect CP
violation (due to mixing): ε
!K ~
where

2
1
"+- + "00
3
3
%
A(K L " # +# - )
BF(K L " # +# - )
$S
=
'!+- =
A(K S " # +# - )
$L
BF(K S " # +# - )
'
&
A(K L " # 0# 0 )
BF(K L " # 0# 0 )
$S
'
!
=
=
0 0
' 00 A(K " # 0# 0 )
$
BF(K
"
#
# )
S
L
S
(
World Average in PDG 2006:
! K = ( 2.232 ± 0.007 ) " 10 -3

Precision: 0.3%!
NB: ~3.7σ shift wrt PDG 2004 after including: KTeV, KLOE, NA48
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
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Kaons’s contribution to the UT: εK

Experimental error on εK ~ 0.3%
… but large errors on constraints of (ρ,η)


Bag parameter from Lattice QCD BK=0.86 ± 0.06 ± 0.14 (16% precision)
Kaon decay constant from leptonic decay rate fK=(159.8 ± 1.5) MeV
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
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The measurements: β
Vub* Vud
VcdVcb*
α
Vtb*Vtd
Vcd Vcb*
The angle β
γ
G. Sciolla – M.I.T.
ββ
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How to measure the CP asymmetry
.
N ( B 0 (t ) ! f CP ) " N ( B 0 (t ) ! f CP )
ACP (t ) =
N ( B 0 (t ) ! f CP ) + N ( B 0 (t ) ! f CP )
e-
Flavor tagging
Q=(30.5 ± 0.5)%
B0
e-
Υ(4S)
BfCP exclusive
reconstruction
e+
µ+
B0
µ- π
Δz~ βγc Δt
G. Sciolla – M.I.T.
π+
Precise Δt determination
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CP violation at the B factories
t=0
B0
mixing
~ e " 2 i!
B
0

N (B 0 (t ) ! f CP ) " N (B 0 (t ) ! f CP )
ACP (t ) =
N (B 0 (t ) ! f CP ) + N (B 0 (t ) ! f CP )
t
= S f sin(#mt ) " C f cos(#mt )
A f CP
ay
c
e
d
fCP
A f CP
(ηf)
Cf =
1" !f
2
1+ !f
2
Sf =
2 Im ! f
1+ !f
2
q Af
!f = "
p Af
When only one diagram contributes to the final state, |λ|=1
"C f = 0
#
$S f = Im !
ACP(t) = ± Imλ sin(Δmt)
(CP violation in interference between mixing and decays in B0 )
G. Sciolla – M.I.T.
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CP violation in B0 decays: sin2β
For some modes, Imλ is directly and simply related to the angles of
the Unitarity Triangle.
J /!
Example:
B0J/ΨKS: the “golden mode”



Theoretically clean
Experimentally clean
Relatively large BF (~10-4)
$ Vtb*Vtd %
" =&
* '
V
V
0
( tb td ) Bmix
B0
KS
$ Vcs*Vcb %
$ Vcd* Vcs %
#i 2 !
=
e
&
&
* '
* '
V
V
V
V
0
( cs cb ) decay ( cd cs ) K mix
η
ACP(t) = sin2β sinΔmt
G. Sciolla – M.I.T.
α
γ
How well do we know the Unitarity Triangle?
β
ρ
17
The golden mode for sin2β:
sin2β in B0
B0J/ψ
J/ψ K0
(π+π−)
KS
~ 500 fb-1
Belle ~500 fb-1
0
_B tag
B0 tag
Nsignal = 7482
sin(2β) = 0.678 ± 0.026
BaBar+Belle Moriond 2007
G. Sciolla – M.I.T.
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Constraints from β on the UT
η
95% CL
from other
measurements
ρ

sin2β is measured with a precision of 3.8%


Most stringent constraint for Unitarity Triangle
Precision is purely dominated by statistical error

Will improve in the near future
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
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The measurements: α
% VtdVtb$ (
! " arg ' #
$ *
& VudVub )
VudVub*
VcdVcb*
αα
Vtd Vtb*
Vcd Vcb*
The angle α
γ
G. Sciolla – M.I.T.
β
How well do we know the Unitarity Triangle?
20
α from Β0ππ, ρρ, ρπ

Not as simple as β in the golden mode: tree and penguin diagrams
d
Tree
W
b

% VtdVtb$ (
! " arg ' #
$ *
& VudVub )
u
u
Vub
Penguin
b
*
g
Vtd
Vtb
W
u
u
d
ACP(t) will have two contributions:
ACP (t ) = S sin(!mt ) " C cos(!mt )

S measures UT angle α

C measures direct CP violation
G. Sciolla – M.I.T.
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Combined constraints on α
Average of BaBar and Belle
+10.7
! = 92.6-9.3
°
(
G. Sciolla – M.I.T.
)
CKM fit
+4.5
! = 100.0-7.3
°
(
How well do we know the Unitarity Triangle?
ρ
)
22
The measurements: γ
VudVub*
VcdVcb*
α
Vtd Vtb*
Vcd Vcb*
% VudVub$ (
! " arg ' #
$ *
V
V
& cd cb )
The angle γ
γγ
G. Sciolla – M.I.T.
β
How well do we know the Unitarity Triangle?
23
% VudVub$ (
! " arg ' #
$ *
V
V
& cd cb )
The angle γ
.
Use

interference between B+ ! D0K + and B+ ! D0K + with both
D0 and D0 decaying to the same final state f
Cabibbo allowed
Cabibbo and color suppressed
VusVcb*
B
B
+
+
VcsVub*
0
A(B ! D K ) " V V " #
+



+
*
us cb
3
A(B + ! D 0 K + ) " VcsVub* " # 3ei$
Only tree diagrams contribute: pure Standard Model process!
Low Branching Fractions: more statistics would help
Best measurements from DKsππ Dalitz analysis
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Summary of γ measurements
ρ
Average of BaBar and Belle
+38
! = 60-24
°
(
G. Sciolla – M.I.T.
)
CKM fit:
+9.3
! = 59.0-3.8
°
(
How well do we know the Unitarity Triangle?
)
25
The measurements: Rb
α
V
Rb !
Vcb
*
ub ud
*
cd cb
V V
ub
V V
Vtb*Vtd
*
Vcd Vcb
γ
G. Sciolla – M.I.T.
β
How well do we know the Unitarity Triangle?
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Semileptonic B Decays
ν
Parton level
W!
b
Hadron level
l
Vub , Vcb
b
B
u, c
2
F
G
2
5
#(b $ u!! ) =
V
m
ub
b
192" 2

!ν
Vub
u
XXuu , X c
Sensitive to hadronic effects


!l!
Theory error not negligible
Γ(bc)/Γ(bu)~50


Vcb precisely measured (±2%)
Vub is the challenge
G. Sciolla – M.I.T.
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|Vub| from Inclusive B→Xu l ν
Inclusive B → Xu l ν
B
!
!l-!
Vub
Xu
Inclusive B → Xulν

Hadronic final state is not specified

bc l ν background is suppressed
using kinematical variables

Partial rate is measured
WA: 4.49±0.19±0.27
χ2/dof = 6.1/6
 theoretical uncertainties ~5%
G. Sciolla – M.I.T.
Precision on V : ±7.3%
How well do we know theub
Unitarity Triangle?
28
|Vub/Vcb|and the Unitarity Triangle
Third most precise constraint in the (ρ,η) plane
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
29
The measurement: Rt
*
ub ud
*
cd cb
V V
V V
Vtb*Vtd
Rt *!
| VcdVcb |
α
Vtd
Vts
γ
β
Rt =
G. Sciolla – M.I.T.
Vtb*Vtd
*
cb
VcdV
!
1" Vtd
# " Vts
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The measurement of Rt
Rt = ! "1
α
γ

Vtd
Vts
β
b
0
d (s)
B
d (s )
t
W
Vtd ( s )
Vtd ( s )
W
t
d (s)
Bd0( s )
b
Bs/Bd oscillations
!md
Vtd
"
!ms
Vts



2
Theory error <5% (LQCD)
Δmd is precisely measured
But Bs mixing is very hard…
G. Sciolla – M.I.T.
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BS mixing at the Tevatron


.

.

.
Flavor tagging
QSST~4.8%
QOST~1.5%
.
Time
reconstruction
σ(ct)~25-70 µm
Reconstruction of BS decay
in hadronic or SL modes
G. Sciolla – M.I.T.
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CDF result
B0 mass[GeV/c2]
!mS = 17.77 ± 0.10 ± 0.07 ps
-1
>5σ
G. Sciolla – M.I.T.
"
Vtd
= 0.2060 ± 0.0007 +0.0080
#0.0070
Vts
How well do we know the Unitarity Triangle?
Exp.
<1%
Theory
~4%
33
Impact of ΔmS on Unitarity Triangle

Measurement vs limit: a factor of 2 improvement
G. Sciolla – M.I.T.
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34
Standard Model or New Physics?
Do all pieces of the puzzle fit?
CP conserving
CP violating
All measurements are consistent:
SM still going strong…
Tree
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Loops
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Standard Model or New Physics?
CP violation in Penguins
Complementary test: measure same angle in channels with different
sensitivity to New Physics

Example β from B0-->J/ΨK0 vs “Penguin Modes” (e.g.: B0φKS)
NP
SM
d


SM predicts same ACP(t); small theory errors
Impact of New Physics could be significant


d
N(η'Ks) ~ 900
BaBar 316 fb-1
New particles in the loop  new CPV phases
Low branching fractions (10-5)

Many final states: φ K0, K+ K− KS, η′ KS, KS KS KS, etc.
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Standard Model or New Physics?
β in penguins vs golden mode
BaBar + Belle average
 A trend is visible
 although each measurement
is compatible with J/ΨKS…
 Naïve average: 0.53±0.05
 ~2.6 σ
 Statistical errors still large…
 More statistics will help
“sin2β”
Golden mode
G. Sciolla – M.I.T.
well do we know the
PenguinHow
modes
Unitarity Triangle?
37
Standard Model or New Physics?
New measurement of |Vtd/Vts|
 |Vtd/Vts| can be measured from decays of Bργ/BK*γ
!
W!
Vtd,Vts ss,d
b
u, c,t
BF(B ! "# )
V
$ td
BF(B ! K*# ) Vts

Recent results from B factories


Vtd
Vts
2
Challenge: BF (B→ργ) ~10-6!
Theory error ~7.5% (LCSR)
= 0.202 +0.017
$0.016 (exp) ± 0.015(th)
! /Sciolla
"#
G.
– M.I.T.
… as expected in the Standard Model…
HowAverage
well do BaBar+Belle
we know the Unitarity Triangle?
38
Conclusion

Precise test of CP violation in the Standard Model



CKM is the dominant source of CP violation at low energy


…thanks to many years of hard work by many experiments!
Tremendous improvement in our knowledge of ρ and η
 Precision on apex ~ 0.04
… since all pieces of the puzzle seem to fit together
Search for New Physics is just getting interesting

Expected effects of NP in loops ~10%



Experimental precision is just getting there…
First hints of NP in penguins? Statistics will tell
Exciting times ahead…



B factories (~2 ab-1 by 2008)
New experiments (e.g.: LHCb, SuperB)
Theoretical progress will be crucial (e.g.: Lattice QCD)
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
.
39
γ from B → DK

GWL (Gronau, Wyler, London)


ADS (Atwood, Dunietz, Soni)


D  CP eigenstate
 Theoretically clean
 Small interference: needs more data
D0KSπ+π-
A( D ! f ) is doubly Cabibbo suppressed
 Larger interference
 Needs more data
Dalitz method (Giri, Grossman, Soffer, Zupan)

Exploits interference pattern in Dalitz plot in DKSπ+π−
 Combines many modes  statistical advantage
 Small systematics due to Dalitz model
Currently
most sensitive
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How well do we know the Unitarity Triangle?
40
% VtdVtb$ (
! " arg ' #
$ *
V
V
& ud ub )
α from Β0ππ, ρπ, ρρ
α
If tree diagram dominates
& Vtb*Vtd Vud *Vub #
!
( = ( '1)$$
*
* !
% VtbVtd VudVub "
α
α
α
ACP(t) = sin2α sinΔmt
α
BF(B 0 " # 0# 0 )
~ 50%
BF(B 0 " # +# + )
…not so small even in B->ρρ…
Penguin
!
Tree
BF(B 0 " # 0 # 0 )
~ 20%
BF(B 0 " # + # + )
ACP (t ) = S sin(!mt ) " C cos(!mt )
α
Tree
W
b
Vub
Large penguin contributions in ππ
Penguin
!
Tree
d
Penguin
b
*
g
Vtd
Vtb
W
u
u
u
u
d
S related to α; C related to direct CPV
α
Isospin analysis a la Gronau-London required to extract α...
G. Sciolla – M.I.T.
How well do we know the Unitarity Triangle?
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