sides and angles of the unitarity triangle soeren prell iowa state university high-energy physics in...
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Sides and Angles of the Unitarity Triangle
Soeren Prell
Iowa State University
High-energy Physics in the LHC Era
3rd International Workshop
January 4-8, 2010
Valparaiso, Chile
Sides and Angles of the Unitarity Triangle (S.Prell) 2
The CKM Matrix• V connects quark mass eigenstates to
weak interaction eigenstates and thus describes coupling strength of quarks to charged current weak interaction
• V first suggested by M. Kobayashi and T. Maskawa in 1973 to explain CP violation in Kaon mixing (Physics Nobel Prize 2008, shared with Y. Nambu); called VCKM to acknowledge N. Cabibbo
HEP 2010
iW -
jGFVij
quark transition
ud us ub
cd cs cb
td ts tb
V V V
V V V V
V V V
'
'
'
d d
s V s
b b
Sides and Angles of the Unitarity Triangle (S.Prell) 3
The CKM Matrix• In 3-generation Standard Model CKM matrix is a unitary 3x3 matrix
– Values of Vij not predicted by SM
– Invariants under quark field rotations are observables (e.g. |Vij|2,VijVik*VlkVlj*)
– VCKM has only 4 independent parameters
• Search for physics beyond the SM by testing unitarity of CKM matrix !
HEP 2010
2 3
2 2 4
3 2
1 / 2 ( )
1 / 2 ( )
(1 ) 1CKM
A i
A O
A i A
V
Wolfenstein’sparameterization
(areas of squares proportional to |Vij|2)
… reflects size of matrix elements
CKM
V
d s b
u
c
t
0.225
Sides and Angles of the Unitarity Triangle (S.Prell) 4
ub
cb
td
ud
cd
t
s
s b
u
cs
t
V
V V
V
V
V
V
V
V
V
The (B) Unitarity Triangle
HEP 2010
* * * 0ub cud bd tdc tbV V VV V V
2
1 ... , .2
etc
ud
cd
V
V
*ub*cb
V
V
* *tb tb
c
td*
cd b cd
V
V
V V
V V td
*ts
V
V
Vud, Vcd and Vtb are well known:Vud from nuclear β decays,Vcd (= Vus) from Kaon decays,Vtb 1 from Vub and Vcb
Determine Vub, Vcb, Vtd and Vts with B decays
Sides and Angles of the Unitarity Triangle (S.Prell) 5
CKM Matrix Element Magnitudes
HEP 2010
Vud
Bd
Bd
Bs B
s
πB
d
e-
νV
us
Vub
Vcd
Vcs B
d D
νe-V
cb
Vtd V
ts Vtbb b
b
b
c
u
b bsd
d st t
tt
All 1st and 2nd row matrix elementsare most precisely determined from leptonic and semi-leptonic decays
Vcb from B → D(*)lν decays
Experiments fit differential B → D(*)lν decay rate for |Vcb|F(1) and |Vcb|G(1) using HQET-based form factor parameterizations– B → D(*) form factor normalizations
from lattice calculations
– Prelim. result from Belle with B- →D*0lν (Dungel @ EPS’09, arXiv:0910.1438, not yet included in average):
ub
cb
td ts
V
V
V V
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 6
3
3
* 3
3
: | | (1) (42.3 0.7 1.3) 10 | | (39.4 1.4(exp) 0.9(FF)) 10
: | | (1) (35.75 0.42) 10 | | (38.8 0.5(exp) 1.0(FF)) 10
cb
cb
cb
cb
B Dl V GV
B D l V FV
*
2* 2 3 1/ 2 2
3
22 3 3/ 2 2
3
( ) | | ( 1) ( )( ( ))48
( ) | | ( ) ( 1) ( ( ))48
Fcb D
Fcb B D D
d GB D l V m w P w F w
dw
d GB Dl V m m m w G w
dw
(1) 1.074 0.018 0.016 (FNAL/MILC (2005)) (1) 0.921 0.013 0.020 (FNAL/MILC (2009))
GF
B →D*lν results
PRD79, 012002 (2009)
PRL100, 231803 (2008)
PRD77, 032002 (2008)
arXiv:0810.1657
3| | (1) (35.0 0.4 2.2) 10cbV F
(*)B Dw v v
Vcb from inclusive B → Xclν decays
• Inclusive rate Γ(B → Xclν) can be described by expansion in powers of 1/mb (HQET, OPE)
• Non-perturbative corrections up to O(1/mb
3) are determined from inclusive distributions in B decays (Elep and mhad in B → Xclν and Eγ in B → Xsγ decays)
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 7
3 | | (41.67 0.44 0.58) 10cbV (~2.3σ larger than Vcb from excl. decays)
BaBar, arXiv:0908.0415
p*l > 0.8 GeV
mhad in B → Xclν
3| | (40.6 1.3) 10cbV My average (S = 2.3)
HFAG, Winter 2009
ub
cb
td ts
V
V
V V
Vub from B → π l ν decays
• Experiments determine |Vub||f+(q2)| from measured B → π l ν rate– |f+(q2)| calculated from theory
(LQCD (LCSR) at high (low) q2)
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 8
23
2 32 22( )
24| ( ) || |F
ub
d GB l p V
qf q
d
PRL101, 081801 (2008)
PLB648, 139 (2007)
arXiv:0812:1414
PRL101, 081801 (2008)
arXiv:0812:1414
PRL99, 041802 (2007)
PRL98, 091801 (2007)
arXiv:0812:1414
0 4( ) (1.36 0.05 0.05) 10BR B l 0.6 30.5| | (3.5 ) 10ub lV
Error dominated by f+(0) calculation
FNAL/MILC + BaBar data, PRD79, 054507 (2009): 3.38 ± 0.36
310ubV
ub
cb
td ts
V
V
V V
arXiv:0907.0379
PRL100, 171802 (2008)
PRL100, 171802 (2008)
PRL100, 171802 (2008)
Vub from inclusive B→Xu l ν decays
• Challenges– mb
5-dependence of Γ(B→Xulν)
– b →c background: Γ(B→Xclν)/ Γ(B→Xulν)~50
• Select B→Xulν enhanced region in phase sp.– use shape function from B→Xsγ Eγ-spectrum
and theory to extrapolate rate to full PS• New Belle multivariate analysis
– Reconstruct other B in hadronic mode– Covers about 90% of B→Xulν PS
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 9
arXiv:0907.0379
Vub (B→πlν)
I can’t average theories, will use |Vub|incl = (4.20 ±0.28)x10-3 (BLNP)
2
2 53
| | (1 had. corr.)192
Fu ub b
GB X l V m
Vub from incl. B→Xulν syst. higher (~1-2σ) than from B→πlν decays
3| | (4.07 0.38) 10ubV My average
ub
cb
td ts
V
V
V V
Sides and Angles of the Unitarity Triangle (S.Prell) 10
Vtd and Vts
HEP 2010
10.507 0.004 psdm
Experimental input: Bd0Bd 0 and Bs
0Bs 0 oscillation frequencies
117.78 0.12 pssm
CDF, PRL 97, 242003 (2006)
D0, PRL 97, 021802 (2006)
ub
cb
td ts
V
V
V V
Sides and Angles of the Unitarity Triangle (S.Prell) 11
Vtd and Vts
HEP 2010
• From neutral B0d(s) mixing
• From radiative B decays: BR(B → ργ) / BR(B → K*γ)
ˆ (216 15) MeV
ˆ (266 18) MeV
d d
s s
B B
B B
f B
f B
-3
-3
| | (8.1 0.6) 10
| | (38.7 2.3) 10
| / | 0.209 0.001 0.006
td
ts
td ts
V
V
V V
| / | 0.21 0.04td tsV V
) )( ) ( (
2
(2 2 2 2
( )2)
2
| | | | ( )ˆ
,6
d s ds sdF B B
td ts tbd Ws
B
t
BG m f BV f m mm V
Improved lattice results:(HPQCD, PRD 80, 014503 (2009))
ˆ1.258 0.033
ˆd d
s s
B B
B B
f B
f B
Some theoretical errorscancel in the ratio:
(errors dominated by theoretical uncertainties)
Sides and Angles of the Unitarity Triangle (S.Prell) 12
UT Apex from Vub, Vcb, Vts and Vtd
HEP 2010
UT from full fit including CKM phases
Measurements of the Unitarity Triangle sides are theoretically limited !
Sides and Angles of the Unitarity Triangle (S.Prell) 13
CKM Phases and Unitarity Triangle Angles
HEP 2010
CKM
V
d s b
u
c
t
γ
ββs
Phases in Wolfenstein convention (areas of squares proport. to |argVij|)
Convention-independent definition:
*
* *
*
*
* *
*
arg arg
arg arg
tb cd cb
ud tb
ud tb
td
ub td
ub tss
cd cb cs cb
V V VV
V VV V
V V
V V
V
V V
V
: NB
Sides and Angles of the Unitarity Triangle (S.Prell) 14
Sensitivity to CKM Phases from Interference
2β(s) from BB box diagrams– no weak phase in
decay amplitudes
2α = 2(π – β – γ)– from BB box
diagram followed by b → u decay
γ– from charged B
b → u decay
HEP 2010
cb
d(s) d(s)
c
sB(s)
0J/ψ
KS(Ф)
KS(Ф)
c
b
d(s)
d(s)
csB(s)
0
J/ψ
t
t
d(s)
bV*td(s)
tdb
dB0 t d
bV*td
d
uu
π -
π+V*ub
d
bd d
uuB0 π -
π+Vub
s
bu u
ucB+ D0
K+ ub
u u
c
sB+
K+
D0Vub
Time-dependent analyses to measure mixing-induced CP-asymmetries:
0 02
0 0
2 02
2 0
2Im ( ) ( )
( ) 1 | |( ) ( )
1 | | ( ) [ sin cos ]
1 | | ( )
CPCP CP
CP CP
CP CPiCP CP
CPCPCP CP
B f B fA t
B f B fA B f
em t m tA B
Sf
S
CC
Sides and Angles of the Unitarity Triangle (S.Prell) 15
β from b →(cc) s decays
HEP 2010
Theor. clean measurement of |S| = sin2β with B → J/ψ K0, J/ψ K*, ψ(2S)KS, ηcKS, & χc1KS by BaBar and Belle
BaBar, PRD 79,072009 (2009)
0.672 0.0230.004 0.019
WA
WA
SC
0.687 0.028 0.0120.024 0.020 0.016
SC (21.1 0.9)
statistically limited
s
Sides and Angles of the Unitarity Triangle (S.Prell) 16
β from b → s(qq ) penguin loop decays
• In SM penguin decay amplitude is dominant and has same weak phase as b→c(cs) amplitude– expect to measure |S| = sin(2b)– SM contributions from suppressed
diagrams expected to be small (Dsin(2b) = sin(2beff)- sin(2b) ~ 0.01-0.1)
• Penguin decays with b → s (qq ) loop sensitive to New Physics from heavy particles – New Physics contributions could cause
large D sin(2b)
HEP 2010
b s
g
t
0B
BaBar, PRD 79, 052003 (2009)
0 0' SB K
0 0' SB K
0 0
0 0
N B N B
N B N B
467M BB
sin 2 0.57 ± 0.08 ± 0.020.08 ± 0.06 ± 0.02
eff
C
s
Sides and Angles of the Unitarity Triangle (S.Prell) 17
β from b → s(qq) penguin loop decays
HEP 2010
• CP asymmetries measured by B factories in 9 different b → s (qq) modes– All measurements of sin2βeff
consistent with sin2βb→c(cs)
– C’s consistent with zero– Naïve average sin2βeff of all b → s
(qq) modes used to be ~3σ lower than sin2β (~2004), now ~1σ
• Some modes (ФK0, η’K0, K0K0K0) believed to have relatively small theoretical uncertainties– My average for clean modes
Theoretically clean modes
s
,sin2 0.59 0.06eff clean
(1.3σ away from sin2β)
Sππ sin2aeff = sin2(a + d )
b → u “tree” b → d “penguin”d
a from B0 → pp
Two sizeable amplitudes (P/T ~ 0.3) :
2 2 2
mixing decay
i i ie e e
g
Determine d from isospin analysis (Gronau & London, PRL 65, 3381 (1990))
PRL 98, 211801 (2007)
Excluded at 95% CL
,
,
0.65 0.070.38 0.06
WA
WA
SC
0.61 0.10 0.04 (5.3 )0.55 0.08 0.05 (5.5 )
SC
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 18
s
a from B → pp, , rr rp0 0 0,
0 6
0 6
6
0 0 0 6
(24.2 3.2) 10
(18.3 3.0) 10
(24.0 2.0) 10(0.73 0.28) 10
Br B
Br B
Br B
PRL 102, 141802 (2009)
+4.44.2= 89.0
o
Also prelim. BaBar result from a1π and K1π (Lombardo @ EPS’09, arXiv:0909.5646)
2008
2009
Excluded by other constraints
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 19
• VV decay B → rr– separate isospin analysis for each
polarization amplitude– fortunately, longitudinal polarization
dominant (>90%)• Small penguin contribution in B → rr• New measurement of BR(B+ → r+r0) from
BaBar stretches isospin triangles
s
0.05 0.17 0.06 0.13
SC
g from B- → D(*)K- Decays
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 20
ubV• Rates of B± → D (*) K± decays are sensitive to γ through inter- ference of b → c and b → u transitions– Need states accessible to D(*)0 and D(*)0
• Several neutral D (*) final states investigated by B factories and CDFGLW : CP eigenstates (pp, KK,etc.)Gronau & London, PLB 253, 483 (1991);Gronau & Wyler, PLB 265, 172 (1991)
ADS: Flavor DCSD states (Kp)Atwood, Dunietz, & Soni, PRL 78, 3257 (1997),Atwood, Dunietz, & Soni, PRD 63, 036005 (2001)
GGSZ: 3-body decays (KS , pp KSKK)Giri, Grossman, Soffer, & Zupan, PRD 68, 054018 (2003)Bondar, PRD 70, 072003 (2004)
New BaBar measurement with first evidence for ADS signal B- → DK-
3.4 σ
Lopez-March @ EPS’09
s
Sides and Angles of the Unitarity Triangle (S.Prell) 21
g from B- → D (*) K- Decays
HEP 2010
• B- → D (*)K- decays with 3-body Dalitz analysis of D → KSπ π, D → KSKK most sensitive to γ– Belle: updated Dalitz analysis
including D*0 → D0γ
Poluektov @ EPS’09
0: SB D K 0: SB D K
1213
10.8 o11.6
(76 4 9)(78.4 3.6 8.9 (model))
o
2008 (prelim.)
2009 (prelim.)
Model error can be reduced to ~2o using CLEO-c measurements of ψ(3770)→DD (PRD 80, 032002 (2009))
s
(75 12)oUTFit
Also, from time-dependent B → D (*)K/p analyses:
2β+γ = (± 90 ± 32)o
Sides and Angles of the Unitarity Triangle (S.Prell) 22
UT from Angles α, β, γ (and εK)
HEP 2010
All measurements of the Unitarity Triangle angles are statistically limited !
Sides and Angles of the Unitarity Triangle (S.Prell) 23
βs from Bs → J/ψ Ф decays
HEP 2010
New physics in BsBs mixing
CDF/PHYS/BOTTOM/CDFR/9787, DØ Note 5928-CONF
s
• D0 and CDF measure βs
with angular dependent fit to decay time distributions of Bs → J/ψ Ф
– Simultaneous fit for ΔΓs and βs
• SM predicts βs very small (~0.02)– sensitive to new physics in Bs mixing
• Prospects– D0 and CDF working on updates with
2x samples– LHCb sensitivity with 0.5 fb-1: σ(βs) = 0.02
Global CKM Fit• Consistency of angles
• Consistency of angles and sides from global fit– Overall good fit (CKMFitter:
global p-value 45%)– ~2σ tension between sin2β
and εK / Vub
• correction to εK will make it worse (Buras, Guadagnoli, PRD78, 033005 (2008))
4.44.289.0
21.1 0.9
75 12
o
o
o
185 13o
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 24
CKM angles Other constraints All constraints
0.0240.027
0.0160.015
UTFit: 0.154 0.022 CKMFitter: 0.139
0.342 0.014 0.342
Sides and Angles of the Unitarity Triangle (S.Prell) 25
Rare Decay: B → τ ν
• Decay B → τ ν is sensitive to Vub
– Decay proceeds via W annihilation in SM
– also sensitive to new physics (e.g. charged Higgs)
• B → τ ν event reconstruction at B factories– Tagging B side
• Full reconstruction of B in hadronic (D(*)π/ρ, etc.) or semi-leptonic mode (D(*)lv)
– Signal B side• Charged tracks• Missing energy due to ν’s • Require (no) additional energy in EM calorimeter (Eextra,EECL)
HEP 2010
2 2 2
22 2( ) 1
8 B u BB
bF BG m m m
fBR VBm
Sides and Angles of the Unitarity Triangle (S.Prell) 26
BR(B → τ ν) Measurements
HEP 2010
• Belle– Hadronic tag– Semileptonic tag
• BaBar– Hadronic tag– Semileptonic tag
4
0.56 +0.460.49 0.51
0.38 +0.350.37 0.37
0.90.8
1.79
1.65
1.8 0.4
1.7 0.8 0.2
Branching fraction( 10 )
Semileptonic tag (arXiv:0912.2453)
4( ) (1.73 0.35) 10BR B World average
10x signalpreliminary
Sides and Angles of the Unitarity Triangle (S.Prell) 27
Unitarity Triangle consistency ?
~2.4σ discrepancy between direct BR(B → τ ν) measurements and global UT analysis
– Theoretical uncertainty from fB is removed in BR(B → τ ν) / Δmd
• discrepancy remains at ~2.5σ (only remaining theoretical error is 12% from B bag factor)
Effect of charged Higgs
HEP 2010
22 2
2
tan( ) ( ) 1 B
SMH
mBR B BR B
m
W. Hou, PRD 48, 2342 (1992)
Sides and Angles of the Unitarity Triangle (S.Prell) 28
Conclusions• Many new measurements regarding quark flavor mixing in the last few
years constrain the Unitarity Triangle with increasing precision• CKM mechanism proven to be dominant mechanism for quark mixing
• describes all current experimental results in quark mixing and CP violation (including measurements of CKM matrix elements (Vud, Vus, Vcd, Vcs, Vtb) not covered in this talk)
• Some intrinsic discrepancies need to be resolved– Vcb and Vub (incl. vs excl. decays)
• A few interesting “tensions” at the 2-3 σ level should be monitored closely in the future– β (J/ψ K0) vs εK and Vub
– B → τν vs β (J/ψ K0) – βs
• Expect significant impact from upcoming experiments (LHCb, Super B factories) and improved theory/lattice calculations mostly on improving γ, βs, Vub, Vtd / Vts
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell) 29
Back-up Slides
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell) 30
Vud from nuclear β Decays
• 0+→0 + super-allowed nuclear β-
decays within same isospin multiplet (pure V decays)
• Error on rad.corrections ∆RV reduced x2
(Marciano and Sirlin, PRL 96, 032002 (2006))
– Still dominant (syst.) error on Vud
• Other Vud measurements compatible, but (7-10 x) less precise– n lifetime (error dominated by gA, most
precise τn measurement 6σ away from earlier results), π decay (stat. limited)
HEP 2010
Before nucleus-dependent corrections …
… and after
Towner & Hardy,PRC 79, 055502 (2009)
'(1 )(1 )R NS CFt ft
3071.81 ± 0.79(stat) ± 0.27 (syst) sFt
5 32
2
ln 2
(1 )e
ud VF R
mV
G Ft
(2.361 ± 0.038)%VR
| | 0.97425 0.00022udV
GF from μ decay
New Penning-trap measurements of
decay energies
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
Sides and Angles of the Unitarity Triangle (S.Prell) 31
Vus from K → πlν (Kl3)
Vus from τ decays– Prelim. BaBar measurement (ICHEP’08) of
BR(τ→Kν)/BR(τ →πν) gives |Vus|=0.2255(23)
– Rate of incl. τ → s decays (CKM’08) gives |Vus| = 0.2165 ± 0.0026(exp) ± 0.0005(theo); 2.6σ smaller than |Vus| from Kl3
HEP 2010
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
}dominated by KL lifetime
2| | (0) 0.21660(47) / ndf 3.0 / 4usV f
(0) 0.964(5)Kf RBC-UKQCD, PRL
100, 141601 (2008)
| | 0.2246 0.0012usV
0
0
( ) (50.56 0.14 0.21) ns
( ) (89.56 0.03 0.07) ps
L
S
K
K
Preliminary measurements τ(KL) and τ(KS) (KLOE, cf. Bocchetta @ Kaon’09, Dreucci @ EPS’09) not yet in average
22 2
(3
)5
23
2| (0) |( | | 12
(1
) )9 Kl K
SU EMEW K
K F Ks l KluKl I
C G MVS f
(experimental input, theory input)
Palutan (FlaviaNet) @ Kaon ‘09
Vus / Vud and combined fit
Ratio Vus / Vud can be determined independently from ratio of K → μν (KLOE, PLB 632, 76 (2006)) and π → μν decay rates
| | ( )0.2387(4)
| | ( )us
ud K
V fK
V f
/ 1.189(7)Kf f HPQCD-UKQCD, PRL100, 062002 (2008)
| | 0.97424 0.00022
| | 0.2252 0.0009ud
us
V
V
| |0.2321(15)
| |us
ud
V
V
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 32
Palutan (FlaviaNet) @ Kaon ‘09
From fit to Vud, Vus and Vud / Vus:
Sides and Angles of the Unitarity Triangle (S.Prell) 33
Vcd from v scattering
Di-muon production by neutrino on nuclei
Semi-leptonic decay D →π l ν– Dominated by D →π form factor
HEP 2010
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
2
2
2( ( ) ( ))| |
3( ( ) ( ))
(0.463 0.034) 10 [CDHS, CCFR, CHARM II]
with ( ) 0.0873 0.0052 (PDG 2008)
cdB V
B BR c X
| | 0.230 0.011cdV
| | 0.234 0.007(exp) 0.025(LQCD)cdV CLEO-c, arXiv:0906.2983
| | 0.231 0.010cdV My average
,
,
d c c s
d c c s
Sides and Angles of the Unitarity Triangle (S.Prell) 34
Vcs from D and Ds Decays
• Semi-leptonic D decay D → K l ν– Dominated by D → K form factor
• Leptonic Ds decays Ds →(μ,τ) ν– New measurements of from CLEO-c – decay constant f(Ds) from LQCD calculation
HEP 2010
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
| | 1.04 0.04csV
| | 0.985 0.01(exp) 0.10(LQCD)csV CLEO-c, arXiv:0906.2983
| | 1.03 0.04cdV My average
| |scs DV f
241 3 MeV [HPQCD/UKQCD, PRL100, 062002 (2008)]260 10 MeV [prelim. FNAL/MILC @ Lattice '09]
242 5 MeV [S = 1.6]
s
s
s
D
D
D
ff
f
[PRD 79, 052001 (2009),PRD 79, 052002 (2009)]
Unitarity of udcs Matrixud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
Inputs: | | 0.97424 0.00022 | | 0.2252 0.0009
| | 0.231 0.010 | | 1.03 0.04ud us
cd cs
V V
V V
Cannot predict 3rd family (Vub too small to matter)
Wolfenstein 0.2252 0.0009
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 35
2 2
2 2
2 2
2 2
| | | | 1 0.0004 0.0007 ( 0.6 )
| | | | 1 0.114 0.083 ( 1.3 )
| | | | 1 0.003 0.005 ( 0.6 )
| | | | 1 0.112 0.082 ( 1.4 )
ud us
cd cs
ud cd
us cs
V V
V V
V V
V V
2 2| | | | 0.0004ud usV V
(equal error contribution to 1st row unitarity check)
Constraints on New Physics– Scalar currents (charged Higgs)– 4th quark generation
• |VuD| < 0.04 @ 95% CL
– Exotic μ decays• BR(Exotic μ decays) < 0.0016 @ 95% CL
(~7x better than bound on μ+ → e+VeVμ)
Sides and Angles of the Unitarity Triangle (S.Prell) 36
• K. Trabelsi for CKMFitter at Beauty 2009
HEP 2010
Sides and Angles of the Unitarity Triangle (S.Prell) 37
Vtb from weak top production
• From weak “single top” production cross-section in pp collisions at the Tevatron– Does not assume unitarity
• 5σ observations by CDF and D0– σ = 2.3 +0.6
-0.5 pb [CDF, arXiv:0903.0885]
– σ = 3.9 ± 0.9 pb [D0, arXiv:0903.0850]
– CDF: |Vtb| = 0.91 ± 0.11(exp) ± 0.07(theo)
– D0: |Vtb| = 1.07 ± 0.12
HEP 2010
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
| | 0.91 0.08tbV
Sides and Angles of the Unitarity Triangle (S.Prell) 38
CKM matrix unitarity check
HEP 2010
-3
-
Inputs: | | 0.97424 0.00022 | | 0.2252 0.0009 | | (4.07 0.38) 10
| | 0.231 0.010 | | 1.03 0.04 | | (40.6 1.3) 10usud ub
cscd cb
V V V
V V V
3
-3 -3 -3 | | (8.1 0.6) 10 | | (38.7 2.3) 10 | | (1.00 0.10) 10tstd tbV V V
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
2 2 2
2 2 2
2 2 2
2 2 2
| | | | | | 1 0.0004 0.0007 ( 0.6 )
| | | | | | 1 0.11 0.08 ( 1.3 )
| | | | | | 1 0.00 0.20 ( 0.0 )
| | | | | | 1 0.003 0.005 ( 0.6 )
|
ud us ub
cd cs cb
td ts tb
ud cd td
V V V
V V V
V V V
V V V
2 2 2
2 2 2
| | | | | 1 0.11 0.08 ( 1.4 )
| | | | | | 1 0.00 0.20 ( 0.0 )
us cs ts
ub cb tb
V V V
V V V
2 -3(40.1 1.1) 10A
From Vcb and Vts
Magnitudes of CKM matrix elements fulfill unitarity well
Mixing-induced CP violation
B0 fCP
B 0
Af
Af
2ie
2
B0
fCPB 0Af
Af
2ie
2
02
0
( )
( )CP
i CPf CP
CP
A B fe
A B f
0 02
0 0
2
2
2Im ( ) ( ) 1 | |( )
( ) ( )1 | |
sin cos 1 | |
CP
CP
CPCP
CP
CP CP CP
CP
ffCP CP
ff
CP CP
ff f f
f
SB f B fA t
B f B f
S m t C m t C
Difference in decayrate for B0 and B0
CP Violation
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 39
Measurement Technique for TDCPVs
z
0
tagBe
4S
0recB
l
-K
B-Flavortagging
Reconstruction of B decays to exclusive
final states
0SK
/J
e
Coherent BB production (p-wave)
z
/z c t
B0
B0
0.3Q
0.56(4 ) 0.43S
HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell) 40