Sides and Angles of the Unitarity Triangle Soeren Prell Iowa State University High-energy Physics in...

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


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


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


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)


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)


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


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


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


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)


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 !


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


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


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


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


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


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


• 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


ubV• Rates of B± → D (*) K± decays are sensitive to γ through interference 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


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


UT from Angles α, β, γ (and εK)

HEP 2010

All measurements of the Unitarity Triangle angles are statistically limited !


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


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


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


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


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)


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


Back-up Slides

HEP 2010


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


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


Palutan (FlaviaNet) @ Kaon ‘09

From fit to Vud, Vus and Vud / Vus:


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


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


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)


• K. Trabelsi for CKMFitter at Beauty 2009

HEP 2010


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


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


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


Date post:	15-Jan-2016
Category:	Documents
Upload:	barry-gaines
View:	216 times
Download:	0 times

Sides and Angles of the Unitarity Triangle Soeren Prell Iowa State University High-energy Physics in...

Documents