Standard Model and CPV: the CKM Unitary Triangle Angles ... - ICTP

CP violation and CKM 

measurements in B decays 

Bob Kowalewski 

University of Victoria and 

LAPP, Annecy 

2008-07-03 Kowalewski - CPT@ICTP 1

Importance of CKM measurements 

Need to pin down “standard standard” physics for many “new new 

physics” physics searches, e.g. K L p0νν: νν 

Improved precision translates 

directly into increased NP reach 

CKM 

parameters 

NP signal will be more credible if seen in multiple 

observables need precise measurements of many 

quantities 


CKM in B physics 

B decays allow direct direct access 

to 2 elements and indirect indirect 

access to 2 others via loops 

Can determine 2 angles and the phase in CKM 

cb| | now known to ~2.5%; only sinθ sin C is known 

better 

|V cb 

⎛V V V ⎞ 

ud us ub 

⎜ ⎟ 

V V V 

⎜ cd cs cb ⎟ 

⎜V V V ⎟ 

⎝ td ts tb ⎠ 


At 

At 

| V 

the 

λ = 

λ = 

ub 

the 

A = 

A = 

| 

1% 

V 

us 

3% 

0. 

809 

and 

→ ρ -η 

Unitarity relation of interest 

V udV ub * +VcdV cb * +VtdV tb * = 0 

Choice of parameters: 

0. 

2257 

V 

cb 

level : 

= sinθ 

level : 

2 

/ λ 

± 

| V 

± 

0. 

024 

td 

| 

plane 

c 

0. 

0021 

Vus γ 

V 

cb 

( 0 , 0) 

( 1, 

0) 

2008-07-03 Kowalewski - CPT@ICTP 4 

η 

R u 

( ρ, η) 

λ , A, 

ρ and η 

α 

R 

cd 

∗ 

ub 

∗ 

cb 

R t 

β 

Vud 

V 

2 

R u = ≈ − ρ + η 

V V 

t 

= 

Unitarity: 1 + R t + R u = 0 

V 

V 

td 

cd 

V 

V 

∗ 

tb 

∗ 

cb 

≈ 

γ = argV 

− 

* 

ub 

, 

2 

( 1− 

ρ) 

+ 

2 

η 

2 

e 

α = π − γ −β 

i γ 

e 

ρ 

−iβ

In all cases many 

different modes 

accessible in e + e - 

|V ub | / |V cb |, 

semileptonic 

B decays 

Direct CP 

asmmetries, e.g. 

B + D 0 K + /D 0 K + 

Observables 

CP asmmetries in 

b uqq transitions 

with BB mixing 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

B d and B s 

oscillations, 

bsγ, bdγ 

CP asmmetries in 

bccs transitions 

with BB mixing 


Trees and loops 

Tree-dominated Tree dominated processes are ~free of new physics 

B 

b 

W 

ℓ 

ν 

q c, u 

q 

New physics, even at a high mass scale, can induce 

effects in loop-dominated loop dominated processes (e.g. W + H + ) 

B 0 

b W d 

t t 

d W b 

B 0 

Compare CKM parameters from tree and loop processes 


B 

b 

q 

B - 

W 

t 

W 

s 

q 

K - 

D 0 

K - 

p

Experimental setting: e + e- Y(4S) Y(4S)BB 

20 MeV above BB threshold; no additional pions 

B mesons have small speed β ~ 0.06 in Y(4S) frame 

Decay products of B and B overlap in detector 

e + e- qq continuum decays also produced 

At asymmetric B factories, B vertices differ by 260μm 260 

qq 

on 

off peak peak 

(q=u,d,s,c) 


2m B 

BB

Belle and BaBar 

World’s World s highest luminosities - 

corresponds to 800 (500 500) ) 10 6 

BB events for Belle (BaBar BaBar) 

BaBar – 

531 fb -1 

Belle – 

817 fb -1 


CP violation in B decay 

Need interference between competing amplitudes 

B0 Decay to CP eigenstate + BB mixing 

Only neutral B mesons 

Clean CKM info if 1 decay amplitude dominates 

CP violation in interfering decay amplitudes 

Need strong interaction phase shift information 

Can exploit D 0 decays to CP 

decays to CP eigenstates, DCSD 

CP violation in BB mixing process – tiny in SM 

Several mechanisms can be present 


CP 

CP 

CP B = e B 

0 + 2iθ 

0 

CP B = e B 

0 −2iθ 

0 

CP Violation in Mixing 

off-shell off-shell 

on-shell on-shell 

arbitrary phase 

⎛ M − Γ M − Γ12⎞ 

= ⎜ ⎟ 

⎝ − Γ − Γ ⎠ 

i i 

2 12 2 

eff * 

M12 i 

2 

∗ 

12 M i 

2 

q q B H B M 

CP violation iff ≠ 1 where = = 

p p M 

2 0 

eff 

0 * i * 

12 − 2 Γ12 

0 

B Heff 0 

B 

i 

12 − 2 Γ12 

HFAG average: |q/p | q/p| | = 1.0025± 1.0025 0.0019 


H

a 

f 

CP 

CP violation in the interference 

between mixing and decay 

fCP 

λf = η CP f ⋅ CP 

p AfCP 

CP eigenvalue −2iβ 

B 

0 

Γ( 

B phys ( t) 

→ f CP ) − Γ( 

B 

( t) 

= 0 

0 

Γ( 

B ( t) 

→ f ) + Γ( 

B 

= 

C 

f 

CP 

phys 

⋅ 

cos( 

Δm 

B 

q 

d 

CP 

A 

0 

t) 

+ S 

f 

≈ e 

CP 

0 

phys 

phys 

( t) 

→ 

( t) 

→ 

⋅ sin ( Δm 

amplitude 

ratio 


B 

d 

f 

f 

CP 

CP 

t) 

) 

) 

0 

B 

mixing 

0 phys 

C 

S 

fCP 

fCP 

= 

Af 

CP 

λ ≠ ± 1 ⇒ Prob( 

Bphys(t) 

→ fCP) 

≠ Prob(B 

(t) → fCP) 

f CP 

0 

phys 

−iMt 

−Γt 

/ 2 

We have |q/p|≈1. If one amplitude 

dominates, |A/A|≈1, but Im(λ)≠0 

0 

B 

[ ( ) ( ) ] 

0 

0 

cos Δmt/ 

2 B + i( 

p/ 

q) 

sin Δmt/ 

2 

( t) 

= e e 

B 

1 − | λ 

1 + | λ 

2Imλ 

= 

1 + | λ 

fCP 

fCP 

Af 

CP 

| 

| 

2 

2 

fCP 

2 

f | 

CP 

fCP

− 

e 

Υ( 

4S) 

Outline of the measurement 

+ 

e 

0 rec 

B 

0 

Btag 

J/ψ 

Δt ≈ 

Δz 

Δz/ 

K s 

B-Flavor Tagging 


βγ 

μ - 

c 

μ + 

Exclusive 

B Meson 

Reconstruction 

(flavor eigenstates) lifetime, mixing analyses 

p - 

p + 

(CP eigenstates) CP analysis 

ℓ - 

K -

β (φ1) ) determination 

Time-dependent Time dependent CP asymmetries in bc transitions 

Golden mode for theory and experiment: experiment: 

B 0Xcc Tree amplitude dominates 

~no additional weak phases 

ccKS,L S,L 

error on S=sin2β: S=sin2 : estimates from 0.001 to 0.017 

Charmonium Xcc cc decays to lepton pairs 

Easy to reconstruct; good definition of decay vertex 

~all K 0 S decays can be reconstructed 

α (φ 2 ) 

Even K 0 L can be used due to kinematic constraints 

γ (φ 3 ) β (φ 1 ) 


Golden modes for β (φ ) 1 

B0 Xcc cc K (*)0 (Xcc cc = J/ψ, J/ , ψ(2S), (2S), χc1, c1, 

ηc; ; K 0 or K *0 K 0p0 ) 

Results compiled by HFAG 

sin2β= 0.714±0.032±0.018 

C=-A= 0.049±0.022±0.017 sin2β= 0.650±0.029±0.018 

C=-A=-0.018±0.021±0.014 

HFAG average: 

sin2β= 0.680±0.025 

C=-A= 0.012±0.020 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


Other β measurements 

Many other modes exhibit Time-dependent Time dependent CP violation 

(TDCPV) yielding β: 

B0DDKS, , DCP CPh0 , DDalitz DDalitzh0 

, K + K-K0 , … 

Analyses of decays involving different spin or Dalitz 

amplitudes give sensitivity to cos2β: cos2 : 

rules out mirror solution for β 

Too many measurements to mention here; significant 

(>3σ) (>3 ) CP asymmetries in 11 individual modes 


Penguin modes for β (φ ) 1 

TDCPV in bqqs penguin decays measures βeff eff in SM; 

e.g. modes B 0φK0 , η ( ’ ) K0 , p0K0 , f 0K0 , K 0K0K0 , etc. 

βeff eff ≠β due to additional EW 

phase; δβ varies per mode 

Interest in bqqs continues, 

consistency with golden modes 

depends on data selection, 

estimate of theory uncertainties 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


f 0 K S

Prospects for β (φ ) 1 

Super-B Super B with 10 36 luminosity (assume 75 ab -1 dataset) 

[projections taken from arXiv:0709.0451] 

sin2β sin2 from charmonium: 

charmonium: 

±0.005 0.005 (detector syst) syst 

Uncertainties of few % in bcʉd modes (stat) 

Uncertainties of few % in bsss modes (theory) 

Self-consistency Self consistency of above modes constrains NP 

Highly accurate knowledge of β pins down CKM 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


TDCPV in bu transitions 

Measuring α (φ ) 2 

Many final states have contributions from >1 amplitude 

(tree, Penguin, color-suppressed color suppressed tree) 

Asymmetries proportional to αeff; eff; 

differs from α by a 

mode-dependent mode dependent offset 

Full isospin amplitude analysis needed to determine δα 

Most useful modes in practice: 

B0 ρ0ρ0 , ρ + ρ- , B + ρ + ρ0 B0 p0p0 , p + p- , B + p + p0 B0 p + p-p0 Dalitz 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


B0 pp 

B pp; pp; 

easy easy 

experimentally (except p0p0 , for which time-dependent 

time dependent 

asymmetry can’t can t readily be measured) 

In each case need isospin analysis 

to determine δα; ; hope for A 00 

hh 8-fold fold ambiguities in solution for α 

analysis (Gronau Gronau, , London PRL65: PRL65:3381(1990)) 

3381(1990)) 

00 á Ahh 

+- 

hh 

BF(B 0 + p p- )=(5.2±0.2)x10 

)=(5.2 0.2)x10-6 BF(B 0 0 p p0 )=(1.3±0.2)x10 

)=(1.3 0.2)x10-6 HFAG 

(big! big!) 

A hh +- /√2 

A hh 00 

A hh +0 = Ahh -0 

BaBar, PRD76:091102(2007) 


A hh +- /√2 

θ 

À 

θ–À = 2 δα 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

No TDCPV 

input in 

B 0 p 0 p 0 

A hh 00

B0 ρρ 

B ρρ; ρρ; 

polarization determines CP eigenvalue 

experiment: ~full longitudinal polarization (CP even) 

Isospin analysis as for pp, pp, 

but ρ0ρ0 easier, smaller 

BF(B 0 + ρ ρ- )=(24.2±3.2)x10 

)=(24.2 

BF(B 0 HFAG 

0 ρ ρ0 )=( 1.1±0.4)x10 

1.1 

Impact of A(B 0 ρ 0 ρ 0 ) 

arXiv:0708.1630 

3.2)x10-6 0.4)x10-6 B 0 ρ 0 ρ 0 

A hh +- /√2 

A hh +- /√2 

A hh +0 = Ahh -0 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


θ 

À 

preliminary 

θ–À = 2 δα 

Angle 

constrained 

by TDCP in 

B 0 ρ 0 ρ 0 

A hh 00 

A hh 00

Main input for α (φ ) 2 

B p + p- : S +- C +- 

Belle -0.61 0.61±0.10 0.10±0.04 0.04 -0.55 0.55±0.08 0.08±0.05 0.05 

BaBar -0.60 0.60±0.11 0.11±0.03 0.03 -0.21 0.21±0.09 0.09±0.02 0.02 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

B ρ + ρ- : S +- 

L C +- 

L fL Belle 0.19±0.30 0.19 0.30±0.08 0.08 -0.16 0.16±0.21 0.21±0.08 0.08 0.941±0.037 

0.941 0.037±0.030 0.030 

BaBar -0.17 0.17±0.20 0.20±0.06 0.06 0.01±0.15 0.01 0.15±0.06 0.06 0.992±0.024 

0.992 0.024±0.026 0.026 


Constraints on α (φ ) 2 

Isospin analyses on pp, pp, 

ρρ; ρρ; 

Dalitz analysis on ρp 

Combined result is 

α = 

UTfit 

91± 

o 

8 

α = 

CKMfitter 

( ) o 6. 

2 

87 . 5 5. 

3 

+ 

− 

α (φ 2 ) 

SuperB projects 1-2° 1 in ρρ, ρρ, 

2° 2 in ρp 

and 3° 3 in pp; pp theory limited 

γ (φ 3 ) β (φ 1 ) 


Direct CP violation 

Interference between competing amplitudes (e.g. tree 

and penguin) involve strong phase shifts uncertainty 

Important special case: CP eigenstates or doubly CKM- 

suppressed decays lead to same final state of D0 and D0 . 

Favored: V cb V us * 

b 

u 

V cs * Vub : suppressed 

s 

u K u 

(*)- 

u 

Common K s 

(*)- 

B- B- final state 

A 

A 

c 

u 

D (*)0 

− 0 

− 

( B →D 

K ) 

B − 

− 0 − 

( B D K ) = rBe e 

→ 

iδ 

iγ 

f 

D (*)0 

Parameters: γ, 

(r B , δ B) per mode 


c 

u 

b

Accessing γ (φ ) 3 

Need interference common final state for D 0 and D0 CP eigenstates (Gronau ronauLondon ondonWyler yler): D 

): D0K + K- , p + p- , KS K p0… Double CKM-suppressed CKM suppressed (Atwood ( twoodDunietz unietzSoni oni): D 

3-body body Dalitz (Giri iriGrossman rossmanSoffer offerZupan upan, 

): D 0 K + p - … 

, Bondar): Bondar): 

Ksp + p-… Measure asymmetries between B + and B - decays and 

ratios of average decay rates to gain sensitivity to 

magnitude (r ( B) ) and phase (δ ( B) ) of amplitude ratio 

These are tree-level tree level decays insensitive to NP 

Self-tagging Self tagging B 0 D (*)0 (*)0K *0 (K *0 

α (φ 2 ) 

*0K + p- ) also measure γ 

TDCPV in B 0D (*)+ h- and D (*) (*)-h + measures sin(2β+γ) sin(2 

γ (φ 3 ) β (φ 1 ) 


Observables for γ (φ ) 3 

GLW: CP +/- +/ eigenstates 

r B, δ B, γ 

8-fold 

ambiguity 

on γ 

ADS: DCSD 

r B, δ B, r D, δ D, γ 

 

 

ADS 

ADS 

Γ 

= 

Γ 

Γ 

= 

Γ 

 

 

Γ 

Γ 

− 

− + 

+ 

( B → D± 

K ) − Γ( 

B → D± 

K ) ± 2rB 

sinδ 

B sin γ 

= 

− 

− + 

2 

( B → D± 

K ) + Γ( 

B → D± 

K ) 1+ 

rB 

± 2rB 

cosδ 

B cosγ 

− 

− + 

+ 

( B → D± 

K ) + Γ( 

B → D± 

K ) 2 

= 1+ 

r 2 cosδ 

cos 

0 

0 

B ± r 

− 

− + 

B B 

( B → D K ) + Γ( 

B → D K ) 

CP± 

= + 

Γ 

Γ 

CP± 

= + 

amplitude 

ratio 

A 

A 

− + − − 

( B →D[ 

K π ] K ) 

− + − − 

( B →D[ 

K π ] K ) 

− + − − + − + + 

( B → [ K π ] K ) − Γ( 

B → [ K π ] K ) 

− + − − + − + + 

( B → [ K π ] K ) + Γ( 

B → [ K π ] K ) 

− + − − + − + + 

( B → [ K π ] K ) + Γ( 

B → [ K π ] K ) 

− − + − + + − + 

( B → [ K π ] K ) + Γ( 

B → [ K π ] K ) 

2rBr 

= 


= r 

2 

B 

D 

+ r 

2 

D 

= 

r 

B 

sin 

 

e 

iδ 

B 

e 

( δ + δ ) 

B 

ADS 

+ 2r 

r 

B 

D 

D 

cos 

−iγ 

sin γ 

γ (φ 3 ) β (φ 1 ) 

r 

α (φ 2 ) 

D 

e 

−iδ 

D 

γ 

( δ + δ ) cosγ 

B 

D

Dalitz method for γ (φ ) 3 

Most precise results from Dalitz method: 

B-[K [KSp + p- ]K (*)- ]K(*) 

; also use D *0 D*0 

0 D p0 , D0γ Amplitude (m + ↔ m- D0 ↔ D0 ) 

A 

± 

at point 

( 2 2 ) ± iγ 

iδ 

B 

m+ 

, m− 

+ rBe 

e 

2 2( 

± 

m m K ) 

( 2 

f m− 

, 

2 ) + 

= f 

m 

Determine f in flavor-tagged 

D *+ D 0 p + decays 

± ⇒ π 

need D 0 decay model (~18 quasi- quasi 

2-body body states) 

Can remove modeling error using 

ψ(3770) (3770)DD data (CLEOc ( CLEOc, , BES) 

BaBar also analyze D 0KSK + K- s 

Belle ADS 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


K S p - 

K S p + p + p-

Dalitz method results 

Quote Cartesian variables: x ±=rB cos(±γ+δ), cos ), y ±=rB sin(±γ+δ) sin( 

x 

y 

x 

y 

− 

− 

+ 

+ 

BaBar [arXiv 

+ 

+ 

− 

− 

0. 

090 

0. 

053 

0. 

067 

0. 

015 

± 

± 

± 

± 

: 0804.2089] 

0. 

043 

0. 

056 

0. 

043 

0. 

055 

± 

± 

± 

± 

0. 

015 

0. 

007 

0. 

014 

0. 

006 

383M BB 

± 

± 

± 

± 

0. 

011 

0. 

015 

0. 

011 

0. 

008 

Belle [arXiv 

B - DK - 

B - DK - 

B + DK + 

Similar results in 

D * K and DK * 

0. 

105 

0. 

177 

0. 

107 

0. 

067 

0. 

047 

0. 

060 

0. 

043 

0. 

059 

0. 

011 

0. 

018 

0. 

011 

0. 

018 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

BaBar dashed, Belle solid 


+ 

+ 

− 

− 

: 0803.3375] 

± 

± 

± 

± 

± 

± 

± 

± 

657M BB

Combined results for γ (φ ) 3 

γ (φ3 ) β (φ1 ) 

Three methods (ADS, GLW and Dalitz) Dalitz) 

can be combined 

for each of B -D 0K- , B-D *0 *0K- and B -D 0K *- 

SuperB: SuperB: 

1-2% 1 2% from all methods combined; 

statistics limited 

α (φ 2 ) 


The left side - |Vub| | / |V | ub cb 

cb | 

The determination of the |V | ub| ub| 

and |V | cb| cb| 

relies on 

semileptonic decays only one hadronic current 

Tree decays – like γ, , insensitive to NP 

Two complementary approaches: 

Exclusive: 

Exclusive: 

X fully reconstructed 

Need form factor normalization (non-perturbative 

(non perturbative) 

Inclusive: : sum over many X 

states, with at most partial 

reconstruction of the X system 

Inclusive 

Use OPE in (1/m b) n 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


B 

b 

q 

W 

X 

ℓ 

ν

Exclusive semileptonic decays 

Conceptually simple – measure F( 

B 

W 

D * 

ℓ 

ν 

measure F(qq 22 )|V cb | 

QCD uncertainties enter calculation of form-factors form factors F 

One form-factor form factor per Lorentz structure in amplitude 

Shapes versus qq 22 can be measured 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

* 

2 2 

( B → D ν ) GF 

V 

2 2 2 

= ( F( 

q ) G( 

q ) 

dΓ l 

cb 

dq 

Normalization from theory uncertainty (~2% now) 


2 

q 2 = (p ℓ +p ν ) 2 

(momentum transfer) 2 

3 

48π 

phase 

space 

form factors

|Vcb| | from BD B 

cb 

* ℓν 

Measure decay rate versus 

4-velocity velocity transfer w and 

determine F(1)|V cb| 

cb and FF slope 

F(w) F(w) 

= F(1)* F(1) * [1 - ρ2 (w-1)+ (w 1)+…] 

Many experiments have done so; 

average has P(χ P 2 ) = 2.6% 

scale cale errors by ◊χ2 /ndf=1.5 

so F(1)|Vcb| 

| = (35.9 ± 0.8)×10 0.8) 10-3 F(1)|V cb 

Latest lattice value is [1] 

F(1) = 0.930 ± 0.023 

Laiho et al., arXiv:0710.1111 

[1] Laiho 

Determine 

V 

( 38. 

6 ± 0. 

9 ± 1. 

0 ) 

Determine 

cb 

= exp th 

× 10 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


−3

Vub 

|Vub| | from B pℓν 

ub 

Use analyticity and unitarity constraints 

plus measured dΓ/dq d /dq2 to fit FF shape; then 

normalize at any q 2 

Fit determines 

|Vub| ub| 

f +(q (q2 =0) = (91 ± 3BF BF ± 6shape FF normalizations |Vub| ub| 

values 

Choose 

= 

( + 0. 

6 ) −3 

3. 

5 × 10 

− 0. 

5 

shape)*10 )*10-5 LCSR 0.26 ± 0.04 

LQCD (FNAL) 0.25 ± 0.03 

LQCD (HPQCD) 0.27 ± 0.03 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

BaBar 

PRL 98 (2007) 091801 

f +(0) (0) |Vub|*10 ub 

35 ± 3 

36 ± 3 

33 ± 3 

|*10 4 


+ 6 

−5 

+ 5 

−4 

+ 4 

−3

Inclusive semileptonic decays γ (φ3 ) β (φ1 ) 

Theoretical tool: Heavy Quark Expansion (OPE) 

1 

Γ ∑ 2m 

4 4 

( B → X ) = ( 2π 

) δ ( p − p ) 

= 

G 

2 

F 

B 

m 

5 

b 

3 

192π 

Quark model result 

( 1+ 

A ) 

Express decay rate as double expansion in αs and 1/m b 

Perturbative corrections are calculable 

EW 

⎫ 

+ ... ⎬ 

⎭ 

α (φ 2 ) 

Non-perturbative 

Non perturbative matrix elements (e.g. μ 2 

p ) arise at 

each order in 1/m b; ; determine in fits moments 


A 

B 

pert 

X 

X 

L 

eff 

B 

2 2 

⎧ μπ 

+ 3μG 

⎨1 

+ 0 − 2 

⎩ 2mb 

2 

Simplified 

form for 

massless X 

First correction O((Λ/m b) 2 )

|Vcb| | from inclusive decays 

cb 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

n n 

Calculate moments (M ( x , Ee ) of inclusive processes bcℓν 

and bsγ for various cuts on lepton (photon) energy: 

n 

M x 

El 

> E 

0 

n 

x 

2 2 3 3 

= τ ∫ B M X dΓ 

= fn 

( E0, 

mb, 

mc, 

μG 

, μπ 

, ρD 

, ρLS 

) 

E 

0 

e or γ 

energy cut 

b-quark quark 

mass 

Kinetic scheme 

Benson, Bigi, Gambino, Mannel, Uraltsev 

(several papers) 

c-quark quark 

mass 

Matrix elements 

appearing at order 

1/m 2 

b and 1/mb 1/m 3 

1S scheme 

Bauer, Ligeti, Luke, Manohar, Trott 

PRD 70:094017 (2004) 

Fit ~60 measured moments from DELPHI, CLEO, BABAR, 

BELLE, CDF to determine ~6 parameters 


Global moment fit results 

Scheme |V cb| (10 -3 ) 

Kinetic 41.68 ± 0.39 ± 0.58 ΓSL 

1S 41.56 ± 0.39 ± 0.08τ B 

Choose 

Vcb 

= 

−3 

( 41. 

6 ± 0. 

6) 

× 10 

Source mb (GeV GeV) 

mb[kin] b[kin (global fit) 4.61 ± 0.03 

mb[kin] b[kin (global fit, no bsγ) 4.68 ± 0.05 

mb[kin] b[kin (bb threshold) 4.56 ± 0.06 

mb[1S] b[1S] (global fit) 4.70 ± 0.03 

mb[1S] b[1S] (global fit, no bsγ) 4.75 ± 0.06 

mb[1S] b[1S] (bb threshold) 4.69 ± 0.03 

arXiv:0803.2158 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

χ 2 /ndf is too good (e.g. 39/62 for 

kinetic, 25/63 for 1S); suggests 

theory errors (included in fit) may 

be overestimated 

m b is crucial for |V ub | 

Use (or not) of bsγ in 

global fit still controversial 


Vub 

|Vub| | from inclusive decays 

ub 

Measurement of inclusive bu SL rate 

requires cuts to suppress large bc 

background 

OPE convergence ruined in limited 

phase space 

Non-perturbative 

Non perturbative distribution f n 

needed; measure it in bsγ 

Other issues: large mb dependence, 

weak annihilation 

Measure many partial rates 

(Ee, , M X, , q 2…) ) and compare 

with calculated rates 

= 

−3 

( 4. 

12 ± 0. 

15 ± 0. 

40) 

× 10 

PDG 2008 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 

BELLE 

hep-ex/0504046 

• Bosch, Lange, Neubert, Neubert, 

Paz (BLNP) 

Phys.Rev.D73,073008(2006) 

• Gambino, Gambino, 

Giordano, Ossola, Ossola, 

Uraltsev (GGOU) 

JHEP 0710:058(2007) 

• Andersen and Gardi (DGE) JHEP 0601:097 (2006) 

• Aglietti, Aglietti, 

Di Lodovico, Lodovico, 

Ferrera, Ferrera, 

Ricciardi (AC) 

arXiv:0711.0860 


α (φ 2 ) 

|Vub| | and |V | 

ub 

cb| | summary cb 

γ (φ3 ) β (φ1 ) 

Determinations from inclusive and exclusive decays are 

independent, both experimentally and theoretically 

Inclusive 

Exclusive : 

| avg has P(χ P( 2 )=3%; 

scale error by ◊χ2 /ndf=2.1 

|Vcb| cb 

: 

Vcb 

V 

V 

= 

cb 

cb 

= 

= 

− 

( 41. 

6 ± 0. 

6) 

× 10 

−3 

( 38. 

6 ± 1. 

3) 

× 10 

−3 

( 41. 

2 ± 1. 

1) 

× 10 

SuperB + theory improvements ~1% on |V | cb|, cb|, 

2-3% 2 3% 

on |V | ub| ub| 

for each of inclusive/exclusive determinations 


3 

V 

V 

ub 

ub 

= 

= 

( 4. 

12 ± 0. 

43) 

( + 0. 

6 ) −3 

3. 

5 × 10 

−0. 

5 

× 10 

−3 

|Vub | avg has P(χ P( 2 )=40% 

Vub 

= 

−3 

( 3. 

95 ± 0. 

35) 

× 10

The long side - |Vtd td | 

Constraints come from precise experimental knowledge 

of BB mixing: 

= 0.507±0.005 0.005 ps -1 (HFAG) 

Δms = 17.77±0.10 

17.77 0.10±0.07 0.07 ps -1 (CDF 

Δm d = 0.507 

(CDF PRL97:242003(2006)) 

PRL97:242003(2006) ) 

Dominant uncertainty in |V | td| td| 

and |V | ts| ts| 

due to non- 

perturbative QCD input 

|Vtd/V td/Vts| 

ts| 

= (0.209 ± 0.006)*10 -3 (PDG) 

Also accessible in radiative decays BK B * γ, Bργ 

Need calculated ratio of form factors 

|Vtd/V td/Vts| 

ts| 

= (0.21 ± 0.04)*10 -3 (PDG) 

α (φ 2 ) 

γ (φ 3 ) β (φ 1 ) 


Constraints on UT 

Putting all constraints together, we determine the apex 

of the UT as 

É = 0.141 +0.029 -0.017 0.017 CKMfitter 

¿ = 0.343 +0.016 

+0.016 -0.016 0.016 

É = 0.147 ± 0.029 

¿ = 0.342 ± 0.016 

0.029 UTfit 

No significant departure from 

SM at present 

Current results from UTfit 

95% c.l. 

bands 


Trees and loops… loops 

Recall that some quantities are determined in tree-level tree level 

processes (e.g. |V | ub|) ub|) 

while others involve BB mixing or 

“penguin penguin” amplitudes. 

Current accuracy is modest; tests NP amplitudes at the 

~100% level 


Unitarity triangle outlook 

SuperB 

scenarios from 

Ciucchini et al. 

“the reality” 


Backup slides

Standard Model and CPV: the CKM Unitary Triangle Angles ... - ICTP

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