recent developments on ckm angles · 2014. 3. 12. · 2)sind b sing 1+(rf d) 2 +2rf d cosd f d...

Recent developments on CKM angles

Wei Wang

Helmholtz-Institut fur Strahlen- und Kernphysik, Bonn

Flavor Physics & CP Violation, Buzios, Rio, 19-24 May 2013(FPCP 2013)

Wei Wang (HISKP) CKM angles Buzios, Rio, 19-24 May 2013 1 / 24

Why are we particularly interested indetermining the CKM angles?


■ Direct search at hadron colliderHiggs vs New particles beyond the SM

■ Flavor PhysicsTest of SMIndirect search of new degree of freedom


Why are we interested in determing CKM angles?

CKM unitarity triangle and

CPV parameter convention

Wolfenstein parametrization Irreducible complex phase

causes CP Violation (CPV)!

Comprehensive test;

measure all the angles and

sides.

B system : very good place, all the angles are O(0.1)!

(β)

(α)

(γ)

b→ u

transition B0-B0 mixing


StatusLeft: evolution plot (UTFit ); Right: HFAG Average of sin(2β/ϕ1) from all experiments.

year

sin

2β sin(2β) ≡ sin(2φ1)

-2 -1 0 1 2 3

BaBarPRD 79 (2009) 072009

0.69 ± 0.03 ± 0.01

BaBar χc0 KSPRD 80 (2009) 112001

0.69 ± 0.52 ± 0.04 ± 0.07

BaBar J/ψ (hadronic) KSPRD 69 (2004) 052001

1.56 ± 0.42 ± 0.21

BellePRL 108 (2012) 171802

0.67 ± 0.02 ± 0.01

ALEPHPLB 492, 259 (2000)

0.84 +-01

.

.80

24 ± 0.16

OPALEPJ C5, 379 (1998)

3.20 +-12

.

.80

00 ± 0.50

CDFPRD 61, 072005 (2000)

0.79 +-00

.

.44

14

LHCbLHCb-PAPER-2012-035

0.73 ± 0.07 ± 0.04

Belle5SPRL 108 (2012) 171801

0.57 ± 0.58 ± 0.06

AverageHFAG

0.68 ± 0.02

H F A GH F A GCKM 2012

PRELIMINARY

β = ϕ1 = (21.5+0.8−0.7)

◦.


Status

Average taken from CKMFitter

(deg)α0 20 40 60 80 100 120 140 160 180

p-va

lue

0.0

0.2

0.4

0.6

0.8

1.0

CKM12 (prel.)

CKMf i t t e r

(BABAR)πρ/ρρ/ππ (Belle)πρ/ρρ/ππ (WA)πρ/ρρ/ππ

CKM fit

(deg)γ0 20 40 60 80 100 120 140 160 180

p-va

lue

0.0

0.2

0.4

0.6

0.8

1.0

Winter 12

CKMf i t t e r

Full Frequentist treatment on MC basis

D(*) K(*) GLW + ADSD(*) K(*) GGSZ Combined

CKM fit

WA

α = ϕ2 = (88.5+4.7−4.4)

◦ γ = ϕ3 = (66 ± 12)◦.α + β + γ = (176 ± 13)◦.


Status

Recent results for γ from B → DK (from HFAG)

BaBar Belle LHCbγ (69+17

−16)◦ (68+15

−14)◦ (71.1+16.6

−15.7)◦

rB 0.092+0.013−0.012 0.112+0.014

−0.015 0.0919+0.0083−0.0082

δB (105+16−17)

◦ (116+18−21)

◦ (112.0+12.6−15.5)

◦

Ref. arXiv:1301.1029 CKM2012 preliminary LHCb-CONF-2012-032

Naive average: γ = (69.3 ± 9.3)◦.α + β + γ = (179.3 ± 10.4)◦.


Development:New Measurements

+ New Channels+ New Effects


New measurements of α/ϕ2:cf talk by Pit VANHOEFER in this conference

New measurements of β/ϕ1:cf talk by Riccardo DE SANGRO in this conference

New measurements of γ/ϕ3:cf talk by Matteo RAMA, Till Moritz KARBACH in this conference

We shall do everything to reduce the errors.


New Channels


γ = ϕ3 constraint via B → DK

Principle Methods and ReferenceD0 or D∗0 → CP eigenstate GLW PLB 253, 483 (1991)

PLB265,172(1991)Enhance CP asymmetry by ADS, PRL78,3357(1997)

suppressed D decay PRD63,036005(2001)Dalitz distribution in three- GGSZ, PRD68,054018(2003)

body D decay (KSπ+π−, etc)

Very clean weak phase information


γ from B → DK∗0,2 in GLW method

In B → DCPK, sensitive to a small ratio of interfering amplitudes.√

2A(B+ → D0±K+) = A(B+ → D0K+)± A(B+ → D0K+),

√2A(B− → D0

±K−) = A(B− → D0K−)± A(B− → D0K−),

Vanishing decay constant for K∗0,2:

⟨K∗−0 (1430)|sγµu|0⟩ = fK∗

0pµ

K∗0∼ 0, ⟨K∗−

2 (1430)|sγµu|0⟩ = 0.

Color-allowed and color-suppressed amplitudes are comparable inB → DK∗

0,2!


γ from B → DK∗0,2 in GLW method

50 60 70 80 90 1002345678

Γ HaL

RC

P+K

0*

50 60 70 80 90 100

-0.5

0.0

0.5

Γ HbL

AC

P+K

0*

50 60 70 80 90 1000.51.01.52.02.53.03.5

Γ HcL

RC

P+K

0*

50 60 70 80 90 100-1.0

-0.5

0.0

0.5

1.0

Γ HdL

AC

P+K

0*

50 60 70 80 90 100

0.8

1.0

1.2

1.4

Γ HeL

RC

P+K

0*

50 60 70 80 90 100

-0.4-0.2

0.00.20.4

Γ HfL

AC

P+K

0*

Large CPasymmetriesare expectedin B → DK0,2.Even betterin B → Dπcounterpart.WW, 1110.5194


Determining γ via Three-body B → KKK andB → Kππ:

Solution Fit 1 Fit 2 Fit 3

I 31+3−2 31 ± 2 31+2

−3

II 76+3−2 78+2

−3 77 ± 3III 261+2

−4 259 ± 3 258+4−3

IV 314 ± 2 315 ± 2 315+3−2

Bhattacharya, Imbeault,

London, 1303.0846

Based on SU(3)symmetry analysis of

the Dalitz plot.cf David LONDON’stalk in this conference

α + β + γ = (187 ± 5.6)◦


New Effects


CPA effects on γ

Large CPA in D0 → (K+K−, π+π−) was observed by LHCb, CDF and Belle (2011, 2012):

indCPa

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

dir

CP

a∆

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02 BaBarCPA∆ Belle Prelim.CPA∆ LHCbCPA∆ CDF Prelim.CPA∆

LHCbΓA BaBar Prelim.ΓA Belle Prelim.ΓA

∆adirCP

= aK+K− ,dirCP − aπ+π− ,dir

CP= (−0.678 ± 0.147)%

Question: How large is the impact on the extraction of γ ifACP ∼ O(0.1 − 1%)?

Warning: Large CPA is not confirmed by the recent LHCb measurement: 1303.2614;LHCb-CONF-2013-003


CPA effects on γ in GLW method

A(D0 → f ) = TfD(1 + rf

De−iγ+iδfD ),

A(D0 → f ) = TfD(1 + rf

Deiγ+iδfD ),

AK+ =

B(B− → D0+K−)−B(B+ → D0

+K+)

B(B− → D0+K−) + B(B+ → D0

+K+)

=1

RK+

[(1 − (rK

B )2)Adir

CP(D0 → f ) +

2rKB (1 + (rf

D)2) sin δK

B sin γ

1 + (rfD)

2 + 2rfD cos δ

fD cos γ

]≡ 2rK

B sin δKB sin γeff /RK

+. (1)

∆γ ≡ γeff − γ = O(AdirCP/rK

B ) ∼ a few degrees!

WW, 1211.4539; Martone, Zupan, 1212.0165; Bhattacharya, London, Gronau, Rosner, 1301.5631


CPA effects on γ

The direct CP asymmetry effects in R+:

RK+ = 2

B(B− → D0+K−) + B(B+ → D0

+K+)

B(B− → D0K−) + B(B+ → D0K+)

= 1 + (rKB )

2 +2rK

B cos δB[(1 + (rfD)

2) cos γ + 2rfD cos δ

fD]

1 + (rfD)

2 + 2rfD cos γ cos δ

fD

≡ 1 + (rKB )

2 + 2rKB cos δK

B cos γeff (2)

-1.0 -0.5 0.0 0.5 1.0

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

ACP H%L

DΓH°L

Depending on the strongphase difference inD → K+K−/π+π− de-cays, the shift of γ can reach0.5◦!


CPA effects on γ in B → DK (D → KSπ+π−)Dalitz plot analysis

Resonance Contribution to γ bias (◦)Amplitude Phase

CF K∗(892) +0.09 ± 0.27 −0.87 ± 2.09CF K∗

0 (1430) −0.05 ± 0.05 −0.23 ± 0.35CF K∗

2 (1430) +0.07 ± 0.12 −0.04 ± 0.07CF K∗(1410) +0.01 ± 0.02 −0.21 ± 0.37ρ(770) +0.27 ± 0.89 −0.24 ± 0.97ω −0.32 ± 0.21 −0.25 ± 0.36f0(980) −0.02 ± 0.13 −0.02 ± 0.38f2(1270) −0.09 ± 0.10 −0.06 ± 0.09f0(1370) −0.09 ± 1.06 +0.01 ± 0.26ρ(1450) −0.02 ± 0.19 −0.09 ± 0.22σ1 −0.31 ± 0.78 −0.09 ± 0.62σ2 −0.07 ± 0.08 −0.04 ± 0.56DCS K∗(892) −0.04 ± 0.24 +0.22 ± 0.15DCS K∗

0 (1430) +0.23 ± 0.44 −0.12 ± 0.21DCS K∗

2 (1430) −0.30 ± 0.56 +0.03 ± 0.04Total −2.65 ± 3.17

Bondar, Dolgov, Poluektov,Vorobiev, arXiv:1303.6305CP violating contributions inD → KSπ+π− decay to the γmeasurement bias


ϕs

V*ts!

_ _

t!

st!

b

b

s _

w!w! Bs!Bs!_!

mixing induced CP violation

CKM ansatz: CPV is due to a complex phase in the quark mixing matrix

Bs

Bs !"#�Bs

Bs

A

A!Į!

= !"#�

A

A!Į!

Bs-Bs mixing

_

ȡs=arg[−VtsVtb*/VcsVcb*]Ď


ϕs from Bs → J/ψϕ

Bs0 B

s0

Bs(Bs)→J/ψ(µ+µ-) φ(K+K-) can proceed directly or through mixing

Angular analysis to disentangle different CP-eigenstates



LHCb

arXiv:1112.3183

SM :φs= −2β

s= −0.04

LHCb :φs= 0.15± 0.18± 0.06

[rad]sφ

0 2 4

]-1

[

ps

sΓ

∆

-0.2

-0.1

0

0.1

0.2 best fit68% CL

90% CL

95% CL

Standard Model

LHCb

Penguin pollutions?



X.Liu, WW, Y.H. Xie,

in preparation.

Bhattacharya, A. Datta, D. London 1209.1413

4φs!

λij=ηi

j q

p

Aij

Aij≡| λi

j| e

−iφij


Conclusions

■ New measurements are reducing the errors and soon we will beable to test the unitarity of CKM:

α + β + γ = 180◦? :: (179.3 ± 10.4)◦.

■ New Channels can provide complementary power and useful toincrease the statistical significance.

■ There are always something unexpected!

Thank you for your attention!


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recent developments on ckm angles · 2014. 3. 12. · 2)sind b sing 1+(rf d) 2 +2rf d cosd f d...

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