Direct CP violation in 3-body B decays

XS2014, Hefei

May 06, 2014

Hai-Yang Cheng

Academia Sinica

in collaboration with Chun-Khiang Chua

2222

Direct CP asymmetries (2-body)

ACP(K-) – ACP(K-

)

Bu/Bd K-

K- K*0 K*-

K- f2(1270) K-

ACP(%)

-8.20.6

295

-378 195 -236

-68+20-18

3711 -134

S

13.7 5.8 4.6 3.8 3.8 3.6 3.4 3.3Bu/Bd K- K*- K-

K-

*

ACP(%)

-145 104 3113 4.02.1

-209

2011

4324

116 4525

S 2.8 2.5 2.4 1.9 1.8 1.8 1.8 1.8 1.8

12.22.2

5.5

Bs K+-

ACP(%)

264

S 7.2

No CP asymmetry observed by LHCb in B- K-

K puzzle: AK is naively expected to vanish

B- K-

ACP(%)

2.22.3

3

Direct CP asymmetries (3-body)

LHCb found evidence of inclusive CP asymmetry in B- , K+K-K-, K+K-

BaBar(%) Belle(%) LHCb(%) Average

3.24.4+4.0-3.7 11.72.11.1 10.52.2

K+ K- K- -1.7+1.9-1.41.4 -4.30.90.8 -3.71.0

K- 2.82.02.3 4.92.62.0 3.20.80.8 3.31.0

K+ K- 0103 -14.14.01.9 -11.94.1

Large asymmetries observed in localized regions of p.s.

ACP(KK) = -0.6480.0700.0130.007 for mKK2 <1.5 GeV2

ACP(KKK) = -0.2260.0200.0040.007 for 1.2< mKK, low2 <2.0 GeV2, mKK, high

2 <15 GeV2

ACP() = 0.5840.0820.0270.007 for m, low2 <0.4 GeV2, m, high

2 > 15 GeV2

ACP(K) = 0.6780.0780.0320.007 for 0.08< m, low2 <0.66 GeV2, mK

2 <15 GeV2

4

K+K+K-

K+K+-

K-+-

5

Zhang, Guo, Yang [1303.3676]

Bhattacharya, Gronau, Rosner [1306.2625]

Xu, Li, He [1307.7186]

Bediaga, Frederico, Lourenco [1307.8164]

Gronau [1308.3448]

Cheng, Chua [1308.5139]

Zhang, Guo, Yang [1308.5242]

Lesniak, Zenczykowski [1309.1689]

Di Salvo [1309.7448]

Xu, Li, He [1311.3714]

Cheng, Chua [1401.5514]

Ying Li [1401.5948]

Bhattacharya, Gronau, Imbeault, London, Rosner [1402.2909]

Wang, Hu, Li, Lu [1402.5280]

Ying Li [1402.6052]

Wen-Fei Wang’s talk on May 8th

Cheng, Chua, Soni [0704.1049]

666

Many three-body B decays have been observed with BFs ~10-5

(BFs ~ 10-6 for B KK & Bs KKK)

useful for extracting CKM angles, CP violation

A(B→P1P2P3)= resonant + nonresonant (NR)

All the quasi-2-body B decays, B→VP,SP (except 00, ) are extracted from Dalitz plot analysis of 3-body decays

NR signal is less than 10% in D decays. Many argued that 3-body B decays are also dominated by resonant contributions

KKKKKKB

KKKKKKKKKKKKB

KKKKKKKKKB

s

SSS

SS

000

000000

,,

,,,,,

,,,,

(LHCb)

77

BaBar Belle

B-→K+K-K- 6824 78±10

B0→K+K-K0 ~ 130

B0→K-KSKS ~ 196

B0→K0+- 22.1+3.6-3.0 41.9+5.3

-5.7

B-→K-+- 17.1+12.5-2.5 34.0+3.0

-2.8

B0→K-+0 19.73.6 15.67.7

B-→+-- 34.9+9.0-6.2

Nonresonant fraction (%)

KKK: 70-90%

K: 35-40% by Belle,

20% by BaBar

K0: 15-20%

: 35%

One of our goals is to identify the origin of NR signals

NR contributions are essential in three-body B decays

A striking feature: Large NR fractions in penguin-dominated modes

Three-body B decays

HYC, Chua, Soni (’07)

P1

P2

P3

P1

P2

P3

All three mesons energetic

All three mesons energetic, but two of them nearly parallel

b

(a)

(b)

8

P1P2

P3

Two energetic (P1, P2) & one soft (P3)

(d)

P2

(c)P1

P3 All three energetic & two of them nearly parallel. The spectatorquark is kicked by a hard gluon to become hard

(b) & (c) mimic 2-body decays

9

Three factorizable amplitudes for B0→K+K-K0

current-induced process: <B0→K0><0→K+K->

transition process: <B0 → K-K0><0→K+>

annihilation process: <B0→0><0→K+K-K0>

b→s b→u

1010

b→u KKKB 000

])()(2[2

|)(|)()(0|)(|)(

13232

1222

021

03

ssmsmrmf

BbupKpKuspK

KBKK

NR

Early attempt: Apply HMChPT to evaluate form factors r and

B0K-

K0

B0

K-

B-

B0

K0

K-

K0

B*0s

B0

K0

B*0s

K-

B-

+,r

+,-,r

r

r

Bajc, Fajfer, Oakes, Pham; Deandrea et al. (’99)(CLY)2; Wise; Burdman, Donoghue

NR contribution of

11

1221 ).( ipppHMChPTtransition

NR eeAA BNR

-- HMChPT is recovered in soft meson limit, p1, p2→0

-- The parameter NR » 1/(2mB) is constrained from B-→+--

NR rates for tree-dominated B→KK, will become too large

For example, Br(B-→K+K-)NR = 3310-6 larger than total BF, 510-6

⇒ HMChPT is applicable only to soft mesons !

Ways of improving the use of HMChPT have been suggested before

We propose to write NR amplitude as

Fajfer et al; Yang, HYC,…

12

b→u

0B

BbuSimms

S

BbuVimms

VBbupp

iSSS

i

iVVV

iR

iii

iii

|)(|1

|

|)(|1

||)(|)()(

2

221

B-

-

-

+

1212

V=, , …, S=f0(980), f0(1370), f0(1500), f(1710),…

Resonant contribution of

1313

b→s

KKKB 000

0||1

|0||

0||1

|0||

2

2

qqSimms

SKKqqKK

qqVimms

VKKqqKK

SSS

R

VVV

R

NRR KKKKKK 000

)()(

0||),( ,0|| ,0||)(

12

*1212

mm

mff

mfVpVfmqqSpfqqpS

SSS

VVSSS

Decay constants for scalar mesons have been evaluated in various approaches Chua,Yang, HYC; C.D. Lu et al

How about the NR contributions ?

1

2221

2

ln)(

,)(

' ,00

s

s

x

s

xesF

imsm

csF

FFFFFFFFFF

iNR

hhh

hh

NRKK

emNRKK

em

ch, x1, x2 fitted from kaon e.m. data

motivated by asymptotic constraint from QCD counting rules

i

sNRNR

iii

KKiii eFF

v

imsm

gfmssKK 23

NR2)'23(

30||

<K+K-|qq|0> can be related to the kaon’s e.m. form factors

qqv

NR

Chua,Hou,Shiau,Tsai (’03)

Brodsky, Farrar (’75)

NR

exp[i/4](3.39+0.18-0.21) GeV

from K+K- spectrum of K+K-KS

from KSKSKS rate 14

The fitted ch agrees with the model (~ decay constant x strong coupling)

15

The decay amplitude of B0 K+K-K0 consists of two pieces:

Nonresonant: <B0 K+K-><0 K0> <B0 K0><0 K+K-> (<B0 K0><0 K+K->)penguin

Resonant: B0 f0K0 K+K-K0 , f0 = f0(980), f0(1500), f0(1710),… B0 VK0 K+K-K0, V = , , ,…

Weak phase: CKM matrix elementsStrong phases: (i) effective Wilson coefficients (ii) propagator (s - m2 + im)-1

(iii) matrix element <M1M2|qq|0> for NR contribution in the penguin sector

16

B-→K+K-K-

BF(10-6)

theory errors: () , (ms, NR, form factors), ()

Large NR rate is penguin-dominated and governed by <K+K-|ss|0>NR

NR rates: mostly from b→s (via <KK|ss|0>)

and a few percentages from b→u transitions

calculable for the first time

17

Belle (’13): Br(B0 K+ K- 0) = (2.170.65)10-6 is a surprise !

We predict a larger rate of +-0 than +-- as the former receives and 0 resonant contributions with BF of order 2010-

6, while only 0 to the latter.

1

200

2)(

)(

a

a

KKBA

KKBA

At short-distance level, we obtain BF ~ 510-8

Long-distance contribution due to B0 +-0 followed by +- K+K- rescattering BF 0.510-6

Recall that Br(B- K+K--) = (5.00.7)10-6

18

Expt (%) Theory(%) 2007

11.72.4 8.7+2.0-2.2 4.4+0.4

-0.4

K+ K- K- -4.31.2 -7.1+2.5-1.6 -10.4+2.1

-1.8

K- 3.21.1 -3.7 -3.3+0.9-0.6

K+ K- -14.14.4 13.1 17.5+2.9-5.1

)(

)(

)(

)( ,

)(

)(

)(

)(

KKB

KB

KBA

KKBA

B

KKKB

KKKBA

BA

CP

CP

CP

CP

U-spin symmetry (s d)

Relative signs between K-K+K- & and between K- & K+K- agree with experiment & U-spin symmetry predictions

However, relative signs between -K+K- & and between K- & K+K- disagree with the data

Xu, Li, He; Bhattacharya, Gronau, Rosner

Inclusive direct CP asymmetries

19

)(

)(

)(

)( ,

)(

)(

)(

)(

KKKB

KB

KBA

KKKBA

B

KKB

KKBA

BA

CP

CP

CP

CP

Naïve U-spin symmetry relations

However, momentum dependence of decay amplitudes should be taken into account

Correlation seen by LHCb:

ACP(K-K+K-) – ACP(K-+-), ACP(-K+K-) – ACP(-+-)

It has been conjectured that CPT theorem & final-state rescattering of +- K+K- may play important roles

isNR

NRsNR

NR eedsppKesspKpK 1212 0||)()( 0||)()( 2121

Xu, Li, He (I, ’13)

FSI

Bediaga et al

Xu, Li, He (II, ’13)

20

410||)()(12

22

2112

s

mmeedsppK Kis

NRNR

12

22

21 410||)()( 12

s

mmeesdppK Kis

NRNR

Fit to B- K-+

U-spin symmetry

U-spin symmetry which relates <K|sd|0> to <KK|ss|0> is badly broken

21

Direct CP violation in 3-body Bu,d decays

Theory (%) Expt (%)

8.7+1.7-1.9 11.72.4

()region 22.5+2.9-3.3 58.48.7

K+ K- K- -7.1+4.8-4.1 -4.31.2

(K+ K-K-)region

-17.7+4.9-2.9 -22.62.2

K- 2.7+0.7-0.8 3.21.1

(K- )region 14.1+13.9-11.7 67.88.5

K+ K- -10.0+2.1-2.7 -14.14.4

(K+K)region -18.2+1.8-1.8 -64.87.2

K- K -9.2+0.0-0.0

K-K+KS -5.5+1.5-1.1

K-KSKS 3.5+0.3-0.2 45

predictions

2222

K+K+K-

K+K+-

K-+-

23

Regional CP asymmetries due to NR contributions

Except K+K-K- the magnitude of local CP asymmetries is substantially reduced by nearby resonances

(ACPregion)NR+RES 22.5+2.9

-3.3 14.1+13.9-11.7 -18.2+1.8

-1.8 -17.7+4.9-2.9

Wang et al. 51.9+16.7-23.9

Zhang, Guo, Yang advocated that local CP violation in +-- arises from interference of 0 with f0(500)

24

BFs & CP violation in 3-body Bs decays

Penguin-dominated modes K0K-+, K0K+ have largest rates, dominated by K*0(1430) resonances

Tree-dominated mode K+K-K0 is predicted to have BF ~ 1.410-6

(10-6)(10-6)

LHCb made first observation of three charmless 3-body Bs decays

ACP(K0K+K-) - 2ACP(K0)

Pen

gu

in-d

om

inated

Tree-d

om

inated

25

U-spin symmetry relations

They cannot be tested by the present available data, but can be checked by dynamical calculations.

U-spin relations are generally not well respected as U-spin symmetry is sometimes badly broken

26

Conclusions

CP asymmetries are the ideal places to discriminate between different models.

Three-body B decays receive sizable NR contributions governed by the matrix elements of scalar densities.

Three sources of strong phases responsible for direct CP violation in 3-body B decays.