CP Violation in Hadronic 3 body B Decays

CP Violation in Hadronic 3 -body B Decays Hai-Yang Cheng Academia Sinica, Taipei in collaboration with Chun-Khiang Chua Future Challenges in Non-Leptonic B Decays Bad Honnef, February 11, 2016

Direct CP asymmetries (3 -body) LHCb (’ 13) found first evidence of inclusive integrated CP asymmetry in B- + - -, K+K-K-, K+K- 2013 LHCb(%) 2014 LHCb(%) + - - 11. 7 2. 1 1. 1 5. 8 0. 9 0. 7 4. 2 K+ K - -4. 3 0. 9 0. 8 -3. 6 0. 4 0. 2 0. 7 4. 3 K+ K - - -14. 1 4. 0 1. 9 -12. 3 1. 7 1. 2 0. 7 5. 6 K- + - 3. 2 0. 8 2. 5 0. 4 0. 7 2. 8 + -: + K -: - Large asymmetries observed in localized small invariant mass regions of p. s. ACPlow(KK ) = -0. 648 0. 070 0. 013 0. 007 for m. KK 2 <1. 5 Ge. V 2 ACPlow(KKK) = -0. 226 0. 020 0. 004 0. 007 for 1. 2< m. KK, low 2 <2. 0 Ge. V 2, m. KK, high 2 <15 Ge. V 2 ACPlow( ) = 0. 584 0. 082 0. 027 0. 007 for m , low 2 <0. 4 Ge. V 2, m , high 2 > 15 Ge. V 2 ACPlow(K ) = 0. 678 0. 032 0. 007 for 0. 08< m , low 2 <0. 66 Ge. V 2, m. K 2 <15 Ge. V 2 2

LHCb (’ 14) measured another local CP asymmetry in the rescattering regions 1. 0 Ge. V < m , KK < 1. 5 Ge. V inclusive rescattering region low invariant mass region + - - 5. 8 0. 9 0. 7 17. 2 2. 1 1. 5 0. 7 58. 4 8. 2 2. 7 0. 7 K+ K- K- -3. 6 0. 4 0. 2 0. 7 -21. 1 0. 4 0. 7 -22. 6 2. 0 0. 4 0. 7 K+ K - - -12. 3 1. 7 1. 2 0. 7 -32. 8 2. 9 0. 7 -64. 8 7. 0 1. 3 0. 7 K- + - 2. 5 0. 4 0. 7 12. 1 1. 2 1. 7 0. 7 67. 8 3. 2 0. 7 Except the K+K-K- mode, local CP asymmetries in low invariantmass region are much larger than that in rescattering region |ACPlow | >> |ACPresc | >> |ACPincl | 3

B- + - 2014 LHCb 2013 LHCb ACPincl( ) = 0. 058 0. 014 inclusive (2013 data: 0. 117 0. 024) ACPres( ) = 0. 172 0. 027 for 1. 0 < m 2 < 2. 25 Ge. V 2 ACPlow( ) = 0. 584 0. 087 for m , low 2 < 0. 4 Ge. V 2, m , high 2 > 15 Ge. V 2 4

B - K - + 2013 LHCb 2014 LHCb ACPincl(K ) = 0. 025 0. 009 inclusive (2013 data: 0. 032 0. 012) ACPres(K ) = 0. 121 0. 022 for 1. 0 < m 2 < 2. 25 Ge. V 2 ACPlow(K ) = 0. 678 0. 085 for 0. 08< m , low 2 < 0. 66 Ge. V 2, m. K 2 < 15 Ge. V 2 5

B- K+ K- 2013 LHCb 2014 LHCb ACPincl(KK ) = -0. 123 0. 022 inclusive (2013 data: -0. 141 0. 044) ACPres(KK ) = -0. 328 0. 041 for 1. 0 < m. KK 2 < 2. 25 Ge. V 2 ACPlow(KK ) = -0. 648 0. 072 for m. KK 2 < 1. 5 Ge. V 2 6

B - K -K + K 2014 LHCb 2013 LHCb ACPincl(KKK) = -0. 036 0. 008 inclusive (2013 data: -0. 043 0. 012) ACPres(KKK) = -0. 211 0. 014 for 1. 0 < m. KK 2 < 2. 25 Ge. V 2 ACPlow(KKK) = -0. 226 0. 022 for 1. 2< m. KK, low 2 < 2. 0 Ge. V 2, m. KK, high 2 < 15 Ge. V 2 7

Zhang, Guo, Yang [1303. 3676] He, Li, Xu [1410. 0476] Bhattacharya, Gronau, Rosner [1306. 2625] Krankl, Mannel, Virto [1505. 04111] Xu, Li, He [1307. 7186] C. Wang, Zhang, Z. Wang, Guo [1506. 00324] Bediaga, Frederico, Lourenco [1307. 8164] Nogueira, Bediaga, Cavalcante, Frederico, Gronau [1308. 3448] Lourenco [1506. 08332] Cheng, Chua [1308. 5139] Bediaga, Magalhaes [1512. 09284] 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] 8

Three-body B decays Large nonresonant (NR) fractions in penguin-dominated B decay modes, recalling that NR signal is less than 10% in D decays Nonresonant fraction (%) Ba. Bar Belle B-→K+K-K- 68 24 78± 10 B 0→K+K-K 0 ~ 130 B 0→K-KSKS ~ 196 B 0→K 0 + - 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 B 0→K- + 0 19. 7 3. 6 15. 6 7. 7 B-→ + - - 34. 9+9. 0 -6. 2 KKK: 70 -90% K : 35 -40% by Belle, 20% by Ba. Bar K 0: 15 -20% : 35% NR contributions are essential in penguin-dominated B decays One of our goals is to identify the origin of NR signals HYC, Chua, Soni (’ 07)

P 2 P 1 All three mesons energetic b P 3 (a) P 2 P 3 All three mesons energetic, but two of them nearly parallel P 1 (b) P 3 P 2 P 1 (c) (b) & (c) mimic quasi-2 -body decays P 3 P 1 P 2 (d) All three energetic & two of them nearly parallel. The spectator quark is kicked by a hard gluon to become hard Two energetic (P 1, P 2) & one soft (P 3) 10

n Receive both resonant & NR contributions n Central 3 -body region can be explored by QCDF or p. QCD n 3 -body decays resemble quasi 2 -body ones through the use of 2 -meson distribution amplitude in the Dalitz-plot regions depicted by [Wang, Hu, Li, Lu (’ 14); Krankl, Mannel, Virto (’ 15)] n Regions with a soft meson emission [Suzuki (`00)] 11

n Most of theory studies focus only on either resonant or NR effects. We discuss both resonant & NR contributions based on factorization. Under the factorization approximation, there are three factorizable amplitudes for B 0→K+K-K 0 Ø current-induced process: <B 0→K 0><0→K+K-> Ø transition process: <B 0 → K-K 0><0→K+> Ø annihilation process: <B 0→ 0><0→K+K-K 0> b→s b→u 12

b→u NR contribution of n Early attempt: Apply heavy meson chiral perturbation theory (HMCh. PT) to evaluate form factors r and Bajc, Fajfer, Oakes, Pham; Deandrea et al. (’ 99) Yan et al. ; Donoghue et al. ; Wise (’ 92) K- B 0 B +, r *0 s K- K 0 B- B 0 K 0 B 0 K- K- K 0 +, -, r B 0 B r *0 s B- r 13

n NR rates for tree-dominated B→KK , will become too large For example, BF(B-→K+K- -)NR = 33 10 -6 larger than total BF, 5 10 -6 6 BF(B-→ + - -)NR = 75 10 -6 larger than total BF, 5. 3 10⇒ HMCh. PT is applicable only to soft mesons ! n Ways of improving the use of HMCh. PT have been suggested before Fajfer et al; Yang, HYC, … n We write tree-induced NR amplitude as p 2 p 1 -- HMCh. PT is recovered in soft meson limit, p 1, p 2→ 0 -- The parameter NR » 1/(2 m. B ) is constrained from B-→ + - - 14

b→s V = , , …, S = f 0(980), f 0(1370), f 0(1500), f(1710), … Decay constants of scalar mesons have been evaluated in various approaches Chua, Yang, HYC (’ 06); C. D. Lu et al. ; Z. G. Wang What about the NR contributions ? 15

<K+K-|q q|0> can be related to the kaon’s e. m. form factors ch, x 1, x 2 fitted from kaon e. m. data Chua, Hou, Shiau, Tsai (’ 03) motivated by asymptotic constraint from QCD counting rules Brodsky, Farrar (’ 75) Fitted ch agrees with the model (~ mass decay constant strong coupling) NR Resonant NR exp[i /4](3. 39+0. 18 -0. 21) Ge. V from K+K- spectrum of K+K-KS from KSKSKS rate Cheng, Chua, Soni (’ 05) 16

The decay amplitude of B 0 K+K-K 0 consists of two pieces: n Nonresonant: <B 0 K+K-><0 K 0> <B 0 K 0><0 K+K-> (<B 0 K 0><0 K+K->)penguin n Resonant: B 0 f 0 K 0 K+K-K 0 , f 0 = f 0(980), f 0(1500), f 0(1710), … B 0 VK 0 K+K-K 0, V = , , , … Weak phase: CKM matrix elements Strong phases: (i) effective Wilson coefficients (ii) propagator (s - m 2 + im )-1 (iii) matrix element <M 1 M 2|qq|0> for NR contribution in the penguin sector 17

B-→K+K-KBF(10 -6) 2. 9 0. 0 theory errors: ( NR) , (ms, NR, form factors), ( ) +0. 5 -0. 5 0. 0 calculable for the first time n Power corrections from QCDF added to Kn 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 tree transitions 18

B-→K- + - 2. 4 0. 0 +0. 6 -0. 5 0. 0 31. 0 3. 8 +1. 7 -1. 6 0. 65 0. 0 +0. 69 -0. 19 0. 0 n Power corrections from QCDF added to K*0 - and 0 Kn Ba. Bar has measured K 0*0(1430) - from B- KS 0 - 0 (2014) with a result consistent with Belle. An issue for QCDF and p. QCD. n If U-spin relation with =0 is used, it will lead to (i) too large BR’s for NR and total, (ii) CP asymmetries with wrong signs. Fit to BR 19

Tree-dominated B-→ + - -, K+K- - n NR B- + - - rate is used to fix the parameter NR n The predicted NR fraction is about 55% for B- K+K- - 20

Direct CP violation in 3 -body B decays n Correlation seen by LHCb: ACP(K-K+K-) – ACP(K- + -), ACP( -K+K-) – ACP( - + -) n U-spin symmetry (s d) predictions for the relative signs between K-K+K- & - + - and between K- + - & -K+K- agree with experiment: Xu, Li, He; Bhattacharya, Gronau, Rosner n However, relative signs between -K+K- & - + - and between K- + - & K-K+K- cannot be fixed from symmetry argument alone 21

Direct CP asymmetries Expt (%) NR Resonant NR + Res ( + - -)incl 5. 8 1. 4 25. 0+4. 9 -4. 1 5. 3+1. 6 -1. 3 8. 3+1. 7 -1. 9 (K+K- -)incl -12. 3 2. 2 -16. 3+0. 9 -0. 8 -10. 2+2. 2 -2. 9 (K- + -)incl 2. 5 0. 9 9. 1+2. 6 -2. 7 6. 9+2. 1 -1. 8 7. 3+2. 1 -2. 0 (K+ K-K-)incl -3. 6 0. 8 -7. 8+1. 9 -1. 7 1. 2+0. 0 -0. 0 -6. 0+2. 0 -1. 5 ( + - -)low 58. 4 8. 7 58. 3+4. 5 -3. 5 4. 5+1. 6 -1. 2 21. 9+3. 0 -3. 3 (K+K- -)low -64. 8 7. 2 -25. 0+3. 9 -6. 0 -4. 9+0. 5 -0. 4 -17. 5+1. 8 -1. 7 (K- + -)low 67. 8 8. 5 48. 9+10. 3 -13. 3 57. 1+8. 0 -16. 6 49. 4+9. 5 -14. 2 (K+ K-K-)low -22. 6 2. 2 -13. 0+3. 4 -3. 4 1. 6+0. 1 -0. 1 -16. 8+4. 5 -3. 9 -25. 6+2. 8 -3. 2 p. QCD (Wang et al. ) : 51. 9+16. 7 -23. 9 36. 7+7. 0 -5. 9 7. 0+1. 8 -1. 5 13. 4+2. 1 -2. 4 ( + - -)resc 17. 2 2. 7 (K+K- -)resc -32. 8 4. 1 -27. 7+4. 3 -6. 5 -5. 6+0. 5 -0. 4 -20. 4+2. 3 -2. 5 (K- + -)resc 12. 1 2. 2 31. 8+6. 5 -8. 1 1. 1+0. 6 -0. 5 4. 1+0. 9 -1. 0 (K+ K-K-)resc -21. 1 1. 4 -10. 8+2. 8 -2. 8 0. 96+0. 02 -0. 02 -3. 8+1. 6 -1. 1

Some issues on CP asymmetries n Final-state rescattering n CP violation in B- 0 n CP asymmetries at large invariant mass regions n The origin of the strong phase for B K , KK 23

Final-state rescattering It has been conjectured that CPT theorem & final-state rescattering of + K+K- may play important roles to explain the CP correlation observed by LHCb. Consider + - & K+K- rescattering and neglect possible interactions Bediaga et al with 3 rd meson Suzuki, Wolfenstein : inelasticity, assuming KK = For numerical calculations, we follow the parameterization of Pelaez and Yndurain 24

Expt (%) NR + Res FSI ( + - -)incl 5. 8 1. 4 8. 3+1. 7 -1. 9 -16. 7 (K+K- -)incl -12. 3 2. 2 -10. 2+2. 2 -2. 9 -19. 5 (K- + -)incl 2. 5 0. 9 7. 3+2. 1 -2. 0 0. 7 (K+ K-K-)incl -3. 6 0. 8 -6. 0+2. 0 -1. 5 -6. 4 ( + - -)low 58. 4 8. 7 21. 9+3. 0 -3. 3 -16. 7 (K+K- -)low -64. 8 7. 2 -17. 5+1. 8 -1. 7 -5. 0 (K- + -)low 67. 8 8. 5 49. 4+9. 5 -14. 2 2. 3 (K+ K-K-)low -22. 6 2. 2 -16. 8+4. 5 -3. 9 -15. 4 ( + - -)resc 17. 2 2. 7 13. 4+2. 1 -2. 4 11. 3 (K+K- -)resc -32. 8 4. 1 -20. 4+2. 3 -2. 5 -6. 9 (K- + -)resc 12. 1 2. 2 4. 1+0. 9 -1. 0 -0. 04 (K+ K-K-)resc -21. 1 1. 4 -3. 8+1. 6 -1. 1 -3. 8 Final-state + - K+Krescattering seems to be in wrong direction 25

CP violation in B- 0 n In naïve factorization, ACP( 0 -) ~ 0. 05. Bar obtained ACP =0. 18+0. 09 -0. 17. However, QCDF, p. QCD, SCET & diagrammatic approach all predict a negative & sizable CP violation for B- 0 -, ACP -0. 20 n LHCb has measured CP asymmetries in regions dominated by vector resonances I: 0. 47 < m( + -)low <0. 77 Ge. V, II: 0. 77 < m( + -)low <0. 92 Ge. V, III: 0. 47 < m( + -)low <0. 77 Ge. V, IV: 0. 77 < m( + -)low <0. 92 Ge. V, cos >0, cos <0, cos <0 ACP changes sign at m( + -) m Summing over regions I-IV yields CP asymmetry consistent with zero with slightly positive central value 26

If we follow QCDF to add power corrections to render ACP -0. 20, then CP violation in + - - induced by , f 0 resonances will become negative Expt (%) NR Resonant NR + Res ( + - -)incl 5. 8 1. 4 25. 0+4. 9 -4. 1 +1. 6 -16. 3 5. 3 -1. 3 +1. 7 -6. 7 8. 3 -1. 9 ( + - -)low 58. 4 8. 7 58. 3+4. 5 -3. 5 +1. 6 4. 5 -16. 8 -1. 2 21. 9 6. 0+3. 0 -3. 3 ( + - -)resc 17. 2 2. 7 36. 7+7. 0 -5. 9 +1. 8 -11. 4 7. 0 -1. 5 0. 4+2. 1 -2. 4 13. 4 An important issue needs to be resolved! 27

CP asymmetries at large invariant mass regions + - K + + K+K- - K+K-K- n ACP is large & positive at m 2( + -)low= 5 -10 Ge. V 2 and m 2( + -)high= 9 -12 Ge. V 2 0. 47 n Negative at m 2( )= 9. 5 -10. 5 Ge. V 2, m 2(K )=10 -18 Ge. V 2 -0. 09 n Large & negative at m 2(KK) =16 -25 Ge. V 2, m 2(K ) = 5 -10 Ge. V 2, 0. 36 positive at m 2(KK)= 7 -14 Ge. V 2, m 2(K ) =5 -13 Ge. V 2 -0. 41 ? n Positive at (i) m 2(KK)low = 3 -5 Ge. V 2, m 2(KK)high =18 -22 Ge. V 2, 0. 11 (ii) m 2(KK)low = 8 -9 Ge. V 2, m 2(KK)high =18 -19 Ge. V 2 0. 41 Predicted CP asymmetries at some large invariant mass regions agree with the data in sign except for K+K- - 28

The origin of the strong phase for B K , KK An additional phase is introduced in B- K- + - in order to accommodate (i) NR rate, (ii) sign of CP asymmetry. What is the origin of this phase? final-state interactions? 29

BFs & CP violation in 3 -body Bs decays LHCb made first observation of three charmless 3 -body Bs decays Penguin-dominated (10 -6) Tree-dominated n Penguin-dominated modes K 0 K- +, K 0 K+ - have largest rates, dominated by K*0(1430) resonances n Tree-dominated mode K+K-K 0 is predicted to have BF ~ 1. 4 10 -6 ACP(K 0 K+K-) - 2 ACP(K 0 + -) 30

Conclusions u Three-body B decays receive sizable NR contributions governed by the matrix elements of scalar densities. u Three sources of strong phases responsible for direct CP violation in 3 -body B decays. u In general, NR contributions alone yield large -violating effects. CP u It is important to pin down the mechanism responsible for regional CP asymmetries. 31

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