Analysis of charmless B decays in Factorization Assisted Topological amplitude approach

Transcription

1 Analysis of charmless B decays in Factorization Assisted Topological amplitude approach Si-Hong Zhou Institute of High Energy Physics,CAS August 24, 2016 Based on work collaorated with Cai-Dian Lu and Qi-An Zhang 1/21

2 Outline Introduction/Motivation Factorization Assisted Topological Amplitude approach Numerical results for B PP,PV decays and Analysis Summary 2/21

3 Rich physics in hadronic B decay Be important for testing the standard model. Exploration of CP violation via the interference of tree and penguin contriutions; Direct access to the parameters of CKM matrix; FCNC processes e sensitive to signals of new physics. The BarBar and Bell experiments and LHC experiment have made great efforts in studying B decays information in the past decades. Non-leptonic B decays are complicated on account of strong interaction effects. 3/21

4 QCD-methods ased on factorization work well for the leading power of 1/m expansion Perturative QCD approach ased on k T factorization; Keum, Li, Sanda, 00 ; Lu, Ukai, Yang, 00 collinear QCD Factorization approach; Beneke, Buchalla, Neuert, Sachrajda, 99º Soft-Collinear Effective Theory. Bauer, Pirjol, Stewart, 01º Unavailale for 1/m power corrections ork well for most of charmless B decays, except for ππ and πk puzzle etc. 4/21

5 Topological diagrammatic approach[cheng, Chiang and Kuo 2015] u (a)t u ()C d, s (c)e u q (d)a q 1. Distinct y weak interaction and flavor flows with all strong interaction encoded, including non-perturative ones. 2. Amplitudes with strong phases extracted from data. 3. Based on flavor SU(3) symmetry. SU(3) reaking effect was lost. 4. B PP, VP and PV fitted separately, = 32 parameters. Less predictive (Phys. Rev. D 91, no. 1, (2015).) Improved y Factorization Assisted Topological amplitude (FAT)approach. keep flavor SU(3) symmetry reaking effect. further reducing the numer of free parameters y fitting all the decay channels 5/21

6 Topological diagrammatic approach[cheng, Chiang and Kuo 2015] u (a)t u ()C d, s (c)e u q (d)a q 1. Distinct y weak interaction and flavor flows with all strong interaction encoded, including non-perturative ones. 2. Amplitudes with strong phases extracted from data. 3. Based on flavor SU(3) symmetry. SU(3) reaking effect was lost. 4. B PP, VP and PV fitted separately, = 32 parameters. Less predictive (Phys. Rev. D 91, no. 1, (2015).) Improved y Factorization Assisted Topological amplitude (FAT)approach. keep flavor SU(3) symmetry reaking effect. further reducing the numer of free parameters y fitting all the decay channels 5/21

7 Factorization Assisted Topological amplitude approach first applied in hadronic D decays [H. n. Li, C. D. Lu and F. S. Yu, Phys. Rev. D 86, (2012),Phys. Rev. D 89, no. 5, (2014)] as in great success to resolve the long-standing puzzle from the large difference of D 0 π + π and D 0 K + K ranching fractions. Also predicted 0.1% of direct CP asymmetry difference etween them. Analysis of Two-ody Charmed B meson decays in Factorization Assisted Topological amplitude approach, S. H. Zhou, Y. B. ei, Q. Qin, Y. Li, F. S. Yu and C. D. Lu, Phys. Rev. D 92, no. 9, (2015) with only 4 parameters and predict more than 100 modes. 6/21

8 Factorization Assisted Topological amplitude approach first applied in hadronic D decays [H. n. Li, C. D. Lu and F. S. Yu, Phys. Rev. D 86, (2012),Phys. Rev. D 89, no. 5, (2014)] as in great success to resolve the long-standing puzzle from the large difference of D 0 π + π and D 0 K + K ranching fractions. Also predicted 0.1% of direct CP asymmetry difference etween them. Analysis of Two-ody Charmed B meson decays in Factorization Assisted Topological amplitude approach, S. H. Zhou, Y. B. ei, Q. Qin, Y. Li, F. S. Yu and C. D. Lu, Phys. Rev. D 92, no. 9, (2015) with only 4 parameters and predict more than 100 modes. 6/21

9 Factorization Assisted Topological amplitude approach in B PP, VP and PV decays (a)t u Color-favored tree emission diagram (T) u ()C It is proved factorization to all order of α s expansion in soft-collinear effective theory. d, s (c)e u q (d)a q T P1P2 = i G F 2 V u V uq a 1 (µ)f p2 (m 2 B m2 p 1 )F BP1 0 (m 2 p 2 ), T PV = 2G F V u V uq a 1 (µ)f V m V F B P 1 (m 2 V )(ε V p B), T VP = 2G F V u V uq a 1 (µ)f P m V A B V 0 (m 2 P )(ε V p B), (1) The SU(3) reaking effect is automatically kept No free parameter 7/21

10 For other diagrams dominated y non-factorization contriutions. e factorize out the decay constants and form factor to keep the SU(3) reaking effect. we extract the amplitude and strong phase from experimental data y χ 2 fit. color-suppressed tree emission diagram(c) u C P1P2 = i G F 2 V u V uq χ C e iφc f p2 (m 2 B m2 p 1 )F BP1 0 (m 2 p 2 ), C V P = 2G F V u V uq χ C e iφc f P m V A B V 0 (m 2 P )(ε V p B), C PV = 2G F V u V uq χ C e iφc f V m V F B P 1 (m 2 V )(ε V p B), (2) ()C χ C and e iφc and χ C e iφc to distinguish cases in which the emissive meson is pseudo-scalar or vector respectively. 8/21

11 The annihilation type diagrams(e and A) d, s u q q (c)e (d)a -exchange topology (E) is non-factorization in QCD factorization approach(nlo) E P1P2 = i G F V u V uq χ E e iφe f B m 2 B (f p 1 f p2 ), 2 E PV,V P = 2G F V u V uq χ E e iφe f B m V ( f Pf V f 2 π f 2 π )(ε V p B), (3) As discussed in conventional topological diagram approach, -annihilation diagram (A) contriution is negligile. 9/21

12 The penguin topological diagrams are grouped into QCD penguin and electro-weak penguin topologies. u,c,t g q q g(z, γ) u,c,t (a)p ()P C(P E) d, s u,c,t g q q u,c,t g q (c)p E (d)p A 10/21

13 color-favored penguin emission diagram (P) u,c,t g q 1. The leading contriution from topology (a)p Pdiagram is similar to diagram T, which is proved factorization in various QCD-inspired approaches. 2.»chiral enhanced¼penguin contriutions need to e fitted. P PP = i G F 2 V t V tq [a 4(µ)+χ P e iφp r χ ]f p2 (m 2 B m2 p 1 )F BP1 0 (m 2 p 2 ), P PV = 2G F V t V tq a 4(µ)f V m V F B P 1 m 2 V(ε V p B ), P VP = 2G F V t V tq [a 4(µ) χ P e iφp r χ ]f P m V A B V 0 (m 2 P )(ε V p B). (4) 11/21

14 power correction to P-penguin annihilation diagram (P A ) u,c,t g q u,c,t g q (a)p (d)pa P A is similar with P and the difference is only at QCD not E. P PP = i G F 2 V t V tq [a 4(µ)+χ P e iφp r χ ]f p2 (m 2 B m2 p 1 )F BP1 0 (m 2 p 2 ), P PV = 2G F V t V tq a 4(µ)f V m V F B P 1 m 2 V(ε V p B ), P V P = 2G F V t V tq [a 4(µ) χ P e iφp r χ ]f P m V A B V 0 (m 2 P)(ε V p B ). (5) The contriution of P A can e included in χ P, except for B PV decays, where we need two more parameters P PV A = 2G F V t V e tq χpa iφp A f B m V ( f Pf V fπ 2 )(ε V p B). (6) 12/21

15 P E diagram is argued smaller than P A diagram, which can e ignored relialy in decay modes not dominated y it, except B s π + π decay. Br(B s π + π ) = (0.76±0.19) 10 6 q d, s u,c,t g q q g(z,γ) u,c,t (c)pe ()PC(PE) The flavor-singlet QCD penguin diagram P C only contriute to the isospin singlet mesons η, η, ω and φ. P PP C P VP C P PV C = i G F 2 V t V tq χpc e iφp C f p2 (m 2 B m 2 p 1 )F BP1 0 (m 2 p 2 ), = 2G F V t V e tq χpc iφp C f P m V A B V 0 (m 2 P)(ε V p B ), = 2G F V t V tq χp C e iφ P C f V m V F1 B P (m 2 V )(ε V p B), (7) 13/21

16 P E diagram is argued smaller than P A diagram, which can e ignored relialy in decay modes not dominated y it, except B s π + π decay. Br(B s π + π ) = (0.76±0.19) 10 6 q d, s u,c,t g q q g(z,γ) u,c,t (c)pe ()PC(PE) The flavor-singlet QCD penguin diagram P C only contriute to the isospin singlet mesons η, η, ω and φ. P PP C P VP C P PV C = i G F 2 V t V tq χpc e iφp C f p2 (m 2 B m 2 p 1 )F BP1 0 (m 2 p 2 ), = 2G F V t V e tq χpc iφp C f P m V A B V 0 (m 2 P)(ε V p B ), = 2G F V t V tq χp C e iφ P C f V m V F1 B P (m 2 V )(ε V p B), (7) 13/21

17 All together we have 14 parameters to e fitted for all B PP,PV and VP decays. Recent update for B PP channels with η η mixing y Hsiao, Chang He, PRD93, (2016), have 12 parameters input parameters V CKM with the olfenstein parameters: λ = ± , A = ρ = 0.117±0.021, η = 0.353± Tale: The decay constants of light pseudo-scalar mesons and vector mesons (in unit of MeV).(5% uncertainty) f π f K f B f Bs f ρ f K f ω f φ /21

18 All together we have 14 parameters to e fitted for all B PP,PV and VP decays. Recent update for B PP channels with η η mixing y Hsiao, Chang He, PRD93, (2016), have 12 parameters input parameters V CKM with the olfenstein parameters: λ = ± , A = ρ = 0.117±0.021, η = 0.353± Tale: The decay constants of light pseudo-scalar mesons and vector mesons (in unit of MeV).(5% uncertainty) f π f K f B f Bs f ρ f K f ω f φ /21

19 Tale: The transition form factors of B meson decays at q 2 =0 and dipole model parameters(10 % uncertainty) F0 B π F0 B K F Bs K 0 F B ηq 0 F Bs ηs 0 F(0) α α F1 B π F1 B K F Bs K 1 F B ηq 1 F Bs ηs 1 F(0) α α A B ρ 0 A B ω 0 A B K 0 A Bs K 0 A Bs φ 0 A(0) α α For the q 2 dependence of the transition form factors, we use the dipole parametrization: F i (q 2 ) = F i (0) q 1 α 2 q 1 +α 4 Mpole 2 2 Mpole 4, 15/21

20 Gloal Fit for all B PP,VP and PV decays 37 ranching Ratios and 11 CP violation oservations data are used for the fit. the est-fitted parameters as: χ C = 0.48±0.06, φ C = 1.58±0.08, χ C = 0.42±0.16, φ C = 1.59±0.17, χ E = 0.057±0.005, φ E = 2.71±0.13, χ P = 0.10±0.02, φ P = 0.61±0.02. χ PC = 0.048±0.003, φ PC = 1.56±0.08, χ P C = 0.039±0.003, φ P C = 0.68±0.08, χ PA = ±0.0008, φ PA = 1.51±0.09, (8) with χ 2 /d.o.f = 45.2/34 = 1.3. Large strong phase This χ 2 per degree of freedom is smaller than the conventional flavor diagram approach. 16/21

21 Predict ranching fractions for B PP,VP and PV and CP violation. Tale: Branching fractions ( 10 6 ) of various B PP decay modes Mode Amplitudes Exp This work π π 0 T,C,P E 5.5 ± ± 0.39 ± 1.02 ± 0.02 π η T,C,P,P C,P E 4.02 ± ± 0.25 ± 0.64 ± 0.01 π η T,C,P,P C,P E 2.7 ± ± 0.21 ± 0.49 ± 0.01 π + π T,E,(P E ),P 5.12 ± ± 0.36 ± 1.31 ± 0.14 π 0 π 0 C,E,P,(P E ),P E 1.91 ± ± 0.30 ± 0.28 ± 0.05 π 0 η C,E,P C,(P E ),P E < ± 0.08 ± 0.08 ± 0.04 π 0 η C,E,P C,(P E ),P E 1.2 ± ± 0.08 ± 0.10 ± 0.03 ηη C,E,P C,(P E ),P E < ± 0.09 ± 0.08 ± ηη C,E,P C,(P E ),P E < ± 0.13 ± 0.14 ± η η C,E,P C,(P E ),P E < ± 0.05 ± 0.07 ± K K 0 P 1.31 ± ± 0.04 ± 0.26 ± 0.01 K 0 K 0 P 1.21 ± ± 0.03 ± 0.25 ± 0.01 π K 0 P 23.7 ± ± 0.6 ± 4.6 ± 0.2 π 0 K T,C,P,P E 12.9 ± ± 0.32 ± 2.35 ± 0.10 ηk T,C,P,P C,P E 2.4 ± ± 0.13 ± 1.19 ± 0.03 η K T,C,P,P C,P E 70.6 ± ± 4.7 ± 11.3 ± 0.22 π + K T,P 19.6 ± ± 0.54 ± 4.0 ± 0.2 π 0 K 0 C,P,P E 9.9 ± ± 0.26 ± 1.96 ± 0.09 ηk 0 C,P,P C,P E 1.23 ± ± 0.10 ± 1.02 ± 0.03 η K0 C,P,P C,P E 66 ± ± 4.5 ± 10.6 ± /21

22 Mode Amplitudes Exp This work π ρ 0 T,C,P,PA,PE 8.3± ±1.81±1.38±0.03 π ω T,C,P,P C,PA,PE 6.9± ±1.46±1.09±0.02 π φ P C,PE < ±0.004±0.055±0.003 π 0 ρ T,C,P,PA,PE 10.9± ±0.73±2.30±0.12 ηρ T,C,P,PC,PA,PE 7.0± ±0.48±1.43±0.07 η ρ T,C,P,PC,PA,PE 9.7± ±0.34±0.97±0.05 π + ρ T,E,P,(PE),PA 14.6± ±0.64±3.20±0.38 π ρ + T,E,P,(PE) 8.4± ±0.47±1.70±0.25 π 0 ρ 0 C,C,E,P,PA,(PE),PE 2± ±0.47±0.09±0.14 π 0 ω C,C,E,P,PA,(PE),PE < ±0.88±0.24±0.07 π 0 φ P C,PE < ±0.002±0.025±0.001 ηρ 0 C,C,E,P,PC,P C,PA,(PE),PE < ±1.15±0.39±0.17 ηω C,C,E,P,PC,P C,PA,(PE),PE ±0.30±0.08±0.09 ηφ P C,PE < ±0.001±0.015± η ρ 0 C,C,E,P,PC,P C,(PE),PE < ±0.77±0.29±0.12 η ω C,C,E,P,PC,P C,(PE),PE ±0.21±0.05±0.06 η φ P C,PE < ±0.0008±0.01± K K 0 P,PA < ±0.06±0.10±0.01 K 0 K P 0.44±0.03±0.09±0.004 K 0 K 0 P 0.41±0.02±0.08±0.004 K 0 K 0 P,PA 0.55±0.05±0.09±0.01 π K 0 P,PA 10.1± ±0.95±1.78±0.15 π 0 K T,C,P,PA,PE 8.2± ±0.51±0.98±0.07 ηk T,C,P,PC,PA,PE 19.3± ±0.8±2.4±0.3 η K T,C,P,PC,PA,PE ±0.44±0.38±0.13 K ρ 0 T,C,P,PE 3.7± ±0.25±0.80±0.04 K ω T,C,P,P C,PE 6.5± ±0.73±1.13±0.06 K φ P,P C,PA,PE 8.8± ±1.21±0.69±0.50 K 0 ρ P 8± ±0.47±1.55±0.07 π + K T,P,PA 8.4± ±0.77±1.46±0.14 π 0 K 0 C,P,PA,PE 3.3± ±0.36±0.65±0.08 ηk 0 C,P,PC,PA,PE 15.9±1 16.6±0.7±2.3±0.3 η K 0 C,P,PC,P C,PA,PE 2.8± ±0.5±0.3±0.1 K ρ + T,P 7± ±0.44±1.65±0.07 K 0 ρ 0 C,P,PE 4.7± ±0.34±0.79±0.04 K 0 ω C,P,P C,PE 4.8± ±0.61±0.95±0.05 K 0 φ P,P C,PA,PE 7.3± ±1.12±0.64± /21

23 Hierarchy B ππ and B πρ T ππ : C ππ : E ππ : P ππ = 1 : 0.47 : 0.29 : 0.32 T ρπ : C πρ : P ρπ : P πρ E = 1 : 0.54 : 0.25 : 0.04 T πρ : C ρπ : P ρπ : P ρπ E = 1 : 0.36 : 0.19 : T > C(C ) > E P > P E. In agreement with those QCD inspired approaches B πk and B πk T πk : C πk : P πk : P πk E = 1 : 0.4 : 6.0 : 0.6 T πk : C K π : P πk : P πk A : P K π E = 1 : 0.37 : 2.87 : 1.44 : P E is even more larger than C P > P A > T > P E > C. 19/21

24 The long-standing puzzles of ππ ranching ratios Theoretically Br(B 0 π 0 π 0 ) < Br(B 0 π 0 ρ 0 ) < Br(B 0 ρ 0 ρ 0 ), ut experimentally it is in the inverse order(sensitive to C). Although some power corrections to C topology were parameterized in QCDF, PQCD and SCET, it is not resolved completely in those factorization approaches. this inverse order can e understood only in the formalism of Glauer gluons, where extra phase was introduced for the pseudo-scalar meson (Goldstone oson) emission diagram. Flavor diagram T C FAT(This work) π 0 emission : χ C = 0.48±0.06, φ C = 1.58±0.08, ρ 0 emission : χ C = 0.42±0.16, φ C = 1.59±0.17, Mode Amplitudes Exp( 10 6 ) This work( 10 6 ) Flavor diagram π 0 π 0 C,E,P,(P E ),P E 1.91 ± ± 0.30 ± 0.28 ± ± /21

25 Summary studied B PP,PV in factorization assisted topological amplitude approach. T was in factorization without free parameters. P E was also included. For most other topological diagrams, the corresponding decay constants, form factors were factorized out from them efore χ 2 fit assisted y factorization hypothesis to indicate the flavor SU(3) reaking effect. Only 14 universal non-perturative parameters to e fitted from all B PP,PV decay channels. the χ 2 per degree of freedom is smaller than the conventional flavor diagram approach. predict ranching fractions and CP asymmetry parameters of nearly 100 B u,d and B s decay modes. The long-standing puzzles of ππranching ratios has een resolved consistently. THANK YOU 21/21