Hadronic B decays from SCET. Christian Bauer LBNL FPCP 2006, Vancouver

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1 Hadronic B decays from SCET Christian Bauer LBNL FPCP 2006, Vancouver

2 Outline of the Talk Introduction Hadronic B deays in SCET Phenomenology of Hadronic B decays Conclusions

3 Introduction

4 Flavor Physics in the SM Decays mediated by electroweak gauge bosons Propagate over distance scale 1/MEW fm Much less than distance of colliding particles 0.1 fm b Charged Current d u u + b Flavor Changing Neutral Current u u d b d u Local 4-fermion operator u

5 Flavor Physics beyond the SM Loop diagrams can get many additional contributions Propagate over distance scale 1/M EW fm Much less than distance of colliding particles 0.1 fm b Charged Current d u u + b Flavor Changing Neutral Current u u d b d u Local 4-fermion operator u

6 The Curse of QCD The weak interaction we are after is masked by QCD effects, which are completely non-perturbative

7 The Curse of QCD The weak interaction we are after is masked by QCD effects, which are completely non-perturbative

8 The Curse of QCD The weak interaction we are after is masked by QCD effects, which are completely non-perturbative Weak interaction effect we are after

9 The Curse of QCD The weak interaction we are after is masked by QCD effects, which are completely non-perturbative Weak interaction effect we are after Non-perturbative effects from QCD

10 The Curse of QCD The weak interaction we are after is masked by QCD effects, which are completely non-perturbative Weak interaction effect we are after Non-perturbative effects from QCD Crucial to understand long distance physics to extract weak flavor physics from these decays

11 Effective Field Theories Separate short distance from long distance effects Short distance physics is calculable perturbatively Long distance physics simplifies in limit ΛQCD/Q 0 Long distance physics is independent of the details of effects at short distances Measure the long distance effects in one process and use results in other processes

12 Hadronic B deays in SCET CWB, Pirjol, Rothstein, Stewart

13 Kinematics π E mb/2 B E mb/2 π Typical size of hadrons 1/Λ QCD E Λ QCD

14 General Idea SCET is effective theory describing interactions of collinear with soft particles Separate distance scales d 1/E and d 1/ΛQCD and study interactions of long distance modes Factorization theorems emerge naturally in SCET Separate d 1/E & d 1/Λ. Study non-perturbative effects in limit ΛQCD/E 0 At leading order, coupling between soft and collinear simple and in many cases absent Factorization is not assumed in SCET. The theory will tell you when amplitudes factorize and when not

15 SCET in pictures π E mb/2 E mb/2 B π 0.1fm 1fm b Heavy b quark almost at rest in B meson u E m b /2 (b) E m b /2 b quark decays into three light quarks, two in the same direction, one in opposing direction u d 1fm! 0.4fm 0.2fm! 1fm energetic quark requires spectator of the B meson to form pion. Factorization more subtle two quarks are very close until far from B meson. Thus no coupling between B and pion

16 Kinematics π E mb/2 B E mb/2 π B meson described by DOF with k µ Λ QCD Interpolating field B q s γ 5 h Pions described by DOF with Interpolating field π k µ (Λ 2 QCD /E π, E π, Λ QCD ) ξ n γ 5 ξ n

17 Relevant Energy scales m b 5 GeV, EΛ 1.3 GeV, Λ 0.5 GeV Integrating out fluctuations ~ mb: Generates local four quark operators

18 Caveat: Charm Penguins Four quark operators two charm quarks b d,s c! s (mv)... c q µ! s ( ) q q Charm quark pair can propagate over long distances Matching at μ mb not all onto local operators How large are these long distance contributions? A cc =[Leading Order] [v α s (2m c )]

19 Relevant Energy scales The relevant scales are m b, EΛ 1.3 GeV, Λ

20 Relevant Energy scales The relevant scales are m b, EΛ 1.3 GeV, Λ π B π

21 Relevant Energy scales The relevant scales are m b, EΛ 1.3 GeV, Λ π B p 2 EΛ π

22 Relevant Energy scales The relevant scales are m b, EΛ 1.3 GeV, Λ Integrating out fluctuations ~ EΛ: Generates so-called jet functions π B p 2 EΛ π

23 Relevant Energy scales The relevant scales are m b, EΛ 1.3 GeV, Λ B Integrating out fluctuations ~ EΛ: Generates so-called jet functions π p 2 EΛ Obtain factorization formula similar in structure to QCDF (BBNS) π

24 Relevant Energy scales The relevant scales are m b, EΛ 1.3 GeV, Λ B Integrating out fluctuations ~ EΛ: Generates so-called jet functions π p 2 EΛ Obtain factorization formula similar in structure to QCDF (BBNS) π Interaction starts at subleading order

25 Universality of jet functions Only a single jet function arises for these decays The same jet function as in semileptonic decays This jet function gets convoluted with B and light meson wave function Define ζ J BL = J ϕ B ϕ L Resums the jet function to all orders in α s ( ΛE) Only rely on perturbation theory in α s (m b )

26 The factorization formula M1 B p 2 EΛ M2

27 The factorization formula M1 B p 2 EΛ M2 Z A = N jf π + ζ Bπ f π Z du dz T 1J (u, z)ζj Bπ (z)φ π (u) ff du T 1ζ (u)φ π (u) + λ (f) c A ππ c c

28 The factorization formula M1 B p 2 EΛ M2 Z A = N jf π + ζ Bπ f π Z du dz T 1J (u, z)ζj Bπ (z)φ π (u) ff du T 1ζ (u)φ π (u) + λ (f) c A ππ c c

29 The factorization formula M1 B p 2 EΛ M2 Z A = N jf π + ζ Bπ f π Z du dz T 1J (u, z)ζj Bπ (z)φ π (u) ff du T 1ζ (u)φ π (u) + λ (f) c A ππ c c

30 The factorization formula M1 B p 2 EΛ M2 Z A = N jf π + ζ Bπ f π Z du dz T 1J (u, z)ζj Bπ (z)φ π (u) ff du T 1ζ (u)φ π (u) + λ (f) c A ππ c c

31 The factorization formula M1 B p 2 EΛ M2 Z A = N jf π + ζ Bπ f π Z du dz T 1J (u, z)ζj Bπ (z)φ π (u) ff du T 1ζ (u)φ π (u) + λ (f) c A ππ c c x2

32 Phenomenology

33 Outline Parameter counting Implications of small phases Determining γ from B ππ Sum rules in B Kπ Full SCET analysis Determination of hadronic parameters Predictions for remaining observables

34 Parameter counting Number of hadronic parameters no expns SU(2) SU(3) SCET +SU(2) SCET +SU(3) ππ 11 7/5 4 15/13 Kπ (6) 4 KK /+0 +3(4)

35 Implications of small phases I Measuring γ from B ππ Amplitudes (using isospin and no EW penguins) A( B 0 π + π ) = e iγ λ u T λ c P A( B 0 π 0 π 0 ) = e iγ λ u C + λ c P 2A(B π 0 π ) = e iγ λ u (T + C)

36 Implications of small phases I Measuring γ from B ππ Amplitudes (using isospin and no EW penguins) A( B 0 π + π ) = e iγ λ u T λ c P A( B 0 π 0 π 0 ) = e iγ λ u C + λ c P 2A(B π 0 π ) = e iγ λ u (T + C) 5 hadronic parameters + γ p c λ c λ u p s λ c λ u Re (P/T ) Im (P/T ) t c T / T + C T C T + C ɛ Im (C/T )

37 Implications of small phases I Measuring γ from B ππ Amplitudes (using isospin and no EW penguins) A( B 0 π + π ) = e iγ λ u T λ c P A( B 0 π 0 π 0 ) = e iγ λ u C + λ c P 2A(B π 0 π ) = e iγ λ u (T + C) 5 hadronic parameters + γ p c λ c λ u p s λ c λ u Re (P/T ) Im (P/T ) t c T / T + C T C T + C ɛ Im (C/T ) Gronau, London ( 90) BR(π + π ) = (5.0 ± 0.4) BR(π 0 π ) = (5.5 ± 0.6) BR(π 0 π 0 ) = (1.45 ± 0.29) C π+ π = 0.37 ± 0.10 S π+ π = 0.50 ± 0.12 C π0 π0 = 0.28 ± 0.40

38 Implications of small phases I Measuring γ from B ππ Amplitudes (using isospin and no EW penguins) A( B 0 π + π ) = e iγ λ u T λ c P A( B 0 π 0 π 0 ) = e iγ λ u C + λ c P 2A(B π 0 π ) = e iγ λ u (T + C) 5 hadronic parameters + γ p c λ c λ u p s λ c λ u Re (P/T ) Im (P/T ) t c T / T + C T C T + C ɛ Im (C/T ) Gronau, London ( 90) BR(π + π ) = (5.0 ± 0.4) BR(π 0 π ) = (5.5 ± 0.6) BR(π 0 π 0 ) = (1.45 ± 0.29) C π+ π = 0.37 ± 0.10 S π+ π = 0.50 ± 0.12 C π0 π0 = 0.28 ± 0.40

39 Implications of small phases I Measuring γ from B ππ Amplitudes (using isospin and no EW penguins) A( B 0 π + π ) = e iγ λ u T λ c P A( B 0 π 0 π 0 ) = e iγ λ u C + λ c P 2A(B π 0 π ) = e iγ λ u (T + C) 5 hadronic parameters + γ p c λ c λ u p s λ c λ u Re (P/T )? Im (P/T ) t c T / T + C T C T + C ɛ Im (C/T ) Gronau, London ( 90) BR(π + π ) = (5.0 ± 0.4) BR(π 0 π ) = (5.5 ± 0.6) BR(π 0 π 0 ) = (1.45 ± 0.29) C π+ π = 0.37 ± 0.10 S π+ π = 0.50 ± 0.12 C π0 π0 = 0.28 ± 0.40

40 Getting rid of one parameter The SCET analysis contains four hadronic parameters Allows us to eliminate one of the 5 in isospin In the limit Λ/E 0 one parameter vanishes Im(C/T)=O(αs,Λ/mb) This allows to use the 5 well measured observables to determine the CKM angle γ

1-CL Extracting γ Hadronic parameters as function of γ isospin bound ε 3 1.5 0.5 20 30 40 50 70 80-0.5 ε 2-1 ε 4-1.5 2 1 ε1 γ 1.2 1 0.8 0.6 0.4 isospin analysis without C 00 CKM fit no " in fit!

41 1-CL Extracting γ Hadronic parameters as function of γ isospin bound ε ε 2-1 ε ε1 γ isospin analysis without C 00 CKM fit no " in fit! (t) = 0 and w/o C 00! (t) < 5 o, 10 o, 20 o and w/o C 00! (t) = 0 and with C o 10 o SCET allowed region isospin bound Flat triangle α (deg) Grossman, Ligeti, Hoecker, Pirjol ( 05) Slightly old data. Including EW penguins, get α=75 5 o

42 Implications of small phases II Define Observables R 1 = 2Br(B π 0 K ) Br(B π K 0 ) 1 = ± R 2 = Br( B 0 π K + )τ B Br(B π K 0 )τ B 0 = ± R 3 = 2Br( B 0 π 0 K0 )τ B Br( B 0 π K 0 )τ B 0 = ± Sum rules for B Kπ 1 1 Lipkin, Gronau, Rosner, Buras et al, Beneke et al 1 = (1 + R 1 )A CP (π 0 K ) = ± = (1 + R 2 )A CP (π K + ) = ± = (1 + R 3 )A CP (π 0 K0 ) = ± = A CP (π K0 ) = 0.02 ± 0.04 Combinations vanish to LO in = ε λ u /λ c, P EW /P R 1 -R 2 +R 3 =O(ε 2 ) Δ 1 -Δ 2 +Δ 3 -Δ 4 =O(ε 2 )

43 Predictions for the R i and Δ i Experimental Results: R 1 +R 2 -R 3 =0.19±0.15 Δ 1 -Δ 2 +Δ 3 -Δ 4 = 0.14±0.15

44 Predictions for the R i and Δ i Experimental Results: R 1 +R 2 -R 3 =0.19±0.15 Δ 1 -Δ 2 +Δ 3 -Δ 4 = 0.14±0.15 SCET Prediction: (modest assumptions about hadronic parameters) R 1 +R 2 -R 3 =O(ε 2 )=0.028±0.021 Δ 1 -Δ 2 +Δ 3 -Δ 4 ε 2 sin(φ i -φ j ) = 0±0.013

45 Predictions for the R i and Δ i Experimental Results: R 1 +R 2 -R 3 =0.19±0.15 Δ 1 -Δ 2 +Δ 3 -Δ 4 = 0.14±0.15 SCET Prediction: (modest assumptions about hadronic parameters) R 1 +R 2 -R 3 =O(ε 2 )=0.028±0.021 Δ 1 -Δ 2 +Δ 3 -Δ 4 ε 2 sin(φ i -φ j ) = 0±0.013 Pretty firm predictions Need better data to check these predictions

46 The B PP predictions Branching ratios K 0 " K _! 0 K _! K! + 0 _ K! K 0 " 0 0 0!! +!! 0 +!! _ The Branching ratios (x10 ) -6 #=83 $ Theory Data

47 The B PP predictions CP asymmetries The CP asymmetries S(! 0! 0) A(!! ) 0 0 A(K _! 0 _ ) 0 A(K! ) 0 0 A(K! ) S(K 0! 0 _ ) A(K! ) C(! +! _+ ) S(! +! _ ) "=83 # Theory Data

48 Adding Isosinglets Williamson, Zupan ( 06) Mode Exp. Theory I Theory II B π η 4.3 ± 0.5 (S = 1.3) 4.9 ± 1.7 ± 1.0 ± ± 1.7 ± 1.2 ± ± ± 0.19 ± 0.21 ± ± 0.19 ± 0.21 ± 0.05 B π η 2.53 ± 0.79 (S = 1.5) 2.4 ± 1.2 ± 0.2 ± ± 1.2 ± 0.3 ± ± ± 0.12 ± 0.10 ± ± 0.10 ± 0.04 ± 0.15 B 0 π 0 η < ± 0.54 ± 0.06 ± ± 0.46 ± 0.03 ± ± 0.10 ± 0.12 ± ± 0.16 ± 0.04 ± 0.90 B 0 π 0 η < ± 0.8 ± 0.3 ± ± 0.5 ± 0.1 ± ± 0.10 ± 0.19 ± 0.24 B 0 ηη < ± 0.38 ± 0.13 ± ± 0.4 ± 0.3 ± ± 0.24 ± 0.21 ± ± 0.22 ± 0.20 ± 0.13 B 0 ηη < ± 0.5 ± 0.1 ± ± 0.7 ± 0.6 ± ± 0.13 ± 0.20 ± 0.04 B 0 η η < ± 0.23 ± 0.03 ± ± 0.4 ± 0.3 ± ± 0.11 ± 0.22 ± 0.29 B 0 K 0 η 63.2 ± 4.9 (S = 1.5) 63.2 ± 24.7 ± 4.2 ± ± 23.7 ± 5.5 ± ± 0.10 (S = 1.5) ± ± ± ± ± ± B 0 K 0 η < ± 4.4 ± 0.2 ± ± 4.4 ± 0.2 ± ± 0.20 ± 0.04 ± ± 0.22 ± 0.06 ± 0.04 B K η 69.4 ± ± 27.0 ± 4.3 ± ± 26.0 ± 7.1 ± ± ± ± ± ± ± ± B K η 2.5 ± ± 4.8 ± 0.4 ± ± 4.5 ± 0.4 ± ± 0.17 (S = 1.4) 0.33 ± 0.30 ± 0.07 ± ± 0.39 ± 0.10 ± 0.04

49 Adding Isosinglets Williamson, Zupan ( 06) Mode Exp. Theory I Theory II B π η 4.3 ± 0.5 (S = 1.3) 4.9 ± 1.7 ± 1.0 ± ± 1.7 ± 1.2 ± ± ± 0.19 ± 0.21 ± ± 0.19 ± 0.21 ± 0.05 B π η 2.53 ± 0.79 (S = 1.5) 2.4 ± 1.2 ± 0.2 ± ± 1.2 ± 0.3 ± ± ± 0.12 ± 0.10 ± ± 0.10 ± 0.04 ± 0.15 B 0 π 0 η < ± 0.54 ± 0.06 ± ± 0.46 ± 0.03 ± ± 0.10 ± 0.12 ± ± 0.16 ± 0.04 ± 0.90 B 0 π 0 η < ± 0.8 ± 0.3 ± ± 0.5 ± 0.1 ± ± 0.10 ± 0.19 ± 0.24 B 0 ηη < ± 0.38 ± 0.13 ± ± 0.4 ± 0.3 ± ± 0.24 ± 0.21 ± ± 0.22 ± 0.20 ± 0.13 B 0 ηη < ± 0.5 ± 0.1 ± ± 0.7 ± 0.6 ± ± 0.13 ± 0.20 ± 0.04 B 0 η η < ± 0.23 ± 0.03 ± ± 0.4 ± 0.3 ± ± 0.11 ± 0.22 ± 0.29 B 0 K 0 η 63.2 ± 4.9 (S = 1.5) 63.2 ± 24.7 ± 4.2 ± ± 23.7 ± 5.5 ± ± 0.10 (S = 1.5) ± ± ± ± ± ± B 0 K 0 η < ± 4.4 ± 0.2 ± ± 4.4 ± 0.2 ± ± 0.20 ± 0.04 ± ± 0.22 ± 0.06 ± 0.04 B K η 69.4 ± ± 27.0 ± 4.3 ± ± 26.0 ± 7.1 ± ± ± ± ± ± ± ± B K η 2.5 ± ± 4.8 ± 0.4 ± ± 4.5 ± 0.4 ± ± 0.17 (S = 1.4) 0.33 ± 0.30 ± 0.07 ± ± 0.39 ± 0.10 ± 0.04

50 Summary Very important to understand hadronic physics to find physics beyond the standard model Effective field theories great tool to separate long distance from short distance effects SCET is effective theory constructed to describe processes with energetic particles Factorization formula can be derived for B PP Predictive power without expansion in α s ( ΛE) Detailed analysis of hadronic B decays available

Hadronic B decays from SCET

Hadronic B decays from SCET Flavor Physics and CP Violation Conference, Vancouver, 26 1 Christian W. Bauer Ernest Orlando Lawrence Berkeley National Laboratory and University of California, Berkeley, CA