Recent progress in B K and ε K in lattice QCD

Recent progress in B K and ε K in lattice QCD Weonjong Lee on behalf of the SWME Collaboration Lattice Gauge Theory Research Center Department of Physics and Astronomy Seoul National University KIAS PPC Workshop, 11/12/2013 Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 1 / 38

Contents 1 Testing the Standard Model Indirect CP violation and B K 2 B K B K on the lattice Data Analysis for B K Continuum extrapolation of B K 3 Conclusion and Future Plan 4 Project: 1998 Present Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 2 / 38

Testing the Standard Model Indirect CP violation and B K CP Violation and B K Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 3 / 38

Testing the Standard Model Indirect CP violation and B K Kaon Eigenstates and ε Flavor eigenstates, K 0 = ( sd) and K 0 = (s d) mix via box diagrams. s W d s u,c,t d u,c,t u,c,t W W d W s d u,c,t s (a) (b) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 4 / 38

Testing the Standard Model Indirect CP violation and B K Kaon Eigenstates and ε Flavor eigenstates, K 0 = ( sd) and K 0 = (s d) mix via box diagrams. s W d s u,c,t d u,c,t u,c,t W W d W (a) s d u,c,t CP eigenstates K 1 (even) and K 2 (odd). K 1 = 1 2 (K 0 K 0 ) K 2 = 1 2 (K 0 + K 0 ) (b) s Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 4 / 38

Testing the Standard Model Indirect CP violation and B K Kaon Eigenstates and ε Flavor eigenstates, K 0 = ( sd) and K 0 = (s d) mix via box diagrams. s W d s u,c,t d u,c,t u,c,t W W d W (a) s d u,c,t CP eigenstates K 1 (even) and K 2 (odd). K 1 = 1 2 (K 0 K 0 ) K 2 = 1 2 (K 0 + K 0 ) Neutral Kaon eigenstates K S and K L. K S = (b) 1 1 + ε 2 (K 1 + εk 2 ) K L = s 1 1 + ε 2 (K 2 + εk 1 ) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 4 / 38

Testing the Standard Model Indirect CP violation and B K Indirect CP violation and direct CP violation Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 5 / 38

Testing the Standard Model Indirect CP violation and B K ε and ˆB K Experiment: ε = (2.228 ± 0.011) 10 3 e iφε, φ ε = 43.52(5). Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 6 / 38

Testing the Standard Model Indirect CP violation and B K ε and ˆB K Experiment: ε = (2.228 ± 0.011) 10 3 e iφε, φ ε = 43.52(5). Relation between ε and ˆB K in standard model. ε = exp(iφ ε ) 2 sin(φ ε ) C ε Imλ t X ˆB K + ξ + ξ LD X = Reλ c [η 1 S 0 (x c ) η 3 S 3 (x c, x t )] Reλ t η 2 S 0 (x t ) λ i = V isv id, x i = m 2 i /M 2 W, C ε = G2 F F 2 K m KM 2 W 6 2π 2 M K ξ = exp(iφ ε ) sin(φ ε ) ImA 0 ReA 0 ξ LD = Long Distance Effect 2% Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 6 / 38

Testing the Standard Model Indirect CP violation and B K ε and ˆB K Experiment: ε = (2.228 ± 0.011) 10 3 e iφε, φ ε = 43.52(5). Relation between ε and ˆB K in standard model. ε = exp(iφ ε ) 2 sin(φ ε ) C ε Imλ t X ˆB K + ξ + ξ LD X = Reλ c [η 1 S 0 (x c ) η 3 S 3 (x c, x t )] Reλ t η 2 S 0 (x t ) λ i = V isv id, x i = m 2 i /M 2 W, C ε = G2 F F 2 K m KM 2 W 6 2π 2 M K ξ = exp(iφ ε ) sin(φ ε ) ImA 0 ReA 0 ξ LD = Long Distance Effect 2% Definition of B K in standard model. B K = K 0 [ sγ µ (1 γ 5 )d][ sγ µ (1 γ 5 )d] K 0 8 3 K 0 sγ µ γ 5 d 0 0 sγ µ γ 5 d K 0 ˆB K = C(µ)B K (µ), C(µ) = α s (µ) γ 0 2b 0 [1 + α s (µ)j 3 ] Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 6 / 38

B K B K on the lattice B K on the lattice Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 7 / 38

B K B K on the lattice B K definition in standard model B K = K 0 [ sγ µ (1 γ 5 )d][ sγ µ (1 γ 5 )d] K 0 8 3 K 0 sγ µ γ 5 d 0 0 sγ µ γ 5 d K 0 ˆB K = C(µ)B K (µ), C(µ) = α s (µ) γ 0 2b 0 [1 + α s (µ)j 3 ] Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 8 / 38

B K B K on the lattice What do we calculate on the lattice? Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 9 / 38

B K Data Analysis for B K Data Analysis for B K Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 10 / 38

B K Data Analysis for B K Data for B K with am d = am s = 0.025 (20 3 64) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 11 / 38

B K Data Analysis for B K N f = 2 + 1 QCD: MILC coarse lattices a (fm) am l /am s geometry ens meas production 0.12 0.03/0.05 20 3 64 564 9 done (SNU) 0.12 0.02/0.05 20 3 64 486 9 done (SNU) 0.12 0.01/0.05 20 3 64 671 9 done (SNU) 0.12 0.01/0.05 28 3 64 274 8 done (BNL) 0.12 0.007/0.05 20 3 64 651 10 done (SNU) 0.12 0.005/0.05 24 3 64 509 9 done (SNU) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 12 / 38

B K Data Analysis for B K N f = 2 + 1 QCD: MILC fine lattices a (fm) am l /am s geometry ens meas production 0.09 0.0062/0.0310 28 3 96 995 9 done (SNU) 0.09 0.0031/0.0310 40 3 96 959 9 done (SNU) 0.09 0.0093/0.0310 28 3 96 950 9 done (SNU) 0.09 0.0124/0.0310 28 3 96 1996 9 done (SNU) 0.09 0.00465/0.0310 32 3 96 665 9 done (SNU) 0.09 0.0062/0.0186 28 3 96 950 9 done (KISTI) 0.09 0.0031/0.0186 40 3 96 701 9 done (SNU) 0.09 0.0031/0.0031 40 3 96 576 9 done (KISTI) 0.09 0.00155/0.0310 64 3 96 790 9 done (KISTI) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 13 / 38

B K Data Analysis for B K N f = 2 + 1 QCD: MILC superfine/ultrafine lattice a (fm) am l /am s geometry ens meas production 0.06 0.0036/0.018 48 3 144 744 9 done (SNU) 0.06 0.0025/0.018 56 3 144 799 9 done (KISTI) 0.06 0.0072/0.018 48 3 144 593 9 done (KISTI) 0.06 0.0054/0.018 48 3 144 617 9 done (SNU) 0.06 0.0018/0.018 64 3 144 826 6.6 (*KISTI) 0.06 0.0036/0.0108 64 3 144 600 0.1 (*SNU) 0.045 0.0030/0.015 64 3 192 747 1 (BNL) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 14 / 38

B K Data Analysis for B K Correlated Bayesian Fitting with SU(2) SChPT (a) X-fit (b) Y-fit MILC, 48 3 144, 642 cnfs, 9 meas at a = 0.06 fm. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 15 / 38

B K Data Analysis for B K Sea quarks and valence quarks Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 16 / 38

B K Continuum extrapolation of B K Continuum extrapolation of B K (1) Fitting functional form: f 1 = c 1 + c 2 (aλ Q ) 2 + c 3 L P Λ 2 X + c 4 S P Λ 2 X f 2 = f 1 + c 5 (aλ Q ) 2 L P Λ 2 + c 6 (aλ Q ) 2 S P X Λ 2 X f 3 = f 1 + c 5 αs 2 + c 6 (aλ Q ) 2 α s + c 7 (aλ Q ) 4 f 4 = f 2 + c 7 α 2 s + c 8 (aλ Q ) 2 α s + c 9 (aλ Q ) 4 Bayesian constraint = prior information: Λ Q = 0.3 GeV Λ X = 1.0 GeV c i = 0 ± 2 for i 2 Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 17 / 38

B K Continuum extrapolation of B K Continuum extrapolation of B K (2) Bayesian Fit to f 1 0.6 0.6 B K 0.58 0.56 0.54 coarse B K 0.58 0.56 0.54 fine 0.52 0.5 fine superfine ultrafine 0.48 0 0.1 0.2 0.3 0.4 0.5 L P 0.52 0.5 0.48 0.3 0.4 0.5 0.6 S P (c) B K vs. L P (d) B K vs. S P We exclude the MILC coarse ensembles in this fit. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 18 / 38

B K Continuum extrapolation of B K Continuum extrapolation of B K (3) Bayesian Fit to f 4 0.6 0.6 B K 0.58 0.56 0.54 coarse B K 0.58 0.56 0.54 fine 0.52 0.5 fine superfine ultrafine 0.48 0 0.1 0.2 0.3 0.4 0.5 L P 0.52 0.5 0.48 0.3 0.4 0.5 0.6 S P (e) B K vs. L P (f) B K vs. S P We exclude the MILC coarse ensembles in this fit. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 19 / 38

B K Continuum extrapolation of B K Continuum extrapolation of B K (4) fit func f 1 f 2 f 3 f 4 χ 2 /dof 1.38 1.38 1.37 1.37 Fitting quality of the Bayesian fits Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 20 / 38

B K Continuum extrapolation of B K Error Budget of B K [ SU(2), 4X3Y, NNNLO] cause error (%) memo statistics 0.62 see text matching factor 4.4 B (2) K (U1) discretization am l extrap 0.78 diff. of B1 and B4 fits am s extrap X-fits 0.33 varying Bayesian priors (S1) Y-fits 0.53 diff. of linear and quad. (F1) finite volume 0.5 diff. of V = and FV fit r 1 0.27 r 1 error propagation (F1) f π 0.4 132 MeV vs. 124.4 MeV Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 21 / 38

B K Continuum extrapolation of B K Current Status of B K (1) SWME: 2011 (PRL): B K (RGI) = ˆB K = 0.727 ± 0.004(stat) ± 0.038(sys) SWME: Lattice 2013 B K (RGI) = ˆB K = 0.7377 ± 0.0046(stat) ± 0.0337(sys) The statistical error remains approximately the same. The systematic error decrease slightly. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 22 / 38

B K Continuum extrapolation of B K Current Status of ε K SWME 2013: (in units of 1.0 10 3 ) ε K = 1.51 ± 0.18 ε K = 1.91 ± 0.21 for Exclusive V cb for Inclusive V cb Experiments: ε K = 2.228 ± 0.011 Hence, we observe 4.0/1.5 σ difference between the SM theory and experiments (exclusive/inclusive process). What does this mean? Breakdown of SM??? Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 23 / 38

B K Continuum extrapolation of B K Error Budget of Exclusive ε K cause error (%) memo V cb 51.6 Exclusive (FNAL/MILC) B K 14.4 SWME η 9.7 Wolfenstein η 3 8.1 η ct m c 6.9 Charm quark mass... Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 24 / 38

B K Continuum extrapolation of B K Current status of B K on the lattice SWME (this work) Aubin et al (2010) RBC-UKQCD (2011) BMW (2011) 0.6 0.7 0.8 0.9 1 1.1 B K (RGI) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 25 / 38

B K Continuum extrapolation of B K NPR (Current Focus) Non-perturbative Renormalization (Jangho Kim): Matching factor error: 4.4% 2.0 3.0% Exceptional Momentum: 2.0 3.0% Non-exceptional Momentum: 2.0 2.5% Basically, we want to trade the truncation error with the statistical error. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 26 / 38

B K Continuum extrapolation of B K Two-loop Perturbation (Current Focus) Two-loop Perturbation: (Jongjeong Kim and Kwangwoo Kim) Matching factor error: 4.4% 0.92% Automated Feynman Rule Generation. Automated Feynman Diagram Generation. Basically, we use non-zero quark masses to regulate the IR divergences. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 27 / 38

Conclusion and Future Plan Grand Challenges in the front Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 28 / 38

Conclusion and Future Plan Tentative Goals (1) 1 V cb, we need to calculate the following semi-leptonic form factors: B Dlν (1) B D lν (2) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 29 / 38

Conclusion and Future Plan Tentative Goals (1) 1 V cb, we need to calculate the following semi-leptonic form factors: B Dlν (1) B D lν (2) 2 We have already implemented a GPU version of the OK action inverter (Yong-Chull Jang). 3 We need to improve the vector and axial current in the same level as the OK action (Yong-Chull Jang, and Jon Bailey). Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 29 / 38

Conclusion and Future Plan Tentative Goals (1) 1 V cb, we need to calculate the following semi-leptonic form factors: B Dlν (1) B D lν (2) 2 We have already implemented a GPU version of the OK action inverter (Yong-Chull Jang). 3 We need to improve the vector and axial current in the same level as the OK action (Yong-Chull Jang, and Jon Bailey). 4 We plan to work on this issue using the OK heavy quark action in collaboration with FNAL and MILC. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 29 / 38

Conclusion and Future Plan Tentative Goals (2) 1 We would like to determine B K directly from the standard model with its systematic and statistical error 2%. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 30 / 38

Conclusion and Future Plan Tentative Goals (2) 1 We would like to determine B K directly from the standard model with its systematic and statistical error 2%. 2 We expect to achieve this goal in a few years using the SNU GPU cluster: David 1, 2, 3 ( 100 Tera Flops), Jlab GPU cluster, and KISTI supercomputers. 3 Basically, we need to accumulate at least 9 times more statistics using the SNU GPU cluster machine. statistical error < 1.0% Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 30 / 38

Conclusion and Future Plan Tentative Goals (2) 1 We would like to determine B K directly from the standard model with its systematic and statistical error 2%. 2 We expect to achieve this goal in a few years using the SNU GPU cluster: David 1, 2, 3 ( 100 Tera Flops), Jlab GPU cluster, and KISTI supercomputers. 3 Basically, we need to accumulate at least 9 times more statistics using the SNU GPU cluster machine. statistical error < 1.0% 4 In addition, we need to obtain the matching factor using NPR (Jangho Kim) and using the two-loop perturbation theory (Kwangwoo Kim). matching error < 1.0% Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 30 / 38

Conclusion and Future Plan Tentative Goals (3) 1 Long-Distance Effect ξ LD 2%: Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 31 / 38

Conclusion and Future Plan Tentative Goals (3) 1 Long-Distance Effect ξ LD 2%: 2 Here, the precision goal is only 10%. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 31 / 38

Conclusion and Future Plan Tentative Goals (3) 1 Long-Distance Effect ξ LD 2%: 2 Here, the precision goal is only 10%. 3 We need N f = 2 + 1 + 1 calculation on the lattice. MILC provides HISQ ensembles with N f = 2 + 1 + 1. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 31 / 38

Conclusion and Future Plan Tentative Goals (3) 1 Long-Distance Effect ξ LD 2%: 2 Here, the precision goal is only 10%. 3 We need N f = 2 + 1 + 1 calculation on the lattice. MILC provides HISQ ensembles with N f = 2 + 1 + 1. 4 As a by-product, a substantial gain is that the charm quark mass dependence might be under control in this way. (Brod and Gorbahn) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 31 / 38

Conclusion and Future Plan Ultimate Goals 1 As a result, we hope to discover a breakdown of the standard model in the level of 5σ or higher precision. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 32 / 38

Conclusion and Future Plan Ultimate Goals 1 As a result, we hope to discover a breakdown of the standard model in the level of 5σ or higher precision. 2 As a result, we would like to provide a crucial clue to the physics beyond the standard model. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 32 / 38

Conclusion and Future Plan Ultimate Goals 1 As a result, we hope to discover a breakdown of the standard model in the level of 5σ or higher precision. 2 As a result, we would like to provide a crucial clue to the physics beyond the standard model. 3 As a result, we would like to guide the whole particle physics community into a new world beyond the standard model. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 32 / 38

Conclusion and Future Plan Thank God for your help!!! Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 33 / 38

Project: 1998 Present SWME Collaboration 1998 Present Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 34 / 38

Project: 1998 Present SWME Collaboration Seoul National University (SNU): Prof. Weonjong Lee Dr. Jon Bailey and Dr. Nigel Cundy (RA Prof.) Dr. Jongjeong Kim (Postdoc) and Dr. Taegil Bae (Staff) 10 + 1 graduate students. Brookhaven National Laboratory (BNL): Dr. Chulwoo Jung Dr. Hyung-Jin Kim (Postdoc) Los Alamos National Laboratory (LANL): Dr. Boram Yoon (Postdoc) University of Washington, Seattle (UW): Prof. Stephen R. Sharpe. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 35 / 38

Project: 1998 Present Lattice Gauge Theory Research Center (SNU) Center Leader: Prof. Weonjong Lee. Research Assistant Prof.: Dr. Jon Bailey Research Assitant Prof.: Dr. Nigel Cundy Postdoctoral Fellow: Dr. Jongjeong Kim 10 + 1 graduate students Secretary: Ms. Sora Park. more details on http://lgt.snu.ac.kr/. Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 36 / 38

Project: 1998 Present Group Photo (2011) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 37 / 38

Project: 1998 Present Group Photo (2013) Weonjong Lee on behalf of the SWME Collaboration (SNU)KIAS PPC 2013 KIAS PPC 2013 38 / 38