Beyond the Standard Model Kaon Mixing with physical light quarks - PowerPoint PPT Presentation

Beyond the Standard Model Kaon Mixing with physical light quarks Julia Kettle 1 Peter Boyle 1 , Nicolas Garron 2 , Renwick Hudspith 3 ,Ava Khamseh 1 , Tobias Tsang 1 RBC-UKQCD 1 University of Edinburgh 2 University of Liverpool 3 York University Lattice 2018, July 2018 1 / 24

The RBC & UKQCD collaborations Tianle Wang University of Liverpool BNL and BNL/RBRC Evan Wickenden Nicolas Garron Yasumichi Aoki (KEK) Yidi Zhao Mattia Bruno MIT University of Connecticut T aku Izubuchi Yong-Chull Jang David Murphy T om Blum Chulwoo Jung Dan Hoying (BNL) Peking University Christoph Lehner Luchang Jin (RBRC) Xu Feng Meifeng Lin Cheng Tu Aaron Meyer University of Southampton Edinburgh University Hiroshi Ohki Jonathan Flynn Shigemi Ohta (KEK) Peter Boyle Vera Guelpers Amarjit Soni Guido Cossu James Harrison UC Boulder Luigi Del Debbio Andreas Juettner T adeusz Janowski Oliver Witzel James Richings Richard Kenway Chris Sachrajda Columbia University Julia Kettle Fionn O'haigan Ziyuan Bai Stony Brook University Brian Pendleton Norman Christ Jun-Sik Yoo Antonin Portelli Duo Guo Sergey Syritsyn (RBRC) T obias T sang Christopher Kelly Azusa Yamaguchi Bob Mawhinney York University (Toronto) Masaaki T omii KEK Jiqun Tu Renwick Hudspith Julien Frison Bigeng Wang 2 / 24

Table of contents Introduction 1 Lattice Implementation 2 Analysis 3 Results 4 Summary 5 3 / 24

Kaon Mixing in the Standard Model c, ¯ u, ¯ ¯ t Oscillation of K 0 to ¯ ¯ K 0 d s ¯ One-loop FCNC W W Mediated by W ± s d Related to indirect CP c, ¯ u, ¯ ¯ t violation OPE separates out a ¯ d s ¯ long-distance 4quark operator Matrix elements of O ∆ S =2 s d calculated with LQCD O ∆ S =2 = [¯ s a γ µ (1 − γ 5 ) d a ][¯ s b γ µ (1 − γ 5 ) d b ] 4 / 24

Beyond the Standard Model Generalized Weak Hamiltonian: 5 3 H ∆ S =2 = � � C i ( µ ) ˜ ˜ C i ( µ ) O i + O i i =1 i =1 Basis of 5 model independent parity-even four-quark operators. O 1 = [¯ s a γ µ (1 − γ 5 ) d a ][¯ s b γ µ (1 − γ 5 ) d b ] O 2 = [¯ s a (1 − γ 5 ) d a ][¯ s b (1 − γ 5 ) d b ] O 3 = [¯ s a (1 − γ 5 ) d b ][¯ s b (1 − γ 5 ) d a ] O 4 = [¯ s a (1 − γ 5 ) d a ][¯ s b (1 + γ 5 ) d b ] O 5 = [¯ s a (1 − γ 5 ) d b ][¯ s b (1 + γ 5 ) d a ] Past calculations by SWME 1 , ETM 2 and RBC-UKQCD 3 . 1 Jang et al 15, Bae et al 14 2 Carrasco et al 15,Bertone et al 10 3 Garron,Hudspith,Lytle 16, Blum et al 14 5 / 24

Simulations 2+1f DWF QCD with Iwasaki Gauge Action 3 lattice spacings 2 ensembles with physical pions New: a − 1 = 2 . 774 GeV m π ≈ 230 MeV am phys a − 1 [GeV] am uni am sea am val name L/a T/a kernel source m π [MeV] n configs s s s l C0 48 96 M Z2GW 1.7295(38) 139 90 0.00078 0.0362 0.0358 0.03580(16) C1 24 64 S Z2W 1.7848(50) 340 100 0.005 0.04 0.03224 0.03224(18) M0 64 128 M Z2GW 2.3586(70) 139 82 0.000678 0.02661 0.0254 0.02539(17) M1 32 64 S Z2GW 2.3833(86) 303 83 0.004 0.03 0.02477 0.02477(18) M2 32 64 S Z2GW 2.3833(86) 360 76 0.006 0.03 0.02477 0.02477(18) F1 48 96 M Z2GW 2.774(10) 234 98 0.002144 0.02144 0.02132 0.02132(17) M and F stand for coarse, medium and fine, respectively, M and S for Moebius and Shamir kernels. Propagators had either Z2 wall (Z2W) or Z2 Gaussian Wall (Z2GW) sources, with latter including source smearing. 6 / 24

Simulations 2+1f DWF QCD with Iwasaki Gauge Action 3 lattice spacings 2 ensembles with physical pions New: a − 1 = 2 . 774 GeV m π ≈ 230 MeV am phys a − 1 [GeV] am uni am sea am val name L/a T/a kernel source m π [MeV] n configs s s s l C0 48 96 M Z2GW 1.7295(38) 139 90 0.00078 0.0362 0.0358 0.03580(16) C1 24 64 S Z2W 1.7848(50) 340 100 0.005 0.04 0.03224 0.03224(18) M0 64 128 M Z2GW 2.3586(70) 139 82 0.000678 0.02661 0.0254 0.02539(17) M1 32 64 S Z2GW 2.3833(86) 303 83 0.004 0.03 0.02477 0.02477(18) M2 32 64 S Z2GW 2.3833(86) 360 76 0.006 0.03 0.02477 0.02477(18) F1 48 96 M Z2GW 2.774(10) 234 98 0.002144 0.02144 0.02132 0.02132(17) M and F stand for coarse, medium and fine, respectively, M and S for Moebius and Shamir kernels. Propagators had either Z2 wall (Z2W) or Z2 Gaussian Wall (Z2GW) sources, with latter including source smearing. 6 / 24

Simulations 2+1f DWF QCD with Iwasaki Gauge Action 3 lattice spacings 2 ensembles with physical pions New: a − 1 = 2 . 774 GeV m π ≈ 230 MeV am phys a − 1 [GeV] am uni am sea am val name L/a T/a kernel source m π [MeV] n configs s s s l C0 48 96 M Z2GW 1.7295(38) 139 90 0.00078 0.0362 0.0358 0.03580(16) C1 24 64 S Z2W 1.7848(50) 340 100 0.005 0.04 0.03224 0.03224(18) M0 64 128 M Z2GW 2.3586(70) 139 82 0.000678 0.02661 0.0254 0.02539(17) M1 32 64 S Z2GW 2.3833(86) 303 83 0.004 0.03 0.02477 0.02477(18) M2 32 64 S Z2GW 2.3833(86) 360 76 0.006 0.03 0.02477 0.02477(18) F1 48 96 M Z2GW 2.774(10) 234 98 0.002144 0.02144 0.02132 0.02132(17) M and F stand for coarse, medium and fine, respectively, M and S for Moebius and Shamir kernels. Propagators had either Z2 wall (Z2W) or Z2 Gaussian Wall (Z2GW) sources, with latter including source smearing. 6 / 24

Source-Sink Time Separations Z 2 (Gaussian) wall sources at every other time slice. Several different ∆ T Bin all data with same ∆ T 7 / 24

Quantities Measured The SM bag parameters: B 1 ( µ ) = � ¯ P |O 1 ( µ ) | P � B i> 1 ( µ ) = ( m s ( µ )+ m d ( µ )) 2 � ¯ P |O i ( µ ) | P � 8 3 m 2 K f 2 N i m 4 K f 2 K K Define a ratio parameter: � f 2 R i ( m 2 � m 2 � ¯ � P |O i ( µ ) | P � � , a 2 , µ ) = P K P � ¯ f 2 m 2 f 2 P |O 1 ( µ ) | P � P K exp P lat such that when a 2 → 0 and m 2 P /f 2 P → m 2 K /f 2 K it reduces to: R i ( µ ) = � ¯ K |O i ( µ ) | K � � ¯ K |O 1 ( µ ) | K � 8 / 24

Correlator Fitting 0.938 8.3 fit result fit result B 4 (t) R 5 (t) 0.936 8.4 0.934 8.5 B 4 0.932 R 5 8.6 0.930 8.7 0.928 8.8 5 10 15 20 25 30 35 40 5 10 15 20 25 30 t / a t / a (a) B 4 ( t ) for C0 (b) R 5 ( t ) for M0. � ¯ C 3 pt ( t,t sink ) C 3 pt ( t,t sink ) → � ¯ P | O i | P � ( t,t sink ) P | O i | P � 2 pt ( t sink − t ) → i C AP 2 pt ( t ) C AP � P | A �� A | P � � ¯ C 3 pt P | O 1 | P � 1 Examples of the fits of correlation functions to measure lattice quantites. 9 / 24

Non-Perturbative Renormalisation We use the Rome-Southampton method with non-exceptional kinematics (RI-SMOM). p 2 p 2 Z RI jk ( µ ) � � O i ( µ ) MS = C MS ← MOM ( µ ) lim O k ( a ) ij Z 2 a 2 → 0 q p 1 p 1 Z RI ( µ ) ˆ P [Λ( p 2 )] | p 2 = µ 2 = Λ( p 2 ) tree p 1 � = p 2 p 2 1 = p 2 2 = ( p 1 − p 2 ) 2 10 / 24

Non-Perturbative Renormalisation Block diagonal structure due to chiral symmetry   Z 11 0 0 0 0 0 Z 22 Z 23 0 0     Z O ∆ S =2 = 0 Z 32 Z 33 0 0     0 0 0 Z 44 Z 45   0 0 0 Z 54 Z 55 Define two intermediate schemes ( γ, γ ) and ( / q, / q ) distiguished by their projectors. The difference between them allows us to quantify a systematic error 11 / 24

Extrapolation to Physical Point and Continuum Simultaneously extrapolate to the continuum and chiral limit in a global fit with form: a 2 , m 2 m 2 0 , m 2 � � � �� � 1 + α i a 2 + β i π ll ll Y , δ m sea = Y , 0 + γ i δ m sea f 2 f 2 f 2 s s π ll ll where we include a term linear strange sea-quark mass: − m phys = ( m sea ) s s δ m sea m phys s s 12 / 24

Ratio Parameter Fits Figure: Preliminary results for R 2 and R 3 in MS at 3 GeV RI-SMOM γ,γ intermediate scheme. Data points have been adjusted to the physical strange-mass and continuum using the fit form and parameters gained from the fit. (m π / 4 π f π ) 2 phys (m π / 4 π f π ) 2 phys C1 M1 / 2 C1 M1 / 2 phys phys M0 M0 C0 F1 C0 F1 16.0 6.0 16.5 5.8 17.0 5.6 17.5 R 2 R 3 5.4 18.0 5.2 18.5 5.0 19.0 19.5 4.8 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.005 0.010 0.015 0.020 0.025 0.030 0.035 m 2 π / (4 πf 2 m 2 π / (4 πf 2 π ) π ) 13 / 24

Ratio Parameter Fits ( not corrected to continuum ) Figure: Preliminary results for R 2 and R 3 in MS at 3 GeV RI-SMOM ( γ,γ ) intermediate scheme. (m π / 4 π f π ) 2 phys (m π / 4 π f π ) 2 phys C1 M1 / 2 C1 M1 / 2 phys phys M0 F1 M0 F1 C0 C0 16.0 7.0 16.5 6.5 17.0 6.0 17.5 R 2 R 3 18.0 5.5 18.5 5.0 19.0 19.5 4.5 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.005 0.010 0.015 0.020 0.025 0.030 0.035 π / (4 πf 2 π / (4 πf 2 m 2 m 2 π ) π ) 14 / 24

Ratio Parameter Fits Figure: Preliminary results for R 4 and R 5 in MS at 3 GeV RI-SMOM γ,γ intermediate scheme. Data points have been adjusted to the physical strange-mass and continuum. (m π / 4 π f π ) 2 phys (m π / 4 π f π ) 2 phys C1 M1 / 2 C1 M1 / 2 phys phys M0 F1 M0 F1 C0 C0 43 11.0 42 41 10.5 40 39 R 4 R 5 10.0 38 37 9.5 36 35 34 9.0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.005 0.010 0.015 0.020 0.025 0.030 0.035 m 2 π / (4 πf 2 m 2 π / (4 πf 2 π ) π ) 15 / 24