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

Beyond the Standard Model Kaon Mixing with physical light quarks

Julia Kettle1

Peter Boyle1, Nicolas Garron2, Renwick Hudspith3,Ava Khamseh1, Tobias Tsang1

RBC-UKQCD

1University of Edinburgh 2University of Liverpool 3York University

Lattice 2018, July 2018

1 / 24

The RBC & UKQCD collaborations

BNL and BNL/RBRC Ziyuan Bai Norman Christ Duo Guo Christopher Kelly Bob Mawhinney Masaaki T

• mii

Jiqun Tu Bigeng Wang University of Connecticut Peter Boyle Guido Cossu Luigi Del Debbio T adeusz Janowski Richard Kenway Julia Kettle Fionn O'haigan Brian Pendleton Antonin Portelli T

• bias T

sang Azusa Yamaguchi Nicolas Garron Jonathan Flynn Vera Guelpers James Harrison Andreas Juettner James Richings Chris Sachrajda Julien Frison Xu Feng Tianle Wang Evan Wickenden Yidi Zhao UC Boulder Renwick Hudspith Yasumichi Aoki (KEK) Mattia Bruno T aku Izubuchi Yong-Chull Jang Chulwoo Jung Christoph Lehner Meifeng Lin Aaron Meyer Hiroshi Ohki Shigemi Ohta (KEK) Amarjit Soni Oliver Witzel Columbia University T

• m Blum

Dan Hoying (BNL) Luchang Jin (RBRC) Cheng Tu Edinburgh University York University (Toronto) University of Southampton Peking University University of Liverpool KEK Stony Brook University Jun-Sik Yoo Sergey Syritsyn (RBRC) MIT David Murphy

2 / 24

Table of contents

1

Introduction

2

Lattice Implementation

3

Analysis

4

Results

5

Summary

3 / 24

Kaon Mixing in the Standard Model

Oscillation of K0 to ¯ K0 One-loop FCNC Mediated by W ± Related to indirect CP violation s ¯ d d ¯ s ¯ u, ¯ c, ¯ t W W ¯ u, ¯ c, ¯ t s ¯ d d ¯ s OPE separates out a long-distance 4quark

• perator

Matrix elements of O∆S=2 calculated with LQCD O∆S=2 = [¯ saγµ(1 − γ5)da][¯ sbγµ(1 − γ5)db]

4 / 24

Beyond the Standard Model

Generalized Weak Hamiltonian: H∆S=2 =

5

• i=1

Ci(µ)Oi +

3

• i=1

˜ Ci(µ) ˜ Oi Basis of 5 model independent parity-even four-quark operators. O1 = [¯ saγµ(1 − γ5)da][¯ sbγµ(1 − γ5)db] O2 = [¯ sa(1 − γ5)da][¯ sb(1 − γ5)db] O3 = [¯ sa(1 − γ5)db][¯ sb(1 − γ5)da] O4 = [¯ sa(1 − γ5)da][¯ sb(1 + γ5)db] O5 = [¯ sa(1 − γ5)db][¯ sb(1 + γ5)da]

Past calculations by SWME1, ETM 2 and RBC-UKQCD 3.

1Jang et al 15, Bae et al 14 2Carrasco et al 15,Bertone et al 10 3Garron,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 = 2.774GeV mπ ≈ 230MeV

name L/a T/a kernel source a−1[GeV] mπ[MeV] nconfigs amuni

l

amsea

s

amval

s

amphys

s

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 = 2.774GeV mπ ≈ 230MeV

name L/a T/a kernel source a−1[GeV] mπ[MeV] nconfigs amuni

l

amsea

s

amval

s

amphys

s

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 = 2.774GeV mπ ≈ 230MeV

name L/a T/a kernel source a−1[GeV] mπ[MeV] nconfigs amuni

l

amsea

s

amval

s

amphys

s

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

Z2 (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:

B1(µ) = ¯

P|O1(µ)|P

8 3 m2 Kf2 K

Bi>1(µ) = (ms(µ)+md(µ))2

Nim4

Kf2 K

¯ P|Oi(µ)|P

Define a ratio parameter: Ri(m2

P

f2

P

, a2, µ) = f2

K

m2

K

• exp

m2

P

f2

P

¯ P|Oi(µ)|P ¯ P|O1(µ)|P

• lat

such that when a2 → 0 and m2

P /f2 P → m2 K/f2 K it reduces to:

Ri(µ) = ¯ K|Oi(µ)|K ¯ K|O1(µ)|K

8 / 24

Correlator Fitting

5 10 15 20 25 30 35 40 t/a 0.928 0.930 0.932 0.934 0.936 0.938 B4

fit result B4(t)

(a) B4(t) for C0

C3pt(t,tsink) CAP

2pt (t)CAP 2pt (tsink−t) →

¯ P |Oi|P P |AA|P

5 10 15 20 25 30 t/a 8.8 8.7 8.6 8.5 8.4 8.3 R5

fit result R5(t)

(b) R5(t) for M0.

C3pt

i

(t,tsink) C3pt

1

(t,tsink) → ¯ P |Oi|P ¯ P |O1|P

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). Oi(µ)MS = CMS←MOM

ij

(µ)

• lim

a2→0

ZRI

jk (µ)

Z2

q

Ok(a)

• ZRI(µ) ˆ

P[Λ(p2)]|p2=µ2 = Λ(p2)tree p1 p2 p1 p2 p1 = p2 p2

1 = p2 2 = (p1−p2)2

10 / 24

Non-Perturbative Renormalisation

Block diagonal structure due to chiral symmetry ZO∆S=2 =       Z11 Z22 Z23 Z32 Z33 Z44 Z45 Z54 Z55       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: Y

• a2, m2

ll

f2

ll

, δmsea

s

• = Y
• 0, m2

π

f2

π

, 0

• 1 + αia2 + βi

m2

ll

f2

ll

+ γiδmsea

s

• where we include a term linear strange sea-quark mass:

δmsea

s

= (msea

s

− mphys

s

) mphys

s

12 / 24

Ratio Parameter Fits

Figure: Preliminary results for R2 and R3 in MS at 3 GeV RI-SMOMγ,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.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 19.5 19.0 18.5 18.0 17.5 17.0 16.5 16.0

R2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 4.8 5.0 5.2 5.4 5.6 5.8 6.0

R3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

13 / 24

Ratio Parameter Fits ( not corrected to continuum )

Figure: Preliminary results for R2 and R3 in MS at 3 GeV RI-SMOM(γ,γ) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 19.5 19.0 18.5 18.0 17.5 17.0 16.5 16.0

R2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 4.5 5.0 5.5 6.0 6.5 7.0

R3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

14 / 24

Ratio Parameter Fits

Figure: Preliminary results for R4 and R5 in MS at 3 GeV RI-SMOMγ,γ intermediate scheme. Data points have been adjusted to the physical strange-mass and continuum.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 34 35 36 37 38 39 40 41 42 43

R4

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 9.0 9.5 10.0 10.5 11.0

R5

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

15 / 24

Bag Parameter Fits

Figure: Preliminary results for B2 and B3 in MS at 3 GeV RI-SMOMγ,γ intermediate scheme. Data points have been adjusted to the physical strange-mass and continuum.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.465 0.470 0.475 0.480 0.485 0.490 0.495 0.500

B2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.70 0.71 0.72 0.73 0.74 0.75 0.76

B3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

16 / 24

Bag Parameter Fits

Figure: Preliminary results for B4 and B5 in MS at 3 GeV RI-SMOMγ,γ intermediate scheme. Data points have been adjusted to the physical strange-mass and continuum.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.850 0.855 0.860 0.865 0.870 0.875 0.880 0.885 0.890

B4

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.685 0.690 0.695 0.700

B5

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

17 / 24

Table of Results

Physical point continuum limit results - with stat error only

• R2

R3 R4 R5 SMOM (γ, γ)

• 18.50(18)

5.529(64) 38.59(37) 10.9(10) (/ q, / q)

• 19.83(19)

5.416(71) 41.12(39) 10.427(96) MS (γ, γ)

• 18.79(19)

5.795(68) 41.46(40) 10.720(99) (/ q, / q)

• 19.38(19)

5.630(73) 42.58(40) 10.424(95) B1 B2 B3 B4 B5 SMOM (γ, γ) 0.5156(12) 0.5125(20) 0.7509(49) 0.9088(33) 0.7789(28) (/ q, / q) 0.5337(12) 0.5115(17) 0.6667(54) 0.9002(29) 0.6968(23) MS (γ, γ) 0.5177(12) 0.4699(18) 0.7089(46) 0.8820(32) 0.6954(23) (/ q, / q) 0.5289(12) 0.4741(16) 0.6555(55) 0.8839(27) 0.6610(21) Values of χ2/dof

• R2

R3 R4 R5 MOM (γ, γ)

• 0.05

0.07 0.97 0.40 (/ q, / q)

• 0.01

0.15 0.73 0.38 ms (γ, γ)

• 0.09

0.14 0.96 0.40 (/ q, / q)

• 0.01

0.16 0.75 0.38 B1 B2 B3 B4 B5 MOM (γ, γ) 1.86 1.36 2.37 0.52 0.92 (/ q, / q) 1.34 1.59 5.74 0.43 1.63 ms (γ, γ) 1.84 0.63 1.50 1.20 1.87 (/ q, / q) 1.32 1.43 6.08 0.57 2.17

18 / 24

Comparison with Previous Results

R MS

2

(3GeV) R MS

3

(3GeV) R MS

4

(3GeV) R MS

5

(3GeV) (γ,γ)(stat only) Garron,Hudspith,Lytle (q,q)(stat only)

PT error ≈ 2%

19 / 24

Comparison with Previous Results

Consistency within errors with previous results.

this work RBC-UKQCD144 RBC-UKQCD165 B

(/ q,/ q) K

(MS, 3GeV) 0.5289(12) 0.5293(17)(106) 0.536(9)(6)(11) R(γ,γ)

2

(MS, 3GeV)

• 18.79(19)
• 19.48(44)(32)(42)

R(γ,γ)

3

(MS, 3GeV) 5.795(68)

• 6.08(15)(18)(14)

R(γ,γ)

4

(MS, 3GeV) 41.5(40)

• 43.11(89)(201)(112)

R(γ,γ)

5

(MS, 3GeV) 10.720(99)

• 10.99(20)(82)(32)

Stat error improved significantly.

4Blum et al, 2014, arXiv:1411.7017 5Garron,Hudspith, Lytle, 2016, arXiv:1609.03334 20 / 24

Tensions in previous results

21 / 24

Tensions in previous results

In Garron et al 6 it was proposed that source of tension come from choice of kinematics in renormalisation.

0.4 0.6 0.8 1

Nf = RBC-UKQCD ’12 2 + 1 2 ETM 2 + 1 + 1 RBC-UKQCD ’16 2 + 1 2 + 1 2 + 1 SWME 2 + 1 RI-MOM SMOM RI-MOM

B4

0.2 0.4 0.6 0.8

Nf = RBC-UKQCD ’12 2 + 1 2 ETM 2 + 1 + 1 RBC-UKQCD ’16 2 + 1 2 + 1 2 + 1 SWME 2 + 1 RI-MOM SMOM RI-MOM

B5

6Garron et al, RBC-UKQCD, 16 arXiv:1609.03334 22 / 24

Summary

Two times smaller statistical error Third lattice spacing in fit Data directly at physical point for first time Systematic error will be dominated by perturbation theory Quantify truncation in perturbation theory by difference between schemes Consistent with previous RBC-UKQCD results with NE schemes Exceptional schemes remain in disagreement (pion pole model suspect)

23 / 24

Acknowledgements

Thanks to all members of RBC-UKQCD for their weekly discussions and comments.

24 / 24

Backup slides

1 / 10

Figure: Preliminary results for R2 and R3 in MS at 3 GeV RI-SMOM(γ,γ) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 19.5 19.0 18.5 18.0 17.5 17.0 16.5 16.0

R2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 4.5 5.0 5.5 6.0 6.5 7.0

R3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

2 / 10

Figure: Preliminary results for R4 and R5 in MS at 3 GeV RI-SMOM(γ,γ) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 28 30 32 34 36 38 40 42 44

R4

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0

R5

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

3 / 10

Figure: Preliminary results for B2 and B3 in MS at 3 GeV RI-SMOM(γ,γ) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60

B2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05

B3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

4 / 10

Figure: Preliminary results for B4 and B5 in MS at 3 GeV RI-SMOM(γ,γ) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92

B4

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.58 0.60 0.62 0.64 0.66 0.68 0.70

B5

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

5 / 10

SM Bag parameter

Figure: Preliminary results for BK in MS at 3 GeV RI-SMOM(γ,γ) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.516 0.517 0.518 0.519 0.520 0.521 0.522 0.523 0.524

B1

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.515 0.520 0.525 0.530 0.535 0.540

B1

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

6 / 10

Results - (/ q, / q)

Figure: Preliminary results for R2 and R3 in MS at 3 GeV RI-SMOM(/

q,/ q) intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 20.0 19.5 19.0 18.5 18.0 17.5 17.0 16.5

R2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 4.8 5.0 5.2 5.4 5.6 5.8

R3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

7 / 10

Results - (/ q, / q)

Figure: Preliminary results for R4 and R5 in MS at 3 GeV RI-SMOM/

q,/ q intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 35 36 37 38 39 40 41 42 43 44

R4

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 8.5 9.0 9.5 10.0 10.5 11.0

R5

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

8 / 10

Results - (/ q, / q)

Figure: Preliminary results for B2 and B3 in MS at 3 GeV RI-SMOM/

q,/ q intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.46 0.47 0.48 0.49 0.50 0.51 0.52

B2

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.64 0.66 0.68 0.70 0.72 0.74 0.76

B3

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

9 / 10

Results - (/ q, / q)

Figure: Preliminary results for B4 and B5 in MS at 3 GeV RI-SMOM/

q,/ q intermediate scheme.

0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.876 0.878 0.880 0.882 0.884 0.886 0.888 0.890 0.892

B4

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys 0.005 0.010 0.015 0.020 0.025 0.030 0.035

m 2

π /(4πf 2 π ) 0.660 0.665 0.670 0.675

B5

(mπ /4πfπ )2

phys

C0 C1 M0 M1/2 F1 phys

10 / 10