[PPT] - QCD QCD W. Sldner, G. Bali (Regensburg) RQCD results on CLS open PowerPoint Presentation

SLIDE 1

QCD

Towards the continuum limit with improved Wilson Fermions employing open boundary conditions –Part 1–

Wolfgang Söldner for RQCD

Regensburg University

Lattice 2016 The 34rd International Symposium on Lattice Field Theory July 29th, 2016

QCD

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 1 / 36

SLIDE 2

QCD Introduction

Motivation

Lattice QCD today more computing power and better algorithms → statistically more precise results increasingly important to control systematics ⇒ obviously, very important: controlled continuum limit Problem when lattice spacing a → 0 ⇒ freezing of topology lattice simulations get stuck in topological sectors problems start at a 0.05 fm ⇒ simple solution: lattice simulations with open boundary conditions

[Lüscher and Schaefer 2011]

→ topology can flow in and out through the boundary

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 2 / 36

SLIDE 3

QCD Introduction

Lattice QCD with Open Boundaries

20 40 60 80 100 120

t

0.50 0.55 0.60 0.65 0.70 0.75 0.80

plaquette action density

Open Boundaries F0k(x)|x0=0 = F0k(x)|x0=T = 0 P+ψ(x)|x0=0 = P−ψ(x)|x0=T = 0, ¯ ψ(x)P−

x0=0 = ¯

ψ(x)P+

x0=T = 0

P± = 1

2(1 ± γ0)

Major Nf = 2 + 1 CLS effort

CLS: HU Berlin, CERN, TC Dublin, Mainz, UA Madrid, Milano Bicocca, Münster, Odense/CP3-Origins, Regensburg, Roma I, Roma II, Wuppertal, DESY Zeuthen

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 3 / 36

SLIDE 4

QCD Simulation Details

Simulation Overview

Lattice Action

Two degenerate light quarks and one strange quark Non-perturbatively improved Wilson action (clover) Tree-level improved Symanzik gauge action

∃ three different quark mass plane trajectories

(1) m = msymm 3m = 2m(ℓ)ight + m(s) = const. ↔

2 κℓ + 1 κs = const. → renormalized 2

mℓ + ms = const. + O(a). (2) ms = ms,ph Strange AWI mass ms = const. → renormalized ms = ms,ph, up to tiny O(a) effects. (3) ms = mℓ (Mainz/Regensburg) For joint non-perturbative renormalization program → simulations with anti-periodic boundary conditions (for a > 0.05 fm)

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 4 / 36

SLIDE 5

QCD Simulation Details

Overview of the simulation strategy

→ 1606.09039]

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

t0m2

π ∼ ml

0.00 0.05 0.10 0.15 0.20 0.25 0.30

t0(2m2

K − m2 π) ∼ ms f ms = f ms, ph physical point ml = ms m = msymm

1 generate the m = msymm trajectory, starting from the ms = mℓ point where m ≈ mph. 2 add points along the symmetric trajectory (mℓ = ms). 3 fit AWI masses (with O(a)-improvement) to a known parametrization, using both trajectories. 4 determine the “physical” point on the m = msymm line, imposing ms/ mℓ = 27.46(44) [FLAG 2] → ms,ph 5 predict κℓ, κs pairs for which ms = ms,ph from the parametrization in order to add ms = ms,ph simulation points.

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 5 / 36

SLIDE 6

QCD Simulation Details

How to predict κs as a function of κℓ for ms fixed I

Average AWI masses:

mj +

mk 2 = mjk = ∂40|Ajk

4 |πjk

20|Pjk|πjk Lattice quark masses: mj = 1 2a 1 κj − 1 κcrit

The Point along the symmetric line (m1 = m2 = mℓ = ms = m3) where
mjk = 0 defines κj = κcrit.

Problem: Different renormalization of flavour-singlet and non-singlet quark mass combinations: Zm(ms − mℓ) = 1 2a 1 κs − 1 κℓ

=

ms − mℓ = ZA ZP 2

m13 −

m12

but:

Zmrmm = Zmrm 2mℓ + ms 3 = 1 6a 2 κℓ + 1 κs − 3 κcrit

= ZA

ZP

m

NB: Due to rm > 1 mℓ < ms can become negative, away from the symmetric line.

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 6 / 36

SLIDE 7

QCD Simulation Details

How to predict κs as a function of κℓ for ms fixed II

3 ms = 2

ms −

mℓ

+ 3

m = Z 2a

2

1 κs − 1 κℓ

+ rm

1 κs + 2 κℓ − 3 κcrit

,

where Z = ZmZP/ZA. Setting ms = ms,ph gives 1 κs = 2 2 + rm 3a Z ms,ph + (1 − rm) 1 κℓ + 3rm 2 1 κcrit

Subtracting the physical point result from both sides of the equation gives:

1 κs = 1 κs,ph + 2(1 − rm) 2 + rm 1 κℓ − 1 κℓ,ph

,

while the target κℓ that corresponds to a given mℓ value can be obtained through 1 κℓ = 1 κℓ,ph + 2a(2 + rm) 3Zrm ( mℓ − mℓ,ph)

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 7 / 36

SLIDE 8

QCD Simulation Details

How to predict κs as a function of κℓ for ms fixed III

Z and κℓ,ph can be obtained from m13 − m12 as a function of κℓ along the m = const. line. Then κs,ph is automatically determined too. Zrm (and κcrit if needed) can be obtained from m as a function of 1/κ along the symmetric m = m = ms = mℓ line. We carry out full order a improvement. In this case four combinations of improvement coefficients (A, B0, C0 and D0) appear. Does the κs prediction strategy work? To be addressed later: Scale setting/tuning; we assumed that the physical point is on the m = msymm trajectory that we simulate (at least up to O(a2) corrections). But is this true?

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 8 / 36

SLIDE 9

QCD Simulation Details

ms = ms,ph: prediction vs. simulation

Predicted and simulated value of physical ms,ph [hep-lat 1606.09039]

1 2 3 4 5 6 7 8

mℓ/

mℓ,ph 0.99 1.00 1.01 1.02

ms/

ms,ph β = 3.4, ms = ms,ph β = 3.55

Mismatch at β = 3.4 due to shift of cA value but still very constant!

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 9 / 36

SLIDE 10

QCD Simulation Details

Nf = 2 + 1 CLS simulations

Great visibility at Lattice 2016 plenaries:

Coordinated Lattice Simulations: HU Berlin, CERN, TC Dublin, Mainz, UA Madrid, Milano Bicocca, Münster, Odense/CP3-Origins, Regensburg, Roma I, Roma II, Wuppertal, DESY Zeuthen

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 10 / 36

SLIDE 11

QCD Simulation Details

CLS ensemble overview

→ JHEP 1502 (2015) 043 [hep-lat 1411.3982]

m = msymm

ms =

ms,ph

150 200 250 300 350 400 450 0.002 0.004 0.006 0.008 0.01 mπ[MeV] a2[fm2] physical U103 H101 U102 H102 U101 H105 N101 S100 C101 D101 D100 D150 B450 S400 N401 H200 N202 N203 S201 N200 D200 N300 N302 J303 J500 J501 150 200 250 300 350 400 450 0.002 0.004 0.006 0.008 0.01 mπ[MeV] a2[fm2] physical H107 H106 C102 N204 N201 D201

U: 128 × 243 B: 64 × 323 H: 96 × 323 S: 128 × 323 C: 96 × 483 N: 128 × 483 D: 128 × 643 J: 192 × 643

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 11 / 36

SLIDE 12

QCD m = msymm line

Tuning details and results for the m = msymm trajectory

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 12 / 36

SLIDE 13

QCD m = msymm line

Tuning strategy: m = msymm

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 φ2 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 φ4 β = 3.4 β = 3.46 β = 3.55 β = 3.7 β = 3.85 φ2 = t0m2

π ∼ ml ,

φ4 = 8t0(m2

K + m2 π/2) ∼ m

At fixed β match lattices with different lattice spacings at flavor symmetric point (i.e. mud = ms → mπ = mK ≈ 415 MeV) The (small) slope of φ4 as a function of φ2 was determined at β = 3.4 from a set of preliminary runs: φ4

mud =ms = 1.15

Physical target (yellow bands):

t0 = 0.1465(21)(13) fm [BMW], mπ = 134.8(3) MeV, mK = 494.2(4) MeV [FLAG 2]
W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 13 / 36

SLIDE 14

QCD m = msymm line

Chiral extrapolation: m = msymm

→ hep-lat 1606.09039

0.0 0.2 0.4 0.6 0.8 1.0 φ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 φ4 m = msymm

ms =

ms,ph ms = mℓ

phys. point

0.0 0.2 0.4 0.6 0.8 1.0 φ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 φ4 m = msymm

ms =

ms,ph ms = mℓ

phys. point

β = 3.4 a ≈ 0.085 fm β = 3.55 a ≈ 0.064 fm

Combination shown is constant to NLO χPT along m = const. Corrections are of higher

rder or O(a).

Dependence on φ2 becomes weaker towards smaller a → mostly lattice artefact? At the physical point we are still within the target range!

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 14 / 36

SLIDE 15

QCD ms = ms,ph line

AWI masses and O(a)-Improvement [hep-lat 1606.09039]

7.295 7.300 7.305 7.310 7.315 1/κℓ 0.000 0.005 0.010 0.015 0.020 0.025 ( ms − mℓ)a m = msymm

ms =

ms,ph

phys. point

7.285 7.290 7.295 7.300 1/κℓ 0.000 0.005 0.010 0.015 0.020 0.025 ( ms − mℓ)a m = msymm

ms =

ms,ph

phys. point

β = 3.4 β = 3.55 Simultaneous fit of light and strange AWI masses m(ℓ,s)(κℓ, κs) from m = msymm and mℓ = ms trajectory Relevant parameters: Z ≡ ZP Zm

ZA

, A, B0 (→ slope is due to Z) use A from Ref. [Korcyl and Bali, arXiv:1607.07090] as input Sums of quark masses are sensitive to Zrm, κcrit , C0, (D0) A, ..., D0 are combinations of rm, bP, bA, bm, dm, ˜ bP, ˜ bA, ˜ bm, ˜ dm

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 15 / 36

SLIDE 16

QCD ms = ms,ph line

Physical point [hep-lat 1606.09039]

7.295 7.300 7.305 7.310 1/κℓ 0.0 0.2 0.4 0.6 0.8 1.0

mℓ/

m m = msymm

ms =

ms,ph

phys. point

7.285 7.290 7.295 7.300 1/κℓ 0.0 0.2 0.4 0.6 0.8 1.0

mℓ/

m m = msymm

ms =

ms,ph

phys. point

β = 3.4 β = 3.55

ms/

mℓ along m = msymm determined from the global fit. physical value = 27.46(44) from [FLAG 2] used to define the physical point.

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 16 / 36

SLIDE 17

QCD ms = ms,ph line

Physical Point II [hep-lat 1606.09039]

Is the FLAG value consistent with our results?

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 8t0,phM 2

π

0.0 0.2 0.4 0.6 0.8 1.0 3M 2

π/(2M 2 K + M 2 π)

m = msymm

ms =

ms,ph

phys. point

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 8t0,phM 2

π

0.0 0.2 0.4 0.6 0.8 1.0 3M 2

π/(2M 2 K + M 2 π)

m = msymm

ms =

ms,ph

phys. point

β = 3.4 β = 3.55 We find consistency with experiment Predicting ms/ mℓ from the experimental pion masses would improve on the FLAG precision. However, we need to analyse additional lattice spacings to take the continuum limit.

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 17 / 36

SLIDE 18

QCD ms = ms,ph line

Fitting Details

Nucleon: Effective mass

5 10 15 20 25 30 35 40 0.28 0.30 0.32 0.34 0.36 0.38

effective mass Ensemble = N300, Run = run4

fit range = [2, 35] N, bin=15

5 10 15 20 25 30 35 40 0.28 0.30 0.32 0.34 0.36 0.38

effective mass

fit range = [2, 30]

5 10 15 20 25 30 35 40

t

0.28 0.30 0.32 0.34 0.36 0.38

effective mass

fit range = [2, 35]

N300 Ensemble mass: mπ = mK ≈ 420 MeV lattice size: 128 × 483 Fitting: Two stage procedure 1 Determine actual fit range where excited state contribution is negligible by double exp fit 2 With determined fit range perform actual fit Autocorrelations → binning analysis, extrapolate error to infinite bin size

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 18 / 36

SLIDE 19

QCD ms = ms,ph line

Fitting Details

Pion: Effective mass

10 20 30 40 50 60 70 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135

effective mass Ensemble = N300, Run = run4

fit range = [4, 66] π, bin=15

10 20 30 40 50 60 70 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135

effective mass

fit range = [4, 34]

10 20 30 40 50 60 70

t

0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135

effective mass

fit range = [4, 52]

N300 Ensemble mass: mπ = mK ≈ 420 MeV lattice size: 128 × 483 Fitting: Two stage procedure 1 Determine actual fit range where excited state contribution is negligible by double exp fit, boundary effects described by sinh 2 With determined fit range perform actual fit Autocorrelations → binning analysis, extrapolate error to infinite bin size

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 19 / 36

SLIDE 20

QCD ms = ms,ph line

Comparing extrapolations m = msymm with ms = ms,ph

Average Hadron Masses Average pion mass: X 2

π = (2M2 K + M2 π)/3

Average octet baryon mass: XN = (MΞ + MΣ + MN)/3 (no Σ0 to circumvent Λ-Σ mixing) Average decuplet baryon mass: X∆ = (2M∆ + MΩ)/3 For the experimental values we take the charge combinations of QCDSF: 1101.5300. All combinations scale in the Gell-Mann–Okubo expansion and NLO ChiPT ∝ m and ∝ (ms − mℓ)2.

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 20 / 36

SLIDE 21

QCD Comparing extrapolations along the two mass trajectories

Pseudoscalar masses m = msymm

preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.0 0.5 1.0 1.5 2.0 m2

M/X2 π,symm

M = π M = K physical point β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.0 0.5 1.0 1.5 2.0 m2

M/X2 π,symm

M = π M = K physical point β = 3.55, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.9 1.0 1.1 1.2 1.3 1.4 1.5 X2

π/X2 π,symm

physical point β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.9 1.0 1.1 1.2 1.3 1.4 1.5 X2

π/X2 π,symm

physical point β = 3.55, m = msymm

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 21 / 36

SLIDE 22

QCD Comparing extrapolations along the two mass trajectories

Pseudoscalar masses m = msymm and ms = ms,ph

preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.0 0.5 1.0 1.5 2.0 m2

M/X2 π,symm

M = π M = K physical point β = 3.4, m = msymm β = 3.4, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.0 0.5 1.0 1.5 2.0 m2

M/X2 π,symm

M = π M = K physical point β = 3.55, m = msymm β = 3.55, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.9 1.0 1.1 1.2 1.3 1.4 1.5 X2

π/X2 π,symm

physical point β = 3.4, m = msymm β = 3.4, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.9 1.0 1.1 1.2 1.3 1.4 1.5 X2

π/X2 π,symm

physical point β = 3.55, m = msymm β = 3.4, ms = ms,ph

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 22 / 36

SLIDE 23

QCD Comparing extrapolations along the two mass trajectories

Octet baryons m = msymm

preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.8 0.9 1.0 1.1 1.2 mB/XN,symm B = N B = Σ B = Ξ B = Λ physical point β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.8 0.9 1.0 1.1 1.2 mB/XN,symm B = N B = Σ B = Ξ B = Λ physical point β = 3.55, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.90 0.95 1.00 1.05 1.10 1.15 XN/XN,symm physical point β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.90 0.95 1.00 1.05 1.10 1.15 XN/XN,symm physical point β = 3.55, m = msymm

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 23 / 36

SLIDE 24

QCD Comparing extrapolations along the two mass trajectories

Octet baryons m = msymm and ms = ms,ph

preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.8 0.9 1.0 1.1 1.2 mB/XN,symm B = N B = Σ B = Ξ B = Λ physical point β = 3.4, m = msymm β = 3.4, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.8 0.9 1.0 1.1 1.2 mB/XN,symm B = N B = Σ B = Ξ B = Λ physical point β = 3.55, m = msymm β = 3.55, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.90 0.95 1.00 1.05 1.10 1.15 XN/XN,symm physical point β = 3.4, m = msymm β = 3.4, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.90 0.95 1.00 1.05 1.10 1.15 XN/XN,symm physical point β = 3.55, m = msymm β = 3.55, ms = ms,ph

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 24 / 36

SLIDE 25

QCD Comparing extrapolations along the two mass trajectories

Decuplet baryons m = msymm

preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.7 0.8 0.9 1.0 1.1 1.2 mB/X∆,symm B = ∆ B = Σ⋆ B = Ξ⋆ B = Ω physical point β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.7 0.8 0.9 1.0 1.1 1.2 mB/X∆,symm B = ∆ B = Σ⋆ B = Ξ⋆ B = Ω physical point β = 3.55, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.85 0.90 0.95 1.00 1.05 1.10 1.15 X∆/X∆,symm physical point β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.85 0.90 0.95 1.00 1.05 1.10 1.15 X∆/X∆,symm physical point β = 3.55, m = msymm

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 25 / 36

SLIDE 26

QCD Comparing extrapolations along the two mass trajectories

Decuplet baryons m = msymm and ms = ms,ph

preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.7 0.8 0.9 1.0 1.1 1.2 mB/X∆,symm B = ∆ B = Σ⋆ B = Ξ⋆ B = Ω physical point β = 3.4, m = msymm β = 3.4, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.7 0.8 0.9 1.0 1.1 1.2 mB/X∆,symm B = ∆ B = Σ⋆ B = Ξ⋆ B = Ω physical point β = 3.55, m = msymm β = 3.55, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.85 0.90 0.95 1.00 1.05 1.10 1.15 X∆/X∆,symm physical point β = 3.4, m = msymm β = 3.4, ms = ms,ph 2 4 6 8 10

mℓ/

mℓ,ph 0.85 0.90 0.95 1.00 1.05 1.10 1.15 X∆/X∆,symm physical point β = 3.55, m = msymm β = 3.55, ms = ms,ph

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 26 / 36

SLIDE 27

QCD Comparing extrapolations along the two mass trajectories preliminary

2 4 6 8 10

mℓ/

mℓ,ph 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90

XN X∆

β = 3.4, ms = ms,ph β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90

XN X∆

β = 3.55, ms = ms,ph β = 3.55, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.35 0.36 0.37 0.38 0.39 0.40

Xπ XN

β = 3.4, ms = ms,ph β = 3.4, m = msymm 2 4 6 8 10

mℓ/

mℓ,ph 0.35 0.36 0.37 0.38 0.39 0.40

Xπ XN

β = 3.55, ms = ms,ph β = 3.55, m = msymm

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 27 / 36

SLIDE 28

QCD t0

t0 (preliminary)

2 4 6 8 10 12

mℓ/

mℓ,ph 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10

t0/t0,ph

m = msymm

ms =

ms,ph ms = mℓ

phys. point

2 4 6 8 10 12

mℓ/

mℓ,ph 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10

t0/t0,ph

m = msymm

ms =

ms,ph ms = mℓ

phys. point

β = 3.4 RQCD(CLS) data β = 3.55 RQCD(CLS) data Compare scale setting relative error on a from mΞ ≈ 0.4%, mΞ⋆ ≈ 0.9%, mΩ ≈ 0.7%, XN ≈ 0.6% ← → from BMW t0 ≈ 1.7% a for β = 3.40: aXN ≈ 0.0833(4) fm ← → from BMW at0 = 0.0854(15) fm a for β = 3.55: aXN ≈ 0.0632(5) fm ← → from BMW at0 = 0.0644(11) fm

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 28 / 36

SLIDE 29

QCD Continuum Extrapolation

Continuum extrapolation along the symmetric line

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 a2/t0 1.00 1.05 1.10 1.15 1.20 1.25 φ4 φ4 = 8t0(m2

K + m2 π/2),m = msymm

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 a2/t0 0.82 0.84 0.86 0.88 0.90 √t0XN √t0XN, m = msymm 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 a2/t0 1.00 1.02 1.04 1.06 1.08 1.10 1.12 √t0X∆ √t0X∆, m = msymm

φ4 (target φ4 = 1.15) was slightly mistuned This is reflected in other quantities As φ4,ph/φ4,symm is subject to O(ma) corrections this was fortunate in some cases, however: → need for correction (see also talk by Rainer Sommer)

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 29 / 36

SLIDE 30

QCD Continuum Extrapolation

Symmetric line continuum extrapolation

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

a2/t0

0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90

XN X∆

XN X∆ , TrM = const.

weak dependence on m allows for a continuum extrapolation

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 30 / 36

SLIDE 31

QCD Continuum Extrapolation

Continuum limit of gA at Mπ ≈ 415 MeV

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

PRELIMINARY

gA a2 [fm2]

RQCD Nf = 2 + 1 Expt

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 31 / 36

SLIDE 32

QCD Continuum Extrapolation

Continuum limit of gA at Mπ ≈ 415 MeV

0.9 1 1.1 1.2 1.3 1.4 1.5 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

PRELIMINARY

gA a2 [fm2]

RQCD Nf = 2 + 1 Expt

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 32 / 36

SLIDE 33

QCD Continuum Extrapolation

Continuum limit of gA at Mπ ≈ 415 MeV

0.9 1 1.1 1.2 1.3 1.4 1.5 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

PRELIMINARY

gA a2 [fm2]

RQCD Nf = 2 + 1 Expt

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 33 / 36

SLIDE 34

QCD Continuum Extrapolation

Continuum limit of gA at Mπ ≈ 415 MeV

0.9 1 1.1 1.2 1.3 1.4 1.5 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

PRELIMINARY

gA a2 [fm2]

RQCD Nf = 2 + 1 Expt

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 34 / 36

SLIDE 35

QCD Summary and Outlook

Disclaimer

The work presented was carried out in collaboration with Sara Collins, Meinulf Göckeler, Fabian Hutzler, Rudolf Rödl, Andreas Schäfer, Enno Scholz, Jakob Simeth, André Sternbeck and Thomas Wurm Code development and software support: Benjamin Gläßle, Piotr Korcyl, Daniel Richtmann Gauge configurations were generated using OPENQCD within CLS We thank all other CLS colleagues who made this possible.

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 35 / 36

SLIDE 36

QCD Summary and Outlook

Summary

Lattice Simulations with Open Boundaries avoid topological freezing as a → 0 long term effort within CLS m = msymm trajectory: Meson/Baryon Spectrum fitting to Gell-Mann–Okubo expansion and SU(3) ChiPT (combined within the other 2 trajectories) in progress

ms =

ms,ph trajectory: Meson/Baryon Spectrum achieved a very constant strange quark mass reasonable overall agreement of quark and hadron masses at the physical point with m = const. trajectory fitting SU(2) and SU(3) ChiPT in progress Strategy allows us to determine SU(2) as well as SU(3) low energy constants to safely extrapolate to the physical quark mass point Outlook extend present study: continuum limit with ≥ 4 lattice spacings nucleon structure and other additional observables

W. Söldner, G. Bali (Regensburg)

RQCD results on CLS open BC ensembles Lattice 2016 36 / 36