[PPT] - Selected new results from the Spectroscopy Selected new results from PowerPoint Presentation

SLIDE 1

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Selected new results from the Spectroscopy in the sextet BSM Model Selected new results from the Spectroscopy in the sextet BSM Model

Chik Him (Ricky) Wong Lattice Higgs Collaboration (LatHC): Zoltán Fodor $, Kieran Holland ∗, Julius Kuti †, Santanu Mondal −, Dániel Nógrádi −, Chik Him Wong $

† University of California, San Diego * University of the Pacific $ University of Wuppertal - Eötvös University

LATTICE 2016

1 / 15

SLIDE 2

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Outline Outline

Review: Sextet model as Composite Higgs candidate Hadron spectroscopy in Isoscalar JPC = 0−+ (η) channel

Fermionic correlator Gluonic operator Improvement using Gradient Flow Preliminary results

Conclusion

2 / 15

SLIDE 3

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 4

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 5

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 6

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 7

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 8

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 9

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 10

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 11

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 12

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Criteria for candidate models in composite Higgs scenario:

Generates Higgs boson consistent with phenomenology Infrared pseudo-Fixed point(IRFP) + Spontaneous χSB ⇒ Models at the edge of Conformal Window

SU(3) Nf = 2 Sextet(Two-index symmetric) Model ψL

ab = ψL ba ≡

uL

ab

dL

ab

, ψR

ab = ψR ba ≡

uR

ab dR ab

a,b = 0,1,2

Why is it interesting?

Very close to Conformal Window “Minimal” model

Spontaneous Chiral Symmetry Breaking: SU(Nf )L ×SU(Nf )R → SU(Nf )V 3 Nambu-Goldstone Bosons (BSM-π) out of N2

f −1 are eaten in Higgs

Mechanism: SU(2)W ×U(1)Y → U(1)em while BSM-f0 is identified as the Higgs boson H N2

f −4 massless BSM-π’s somehow gains masses from additional

interactions, but far separated from the eaten massless 3, yet not a concern if Nf = 2 ⇒ Sextet is “Minimal” realization and hence appealing

3 / 15

SLIDE 13

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 14

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 15

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 16

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 17

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 18

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 19

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ 4 / 15

SLIDE 20

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Consistent with χSB

Static Quark Potential: Confining (Fodor et al, PoS (Lattice 2012) 025) Chiral condensate: Non-zero (Fodor et al, PoS (LATTICE 2013) 089) β function of gR : No IRFP is observed (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503 )

Hadron Spectroscopy

Action: Tree-level Symanzik-Improved 2-stout ρ = 0.15 smeared gauge action with Staggered Nf = 2 Sextet SU(3) fermions Previously:(Fodor et al, PoS (LATTICE 2014) 244)

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ

Light Higgs f0 LHC-reachable resonance candidates ρ, a0, a1 Baryon N: Its spectrum is crucial for predicting relic abundance in the early Universe and dictates how to embed into SM (Fodor et al, Phys.Rev. D94 (2016) no.1, 014503)

5 / 15

SLIDE 21

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Taste breaking

Goldstone spectrum depends on m with different slopes ⇒ Taste breaking pattern is different from QCD

0.002 0.004 0.006 0.008

m

0.02 0.04 0.06 0.08

M

2

P I V T A

β=3.20

0.002 0.004 0.006 0.008

m

0.02 0.04 0.06 0.08

M

2

P I V T A

β=3.25

χPT analysis is complicated by Taste breaking

6 / 15

SLIDE 22

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Taste breaking

Goldstone spectrum depends on m with different slopes ⇒ Taste breaking pattern is different from QCD

0.002 0.004 0.006 0.008

m

0.02 0.04 0.06 0.08

M

2

P I V T A

β=3.20

0.002 0.004 0.006 0.008

m

0.02 0.04 0.06 0.08

M

2

P I V T A

β=3.25

χPT analysis is complicated by Taste breaking

6 / 15

SLIDE 23

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Taste breaking

Goldstone spectrum depends on m with different slopes ⇒ Taste breaking pattern is different from QCD

0.002 0.004 0.006 0.008

m

0.02 0.04 0.06 0.08

M

2

P I V T A

β=3.20

0.002 0.004 0.006 0.008

m

0.02 0.04 0.06 0.08

M

2

P I V T A

β=3.25

χPT analysis is complicated by Taste breaking

6 / 15

SLIDE 24

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Taste breaking

Gradient Flow ( Martin Luescher Commun.Math.Phys.293:899-919,2010 ) restores taste Mixed action analysis using Gradient Flow is under development

7 / 15

SLIDE 25

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Taste breaking

Gradient Flow ( Martin Luescher Commun.Math.Phys.293:899-919,2010 ) restores taste Mixed action analysis using Gradient Flow is under development

7 / 15

SLIDE 26

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Sextet model as Composite Higgs candidate Sextet model as Composite Higgs candidate

Taste breaking

Gradient Flow ( Martin Luescher Commun.Math.Phys.293:899-919,2010 ) restores taste Mixed action analysis using Gradient Flow is under development

7 / 15

SLIDE 27

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Where is Mη (Isoscalar JPC = 0−+)?

π = ¯ ψ γ5 C ψ , ψ = (u,d)T: NG boson ∂µjµ

5 ∼ mj5 ⇒ lim m→0M2 π = 0

η = ¯ ψ γ5 ψ , ψ = (u,d)T: would-be NG boson, but mass generated by U(1)A anomaly ∂µjµ

5 ∼ 2Nf (Nc ±2)q,

+: Symmetric, −: Anti-symmetric Witten-Veneziano formula ( E. Witten, G. Veneziano Nucl. Phys. B 159, 213,269 (1979)) predicts much higher mass than QCD in the chiral limit M2

η ∼ 6(Nc ±2)

f 2

π

χt|Nf =0, χt|Nf =0 =

dxq(0)q(x)|Nf =0

8 / 15

SLIDE 28

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Where is Mη (Isoscalar JPC = 0−+)?

π = ¯ ψ γ5 C ψ , ψ = (u,d)T: NG boson ∂µjµ

5 ∼ mj5 ⇒ lim m→0M2 π = 0

η = ¯ ψ γ5 ψ , ψ = (u,d)T: would-be NG boson, but mass generated by U(1)A anomaly ∂µjµ

5 ∼ 2Nf (Nc ±2)q,

+: Symmetric, −: Anti-symmetric Witten-Veneziano formula ( E. Witten, G. Veneziano Nucl. Phys. B 159, 213,269 (1979)) predicts much higher mass than QCD in the chiral limit M2

η ∼ 6(Nc ±2)

f 2

π

χt|Nf =0, χt|Nf =0 =

dxq(0)q(x)|Nf =0

8 / 15

SLIDE 29

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Where is Mη (Isoscalar JPC = 0−+)?

π = ¯ ψ γ5 C ψ , ψ = (u,d)T: NG boson ∂µjµ

5 ∼ mj5 ⇒ lim m→0M2 π = 0

η = ¯ ψ γ5 ψ , ψ = (u,d)T: would-be NG boson, but mass generated by U(1)A anomaly ∂µjµ

5 ∼ 2Nf (Nc ±2)q,

+: Symmetric, −: Anti-symmetric Witten-Veneziano formula ( E. Witten, G. Veneziano Nucl. Phys. B 159, 213,269 (1979)) predicts much higher mass than QCD in the chiral limit M2

η ∼ 6(Nc ±2)

f 2

π

χt|Nf =0, χt|Nf =0 =

dxq(0)q(x)|Nf =0

8 / 15

SLIDE 30

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Where is Mη (Isoscalar JPC = 0−+)?

π = ¯ ψ γ5 C ψ , ψ = (u,d)T: NG boson ∂µjµ

5 ∼ mj5 ⇒ lim m→0M2 π = 0

η = ¯ ψ γ5 ψ , ψ = (u,d)T: would-be NG boson, but mass generated by U(1)A anomaly ∂µjµ

5 ∼ 2Nf (Nc ±2)q,

+: Symmetric, −: Anti-symmetric Witten-Veneziano formula ( E. Witten, G. Veneziano Nucl. Phys. B 159, 213,269 (1979)) predicts much higher mass than QCD in the chiral limit M2

η ∼ 6(Nc ±2)

f 2

π

χt|Nf =0, χt|Nf =0 =

dxq(0)q(x)|Nf =0

8 / 15

SLIDE 31

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Fermionic correlator η(τ)η(τ0) ≡ −C(τ −τ0)+2D(τ −τ0)

Involves disconnected contribution D(τ −τ0) which are costly In the limit τ −τ0 → ∞, −C(τ −τ0) ∝ Aπe−Mπ(τ−τ0) 2D(τ −τ0) ∝ −Aπe−Mπ(τ−τ0) +Bηe−Mη(τ−τ0) (Mπ < Mη) Cancellation of large pion contribution ⇒ Noisy

9 / 15

SLIDE 32

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Fermionic correlator η(τ)η(τ0) ≡ −C(τ −τ0)+2D(τ −τ0)

Involves disconnected contribution D(τ −τ0) which are costly In the limit τ −τ0 → ∞, −C(τ −τ0) ∝ Aπe−Mπ(τ−τ0) 2D(τ −τ0) ∝ −Aπe−Mπ(τ−τ0) +Bηe−Mη(τ−τ0) (Mπ < Mη) Cancellation of large pion contribution ⇒ Noisy

9 / 15

SLIDE 33

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Fermionic correlator η(τ)η(τ0) ≡ −C(τ −τ0)+2D(τ −τ0)

Involves disconnected contribution D(τ −τ0) which are costly In the limit τ −τ0 → ∞, −C(τ −τ0) ∝ Aπe−Mπ(τ−τ0) 2D(τ −τ0) ∝ −Aπe−Mπ(τ−τ0) +Bηe−Mη(τ−τ0) (Mπ < Mη) Cancellation of large pion contribution ⇒ Noisy

9 / 15

SLIDE 34

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Fermionic correlator η(τ)η(τ0) ≡ −C(τ −τ0)+2D(τ −τ0)

Involves disconnected contribution D(τ −τ0) which are costly In the limit τ −τ0 → ∞, −C(τ −τ0) ∝ Aπe−Mπ(τ−τ0) 2D(τ −τ0) ∝ −Aπe−Mπ(τ−τ0) +Bηe−Mη(τ−τ0) (Mπ < Mη) Cancellation of large pion contribution ⇒ Noisy

9 / 15

SLIDE 35

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Gluonic operator (H. Fukaya, Phys. Rev. D 92, 111501 2015)

Mη can be extracted from the topological charge density: q(x) = 1 32π2 εµνρσTr Fµν

cl Fρσ cl (x)

lim

r→large−q(x)q(y) ∝ K1( Mηr )

r , r ≡ |x−y| Fµν

cl : Field Strength Tensor (clover term)

K1: Modified Bessel function of the second kind Does not couple directly to pions ⇒ Quieter No inversions of Dirac operator ⇒ Cheaper Further speed-up by FFT q(x)q(y) = 1 4π2

|˜

q(k)|2eik(x−y)d4k

10 / 15

SLIDE 36

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Gluonic operator (H. Fukaya, Phys. Rev. D 92, 111501 2015)

Mη can be extracted from the topological charge density: q(x) = 1 32π2 εµνρσTr Fµν

cl Fρσ cl (x)

lim

r→large−q(x)q(y) ∝ K1( Mηr )

r , r ≡ |x−y| Fµν

cl : Field Strength Tensor (clover term)

K1: Modified Bessel function of the second kind Does not couple directly to pions ⇒ Quieter No inversions of Dirac operator ⇒ Cheaper Further speed-up by FFT q(x)q(y) = 1 4π2

|˜

q(k)|2eik(x−y)d4k

10 / 15

SLIDE 37

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Gluonic operator (H. Fukaya, Phys. Rev. D 92, 111501 2015)

Mη can be extracted from the topological charge density: q(x) = 1 32π2 εµνρσTr Fµν

cl Fρσ cl (x)

lim

r→large−q(x)q(y) ∝ K1( Mηr )

r , r ≡ |x−y| Fµν

cl : Field Strength Tensor (clover term)

K1: Modified Bessel function of the second kind Does not couple directly to pions ⇒ Quieter No inversions of Dirac operator ⇒ Cheaper Further speed-up by FFT q(x)q(y) = 1 4π2

|˜

q(k)|2eik(x−y)d4k

10 / 15

SLIDE 38

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Gluonic operator (H. Fukaya, Phys. Rev. D 92, 111501 2015)

Mη can be extracted from the topological charge density: q(x) = 1 32π2 εµνρσTr Fµν

cl Fρσ cl (x)

lim

r→large−q(x)q(y) ∝ K1( Mηr )

r , r ≡ |x−y| Fµν

cl : Field Strength Tensor (clover term)

K1: Modified Bessel function of the second kind Does not couple directly to pions ⇒ Quieter No inversions of Dirac operator ⇒ Cheaper Further speed-up by FFT q(x)q(y) = 1 4π2

|˜

q(k)|2eik(x−y)d4k

10 / 15

SLIDE 39

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Gluonic operator (H. Fukaya, Phys. Rev. D 92, 111501 2015)

Mη can be extracted from the topological charge density: q(x) = 1 32π2 εµνρσTr Fµν

cl Fρσ cl (x)

lim

r→large−q(x)q(y) ∝ K1( Mηr )

r , r ≡ |x−y| Fµν

cl : Field Strength Tensor (clover term)

K1: Modified Bessel function of the second kind Does not couple directly to pions ⇒ Quieter No inversions of Dirac operator ⇒ Cheaper Further speed-up by FFT q(x)q(y) = 1 4π2

|˜

q(k)|2eik(x−y)d4k

10 / 15

SLIDE 40

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Improvement from Gradient Flow Cut-off effects can be reduced by the lattice version of Gradient Flow with Wilson operator ∂tAµ(t,x) = −∂SYM ∂Aµ Smooths links similar to diffusion equation with diffusion length √ 8t in lattice units Correlator is distorted by footprint ⇒ Fitting range of r should be far enough r >> 2 √ 8t

2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-10
5e-11

5e-11 1e-10

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001 2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-09 1e-08

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001

11 / 15

SLIDE 41

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Improvement from Gradient Flow Cut-off effects can be reduced by the lattice version of Gradient Flow with Wilson operator ∂tAµ(t,x) = −∂SYM ∂Aµ Smooths links similar to diffusion equation with diffusion length √ 8t in lattice units Correlator is distorted by footprint ⇒ Fitting range of r should be far enough r >> 2 √ 8t

2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-10
5e-11

5e-11 1e-10

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001 2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-09 1e-08

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001

11 / 15

SLIDE 42

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Improvement from Gradient Flow Cut-off effects can be reduced by the lattice version of Gradient Flow with Wilson operator ∂tAµ(t,x) = −∂SYM ∂Aµ Smooths links similar to diffusion equation with diffusion length √ 8t in lattice units Correlator is distorted by footprint ⇒ Fitting range of r should be far enough r >> 2 √ 8t

2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-10
5e-11

5e-11 1e-10

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001 2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-09 1e-08

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001

11 / 15

SLIDE 43

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Hadron spectroscopy in η channel Hadron spectroscopy in η channel

Improvement from Gradient Flow Cut-off effects can be reduced by the lattice version of Gradient Flow with Wilson operator ∂tAµ(t,x) = −∂SYM ∂Aµ Smooths links similar to diffusion equation with diffusion length √ 8t in lattice units Correlator is distorted by footprint ⇒ Fitting range of r should be far enough r >> 2 √ 8t

2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-10
5e-11

5e-11 1e-10

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001 2 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-09 1e-08

<q(x)q(y)>

tf=1.0 tf=2.0 tf=3.5 tf=5.0

64

3x96, β=3.2500, m=0.001

11 / 15

SLIDE 44

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=4.5

64

3x96, β=3.2500, m=0.001

<q(x)q(y)>=A*K1(Mη r)/r

A=6.4(2) x 10

9,Mη=0.418(2), χ

2/dof=0.2

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

64

3x96, β=3.2500, m=0.001

<q(x)q(y)>=A*K1(Mη r)/r

A=6.6(2) x 10

9,Mη=0.419(2), χ

2/dof=0.3

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.5

64

3x96, β=3.2500, m=0.001

<q(x)q(y)>=A*K1(Mη r)/r

A=6.3(2) x 10

9,Mη=0.416(2), χ

2/dof=0.5

3 3.5 4 4.5 5 5.5 6

tf

0.3 0.35 0.4 0.45 0.5

Mη 64

3x96, β=3.2500, m=0.001

12 / 15

SLIDE 45

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

Mη can be as heavy as > 3 TeV Measurements from more ensembles at different volumes, β’s and m’s are available and accumulating

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.001 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.0015 4 6 8 10 12 14 16 18 20

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.002

Further analysis:

The effects of finite volume and fixed topology Cross-check by time-slice-to-time-slice correlator lim

|x4−y4|→large− ∑

x ,

y

q(x)q(y) ∝ e−Mη|x4−y4| The mixing between η and pseudoscalar glueball

13 / 15

SLIDE 46

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

Mη can be as heavy as > 3 TeV Measurements from more ensembles at different volumes, β’s and m’s are available and accumulating

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.001 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.0015 4 6 8 10 12 14 16 18 20

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.002

Further analysis:

The effects of finite volume and fixed topology Cross-check by time-slice-to-time-slice correlator lim

|x4−y4|→large− ∑

x ,

y

q(x)q(y) ∝ e−Mη|x4−y4| The mixing between η and pseudoscalar glueball

13 / 15

SLIDE 47

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

Mη can be as heavy as > 3 TeV Measurements from more ensembles at different volumes, β’s and m’s are available and accumulating

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.001 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.0015 4 6 8 10 12 14 16 18 20

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.002

Further analysis:

The effects of finite volume and fixed topology Cross-check by time-slice-to-time-slice correlator lim

|x4−y4|→large− ∑

x ,

y

q(x)q(y) ∝ e−Mη|x4−y4| The mixing between η and pseudoscalar glueball

13 / 15

SLIDE 48

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

Mη can be as heavy as > 3 TeV Measurements from more ensembles at different volumes, β’s and m’s are available and accumulating

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.001 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.0015 4 6 8 10 12 14 16 18 20

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.002

Further analysis:

The effects of finite volume and fixed topology Cross-check by time-slice-to-time-slice correlator lim

|x4−y4|→large− ∑

x ,

y

q(x)q(y) ∝ e−Mη|x4−y4| The mixing between η and pseudoscalar glueball

13 / 15

SLIDE 49

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

Mη can be as heavy as > 3 TeV Measurements from more ensembles at different volumes, β’s and m’s are available and accumulating

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.001 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.0015 4 6 8 10 12 14 16 18 20

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.002

Further analysis:

The effects of finite volume and fixed topology Cross-check by time-slice-to-time-slice correlator lim

|x4−y4|→large− ∑

x ,

y

q(x)q(y) ∝ e−Mη|x4−y4| The mixing between η and pseudoscalar glueball

13 / 15

SLIDE 50

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Preliminary Results Preliminary Results

Mη can be as heavy as > 3 TeV Measurements from more ensembles at different volumes, β’s and m’s are available and accumulating

4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.001 4 6 8 10 12 14 16 18 20 22

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.0015 4 6 8 10 12 14 16 18 20

r=|x-y|

1e-14 1e-13 1e-12 1e-11

<q(x)q(y)>

tf=5.0

56

3x96, β=3.2000, m=0.002

Further analysis:

The effects of finite volume and fixed topology Cross-check by time-slice-to-time-slice correlator lim

|x4−y4|→large− ∑

x ,

y

q(x)q(y) ∝ e−Mη|x4−y4| The mixing between η and pseudoscalar glueball

13 / 15

SLIDE 51

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Conclusion Conclusion

The sextet model remains an interesting candidate model of Composite Higgs scenario (More details can be found on Julius Kuti’s talk on Mon) More comprehensive and better analysis tools , e.g. mixed action analysis, are being developed Sextet Mη is extracted from the topological charge density correlator after Wilson Gradient Flow Sextet Mη appears to be heavy, and further investigation is ongoing

14 / 15

SLIDE 52

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Conclusion Conclusion

The sextet model remains an interesting candidate model of Composite Higgs scenario (More details can be found on Julius Kuti’s talk on Mon) More comprehensive and better analysis tools , e.g. mixed action analysis, are being developed Sextet Mη is extracted from the topological charge density correlator after Wilson Gradient Flow Sextet Mη appears to be heavy, and further investigation is ongoing

14 / 15

SLIDE 53

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Conclusion Conclusion

The sextet model remains an interesting candidate model of Composite Higgs scenario (More details can be found on Julius Kuti’s talk on Mon) More comprehensive and better analysis tools , e.g. mixed action analysis, are being developed Sextet Mη is extracted from the topological charge density correlator after Wilson Gradient Flow Sextet Mη appears to be heavy, and further investigation is ongoing

14 / 15

SLIDE 54

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

Conclusion Conclusion

The sextet model remains an interesting candidate model of Composite Higgs scenario (More details can be found on Julius Kuti’s talk on Mon) More comprehensive and better analysis tools , e.g. mixed action analysis, are being developed Sextet Mη is extracted from the topological charge density correlator after Wilson Gradient Flow Sextet Mη appears to be heavy, and further investigation is ongoing

14 / 15

SLIDE 55

Selected new results from the Spectroscopy in the sextet BSM Model Chik Him (Ricky) Wong Outline Review η Spectroscopy

Correlator construction Improvement using Gradient Flow Preliminary Results

Conclusion

12 12.5 13 13.5 14 14.5 rmin 0.1 0.2 0.3 0.4 0.5 mfit(rmin) tf=4.0 64

3x96, β=3.2500, m=0.001, rmax=20

15 / 15