Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling...

29
Introduction 8-flavor QCD with regards to WTC (LatKMI, Preliminary) SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary) Summary and Future Perspective Strongly Interacting Gauge Theory and Physics Beyond Standard Model Mass Anomalous Dimension γ Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Tel Aviv, June. 25, 2015 Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Transcript of Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling...

Page 1: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Strongly Interacting Gauge Theoryand Physics Beyond Standard Model

Mass Anomalous Dimension γ

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.))

Tel Aviv, June. 25, 2015

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 2: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Motivation

The Higgs boson with MH ' 125 GeV is discovered (2012, LHC-CERN)!

The LHC second-run has started!

Why Not Investigate The Origin of EWSB?

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 3: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Strong Dynamics: Origin of EWSB

Questions/Answers: New Strong Dynamics

1 Physical Contents of Higgs?Composite Higgs(c.f. σ, Cooper-Pair).

2 Physics of Electroweak (EW) Symmetry Breaking?Chiral Symmetry Breaking.

3 Fine-Tuning Problem for MH = 125 GeV?Log (partly Power-Low) corrections for MH = 125 GeV.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 4: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Many Flavor QCD and Walking

0

(g)

g

Chiral S

SB

IRFP

g

IRFPwalking

Chiral S

SB

log μ

β

b0 > 0

b1 < 0

Beta function of Nf flavor in SU(Nc = 3) gauge theory:β(g) = dg(µ)/dµ = −b0(Nf ,Nc)g 3 − b1(Nf ,Nc)g 5 + · · · .In 8 . Nf . 12, Walking Dynamics(Schwinger Dyson Analyses, Yamawaki et.al.(’86), Holdom (’85)).

Stable (light) Higgs: Techni-Dilaton (PNGB for Scale Sym Breaking).

SM-lepton/quark masses: Enhancement by Factor (ΛETC/ΛEW)γ

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 5: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Subject: Mass Anomalous Dimension

We investigate the mass anomalous dimension γ in many flavor QCD by using

Lattice Gauge Theory with Monte Carlo Simulations(Latest 8-Flavor Results in LatKMI Collaboration).

Schwinger-Dyson (SD) Equations(Miura-Nagai-Shibata, UV/IR Cutoff Effects).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 6: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Table of Contents

1 Introduction

2 8-flavor QCD with regards to WTC (LatKMI, Preliminary)SetupsHightlightScaling Property of Mass Spectrum

3 SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Some IntroductionIR Cutoff Effects

4 Summary and Future Perspective

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 7: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

LatKMI Collaboration

Y. Aoki (KMI, Nagoya Univ)T. Aoyama (KMI, Nagoya Univ)E. Bennett (Swansea Univ (UK))M. Kurachi (KEK)T. Maskawa (KMI, Nagoya Univ)K. Miura (CPT, Aix-Marseille Univ (RF) / KMI, Nagoya-Univ)K-i. Nagai (KMI, Nagoya Univ)H. Ohki (RIKEN)T. Yamazaki (Tsukuba Univ)K. Yamawaki (KMI, Nagoya Univ)E. Rinaldi (LLNL (US))A. Shibata (KEK)

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 8: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Setups I

Lattice Action: Nf = 8 HISQ Action+ Tree-level Symanzik Gauge Action with β = 3.8.

Argolithm: HMC with Hasenbush pre-conditioning.Observables: Fπ, Mπ, Mρ, Ma1, MN , VPF, · · · .Code etc: MILC ver.7.6.3 with some modifications, SciDac Libraly.Computer: KMI HPC Cluster ϕ,

Nagoya-Univ-ITC CX400,Kyushu-Univ-RIIT CX400/HA8000.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 9: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Setups II

F: New Configs. F: Updates, O(104) Configs.

mf � L 42 36 30 24 18 120.012 F0.015 F F0.02 F F F0.03 F F F0.04 F F F0.05 F F F F0.06 F F F0.07 F F F F0.08 F F F0.09 F0.10 F F F0.12 F0.14 F0.16 F

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 10: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Nf = 8 Flavor Singlet Scalar σ I (Update from LatKMI PRD 2014)

0 0.01 0.02 0.03 0.04 0.05 0.06m

f

0

0.1

0.2

0.3

0.4

0.5m

σ L=42σ L=36σ L=30σ L=24σ L=18π

ρ(PV)

Light σ ∼ Dilaton (PNGB for Broken Scale Symm.)

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 11: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Nf = 8 Flavor Singlet Scalar σ II (Update from LatKMI PRD 2014)

0 0.01 0.02 0.03 0.04 0.05 0.06m

f

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ L=42σ L=36σ L=30σ L=24σ L=18π

ρ(PV)

Light σ ∼ SM Higgs (125 GeV)?(c.f. LatHC Collab. (’14), Hietanen et.al. (’14), Athenodorou et.al. (’15)).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 12: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Nf = 8 S-Parameter

?EW EW

ΠV−A ∼

S ≡ 4πΠ′V−A(Q

2 → 0)

The result S ∼ 0.25− 0.275 is smaller than that SQCD,Nf=2 ∼ 0.43.

Walking ∼ Weaker Chiral SSB ∼ V-A Doubling(c.f. LSD-Collab. (’14), Knecht et.al. (Large Nc ’98)).

Still much larger than Sexp = 0.03(10).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 13: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

FSHS: Individual Fits

0

5

10

15

20

25

2 3 4 5 6 7

Fit: L Mh = c0 + c1 L mf1/(1+γ)

L M

h

X = L mf1/(1+γ)

MN

Fπ Mπ Mρ MN

γ 1.003(5) 0.627(2) 0.896(11) 0.810(11)χ2/dof 2.34 15.26 1.41 2.58

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 14: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

FSHS: Simultaneous Fits

2

3

4

5

6

2 3 4 5 6

Fit: L Mh = c0 + c1 L mf1/(1+γ)

(L M

h -

c0)/

c1

L mf1/(1+γ)

MN

Fit

(γ, χ2/dof) = (0.709(2), 124.96).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 15: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

FSHS: Simultaneous Fits with Mass Collection

3

3.5

4

4.5

5

5.5

6

6.5

3 3.5 4 4.5 5 5.5 6 6.5

Fit: L Mh = c0 + c1 L mf1/(1+γ)

+ c2 L mfα

(L M

h -

(c

0 +

c2 L

mfα

))/c

1

L mf1/(1+γ)

MN

Fit

(γ, χ2/dof) = (0.893(15), 3.26) for α = 1.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 16: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

FSHS: Simultaneous Fits with A-Hasenfratz Type Collection

Fit Ansatz: Cheng-Hasenfratz-Liu (’14).

3.5

4

4.5

5

5.5

6

6.5

7

3.5 4 4.5 5 5.5 6 6.5 7

Fit: L Mh = (1 + c2 mω

f )(c0 + c1 L mf1/(1+γ)

)(L

Mh/(

1 +

c2 m

ω f )

- c

0)/

c1

L m1/(1+γ)f

MN

Fit

(γ, χ2/dof) = (1.014(35), 2.46) for ω = 0.35.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 17: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

FSHS: Simultaneous Fits with Frascati-Groningen Type Collection

Fit Ansatz: Lombardo-Miura-Silva-Pallante (’14).

2

2.5

3

3.5

4

4.5

5

5.5

2 2.5 3 3.5 4 4.5 5 5.5

Fit: L Mh = c0 + c1 L mf1/(1+γ)

+ c2 L exp[-kX](L

Mh -

(c 0

+ c

2 L

e-k

X))

/c1

X = L m1/(1+γ)

MN

Fit

(γ, χ2/dof) = (0.617(2), 12.80) for k = 0.1.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 18: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Nf = 8 String Tension

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.02 0.04 0.06 0.08 0.1

stri

ng1/

2 a

mfa

L=42L=30L=24L=18L=36

conformal fit: all range

√string · a = C(mf a)1/(1+γ),

(γ, χ2/dof) = (0.97(4), 0.68).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 19: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

SetupsHightlightScaling Property of Mass Spectrum

Summary on Nf = 8 QCD

FSHS Individual Fπ Mπ Mρ MN

γ 1.003(5) 0.627(2) 0.896(11) 0.810(11)χ2/dof 2.34 15.26 1.41 2.58

FSHS Simultaneous γ χ2/dof

LMh = c0 + c1X , X = Lm1/(1+γ)f 0.709(2) 124.96

LMh = c0 + c1X + c2Lmα=1f 0.893(15) 3.26

LMh = c0 + c1X + c2Lmα=2f 0.772(5) 19.38

LMh = (1 + c2mω=0.35f )(c0 + c1X ) 1.014(35) 2.46

LMh = c0 + c1X + c2L exp(−kX )|k=0.1 0.617(2) 12.80

For mf ∈ [0.012, 0.03], the quadratic fit (motivated by ChPT) works for allmeasured operators. However, Nf (Mπ/(4πF/

√2))2 & 6 and FL . 0.85.

For the same mf range, the naive hyper-scaling fit also works except fewcases with somewhat larger χ2/dof. The γ is operator dependent.

Nf = 8 QCD: Having Light σ, Showing Quasi-Conformal Nature with γ ∼ 1.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 20: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

Motivation: Lattice Results on γ in Color SU(Nc = 3) with Nf = 12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

[FG]

[0]

[1]

[2]

[3], β=3.7

[3], β=4.0

[4]

[5]

perturb.2l3l-MS4l-MS −−

γ

[FG] Nunes et.al. (’14), [0] Deuzemann et.al. (’09), [1] LSD-Collab (’11), (using data provided in [7]), [2] DeGrand

(’11), (using data provided in [7]), [3] LatKMI (’12), [4] Cheng et.al. (’13), [5] Itou (’13), [6] Shrock (’13) [7]

Fodor et.al. (’11).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 21: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

SD with Too-Loop Improved Ladder Approx.

γµg γνg

−1= +

−1

0

1

2

3

4

5

6

-40 -20 0 20 40

α =

g2/(

)

log[µ/Λ]

α = αcrNf = 9

Nf = 10

Nf = 11

Nf = 12

Nf ≥ 8.05: Banks-Zaks (BZ) Infra-Red Fixed Point (IRFP, α∗).

Nf & 12: Conformal Window with α∗ ≤ αcr = π/(3C2[F ]).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 22: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

SD with ΛUV/IR

γµg γνg

−1= +

−1

iS−1F (q) =

[A(p2)6p − Σ(p2)

](Fermion Invers-Prop.) ,

mp(m0,ΛUV/IR) = Σ(p2 = mp;m0,ΛUV/IR) , (Pole Mass, SD-Output) ,

f 2π (m0,ΛUV/IR) =Nc

4π2

∫dz z

(1− 1

4z d

dz

)Σ2(z)(

z + Σ2(z))2 , (Pagels-Stoker) .

State of The Arts (c.f. Previous Work (LatKMI ’09))

The full momentum dependence of the two-loop running coupling g(ΛUV/IR vs scales encoded in g).

Wide range probe in the parameter space(ΛIR/Λ ∈ [10−8, 2.5] and ΛUV/Λ ∈ [1.0, 20] including fπ/ΛIR ∼ fπL ∼ 1).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 23: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

Nf = 12 fπ vs m0

1e-04

1e-03

1e-02

1e-01

1e+00

1e+01

1e-05 1e-04 1e-03 1e-02 1e-01 1e+00 1e+01

ΛUV/Λ = 20, Nf = 12f π

m0/Λ

ΛIR/Λ = 1.0e-8ΛIR/Λ = 1.0e-2

ΛIR/Λ = 0.1ΛIR/Λ = 1.0ΛIR/Λ = 2.5

Mh = Cm1/(1+γm)0 , Mh = mp or fπ . (1)

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 24: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

Nf = 12 γm vs ΛIR

Mh = Cm1/(1+γm)0 , Mh = mp or fπ . (2)

0

0.2

0.4

0.6

0.8

1e-08 1e-06 1e-04 1e-02 1e+00 1e+01

γ m

ΛIR/Λ

ΛUV/Λ=20, Nf = 12, mass fit range [0.001, 0.1]

using mp data

using fπ data

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 25: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

SD-Based FSHS: Formulation

m0

ZUVmp=

Aωm (yIR)Dωm (yΛ)(1+yIR1+yΛ

)(1−ωm)/2+ (ωm ↔ −ωm)

Aωm (yIR)Nωm (max{1, yIR})(

1+yIR1+max{1,yIR}

)(1−ωm)/2+ (ωm ↔ −ωm)

,

Aωm (y) =1 + ωm

2ωmF[−1 + ωm

2,−1 + ωm

2, 1 + ωm;

1

1 + y

],

Dωm (y) =1 + ωm

2F[1− ωm

2,

1− ωm

2, 1− ωm;

1

1 + y

],

Nωm (y) = F[1− ωm

2,

3− ωm

2, 1− ωm;

1

1 + y

], (3)

ωm = 1− γm , (yIR, yΛ) =(Λ2

IR

m2p,

Λ2

m2p

). (4)

m̂p

Λ̂IR

=

{CX(γm,Z

UVm ) · X , X ≡ m̂

1/(1+γm)0 /Λ̂IR (ΛIR � mp � Λ) ,

CY(γm,ZUVm ) · Y , Y ≡ m̂0/Λ̂

−(1+γm)IR (mp � ΛIR � Λ) .

(5)

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 26: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

Nf = 12 SD-Based FSHS I

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 27: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Some IntroductionIR Cutoff Effects

Nf = 12 SD-Based FSHS II

m̂p

Λ̂IR

=

{CX(γm,Z

UVm ) · X , X ≡ m̂

1/(1+γm)0 /Λ̂IR (ΛIR � mp � Λ) ,

CY(γm,ZUVm ) · Y , Y ≡ m̂0/Λ̂

−(1+γm)IR (mp � ΛIR � Λ) .

(6)

1e-04

1e-02

1e+00

1e+02

1e+04

1e+06

1e+08

1e-02 1e+00 1e+02 1e+04 1e+06 1e+08

ΛUV/Λ = 20, Nf = 12

f π/Λ

IR

X(γm = 0.60)

ΛIR = 1.0e-8

ΛIR = 1.0e-3

ΛIR = 0.1

ΛIR = 0.4

ΛIR = 2.5

c.f. fπL in recent lattice results: [1] Fodor et.al. (’11), [2] Cheng et.al. (’14), [3] DeGrand (’11).

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 28: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

Summary

8-flavor QCD (LatKMI)

Having Light σ, Showing Quasi-Conformal Nature with γ ∼ 1.

A viable candidate of Walking Technicolor Model (One-Family Model).

SD with ΛUV/IR (Miura-Nagai-Shibata)

The γ is strongly suppressed when the IR cutoff ΛIR gets comparable tothe scale (mp, fπ).

The SD-based FSHS allows us to avoid the suppression, explains how twoslopes in FSHS result from the IR cutoffs.

The fomulas applicable for lattice mass spectra are desirable.

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model

Page 29: Strongly Interacting Gauge Theory and Physics Beyond ...julian.tau.ac.il/CECAM/Miura.pdf · Scaling Property of Mass Spectrum 3 SD Studies on with UV/IR Cuts (Miura-Nagai-Shibata,

Introduction8-flavor QCD with regards to WTC (LatKMI, Preliminary)

SD Studies on γ with UV/IR Cuts (Miura-Nagai-Shibata, Preliminary)Summary and Future Perspective

LABEX-OCEVU Project in CPT Aix-Marseille Univ: Muon (g − 2)

γ

muon muon

= −ie[γνF1(q2) +

iσνρqρ2mmuon

F2(q2)]

aµ = (g − 2)/2 → F2(0)

∋ ΠhadV

γ?

EW EWΠV−A ∼

S ≡ 4πΠ′V−A(Q

2 → 0)

There exists 3.3σ deviation between aexpµ and aSMµ .

Kohtaroh Miura (CPT, Aix-Marseille Univ. (KMI, Nagoya Univ.)) Strongly Interacting Gauge Theory and Physics Beyond Standard Model