Introduction
Main Result

Lattice Study for Conformal and Walking Dynamicsin Large Nf Gauge Theory
A Potential Interest for Use of New Fermions

Kohtaroh MiuraA , M. LombardoA , E. PallanteB
A. DeuzemanC , and T. SilvaB
Laboratori Nazionali di Frascati - INFNA
Rijksuniversiteit GroningenB
University of BernC

Flash Talk at YITP, Feb. 17, 2011

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Gauge Theory with IRFP

S[g]

S[g0]

µµ0
B(g , Nc , Nf ) = µ(1)gg∗ Conformal

B(g)IRFPg∗dg.
dµgµKohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Motivation: Walking Technicolor ModelhΨ̄Ψi|ETC= exphΨ̄Ψi|TC»Z ΛETCΛTC–„«γ[g∗2 ]ˆ 2 ˜ Conformal
ΛETC.
d(log µ) γ g (µ) −−−−−→
ΛTC(2)

Composite Higgs: To avoid Higgs mass hierarchy problem.
Walking Dynamics: To make masses of SM fermions (63 ν)
without large FCNC current.

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge ThIntroduction
Main Result

Motivation: Walking Technicolor ModelhΨ̄Ψi|ETC= exphΨ̄Ψi|TC»Z ΛETCΛTC–„«γ[g∗2 ]ˆ 2 ˜ Conformal
ΛETC.
d(log µ) γ g (µ) −−−−−→
ΛTC(2)

Composite Higgs: To avoid Higgs mass hierarchy problem.
Walking Dynamics: To make masses of SM fermions (63 ν)
without large FCNC current.

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Motivation: Walking Technicolor ModelhΨ̄Ψi|ETC= exphΨ̄Ψi|TC»Z ΛETCΛTC–„«γ[g∗2 ]ˆ 2 ˜ Conformal
ΛETC.
d(log µ) γ g (µ) −−−−−→
ΛTC(2)

Composite Higgs: To avoid Higgs mass hierarchy problem.
Walking Dynamics: To make masses of SM fermions (63 ν)
without large FCNC current.

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Strategy

We investigate finite T chiral phase transitionsin Nf = 0, 4, 6, 8, and 12 cases, (and more and more in future).
The lower edge of the conformal window is extracted
from a vanishing Tc (Nf ).
How we compare theories with different number of flavors?
Analytic guide: Functional Renormalization Group(J. Brawn and H. Gies (’06)).

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Strategy

We investigate finite T chiral phase transitionsin Nf = 0, 4, 6, 8, and 12 cases, (and more and more in future).
The lower edge of the conformal window is extracted
from a vanishing Tc (Nf ).
How we compare theories with different number of flavors?
Analytic guide: Functional Renormalization Group(J. Brawn and H. Gies (’06)).

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Strategy

We investigate finite T chiral phase transitionsin Nf = 0, 4, 6, 8, and 12 cases, (and more and more in future).
The lower edge of the conformal window is extracted
from a vanishing Tc (Nf ).
How we compare theories with different number of flavors?
Analytic guide: Functional Renormalization Group(J. Brawn and H. Gies (’06)).

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

IntroductionMain Result

Strategy

We investigate finite T chiral phase transitionsin Nf = 0, 4, 6, 8, and 12 cases, (and more and more in future).
The lower edge of the conformal window is extracted
from a vanishing Tc (Nf ).
How we compare theories with different number of flavors?
Analytic guide: Functional Renormalization Group(J. Brawn and H. Gies (’06)).

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Critical Flavor Number Nf∗am=0.02
0.25
Fit, exp=2.54
N f*βref=4.0

R(Nf)/R(0)

0.2
0.15
0.1
0.05
04681012

Nf

Figure: R(Nf ) ≡ Tc /Λref (Nf )Tc (Nf )=K |Nf − Nf∗ |2.54 ,Nf∗=

10.5 ± 0.4 ,(Braun-Geis (’11))(Presnt Work)

(3)
(4)

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th

Introduction
Main Result

Welcome to Talk

Details are on Feburuary 20 (Mon),
10:45 - 11:15 !!

Kohtaroh MiuraA , M. LombardoA , E. PallanteB A. DeuzemanC , and T. SilvaBLattice Study for Conformal and Walking Dynamics in Large Nf Gauge Th