The KMI project · 2013-12-13 · The KMI project Yasumichi Aoki [Kobayashi-Maskawa Institute(KMI), Nagoya University] - at KMI2013 International Symposium - Dec. 11, 2013 Kobayashi-Maskawa

The KMI project

Yasumichi Aoki [Kobayashi-Maskawa Institute(KMI), Nagoya University]

- at KMI2013 International Symposium -

Dec. 11, 2013

Kobayashi-Maskawa Institutefor the Origin of Particles and the Universe素粒子宇宙起源研究機構

素粒子宇宙起源研究機構

Kobayashi-Maskawa Institute for the Origin of Particles and the Universe




'

KMI high performance computer '

KMI high performance computer

• purpose

• strong gauge dynamics, especially for BSM physics

• solve the non-perturbative dynamics quantitatively

• allows to test the theory against experiments: EW measurements, LHC

'


• purpose




• uniqueness

• setting main target as BSM physics ↔ QCD dedicated computers

'


• purpose




• uniqueness

• setting main target as BSM physics ↔ QCD dedicated computers

• operation policy

• promote a few projects to grant large resource to maximize the outcome

• while allowing small projects for test phase use / non-demanding tasks

• anybody can use under collaboration with PI in KMI or Nagoya Univ.

'

KMI computer　 '

KMI computer　 '

KMI computer　

• non GPU nodes

• 148 nodes

• 2x Xenon 3.3 GHz

• 24 TFlops (peak)

'

KMI computer　

• non GPU nodes

• 148 nodes



• GPU nodes

• 23 nodes

• 3x Tesla M2050


'

KMI computer　

• non GPU nodes

• 148 nodes



• GPU nodes

• 23 nodes

• 3x Tesla M2050


• 62 TFlops (peak; comparable to Japanese top 20 of top500 list @ 2012.10)

'

inauguration March 2, 2011'

Inauguration Ceremony of March 2nd, 2011

'

Infrastructure for global data sharing: JLDG

• Japan Lattice Data Grid server @ KMI connected to other site with SINET vpn

2

JLDGy½

priority projects

• 2/3 of whole resource is granted to these 4 projects

• rest ~10 small projects

7 Research groups and users

7.1 List of research groups

Group Project title PI Members

sc-su2phase Lattice study of quantum-mechanical dynamics oftwo-color QCD with six flavors of quarks

M. Hayakawa K. Ishikawa, Y. Osaki, S. Takeda,M. Tomii, N. Yamada

scgt8 Exploring for walking technicolor model with 8-flavor SU(3) gauge theory

T. Aoyama,T. Yamazaki

Y. Aoki, K. Hasebe, M. Kurachi,T. Maskawa, K. Miura, K.-i. Na-gai, H. Ohki, E. Rinaldi, A. Shi-bata, K. Yamawaki

scgt12 Phase structure near the chiral phase boundary inmany flavor QCD

Y. Aoki,H. Ohki

T. Aoyama, K. Hasebe, M. Ku-rachi, T. Maskawa, K. Miura, K.-i. Nagai, E. Rinaldi, A. Shibata,K. Yamawaki, T. Yamazaki

scgtmeas Nonperturbative computation of the spectroscopyin SU(3) gauge theory

M. Kurachi,K.-i. Nagai

Y. Aoki, T. Aoyama, K. Hasebe,T. Maskawa, K. Miura, H. Ohki,E. Rinaldi, A. Shibata, K. Ya-mawaki, T. Yamazaki

sc-ov Study on acceleration of lattice QCD simulationwith chiral fermions

M. Hayakawa K. Ishikawa, Y. Osaki, S. Takeda,M. Tomii, H. Matsufuru, N. Ya-mada

sc-su2wg Lattice study of running gauge constant and massanomalous dimension in two-color QCD with sixflavors of quarks

M. Hayakawa K. Ishikawa, Y. Osaki, S. Takeda,N. Yamada

scgt16 Study of SU(3) gauge theory with infrared confor-mal symmetry



scexotic Study of exotic hadrons on the lattice C. Nonaka M. Wakayama

scyukawa Nonperturbative analysis of strong couplingYukawa-model on the lattice

K.-i. Nagai K. Ogawa

scchiral Numerical study of SU(2) gauge theories with chi-ral invariant lattice action

K.-i. Nagai N. Yamada, H. Matsufuru

scftptwt Finite temperature phase transition in a walkingtechnicolor model

Y. Aoki,K.-i. Nagai

T. Aoyama, K. Hasebe, M. Ku-rachi, T. Maskawa, K. Miura,H. Ohki, E. Rinaldi, A. Shibata,K. Yamawaki, T. Yamazaki

schydro Study of heavy-ion collisions based on a relativistichydrodynamic model

C. Nonaka Y. Akamatsu

scgt4vec Vector meson mass in four-flavor SU(3) gauge the-ory

M. Kurachi,H. Ohki

Y. Aoki, T. Aoyama, K. Hasebe,T. Maskawa, K. Miura, K.-i. Na-gai, E. Rinaldi, A. Shibata,K. Yamawaki, T. Yamazaki

sc-thermo Study of thermal phase transition of many flavorQCD


sceoo Low energy spectra in 8 flavor SU(2) gauge theory H. Ohki K. Ogawa, E. Rinaldi

5

priority projects












Y. Aoki,H. Ohki


















Y. Aoki,K.-i. Nagai





M. Kurachi,H. Ohki





5

LatKMI collaboration:KMI’s flagship project

priority projects












Y. Aoki,H. Ohki


















Y. Aoki,K.-i. Nagai





M. Kurachi,H. Ohki





5

LatKMI collaboration:KMI’s flagship project

e/μ anomalous magnetic moment → talk by Aoyama (Today)

sub system and COSMOS @ KMI

• ctpl1 & ctpl2 COSMOS

'



'

LatKMI



'

LatKMI

QCD hydrodynamics→ talk by Nonaka (Thursday)



'

LatKMI

QCD hydrodynamics→ talk by Nonaka (Thursday)

large scale structure formation

→ talk by Hikage (Thusday)

LatKMI collaboration

• YA, T.Aoyama, M.Kurachi, T.Maskawa, K.Miura, K.Nagai,

H.Ohki, K.Yamawaki, T.Yamazaki

• E. Rinaldi A.Shibata







LatKMI mission

• (kick off meeting at 28 Sep. 2010; computer installment 2 Mar. 2011)

• mission focused as time goes by...

• find / understand (near) conformal dynamics in gauge theory (late 2010)

• /w state-of-the-art lattice discretization (HISQ) and large scale computation

• find conformal window in SU(3) gauge theory w. Nf m=0 fundamental fermions

• find a walking technicolor theory in SU(3) gauge theory

• investigate Nf=8 in some detail

• investigate flavor singlet scalar in SU(3) gauge theory ⇔ Higgs

• test Nf=8 against experiment

Physics motivation: new physics

Standard Model

Physics motivation: new physicsq1

q2

q3

q4

q5

q6

q7

q8{ G

techni-quarks techni-glueon

• New techni sector

• QCD like interaction

QCD

Standard Model


q2

q3

q4

q5

q6

q7

q8{ G




• weakly coupled with SM sector

QCD

Standard Model


q2

q3

q4

q5

q6

q7

q8{ G





• resemble Higgs mechanism

QCD

Standard Model


q2

q3

q4

q5

q6

q7

q8{ G





• resemble Higgs mechanism

• produce Higgs like particle

QCD

Standard Model

qq-

Walking Technicolor (WTC)

• a candidate of the new physics beyond the Standard Model of particles

• could replace Higgs sector of the Standard Model

• Higgs sector is a low energy effective theory of WTC

• free from the gauge hierarchy problem (naturalness)

• gives explanation of the electro-weak gauge symmetry breaking,

• thus origin of mass of the elementary particles

• “Higgs” = pseudo Nambu-Goldstone boson

• due to breaking of the approximate scale invariance

➡Techni Dilaton (Yamawaki, Bando, Matsumoto)

difficulty compared with ordinary QCD


• QCD

• one dynamical scale

• non-zero quark mass

• vast experimental results


• QCD




• WTC

• multiple scale : separated

• zero quark mass is the target

• one exp. result: Higgs mass


• QCD




• WTC




• Rich structure


• QCD




• WTC




• Rich structure

• New concepts


• QCD




• WTC




• Rich structure

• New concepts

➡ developing field


• QCD




• WTC




• Rich structure

• New concepts

➡ developing field

➡ still controversies

LatKMI publications

• LatKMI, PRD 85 (2012), “Study of the conformal hyperscaling relation through the Schwinger-Dyson equation” [non-lattice]

• LatKMI, PRD 86 (2012), “Lattice study of conformality in twelve-flavor QCD”

• LatKMI, PRD 87 (2013), “Walking signals in Nf=8 QCD on the lattice”

• LatKMI, PRL 111 (2013), “Light composite scalar in twelve-flavor QCD on the lattice”

LatKMI publications

• LatKMI, PRD 85 (2012), “Study of the conformal hyperscaling relation through the Schwinger-Dyson equation” [non-lattice]

• LatKMI, PRD 86 (2012), “Lattice study of conformality in twelve-flavor QCD”

• LatKMI, PRD 87 (2013), “Walking signals in Nf=8 QCD on the lattice”


models being studied:

• SU(3)

• fundamental: Nf=6, 8, 10, 12, 16

• sextet: Nf=2

• SU(2)

• adjoint: Nf=2

• fundamental: Nf=8

• SU(4)

• decuplet: Nf=2

PoS(Lattice 2010)004

Conformal window Luigi Del Debbio

conformal window: SU(3) with n f = 16,12,10,9,8,6 flavors in the fundamental representation,SU(2) with n f = 6 flavors in the fundamental, SU(2) with n f = 2 flavors in the adjoint represen-tation, and SU(3) with n f = 2 flavors in the two-index symmetric (sextet) representation. At theseearly stages of the nonperturbative studies of the conformal window it is important to try to identifya paradigm to guide the numerical investigations, rather than trying to get exhaustive results on onespecific theory.

Fund

2A

2S Adj

Ladder

� = 1 � = 2

Ryttov & Sannino 07

SU(N) Phase Diagram

Dietrich & Sannino 07

Sannino & Tuominen 04

Figure 3: Boundaries of the conformal window for SU(N) gauge theories with n f species of Dirac fermions.The four bands represent respectively fermions in the fundamental (Fund), adjoint (A) and two-index sym-metric and antisymmetric (2S,2A) representations. The upper limit of each band corresponds to the numberof flavors where asymptotic freedom is lost, as obtained from one-loop perturbative computations. Thelower limit of each band yields the number of flavors above which the theories develop an IR fixed point.The location of these lower limits relies upon assumptions about the nonperturbative dynamics of the theo-ries. Lattice simulations can provide first-principle evidence in favour (or against) this picture, and computethe critical exponents that characterize the fixed points. Figure courtesy of F. Sannino.

2. Tools

Numerical tools that were originally designed for investigating lattice QCD have been used inorder to identify the existence of IRFPs. We describe briefly the main ideas, the observables thatare used in the different approaches, and their expected behaviour in the presence of an IRFP. Foreach case we try to emphasize the sources of systematic errors that need to be kept under controlin order to draw robust conclusions from numerical data.

2.1 Phase structure of the lattice theories.

Lattice simulations are performed by discretizing the action of a given theory on a Euclideanspace-time lattice. At weak coupling the RG flow can be computed perturbatively, and the relevantparameters are easily identified. For an asymptotically-free gauge theory, g = 0 is an UV fixedpoint that defines the usual continuum limit of the lattice theory. The IRFP that we are seeking isa fixed point on the massless renormalized trajectory that originates from the continuum limit. As

7

F.Sannino


• SU(3)

• fundamental: Nf=6, 8, 10, 12, 16

• sextet: Nf=2

• SU(2)

• adjoint: Nf=2


• SU(4)

• decuplet: Nf=2




Fund

2A

2S Adj

Ladder

� = 1 � = 2

Ryttov & Sannino 07

SU(N) Phase Diagram




2. Tools




7


• SU(3)

• fundamental: Nf=6, 8, 10, 12, 16

• sextet: Nf=2

• SU(2)

• adjoint: Nf=2


• SU(4)

• decuplet: Nf=2




Fund

2A

2S Adj

Ladder

� = 1 � = 2

Ryttov & Sannino 07

SU(N) Phase Diagram




2. Tools




7

a crude analysis: Fπ/Mπ vs Mπ leads to a likely scenario

0 0.2 0.4 0.6 0.8 1mpi

0.18

0.2

0.22

0.24

0.26

0.28

0.3

fpi(m

f)/m

pi(m

f)

L=12L=18L=24L=30L=36

fpi/mpi vs mpiL^3x(4L/3)Nf=8

Nf=4, β=3.7 Nf=12

f⇡/M⇡

Conformal: flat behaviorSχSB: divergent

Nf=8

• chiral symmetry

mf # trj. M! M" F!

0.04 700 0.3024(16) 0.3777(47) 0.0633(6)

0.05 600 0.3513(12) 0.4332(19) 0.0738(8)

0.06 500 0.3994(15) 0.4888(14) 0.0840(7)

0.08 500 0.4875(9) 0.5965(10) 0.1017(6)

0.1 500 0.5670(7) 0.6927(14) 0.1167(3)

0.12 500 0.6460(7) 0.7899(22) 0.1328(4)

0.16 400 0.7877(6) 0.9549(14) 0.1586(5)

0.2 400 0.9193(6) 1.1049(22) 0.1821(6)

TABLE V. The results of the spectra on V =

303 ! 40 at ! = 3.7. {tab:5}

mf # trj. M! M" F!

0.05 600 0.3163(27) 0.3693(49) 0.0633(9)

0.06 600 0.3634(15) 0.4336(22) 0.0729(4)

0.08 600 0.4508(12) 0.5311(21) 0.0898(7)

0.1 600 0.5227(9) 0.6174(21) 0.1017(7)

0.12 600 0.5966(10) 0.7027(22) 0.1149(7)

0.16 500 0.7308(8) 0.8519(12) 0.1380(7)

0.2 500 0.8568(6) 0.9921(6) 0.1585(8)

TABLE VI. The results of the spectra on

V = 303 ! 40 at ! = 4. {tab:6}

0 0.1 0.2 0.3 0.4 0.5a M

π

0.3

0.35

0.4

0.45

0.5

F π/Μ

π

16^3 x 24

FIG. 2. Dimension-less ratio F!/M! as a function of M! for Nf = 4 at ! = 3.7. Due to the

spontaneous chiral symmetry breaking, the ratio diverges in the chiral limit. {fig:ratio_mf_nf4}

dependence.

Similar observation can be made for the other ratio M"/M! shown in the right panel of

Fig. 3. Here, the flattening is observed for ! = 3.7 again, however the range is wider than

F!/M!. In this case ! = 4 shows the flattening, also. The di!erence of the constant is made

possible due to a discretization e!ect.

In the following sections, further detailed study using these data are performed. From

the observation here, we note that the only the smaller mass data would qualify the hyper

scaling test if there is any, if only a leading mass dependence is taken into account. Further,

11

Nf=4

• chiral symmetry• conformality

Nf=12Recent study of LatKMI Collaboration

Nf = 12: PRD86(2012)054506; Nf = 8: arXiv:1302.6859

Chiral broken Conformal

0 0.1 0.2 0.3 0.4 0.5mπ

0.25

0.3

0.35

0.4

0.45

0.5

0.55

F π/m

π

Nf=4 β=3.7

0 0.2 0.4 0.6 0.8 1mπ

0.19

0.2

0.21

0.22

F π/m

π

Nf=12 β=3.7

0 0.2 0.4 0.6 0.8 1mπ

0.2

0.24

0.28

F π/m

π

Nf=8 β=3.8

12-b

Baryon acoustic oscillations as a probe of dark energy High-performance parallel computer system, " ".

Exploring the nature of the Higgs boson as a composite of more fundamental particles using lattice simulations

9

The rapid development of computers has altered the landscape

of computational science. Using supercomputers we clarify

complicated physical phenomena quantitatively and develop

new research areas, which could only be dreamed about a

decade ago.

The discovery of the Higgs boson in the LHC experiments

provides a clue to how elementary particles like quarks and

leptons acquire mass, which is a fundamental problem in

modern particle physics. Our group tries to clarify this unknown

mechanism and to understand the Higgs particle as a

composite of more fundamental particles. We use the KMI

high-performance parallel computer, “ ”, which consists of

��

��

��

dimensional lattice. Additionally, we work on verifying the

Standard Model via quantum chromodynamics (QCD)

simulations on the lattice, directly calculating the nuclei from

QCD. Furthermore, we investigate the phase structure of QCD

and the nature of hadronic phase in the high-temperature and

high-density region, which are directly related to the quark-

gluon matter found in high-energy heavy-ion collisions.

Modern cosmological surveys strive to elucidate the nature of

dark energy and dark matter occupying 96% of the total

energy in the universe. To illuminate the dark side of the

universe, we develop a precise theoretical framework that

describes the growth of cosmic structure using large-scale

cosmological simulations. We actively participate in the galaxy

imaging and redshift survey using Subaru telescope, called

the "SuMIRe" project.

Computational Theoretical Physics Laboratory

New research areas for the physics of particles and

the universe are explored by utilizing high-performance parallel computers.

Hadron spectrum: response to mass (mf) deformation

• IR conformal phase:

• coupling runs for μ<mf: like nf=0 QCD with ΛQCD~mf

• multi particle state : MH ∝ mf1/(1+γm*); Fπ ∝ mf1/(1+γm*) (criticality @ IRFP)

• SχSB phase:

• ChPT

• at leading: Mπ2 ∝ mf, ; Fπ = F + c mf

Hadron spectrum: response to mass (mf) deformation

• IR conformal phase:

• coupling runs for μ<mf: like nf=0 QCD with ΛQCD~mf

• multi particle state : MH ∝ mf1/(1+γm*); Fπ ∝ mf1/(1+γm*) (criticality @ IRFP)

• SχSB phase:

• ChPT

• at leading: Mπ2 ∝ mf, ; Fπ = F + c mf

Detailed analysis of Fπ vs mf


PRD86(2012)054506; arXiv:1302.6859

Chiral broken F! ! F "= 0 Conformal F! ! Cm1/(1+")f

0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

• conformality

•

• γ~0.5

Recent study of LatKMI CollaborationPRD86(2012)054506; arXiv:1302.6859


0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a


PRD86(2012)054506; arXiv:1302.6859


0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

• chiral symmetry

•



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a



9





decade ago.








��

��

��





















PRD86(2012)054506; arXiv:1302.6859


0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

• conformality

•

• γ~0.5



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a


PRD86(2012)054506; arXiv:1302.6859


0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

• chiral symmetry

•



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

Nf=8



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a• chiral symmetry

• 　　　　　　 mf→0

• intermediate mf

• γ~0.9



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2F π Cmf

1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a



9





decade ago.








��

��

��





















PRD86(2012)054506; arXiv:1302.6859


0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

• conformality

•

• γ~0.5



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a


PRD86(2012)054506; arXiv:1302.6859


0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

• chiral symmetry

•



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a

Nf=8



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a• chiral symmetry

• 　　　　　　 mf→0

• intermediate mf

• γ~0.9



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2F π Cmf

1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a



0 0.01 0.02 0.03 0.04 0.05mf

0.04

0.08

0.12

0.16

F π

Nf=4 β=3.7

0 0.05 0.1 0.15 0.2mf

0

0.05

0.1

0.15

0.2

F π Cmf1/(1+γ) [0.05-0.2]

Nf=12 β=3.7

0 0.04 0.08 0.12 0.16mf

0

0.04

0.08

0.12

0.16

0.2

F π quad [0.015-0.04]Cmf

1/(1+γ) [0.08-0.16]

Nf=8 β=3.8

13-a



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detailed analysis is presented by Ohki & Nagai

crucial difference between Nf=8 and 12

• conformal ↔ broken chiral symmetry picture:

• property should emerge in the mf→0, V→∞ limit

• Nf=12

• conformal hypothesis:

• getting better in mf→0, V→∞

• broken chiral symm. analysis: fπ(mf→0)≠0; but very long extrapolation

• Nf=8

• conformal hypothesis

• good for intermediate mf ↔ getting worse in mf→0

• broken chiral symm. analysis: fπ(mf→0)≠0; better controlled than nf=12

crucial difference between Nf=8 and 12

• conformal ↔ broken chiral symmetry picture:

• property should emerge in the mf→0, V→∞ limit

• Nf=12

• conformal hypothesis:

• getting better in mf→0, V→∞

• broken chiral symm. analysis: fπ(mf→0)≠0; but very long extrapolation

• Nf=8

• conformal hypothesis

• good for intermediate mf ↔ getting worse in mf→0

• broken chiral symm. analysis: fπ(mf→0)≠0; better controlled than nf=12

Nf=8: an interpretation


• What’s observed:

• chiral symmetry spontaneously broken for mf→0

• hyperscaling for intermediate mf

• largish γ ~ 0.6-1 for various observables






• can be interpreted as “walking”:







• probing energy scale with μ~mf → schematic picture

3

QCDf

α(µ)

µ

α*

mf mD Λm

FIG. 1. Schematic two-loop/ladder picture of the gauge coupling of the massless large Nf QCD as a walking gauge theory inthe S!SB phase near the conformal window. mD is the dynamical mass of the fermion generated by the S!SB. The e!ects ofthe bare mass of the fermion mf would be qualitatively di!erent depending on the cases: Case 1: mf ! mD (red dotted line)well described by ChPT, and Case 2: mf " mD (blue dotted line) well described by the hyper scaling.

finite box L3 and lattice spacing a, which do not exist in the continuum theory we are interested in. Among othersthe fermion bare mass mf obviously distorts the ideal behavior of the breaking of the scale symmetry in a way similarto the continuum theory. Then, disregarding the e!ects of the lattice parameters L and a for the moment, we mayimagine possible e!ects of the fermion bare mass on the walking coupling of our target of study as in Fig. 1, which issuggested by the two-loop/ladder analysis.Case 1. mf ! mD ! "QCD (red dotted line in Fig. 1): The chiral perturbation theory should hold in a way similarto the real-life QCD with light quarks.Case 2. mD ! mf ! "QCD (blue dotted line in Fig. 1): The conformal hyperscaling relation should hold approxi-mately with a large anomalous dimension !m " 1.Actually, the S"SB order parameter to be measured on the lattice is not mD but would be the decay constant F! ofthe Nambu-Goldstone boson # extrapolated to the chiral limit: F = F!(mf = 0) which would be expected roughlythe same as mD: mD = O(F ).There is a caveat about the approximate hyperscaling relation to be expected in the Case 2 (mD ! mf ! "QCD ):

There are two infrared mass parameters mD and mf which violate the infrared conformality and hence the possiblehyperscaling relations for the physical mass quantities measured from the spectrum should not be universal butdo depend on both of them in non-universal ways, in sharp contrast to the hyperscaling relation in the conformalwindow where all the mass parameters from the spectra reflects the deformation by the unique infrared scale-violatingparameter mf in a universal way. In particular, when mf is getting close to the region in Case 1, where # mass M!

and the other quantities such as $ mass M" and F! behave qualitatively di!erent towards the chiral limit: M! # 0while the others remain non-zero.To date, some groups carried out lattice studies on 8-flavors, with Wilson fermions [10, 11, 23] and with staggered

fermions [12, 15, 24, 25, 30–33]. The Refs. [10, 11, 23] concluded the Nf = 8 is in the conformal window, but Refs[12, 15, 24, 25, 30, 31] concluded that the Nf = 8 resides on the chiral broken phase. Even if Nf = 8 is in the chiralbroken phase, it has not been investigated whether the behavior of this system is QCD like or the walking with thelarge anomalous mass dimension.In this paper we study the meson spectrum by simulating the Nf = 8 QCD, based on yet another lattice fermion,

Highly Improved Staggered Quark (HISQ) [34], applied to Nf = 8 for the first time. Preliminary reports were givenin Ref. [35]. HISQ action improves the behavior towards the continuum limit through the improvement of the flavorsymmetry. The salient feature of our collaboration is that we have been investigating Nf = 4, 8, 12, 16 on the settingof HISQ action with the same systematics in order to study the Nf -dependence of the physics systematically [21, 35].Thus our analyses for Nf = 8 are made in comparison with those for other flavors of our group.We first show the data of the meson spectrum, M! and F!, as well as M" and the chiral condensate $%̄%% for

&(& 6/g2) = 3.8 on the L3 ' T lattice with and L = 12 ( 36 and T = 16 ( 48, and mf = 0.015 ( 0.16. We thenanalyze the data based on the Chiral Perturbation Theory (ChPT) [36], particularly for small mf : mf = 0.015( 0.04(corresponding to Case 1 in Fig. 1 in the above). We find that the ChPT analysis is self-consistent and find a resultconsistent with non-zero value of F and M" and vanishing of M! in the chiral limit extrapolation based on the ChPT(we also estimate the e!ects of the chiral logarithm). The chiral condensate is also non-zero value in the chiral limitextrapolation, which neatly coincides with the Gell-Mann-Oakes-Renner (GMOR) relation obtained from the # datain the chiral limit extrapolation.








• if Nf=8 is close to conformal transition point nfc, γ ~ γm ~ 1

3

QCDf

α(µ)

µ

α*

mf mD Λm
















• walking: a solution to classical technicolor problem: quark mass ↔ FCNC

3

QCDf

α(µ)

µ

α*

mf mD Λm

















• Next interesting direction → prediction (postdiction) of spectrum

3

QCDf

α(µ)

µ

α*

mf mD Λm

















• Next interesting direction → prediction (postdiction) of spectrum

3

QCDf

α(µ)

µ

α*

mf mD Λm








details presented by Nagai

Physics motivation: new physics


q2

q3

q4

q5

q6

q7

q8{ G



q2

q3

q4

q5

q6

q7

q8{ G


other composites


q2

q3

q4

q5

q6

q7

q8{ G


other composites

• prediction of other composites

➡compare with experiments → LHC

Nf=8 spectrum

• with input Fπ = 246 /√N GeV (N: # weak doublet in techni-sector)

• prediction: (with only technicolor dynamics)

• for example: for one family model: N=4

• Higgs mass ?

• 125 GeV (LHC) seems very light for technicolor

• 0++: one of the difficult quantities on the lattice

• multi-faceted nature of Nf=8 adds another difficulty: delicate chiral extrapl.

➡ first analyze simpler Nf=12, which shares “conformality” → techni dilaton

➡Is 0++ state light in (mass deformed) Nf=12 theory ?

M⇢/F⇡ = 7.7(1.5)(+3.8�0.4)

M⇢ = 970(+515�195) GeV

flavor singlet scalar spectrum in Nf=12 theory

4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ

FIG. 3: Fermionic m! and gluonic mG e!ective masses (re-spectively from correlators in Eq. (4) and Eq. (5)) for L = 24and mf = 0.06. The fitted masses are highlighted by dashedand dotted-dashed lines for the gluonic correlators and dottedlines for the fermionic one. Systematics e!ects on the gluonicmass are not relevant given the larger statistical error.

0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m

π (L=30)σ (L=24)σ (L=30)σ (L=36)G (L=24)hyperscaling fit

FIG. 4: The mass of the flavor–singlet scalar meson ! (seeTable I) compared to the mass of the pseudo–scalar " stateand the mass mG from gluonic operators. Errors are statis-tical and systematics added in quadrature. The hyperscalingcurve is described in the text. The triangle and filleds squaresymbols are slightly shifted for clarity.

each parameter. For m! on the largest two volumes ateach mf , finite size e!ects are negligible in our statis-tics. For a check of consistency with the hyperscaling ofm", we fit m! on the largest volume data at each mf

using the hyperscaling form m! = C(mf )1/1+# with afixed ! = 0.414 estimated from m" [10], which gives areasonable value of "2/dof = 0.12. The fit is shown inFig.4. We remind here that the fitted data points havem"L > 11.5, as can be checked from Table. I. We also es-timate the ratio m!/m" at each parameter and report itin Table I. All the ratios are smaller than unity by morethan one standard deviation including the systematic er-ror, except the one atmf = 0.06 on L = 30, as previouslyexplained. A constant fit with the largest volume data at

each mf gives 0.86(3). These results are consistent withthe theory being infrared conformal. Moreover they donot show an abnormal mf dependence of m! similar tothe one observed in Ref. [23], by which an e!ect of anunphysical phase boundary would have been suspected.

To summarize, we performed the first study of thescalar flavor–singlet state in Nf = 12 QCD usingfermionic and gluonic interpolating operators. The moststriking feature of the measured scalar spectrum is theappearance of a state lighter than the # state, as it isshown in Fig. 4. Such a state appears both in gluonicand fermionic correlators at small bare fermion mass.Clear signals in our simulations were possible thanks tothe following salient features: 1. Small taste–symmetrybreaking, 2. E"cient noise–reduction methods, 3. Largeconfiguration ensembles, and 4. Slow damping of D(t)thanks to small m!.

We regard the light scalar state observed for Nf = 12in this study, as a reflection of the dilatonic nature of theconformal dynamics, since otherwise the p–wave boundstate (scalar) is expected to be heavier than the s–waveone (pseudo–scalar). Thus, it is a promising signal fora walking theory, where a similar conformal dynamics ina wide infrared region should be operative in the chirallimit to form a dilatonic state with mass of O(F"), insuch a way that the tiny spontaneous–breaking–scale F"

plays the role of mf (cfr. Ref. [11]).

While further investigation of the scalar state in Nf =12 QCD, such as a possible lattice spacing dependence,is important, the most pressing future direction is tolook at more viable candidates for walking technicolormodels. For example, it will be interesting to investi-gate the scalar spectrum of the Nf = 8 SU(3) theory,which was shown to be a good candidate for the walkingtechnicolor [11], where the scalar state could be identi-fied with the technidilaton, a pseudo Nambu–Goldstoneboson coming from the dynamical breaking of conformalsymmetry. There actually exists an indication of such alight scalar in Nf = 8 QCD [38].

Acknowledgments.– Numerical simulation has been car-ried out on the supercomputer system $ at KMI inNagoya University, and the computer facilities of the Re-search Institute for Information Technology in KyushuUniversity. This work is supported by the JSPSGrant-in-Aid for Scientific Research (S) No.22224003,(C) No.23540300 (K.Y.), for Young Scientists (B)No.25800139 (H.O.) and No.25800138 (T.Y.), and alsoby Grants-in-Aid of the Japanese Ministry for Scien-tific Research on Innovative Areas No.23105708 (T.Y.).E.R. was supported by a SUPA Prize Studentship anda FY2012 JSPS Postdoctoral Fellowship for ForeignResearchers (short-term). We would like to thankLuigi Del Debbio and Julius Kuti for fruitful discussions.



9





decade ago.








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��

��




















• with very high statistics

• thanks to φ

• and other computers

4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ


0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m













9





decade ago.








��

��

��





















• thanks to φ


• signal obtained !

4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ


0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m













9





decade ago.








��

��

��





















• thanks to φ



• π was lightest in QCD (Nf=2)

• results by SCALAR Collab. 0 0.05 0.1 0.15m

q

0

0.5

1

1.5

2

mh

ad

!"#

nf=2 QCD

SCALAR Collaboration



9





decade ago.








��

��

��





















• thanks to φ




• results by SCALAR Collab.

4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ


0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m













9





decade ago.








��

��

��





















• thanks to φ





• σ is lightest for Nf=12: LatKMI is the first to show this !

4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ


0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m













9





decade ago.








��

��

��





















• thanks to φ






• mechanism to make the composite scalar light is working

4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ


0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m













9





decade ago.








��

��

��





















• thanks to φ






• mechanism to make the composite scalar light is working


4

0 2 4 6 8 10t

0

0.2

0.4

0.6

0.8

1

mef

f

Gσ


0 0.02 0.04 0.06 0.08 0.1 0.12mf

0

0.1

0.2

0.3

0.4

0.5

0.6

m













9





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��

��

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scalar (Higgs) in Nf=8 theoryBaryon acoustic oscillations as a probe of dark energy High-performance parallel computer system, " ".


9





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scalar (Higgs) in Nf=8 theory

• preliminary results reported at Lattice 2013A light composite scalar in eight-flavor QCD on the lattice Hiroshi Ohki

0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ

Figure 4: Fit result of the chiral extrapolation formσ . For comparison, other spectra of mπ and mρ and theirchiral fits in Ref. [6] are also shown.

References

[1] K. Yamawaki, M. Bando and K. -i. Matumoto, Phys. Rev. Lett. 56, 1335 (1986).

[2] S. Matsuzaki and K. Yamawaki, Phys. Lett. B 719, 378 (2013); Phys. Rev. D 86, 115004 (2012);S. Matsuzaki, arXiv:1304.4882 [hep-ph].

[3] J. Kuti, PoS LATTICE 2013 004 (2013); J. Giedt, PoS LATTICE 2012 006 (2012); E. T. Neil, PoSLATTICE 2011, 009 (2011), and references therein.

[4] Y. Aoki, T. Aoyama, M. Kurachi, T. Maskawa, K. -i. Nagai, H. Ohki, E. Rinaldi, A. Shibata,K. Yamawaki and T. Yamazaki (LatKMI collaboration), arXiv:1305.6006 [hep-lat]; arXiv:1302.4577[hep-lat].

[5] Y. Aoki, T. Aoyama, M. Kurachi, T. Maskawa, K. -i. Nagai, H. Ohki, A. Shibata, K. Yamawaki andT. Yamazaki (LatKMI collaboration), Phys. Rev. D 86 (2012) 054506.

[6] Y. Aoki, T. Aoyama, M. Kurachi, T. Maskawa, K. -i. Nagai, H. Ohki, A. Shibata, K. Yamawaki and T.Yamazaki (LatKMI collaboration), Phys. Rev. D 87 (2013) 094511, arXiv:1302.6859 [hep-lat].

[7] G. W. Kilcup and S. R. Sharpe, Nucl. Phys. B 283, 493 (1987).

[8] L. Venkataraman and G. Kilcup, [hep-lat/9711006].

[9] E. B. Gregory, A. C. Irving, C. M. Richards and C. McNeile, Phys. Rev. D 77, 065019 (2008).

[10] C. McNeile, A. Bazavov, C. T. H. Davies, R. J. Dowdall, K. Hornbostel, G. P. Lepage andH. D. Trottier, Phys. Rev. D 87, no. 3, 034503 (2013).

[11] X. -Y. Jin and R. D. Mawhinney, PoS LATTICE 2011, 066 (2011) [arXiv:1203.5855 [hep-lat]].

[12] Y. Aoki, T. Aoyama, M. Kurachi, T. Maskawa, K. Miura, K. -i. Nagai, H. Ohki, E. Rinaldi,A. Shibata, K. Yamawaki and T. Yamazaki (LatKMI collaboration), PoS LATTICE 2013, 073 (2013)

7

LatKMI PoS2013



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decade ago.








��

��

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• preliminary results reported at Lattice 2013

• σ is as light as π

A light composite scalar in eight-flavor QCD on the lattice Hiroshi Ohki

0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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��

��

��






















• far lighter than ρ


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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• mf→0 is what we want to know


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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• mσ/fπ= 4±4


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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��

��

��
























• mσ/fπ= 4±4

• 1 family model : mσ=0～500 GeV


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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��

��
























• mσ/fπ= 4±4


• large error


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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��

��

��
























• mσ/fπ= 4±4


• large error

• more statistics, points are being added


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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��

��

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• mσ/fπ= 4±4


• large error


• further effort will be required


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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LatKMI PoS2013



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��

��

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• mσ/fπ= 4±4


• large error


• further effort will be required


0 0.01 0.02 0.03 0.04mf

0

0.1

0.2

0.3

0.4

0.5

0.6

mσ

L=30L=24L=18mρ

mπ


References













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��

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��



















details and updates to be presented by Yamazaki

Summary and Outlook

• KMI high performance computer φ has been used for 2.5 years, probing BSM possibilities for electro-weak symmetry breaking, through strong dynamics, producing interesting results.

• Results from LatKMI collaboration

• 1st to show light composite scalar in Nf=12

• Nf=8 is a candidate walking technicolor theory

• 1st to find light scalar in Nf=8, which could realize 125 GeV Higgs

Summary and Outlook

• Solidness of the emerging picture will have to be investigated further:

• precision needs to be improved

• towards LHC run2 (2015-)

• controversial pictures (conformal window) from different collaborations

• Calculation / technology development for other quantities are underway

• S parameter: new method proposed for vacuum polarization function

• low energy parameters in π and σ as effective light elements

• Scaler (Higgs) decays need to be investigated

• Finite Temperature ↔ Baryogenesis

• Property of Dark Matter candidate: techni-baryon...

Thank you very much for your attention !

Documents

The KMI project · 2013-12-13 · The KMI project Yasumichi Aoki [Kobayashi-Maskawa Institute(KMI), Nagoya University] - at KMI2013 International Symposium - Dec. 11, 2013 Kobayashi-Maskawa