スライド - 名古屋大学 素粒子宇宙起源研究機構（KMI）

N f =8
2013326

Higgs(-like) boson

Higgs(-like) boson

SM Higgs

SM Higgs
Hierarchy problem
Triviality
Vacuum stability
QCD

SM Higgs
Hierarchy problem
Triviality
Vacuum stability
QCD
The most conservative scenario for the EWSB is still

Nf=8 SU(3)
Chiral restoration point
--- walking behavior
arXiv:1302.6859, LatKMI Collaboration
Extended Technicolor
(~125 GeV)

Ladder picture
Bethe-Salpeter equation for a
q¯q
bound state
p + q 2
p + q 2 k + q 2
q
( p ; q )
( k ;q )
p q q q 2 p 2 k 2
q
µ
( )
6
( )
1
0
1
2
3
N f = 9
N f = 10
N f = 11
N f = 12
5
4
3
2
1
0 1 2 3 4 5
Large Nf 2-loop running coupling
0
15 10 5 0 5 10 15
log µ

Ladder picture
( M A,V,S,P / ) 2
F p
M A
spectrum N f
(↵ ⇤ )
200
150
(
(
(
(
M V
M S
M P
/
/
/
/
F p
F p
F p
F p
)
)
)
)
2
2
2
2
axial-vector
100
vector
50
scalar
0
cr
0.8 0.85 0.9 0.95 1
N cr
f N f
*
Harada, Kurachi, Yamawaki, PRD 68 (2003) 076001

Ladder picture
N f (↵ ⇤ )
spectrum
14
12
M A,V,S f P
M V f P
axial-vector
M
A
M S
f
P
f P
10
vector
8
6
4
scalar
2
0
cr
1 1.2 1.4 1.6 1.8 2 2.2 2.4
N cr
f N f
*
Kurachi, Shrock, JHEP 0612 (2006) 034

Ladder picture
p + q 2
p + q 2 k + q 2
q
( p ; q )
( k ;q )
p q q q 2 p 2 k 2
q
Note: Ladder
flavor non-singlet mesons
singlet state glueball
mixing flavor-singlet scalar

Fully nonperturbative calculation
(Lattice!!)

Lattice setup
Nf=8, SU(3) gauge theory
Tree-level Symanzik gauge action
Highly Improved Staggered Quarks (HISQ)
Parameter set
(⌘ 6/g 2 )=3.8, m f =0.06, V= 24 3 ⇥ 32
Disconnected correlator measurement
7600 configurations (from 15200 thermalized trajectories)
Stochastic estimator with 64 gaussian noises
Venkataraman-Kilcup variance reduction technique

N C =3,N f =8, =3.8, m f =0.06, V= 24 3 ⇥ 32
Connected
0.0001
1e-05
1e-06
1e-07
1e-08
1e-09
1e-10
C(t)
scalar interpolating ¯
operator couples to 2 states
-C(t)
0 + 0
1e-11
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t

N C =3,N f =8, =3.8, m f =0.06, V= 24 3 ⇥ 32
Connected
C(t)
“Pick up”
0.0001
1e-05
state: 0 + C + (2t) ⌘ 2C(t)+C(t + 1) + C(t 1)
- C(t)
- C +
(t)
1e-06
1e-07
1e-08
1e-09
1e-10
1e-11
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t

N C =3,N f =8, =3.8, m f =0.06, V= 24 3 ⇥ 32
Disconnected
1e-06
D(t)
1e-07
1e-08
1e-09
1e-10
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t

N C =3,N f =8, =3.8, m f =0.06, V= 24 3 ⇥ 32
Full scalar correlator
⇠ SCL(t) =
C + (t)+2D + (t)
where
D + (2t) ⌘ 2D(t)+D(t + 1) + D(t 1)
0.0001
SCL(t)
2D +
(t)
- C +
(t)
1e-06
1e-08
1e-10
0 5 10 15
t

N C =3,N f =8, =3.8, m f =0.06, V= 24 3 ⇥ 32
Effective mass plot
1.2 Connected only
Disconnected only
1
Scalar (full)
0.8
0.6
0.4
0.2
0
0 2 4 6 8 10 12 14
t

N C =3,N f =8, =3.8, m f =0.06, V= 24 3 ⇥ 32
Effective mass plot
NG boson
1.2 Connected only
Disconnected only
1
Scalar (full)
0.8
0.6
0.4
0.2
0
0 2 4 6 8 10 12 14
t
M ⇡
arXiv:1302.6859[hep-lat]
LatKMI Collaboration
(F ⇡ ⇠ 0.1)

Summary
First lattice study of the flavor-singlet scalar in Nf=8 QCD
Several tequniques + high statistics →
(⌘ 6/g 2 )=3.8, m f =0.06, V= 24 3 ⇥ 32
NG boson
Future direction
Larger volumes, smaller fermion masses
chiral limit M ! F
Gluonic operator study
lightest scalar meson glueball mix )

ackups

Spectrum other than flavor-singlet scalar
arXiv:1302.6859[hep-lat], LatKMI Collaboration
(⌘ 6/g 2 )=3.8, m f =0.06, V= 24 3 ⇥ 32

0
B
@
1
u
d
u
d
u
d
C
e A
⌫ e
0
B
@
1
c
s
c
s
c
s
C
µ A
⌫ µ
0
B
@
1
t
b
t
b
t
b
C
⌧ A
⌫ ⌧
0
B
@
1
U 1
D 1
U 1
D 1
U 1
D 1
C
E 1
A
N 1
0
B
@
1
U NTC
D NTC
U NTC
D NTC
U NTC
D NTC
C
E NTC
A
N NTC
SU(3 + N TC )
{ { { {
SU(2 + N TC )
⇤ 1
⇤ 2
⇤ 3
SU(1 + N TC )
SU(N TC )
SU(N TC )