Report on the
NPR projects and
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
Lattice values
Chiral behavior
Report on the NPR projects and B K in N f = 2 + 1
DWQCD
Operator mixing
NPR
Jun Noaki
23rd Jan. 2006, Edinburgh
Report on the
NPR projects and
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
Lattice values
Chiral behavior
Operator mixing
NPR
-2
q
Z ZQ
NPR projects,
report & proposal
(tree)
Report on the
NPR projects and
Overview
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
• Rome-Southampton Method
Lattice values
lattice
Chiral behavior
tree
Operator mixing
NPR
-1
Z q ZΓ
p
p
=
latt
Z −1
q Z Γ ΛΓ ( p) = 1
• Target
- Z q = Λ A Z A : quark mass (Azusa)
- PDA operators (1st & 2nd derivatives)
- Z BK = Z ∆S=2 /Z 2
A
- other ideas?
Report on the
NPR projects and
Chroma is equivalent with CPS
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
Lattice values
Chiral behavior
• Iwasaki β = 2.13, 163 × 32, Ls = 8, mu = ms = msea = 0.04
• Same #traj (20 configs.) and same latt. momenta (376 of them)
Operator mixing
NPR
ΛV
1.4
1.2
UK hadron (Chroma)
CPS
ΛA=Zq/ZA
ΛV=Zq/ZV
Axial vector
1.1
1.3
1.2
1
UK hadron (Chroma)
CPS
0.9
1.1
1
ΛA
Vector
0
0.5
1
1.5
2
platt
2
2.5
0.8
0
0.5
1
1.5
2
platt
2
2.5
Report on the
NPR projects and
Chroma is equivalent with CPS (2)
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
ΛS
Lattice values
Chiral behavior
2
ΛP
Scalar
4
Pseudo scalar
Operator mixing
NPR
3.5
UK hadron (Chroma)
CPS
1.8
UK hadron (Chroma)
CPS
3
ΛP=Zq/ZP
ΛS=Zq/ZS
1.6
1.4
2.5
2
1.2
1
1.5
0
0.5
1
1.5
2
platt
2
2.5
1
0
0.5
1
1.5
2
platt
2
2.5
Report on the
NPR projects and
Chroma is equivalent with CPS (3)
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
ΛVV+AA
Lattice values
ΛVV+AA;VV−AA
Chiral behavior
VV+AA
Operator mixing
VV+AA; VV−AA
1.6
0.35
NPR
UK hadron (Chroma)
CPS
1.5
0.3
0.25
1.4
UK hadron (Chroma)
CPS
ΛVV+AA; VV−AA
ΛVV+AA=Zq/ZBK
0.2
1.3
1.2
0.15
0.1
0.05
1.1
1
0
−0.05
0
0.5
1
1.5
2
platt
2
2.5
0
0.5
1
1.5
2
platt
2
2.5
Report on the
NPR projects and
PDA operators
B K in N f = 2 + 1
DWQCD
Jun Noaki
(See Andreas’s talk for the detail of the lattice values.)
NPR projects
BK
Lattice values
Chiral behavior
Operator mixing
NPR
• 1st moment: Oρµ = ψ̄γρ γ5
↔
Dµ ψ
À
¿
←
→
F.T. S(z|x)γρ γ5 D x,µ S(x|y) − S(z|x) D x,µ γρ γ5 S(x|y)
←
←
CG with momentum source: M y,x0 S(x0 |x) Dµ,x = δ y,x Dµ,x
#µ = 4 sources
• 2nd moment:
←
←
→
←
↔ ↔
Oρµν = ψ̄γρ γ5 Dµ Dν ψ
S(z|x) D x,µ D x,ν γρ γ5 S(x|y) 12 sources
S(z|x) D x,µ D x,ν γρ γ5 S(x|y) 16 sources
• mixing operator (2nd moment):
ordinary point source
Totally 33 sources
Õρµν = ∂µ ∂ν ψ̄γρ γ5 ψ
Report on the
NPR projects and
B K in N f = 2 + 1
New run on Iwasaki, β = 2.13, 163 × 32, L s = 16
DWQCD
Jun Noaki
• Point source (256node)
NPR projects
BK
Lattice values
Chiral behavior
Operator mixing
NPR
Ensemble
md /ms = 0.01/0.04
md /ms = 0.02/0.04
md /ms = 0.03/0.04
#traj.
1000-1260/20 (running)
1000-2820/20 (pending)
1000-3420/20 (done)
time/config
90min
70min
70min
• 1st derivative source (256node, 4 sources)
md /ms = 0.01/0.04
md /ms = 0.02/0.04
md /ms = 0.03/0.04
(not yet)
(not yet)
1000-1160/20 (running)
320min
260min
240min
• 2st derivative source (256 machine, 28 sources)
md /ms = 0.01/0.04
md /ms = 0.02/0.04
md /ms = 0.03/0.04
(100 confs)
(100 confs)
(100 confs)
≈ 36 hr
≈ 24 hr
≈ 20 hr
N.B. If we do not calc m f = ms propagator, much time is saved.
Report on the
NPR projects and
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
0
Lattice values
Chiral behavior
s
Operator mixing
NPR
s
K0
Kaon B-parameters,
Q ∆ s=2
d
report & discussion
K0
d
Report on the
NPR projects and
Overview
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
Lattice values
Chiral behavior
• Iwasaki, β = 2.13, 163 × 32, Ls = 16
Operator mixing
Ensemble
NPR
md /ms = 0.01/0.04
md /ms = 0.02/0.04
md /ms = 0.03/0.04
-t
d
s
u
u
0
#traj./step
1000-2120 / 20
1000-2820 / 20
1000-2980 / 20
B PS =
t
D
8
3
# config.
57
92
100
P(−t)Q∆S=2 (0)P(t)
E
hP(−t) A4 (0)i h A4 (0)P(t)i
Q∆S=2 = (s̄d)V−A (s̄d)V−A
Report on the
NPR projects and
Plateaus (point-point)
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
1.5
md=0.03
1.0
BK
Lattice values
Chiral behavior
Operator mixing
0.5
NPR
0.0
1.5
md=0.02
1.0
0.5
0.0
1.5
md=0.01
1.0
0.5
0.0
0
5
t
10
15
Report on the
NPR projects and
Chiral behavior(1)
B K in N f = 2 + 1
DWQCD
Chiral expansion
Jun Noaki
Bfull
K
NPR projects
BK
=
h
B 1−
1
(4π f )2
i
L(mπ , mK ) + ξ1 m2π + ξ2 m2K + O(m4 )
Lattice values
Chiral behavior
Operator mixing
NPR


m2η
m2K
m2π  m2π
m2π 

 ln
2
1 +
L(mπ , mK ) =
+
2m
+
ln

K
2 
2
m2K  Λ2χ
Λ2χ


2

m2  m
7 − π  ln η


m2K  Λ2χ
BK, Full SU(3)
0.8
0.7
0.6
Large ambiguity in getting
physical point
0.5
0.4
0.3
0
0.01
0.02
mlight
0.03
0.04
Report on the
NPR projects and
Chiral behavior(2)
B K in N f = 2 + 1
DWQCD
Jun Noaki
N f = 2 + 1 partially quenched ChPT Van de Water & Sharpe, 2005
NPR projects
BK
Lattice values
Chiral behavior
Operator mixing
PQ
B PS
NPR

 2 

 mPS 
6

 + η m2 + η (2m2 + m2 ) + O(m4 )
= B 1 −
ln 
1 PS
2

DD
SS
(4π f )2
Λ2χ 
BPS, all available valence masses
0.8
0.7
Now filling the gap of data
points.
0.6
0.5
0.4
0.3
B , η1 , η2 ⇒ mPS = mK
msea=0.01
msea=0.02
msea=0.03
0
0.01
0.02
(mval1+mval2)/2
0.03
0.04
Report on the
NPR projects and
B K in N f = 2 + 1
Operator mixing with wrong chirality
DWQCD
Jun Noaki
Bren
K
NPR projects
BK
Z VV+AA
+
Z VV+AA; VV−AA · Blatt VV−AA
+
+
+
Z VV+AA; SS−PP · Blatt SS−PP
Z VV+AA; SS+PP · Blatt SS+PP
Z V+AA; TT
· Blatt TT
Lattice values
Chiral behavior
Operator mixing
NPR
· Blatt VV+AA
=
15
VV−AA
VV+AA
SS−PP
SS+PP
TT
10
5
0
−5
−10
−15
0
0.01
0.02
md
0.03
0.04
Report on the
NPR projects and
NPR to solve mixing ( ms /md = 0.04/0.03)
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
VV+AA; TT
VV+AA; VV−AA
0.8
0.1
0.0
0.6
BK
Lattice values
−0.1
Chiral behavior
Operator mixing
0.4
−0.2
NPR
−0.3
0.2
−0.4
0
−0.5
0
0.5
1
1.5
2
0
0.5
2
latt
p
1
2
platt
1.5
2
1.5
2
VV+AA; SS+PP
VV+AA; SS−PP
0.2
0.00
0.1
−0.10
0
−0.1
−0.20
0
0.5
1
2
platt
1.5
2
−0.30
0
0.5
1
2
platt
Report on the
NPR projects and
Z BK
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
Lattice values
• ms /md = 0.04/0.03, 1200-1980/20 traj. (40 confs.)
VV+AA; VV+AA
1.2
Chiral behavior
Operator mixing
NPR
1
0.8
0.6
0.4
0
0.5
1
2
platt
1.5
- More momenta
- Need to take chiral extrapolation
2
Report on the
NPR projects and
To do
B K in N f = 2 + 1
DWQCD
Jun Noaki
NPR projects
BK
Lattice values
Chiral behavior
Operator mixing
NPR
• Smearing effect?
• Analysis with new ME data (w/ meson, PDA, Kl3)
- lighter mass ( mval = 0.01 ?) is expensive
- more data points → LECs → physical point
• Analysis with new NPR data (soon available)
- RGI value
- chiral extrapolation
• Time scale?
- All raw data will be available by the end of February