Staggered Heavy-Light Physics
Update
Fermilab/MILC
Paul Mackenzie
Fermilab Theoretical Physics
mackenzie@fnal.gov
Edinburgh
March, 2005
The Fermilab/MILC heavy/light project
B and D mesons with staggered light quarks and Fermilab
heavy quarks on unquenched improved staggered gauge fields.
Lattice QCD/Experiment (no free parameters!):
Tests:
Before
Now
f&
fK
3m% # mN
m$
2mB # m!
s
"(1P-1S)
!(1D-1S)
!(2P-1S)
!(3S-1S)
!(1P-1S)
0.9
1
1.1
quenched/experiment
0.9
1.0
1.1
(nf = 2+1)/experiment
light mesons and
baryons
Part of larger program of
heavy-light mesons
phenomenology with unquenched
heavyonium
fermions with Fermilab,
Find staggered
agreement with
expt MILC,
(at last!) and
when HPQCD.
correct dyn. quark
content is present.
Quenched
approx.
has syst.
errors
10% and internal
inconsistency.
Davies et al, hep-lat/0304004 + Toussaint,Davies, LAT04
5
Initial results were at a=0.125
fm; now doing other lattice spacings.
Paul Mackenzie
Why staggered fermions?
0.9
unquenched lattice data
quadratic
s
0.7
3/2
r0 !P
Wilson fermions have a hard
time reaching below mu~ms/2.
r0 fPS / ZA
0.8
0.6
0.5
chiral log + quadratic
chiral log below 300 MeV
chiral log below 500 MeV
0.4
0.0
2.0
4.0
(r0mPS)
Hard to reduce chiral
extrapolation uncertainties
below 10% from there.
2
6.0
fπ and fK fits extrapolated
to larger
masses: JLQCDFigure
Wilson
fermions,
Figure 3. Uncertainty in the chiral extrapoladecay c
tion.
0.13
regions.
two-flavor QCD result is significantly higher than
the chir
0.12
the quenched
result 1.081(5)(17) [7] and closerNote:
to
as large
the physical fvalue 1.22, the uncertainty is still– Masses ≥ ms /2 ba
K
sizable.0.11
– High-mass fπ s line
10%wo
hig
! msconstant
This
For the heavy-lightmsea
decay
the predic- extrapolate
/2.3
=
0.1
u,d
s /4.5
two fπ s p
ex
tion of ChPT is available
inmthe
heavy quark limit– Lowest puter
late
linearly
to
with
by the G
for quenched,
partially quenched and full QCD
0.09 fπ
(Nos. 1
[8,9]. The chiral logarithm appears with a def1364025
inite coefficient0.2
but0.4
including
an additional
cou0.6 0.8
1
∗
is suppo
pling constant g describing
the B Bπ interaction.
mval
u,d /ms
The chiral extrapolation of fB and fBs including
the chiral logarithm is shown
in Figure
4 with
REFER
Improved
staggered
fermions,
Lattice QCDand Ex
two representative values
of g. As in the pion de-High-Precision
MILC/HPQCD/UKQCD,
Fermilab.
1. T. K
cay constant, the uncertainty in the chiral limit
thes
is enhanced by the chiral logarithm.
2. J. G
The ratio fBs /fB is needed in the extraction
158
of the CKM matrix element |Vtd /Vts |. Since the
465
bulk of systematic errors cancels in the ratio, one
3. S. A
may expect better accuracy than the determinaPhy
tion of |Vtd | solely from ∆Md . Our preliminary
4. S.R
result varies from 1.24 (quadratic fit) to 1.38 (chi5. M.F
ral log, g = 0.59). It suggests that the ratio and
D5
Overlap/domain wall fermions have good chiral behavior, but are
slower. Staggered fermions will get to higher precision faster.
Paul Mackenzie
Semileptonic decays.
"l
W
BK Ansat!
•
l+
Vcs , Vcd
D
To provide for the presence of nearby vector meson poles
in form factors, Becirevic and Kaidalov proposed the
parametrization
2
f+ (q ) =
2
f0 (q ) =
•
+
f (0)
(1−q 2 /m2D∗ )(1−αq 2 /m2D∗ )
f (0)
(1−q 2 /m2D∗ /β)
Builds in the closest pole, and has parameters for the slop.
K, !
• Analysis method
•
•
•
•
calculate matrix elements for various (mq, p).
use BK to interpolate to fiducial values of E, same for
each ensemble.
use partially quenched staggered χPT for chiral
extrapolation.
use BK to extrapolate to full kinematic range.
Paul Mackenzie
USQCD Allocations Workshop, January, 2005
D
! and D
K results (hep-ph/0408306, accepted for PRL)
! Vµ D
f
q2
pD
m2D
p!
m2!
q2
µ
f0 q2
q
m2D
m2!
q2
qµ
1.5
1
f0
f+
experiment
D!>!
0.5
1.5
1
0
1
2
f0
f+
experiment
D!>K
0.5
fD
Paul Mackenzie
!
0
0
0 64 3 6
21
2
2
q [GeV ]
fD
K
0
0 73 3 7
USQCD Allocations Workshop, January, 2005
Comparison to FOCUS experiment for D
f
q2
f
K decay
0 vs q2 :
(provided by FOCUS collab.)
Paul Mackenzie
USQCD Allocations Workshop, January, 2005
• An alternative is to avoid BK altogether, and use
χPT to extrapolate jointly in (mq, E):
&'!()*+,-).)/0*1*-2(/)345--6*$--)/7+8.)716+-).)/0*1*-28+,5
"$%
"
9!
9:
+;<+81=+.7
>!?!
!$%
•
!
"
#
2
2
q (GeV )
2
Consistent, but no-BK has larger error in low q
(high E) region.
Ci (mQ , m0 a) − Ci (mQ ) = a
fi (m0 a).
Discretization
the usual
counting ofEffects
powers of a (common parlance from Symanzik)
dependence. For Wilson fermions limm0 a→0 fi = constant. But as m0
to think
of
some
or
all
of
the
powers
of
a
being
replaced
by
powers
For heavy-light use HQET to order and estimate
final expression for the discretization errors is
errori = fi (m0 a)(aΛQCD )dim Oi −4 .
cit calculations of the fi for the O(a) and O(a2 ) errors at the tree lev
hem to estimate the O(αs a) and O(a2 ) discretization errors.
kind of thing
can be
written
out for? currents, but I won’t do that in
What
would
you
use
for
Λ
QCD
•
that the leading current is of dimension 3, so the power appearing var
where •Vµ,i
is the
correction
the appears
HQET in
description
Based
on ith
estimates
of the in
Λ that
the heavy- of the vector c
quark expansion, from lattice, sum rules, and experiment,
the sensible range is
2
•
ΛQCD = 500–700 MeV
.
Λ (MeV):
errorB [O(αs a) Lagrangian]
error3 [O(αs a) current]
2
errorE [O(a ) Lagrangian]
(cE = 0)
2
errorX [O(a ) current]
(d1 off)
2
errorY [O(a ) current]
temporal total
spatial total
400
1.8
1.1
0.4
1.1
0.9
1.3
0.4
2.8
3.2
500
2.2
1.4
0.6
1.6
1.3
2.0
0.6
3.6
4.1
600
2.6
1.7
0.9
2.4
1.9
2.8
0.8
4.7
5.3
700
3.1
2.0
1.2
3.2
2.6
3.9
1.1
5.9
6.6
800
3.5
2.2
1.5
4.2
3.4
5.0
1.5
7.2
7.8
900
3.9
2.5
1.9
5.3
4.3
6.4
1.8
8.7
9.4
1000
4.4
2.8
2.4
6.6
5.4
7.9
2.3
10.5
11.2
Pending
studies
on finer
lattices,
we quoted sum in
ld, Phys.
Rev. D
62, 014505
(2000)
[arXiv:hep-lat/0002008].
quadrature
currents,
ΛQCD = 700 MeV
al., Phys.
Rev. D of
65,both
094513
(2002)at[arXiv:hep-lat/0112044];
Phys.
hep-ph/0408306
• D → Klν
D→K
f+
(0) = 0.73(3)(7)
D→K
f+
(0)
dominant error:
heavy quark
discretization
= 0.78(5) [BES, hep-ex/0406028]
• D → πlν:
D→π
f+
(0) = 0.64(3)(6)
D→π
f+
(0)
D→π
f+
(0)
=
=
D→K
0.87(3)(9)f+
D→K
0.86(9)f+
[CLEO,
hep-ex/0407035]
First heavy-light on fine lattices (a=0.09 fm).
Repeating the coarse lattice calculations on the fine lattices
(4 time sources / configuration) will take most of this year.
01!211(3+456
!/
789+:;/!!4<97=4<5>1+:;$!!4<97((!,?/((()5 (>+1+@(@<(/"%/*+,-
#
/=#
5 (7AA(((B789+((@19C?#&D
!/=#
5 7'+>'(B789+((@19C?#&D
/=#
5 (7AA(((B789+((@19C?#$D
!/=#
5 7'+>'(B789+((@19C?#$D
/=#
5 (7AA(((B4<5>1+D
!/=#
5 7'+>'(B4<5>1+D
/".
/
!".
!
!
!"#
#
!"$
#
' ()*+, -
!"%
!"&
Little lattice spacing dependence seen at level of statistical errors, ~ 5%.
Look at coarser lattice spacings to improve discretization uncertainty
estimate.
Paul Mackenzie
Unquenched, improved staggered (”asqtad”) data sets
Operations counts for unquenched improved staggered configuration generation.
a (fm)
m light
m heavy
Ns
Nt
Volume
CG l
CG h
Ops/site
steps
Ops/traj
traj
TF years
0.18
0.0492
0.0328
0.0164
0.0082
0.082
16
16
16
16
48
48
48
48
196608
196608
196608
196608
170
170
170
500
142
142
142
142
1164472
1164472
1164472
1556182
50
50
100
200
1.14E+13
1.14E+13
2.29E+13
6.12E+13
3000
3000
3000
3000
0.0011
0.0011
0.0022
0.0058
0.15
0.0484
0.029
0.0194
0.0097
0.0048
0.0484
16
16
16
16
16
48
48
48
48
48
196608
196608
196608
196608
196608
138
206
281
430
890
138
138
138
138
138
1121740
1202456
1291481
1468344
2014364
100
100
100
150
333
2.21E+13
2.36E+13
2.54E+13
4.33E+13
1.32E+14
3000
3000
3000
3000
3000
0.0021
0.0023
0.0024
0.0041
0.0126
0.125
"coarse"
0.04
0.03
0.02
0.01
0.007
0.005
0.05
0.05
0.05
0.05
0.05
0.05
20
20
20
20
20
24
64
64
64
64
64
64
512000
512000
512000
512000
512000
884736
170
212
253
426
583
893
142
142
127
127
127
143
1164472
1214326
1245188
1450539
1636898
2023860
50
50
75
150
200
333
2.98E+13
3.11E+13
4.78E+13
1.11E+14
1.68E+14
5.96E+14
3000
3000
3000
3000
3000
3000
0.003
0.003
0.005
0.011
0.016
0.057
0.09
"fine"
0.0124
0.0062
0.0031
0.031
0.031
0.031
28
28
40
96
96
96
2107392
2107392
6144000
352
687
1400
189
189
189
1436295
1833940
2680271
125
250
500
3.78E+14
9.66E+14
8.23E+15
3000
3000
3000
0.036
0.092
0.786
0.06
0.008
0.004
0.002
0.02
0.02
0.02
42
42
60
144
144
144
10668672
10668672
31104000
355
1030
1050
300
300
300
1571613
2372838
2396578
188
375
750
3.15E+15
9.49E+15
5.59E+16
3000
3000
3000
0.301
0.907
5.339
Fermilab
Supercomputers
QCDOC
Ops/site=1187*(CG l + CG h)+794128.
Paul Mackenzie
First results on coarser lattices.
(a=0.18 fm. “extra coarse”.)
At a minimum, a good sanity check on errors
estimated from the fine and coarse lattices.
-1
a (GeV)
r1 (potential)
psi 1P1S
Upsilon 1P1S
Upsilon 2S1S
B_c
Paul Mackenzie
1.105 (50)
1.097 (+97/-22)
1.122 (19)
1.139(43)
1.13
Statistical errors only.
USQCD Allocations Workshop, January, 2005
hep-ph/0408306
dominant error:
heavy quark
discretization
• D → Klν
D→K
f+
(0) = 0.73(3)(7)
D→K
f+
(0) = 0.78(5) [BES, hep-ex/0406028]
• D → πlν:
D→π
f+
(0)
D→π
f+
(0)
D→π
f+
(0)
= 0.64(3)(6)
D→K
= 0.87(3)(9)f+
=
D→K
0.86(9)f+
[CLEO, hep-ex/0407035]
fD and fDs
We’re concentrating on charm before bottom
because of the pending revolution in charm data
from CLEO.
Samples of current work in
progre
CLEO expects:
Semileptonic decays to 1%.
Decay constants to 2%.
New tests of lattice methods from CKM
independent amplitude ratios:
New high precision experimental data for Vcd and Vcs.
Taking data now, results in about a year.
Paul Mackenzie
USQCD Allocations Workshop, January, 2005
Quark masses used.
Lots of partially quenched
valence masses from a
multimass inverter.
Partially quenched, finite a
staggered chiral
perturbation theory,
Bernard and Aubin.
One-loop corrections,
Nobes and Trottier.
Paul Mackenzie
Simone, Lattice 2004
Fermilab/MILC
USQCD Allocations Workshop, January, 2005
8
0.030/0.05
The SχPT fit
Ensemble 0.030/0.05
The mass plane
Fit including staggered discretization effects.
Fit without discretization effects.
LATTICE 2004
Paul Mackenzie
June 2004
USQCD Allocations Workshop, January, 2005
8
The SχPT fit
Ensemble 0.030/0.05
The mass plane
Fit including staggered discretization effects.
Fit without discretization effects.
LATTICE 2004
Paul Mackenzie
June 2004
USQCD Allocations Workshop, January, 2005
9
The SχPT fit
Ensemble 0.020/0.05
The mass plane
Fit including staggered discretization effects.
Fit without discretization effects.
LATTICE 2004
Paul Mackenzie
June 2004
USQCD Allocations Workshop, January, 2005
10
The SχPT fit
Ensemble 0.010/0.05
The mass plane
Fit including staggered discretization effects.
Fit without discretization effects.
LATTICE 2004
Paul Mackenzie
June 2004
USQCD Allocations Workshop, January, 2005
11
The SχPT fit
Ensemble 0.007/0.05
The mass plane
Fit including staggered discretization effects.
Fit without discretization effects.
LATTICE 2004
Paul Mackenzie
June 2004
USQCD Allocations Workshop, January, 2005
12
The SχPT fit
Ensemble 0.005/0.05
The mass plane
Fit including staggered discretization effects.
Fit without discretization effects.
LATTICE 2004
Paul Mackenzie
June 2004
USQCD Allocations Workshop, January, 2005
extrapolate along full QCD
16
Results
NARY
g systematic errors in quadrature,
√
fDs mDs
√
fD mD
= 1.20 ± .06 ± .06
Result
from
fit
+5to all data:
f
= 263 ± 24 MeV
Ds
fD =
Paul Mackenzie
−9
+10
224−14
± 22
MeV
USQCD Allocations Workshop, January, 2005
16
Results
IMINARY
ning systematic errors in quadrature,
√
fDs mDs
√
fD mD
= 1.20 ± .06 ± .06
fDs = 263+5
−9 ± 24
fD = 224+10
−14 ± 22
MeV
MeV
e
ing now
the dominant uncertainty. Need matching
Paul Mackenzie
USQCD Allocations Workshop, January, 2005
CKM matrix with LQCD(n f
3)
(from semileptonic decays)
Vud
Vus
0 225 2 1
Vcd
Vcs
0 24 3 2
0 97 10 2
Vtd
Vts
Vub
35 5 5
10
3
10
2
Vcb
39 1 3
Vtb
value(lat.err)(exp.err)
5/9 determined with LQCD(n f
Paul Mackenzie
3)+Exp’t !!!!!
Full CKM matrix with LQCD(n f
3)
(from semileptonic decays)
Vud
Vus
0 9744 5 3
0 225 2 1
Vcd
Vcs
0 24 3 2
0 97 10 2
Vtd
Vts
81 27
10
3
38 4 3
Vub
35 5 5
10
3
10
2
Vcb
39 1 3
Vtb
10
2
0 9992 0 1
value(lat.err)(exp.err)
9/9 fully determined !!!!!!!!!
!
Paul Mackenzie
Wolfenstein parameters with LQCD(n f
0 225 2 1
A 0 77 2 7
" 0 16 28
3)
# 0 36 11
Paul Mackenzie