Puttin’ on the HISQ Andreas S. Kronfeld Fermilab & IAS TU München Lattice Meets Continuum: QCD Calculations in Flavor Physics Kulturhaus Lÿz, Siegen | September 18–20, 2017
Puttin’ on the HISQ
Andreas S. KronfeldFermilab & IAS TU München
Lattice Meets Continuum: QCD Calculations in Flavor PhysicsKulturhaus Lÿz, Siegen | September 18–20, 2017
huh?
• “Puttin’ on the Ritz” — song by Irving Berlin from a film of the same name, with dancing from Fred Astaire:
Come with me and we'll attend The jubilee, and see them spend Their last two bits Puttin’ on the Ritz
• HISQ = Highly Improved Staggered Quark
• Some soon-to-appear results from the Fermilab Lattice and MILC Collaborations, using MILC’s 2+1+1 ensembles
• Maybe a little cabaret.
2
huh?
• “Puttin’ on the Ritz” — song by Irving Berlin from a film of the same name, with dancing from Fred Astaire:
Come with me and we'll attend The jubilee, and see them spend Their last two bits Puttin’ on the Ritz
• HISQ = Highly Improved Staggered Quark
• Some soon-to-appear results from the Fermilab Lattice and MILC Collaborations, using MILC’s 2+1+1 ensembles
• Maybe a little cabaret.
2
Ritz: a brand of crackers, as
well as a fancy New York hotel
Outline
• Recap Fermilab Lattice MILC Collaborations’ work on the 2+1-flavor ensembles—asqtad = a2 tadpole-improved (staggered).
• Note some things we did “differently” and one thing still underway.
• Present MILC’s 2+1+1-flavor HISQ ensembles—lattice spacings as small as a = 0.03 fm.
• Ongoing work on αs and mc from charmonium correlators.
• Ongoing work on D- and B-meson decay constants, as well as mQ from heavy-light meson masses.
• Some frightened outlook.
3
asqtad
asqtad Ensembles: 2+1 MILC, arXiv:0903.3598 + earlier
a (fm) size aml/ams # confs # sources≈ 0.15 163×148 0.0097/0.0484 628 24≈ 0.12 203×164 0.02/0.05 2052 4≈ 0.12 203×164 0.01/0.05 2256 4≈ 0.12 203×164 0.007/0.05 2108 4≈ 0.12 243×164 0.005/0.05 2096 4≈ 0.09 283×196 0.0124/0.031 1992 4≈ 0.09 283×196 0.0062/0.031 1928 4≈ 0.09 323×196 0.00465/0.031 984 4≈ 0.09 403×196 0.0031/0.031 1012 4≈ 0.09 643×196 0.00155/0.031 788 4≈ 0.06 483×144 0.0072/0.018 576 4≈ 0.06 483×144 0.0036/0.018 672 4≈ 0.06 563×144 0.0025/0.018 800 4≈ 0.06 643×144 0.0018/0.018 824 4≈ 0.045 643×192 0.0028/0.014 800 4
5
asqtad Ensembles: 2+1
0.0 0.090.06 0.15 0.180.12a (fm)
0.00
0.10
0.20
0.30
0.40
0.50
ml/m
h
6
❋
asqtad Results• Unquenched lattice QCD works [hep-lat/0304004]!
• Predictions: f+D→K(q2) [hep-lat/0408306], Bc mass [hep-lat/0411027], fD & fDs [hep-lat/0506030]!
• Decay constants for B → lν:, D(s) → lν [arXiv:1112.3051].
• Form factors for K → πlν: |Vus| [arXiv:1212.4993] — HISQ on asqtad.
• Zero-recoil form factor for B → D*lν: |Vcb| [arXiv:0808.2519, arXiv:1403.0635].
• Form factors for B → Dlν: BSM [arXiv:1206.4992] & |Vcb| [arXiv:1503.07237].
• Form factors for B → πlν: |Vub| [arXiv:0811.3640, arXiv:1503.07839].
• f+,0,T for B → K/πl+l−: [arXiv:1507.01618, arXiv:1509.06235, arXiv:1510.02349].
• Neutral-meson mixing [arXiv:1205.7013, arXiv:1602.03560, arXiv:1706.04622].
7
CLEO, BaBar, and f+D→K(q2)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
q2/mDs*2
0
0.5
1
1.5
2
2.5f +(q
2 )q2
max/mDs*2
lattice QCD [Fermilab/MILC, hep-ph/0408306]experiment [Belle, hep-ex/0510003]experiment [BaBar, 0704.0020 [hep-ex]]experiment [CLEO-c, 0712.0998 [hep-ex]]experiment [CLEO-c, 0810.3878 [hep-ex]]
D → Klν
8
CLEO, BaBar, and f+D→K(q2)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
q2/mDs*2
0
0.5
1
1.5
2
2.5f 0(q
2 ), f +(q
2 )q2
max/mDs*2
lattice QCD [Fermilab/MILC, hep-ph/0408306]lattice QCD [HPQCD, arXiv:1305.1462]experiment [CLEO-c, 0906.2983 [hep-ex]]experiment [CLEO-c, 0906.2983 [hep-ex]]
D → Klν
8
Precision of Decay Constants
9
Dsexpt/CKM
QCD
Bexpt/CKM
QCD
Kexpt/CKM
QCD0 2 4 6 8 10 12 14 16 18
t
150
200
250
300
MeV
BKDs
years since 2000
Coefficients and Correlations: B → Kl+l–
• arXiv:1509.06235, arXiv:1503.07839, arXiv:1507.01618.
• Use this!!!
10
b+0
b+1
b+2
b0
0
b0
1
b0
2
bT0
bT1
bT2
mean 0.466 �0.885 �0.213 0.292 0.281 0.150 0.460 �1.089 �1.114
error 0.014 0.128 0.548 0.010 0.125 0.441 0.019 0.236 0.971
b+0
1 0.450 0.190 0.857 0.598 0.531 0.752 0.229 0.117
b+1
1 0.677 0.708 0.958 0.927 0.227 0.443 0.287
b+2
1 0.595 0.770 0.819 �0.023 0.070 0.196
b0
0
1 0.830 0.766 0.582 0.237 0.192
b0
1
1 0.973 0.324 0.372 0.272
b0
2
1 0.268 0.332 0.269
bT0
1 0.590 0.515
bT1
1 0.897
bT2
1
Correlation Matrix: BBBBB Mixing
11
f 2Bd
B(1)Bd
f 2Bd
B(2)Bd
f 2Bd
B(3)Bd
f 2Bd
B(4)Bd
f 2Bd
B(5)Bd
f 2Bs
B(1)Bs
f 2Bs
B(2)Bs
f 2Bs
B(3)Bs
f 2Bs
B(4)Bs
f 2Bs
B(5)Bs
f 2Bd
B(1)Bd
1 0.415 0.124 0.320 0.297 0.845 0.417 0.142 0.323 0.308
f 2Bd
B(2)Bd
1 0.332 0.349 0.281 0.416 0.841 0.348 0.360 0.295
f 2Bd
B(3)Bd
1 0.204 0.119 0.133 0.316 0.954 0.203 0.125
f 2Bd
B(4)Bd
1 0.457 0.343 0.380 0.232 0.848 0.468
f 2Bd
B(5)Bd
1 0.312 0.300 0.140 0.449 0.879
f 2Bs
B(1)Bs
1 0.464 0.175 0.385 0.357
f 2Bs
B(2)Bs
1 0.368 0.437 0.354
f 2Bs
B(3)Bs
1 0.257 0.169
f 2Bs
B(4)Bs
1 0.508
f 2Bs
B(5)Bs
1
B0(s)-B
0(s)
• These results (plus those of the competition!) have shrunk the decay and mixing rate bands:
CKM Unitarity Triangle
12
plot by Lunghi
• These results (plus those of the competition!) have shrunk the decay and mixing rate bands:
CKM Unitarity Triangle
12
Latest from HFLAV
plot by Lunghi
A First Look: B → Dlν at Nonzero Recoil
• Alejandro Vaquero Avilés-Casco [for Fermilab Lattice and MILC], talk at Lattice 2017.
• Bernlochner, Ligeti, Papucci, & Robinson [arXiv:1708.07134] already using this!!
13
Results: double ratio RA1 and hA1
Double ratio Single ratio
Alejandro Vaquero (University of Utah) B ! D?`⌫ at w > 1 June 19th , 2017 17 / 22
PRELIMINARY
Results: ratios R0, R1 and hA2, hA3
hA2(w) h
A3(w)
Alejandro Vaquero (University of Utah) B ! D?`⌫ at w > 1 June 19th , 2017 20 / 22
PRELIMINARYResults: ratios R0, R1 and hA2, hA3
hA2(w) h
A3(w)
Alejandro Vaquero (University of Utah) B ! D?`⌫ at w > 1 June 19th , 2017 20 / 22
PRELIMINARY
Results: XV and hV
Ratio
hD?(p?)|V1
��B(0)↵
hD?(p?)|A1
��B(0)↵ =
rw � 1
w + 1
hV
(w)
hA1(w)
Blue: smeared daughter meson. Red: unsmeared daughter meson.
Alejandro Vaquero (University of Utah) B ! D?`⌫ at w > 1 June 19th , 2017 21 / 22
PRELIMINARY
HISQ [Follana et alia, hep-lat/0610092]
HISQ Ensembles: 2+1+1 MILC, arXiv:1212.4768 + further runs
15
a (fm) size aml/ams/amc # confs # sources notes≈ 0.15 163×148 0.0130/0.065/0.838 1020 4≈ 0.15 243×148 0.0064/0.064/0.828 1000 4≈ 0.15 323×148 0.00235/0.0647/0.831 1000 4 physical≈ 0.12 243×164 0.0102/0.0509/0.635 1040 4≈ 0.12 323×164 0.00507/0.0507/0.628 1020 4 also 243, 403
≈ 0.12 483×164 0.00184/0.0507/0.628 999 4 physical≈ 0.12 243×164 0.01275/0.01275/0.640 1020 4 ms = ml
≈ 0.12 323×164 0.00507/0.0307/0.628 1020 4 ms < ms
≈ 0.12 323×164 0.00507/0.012675/0.628 1020 4 ms << ms
≈ 0.09 323×196 0.0074/0.037/0.440 1005 4≈ 0.09 483×196 0.00363/0.0363/0.430 999 4≈ 0.09 643×196 0.0012/0.0363/0.432 484 4 physical≈ 0.06 483×144 0.0048/0.024/0.286 1016 4≈ 0.06 643×144 0.0024/0.024/0.286 572 4≈ 0.06 963×192 0.0008/0.022/0.260 842 6 physical≈ 0.042 643×192 0.00316/0.0158/0.188 1167 6≈ 0.042 1443×288 0.000569/0.01555/0.1827 429 6 physical≈ 0.03 963×288 0.00223/0.01115/0.1316 724 4
16
16
used in Wingate’s talk
Frozen Topology
• Continuum gauge fields: topological charge Q cannot change with an infinitesimal change in the gauge field.
• Evolution of lattice gauge fields in CPU time consists of small steps that (in physical units) become smaller and smaller as lattice spacing a → 0.
• Some reactions:
• “Oh, my! Physics is now impossible!”—anonymous
• “Physical quantities will suffer a systematic error, and we need to either correct for this error or account for it in our error budgets.” —Bernard & Toussaint [arXiv:1707.05430]
17
Good vs. Bad Sampling
18
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
19
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
spacetime volume V = L3T
19
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
vev of Q2 in θ = 0 vacuum
spacetime volume V = L3T
19
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
Q of fixed-Q sector, or average of Q2 in a simulation
vev of Q2 in θ = 0 vacuum
spacetime volume V = L3T
19
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
Q of fixed-Q sector, or average of Q2 in a simulation
vev of Q2 in θ = 0 vacuum
spacetime volume V = L3T
topological susceptibility: χT = Q2/V
in χPT, χT ∝ fπ2 Mπ2 if MπL ~ const, χTV ∝ fπ2 LT
19
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
Q of fixed-Q sector, or average of Q2 in a simulation
vev of Q2 in θ = 0 vacuum
spacetime volume V = L3T
topological susceptibility: χT = Q2/V
in χPT, χT ∝ fπ2 Mπ2 if MπL ~ const, χTV ∝ fπ2 LT
pre-factor from mq dependence
19
12cT
1V
✓1� Q2
hQ2i
◆
• Instead of exponential volume effects, poorly sampled topological charge leads to effects suppressed by
Q of fixed-Q sector, or average of Q2 in a simulation
vev of Q2 in θ = 0 vacuum
spacetime volume V = L3T
topological susceptibility: χT = Q2/V
in χPT, χT ∝ fπ2 Mπ2 if MπL ~ const, χTV ∝ fπ2 LT
References: Leutwyler, Smilga [PRD46 (1992) 5607]; Brower et alia [hep-lat/0302005]; Aoki et alia [arXiv:0707.0396]; Aoki, Fukaya [arXiv:0906.4852].
pre-factor from mq dependence
19
Typical Corrections Bernard & Toussaint, arXiv:1707.05430
• Must be carried out for every ensemble generated.20
ml = ms/5 ml = physical
1.30 0.65
fK/fπ 1.20508(0.00250) [–0.01271]
1.19680(0.00114) [0.00015]
aMπ0.031147(0.000172)
[–0.000707]0.028964(0.000020)
[0.000008]
aMD0.048858(0.000261)
[–0.000552] 0.045389(0.000245)
[0.000006]
afD0.409786(0.000391)
[–0.000044] 0.400678(0.000258)
[0.000001]
aMDs0.054828(0.000068)
[–0.000001] 0.053582(0.000025)
[0.000000]
afDs0.430966(0.000116)
[–0.000004] 0.422041(0.000037)
[0.000000]
hQ2iens/hQ2icPT
Typical Corrections Bernard & Toussaint, arXiv:1707.05430
• Must be carried out for every ensemble generated.20
ml = ms/5 ml = physical
1.30 0.65
fK/fπ 1.20508(0.00250) [–0.01271]
1.19680(0.00114) [0.00015]
aMπ0.031147(0.000172)
[–0.000707]0.028964(0.000020)
[0.000008]
aMD0.048858(0.000261)
[–0.000552] 0.045389(0.000245)
[0.000006]
afD0.409786(0.000391)
[–0.000044] 0.400678(0.000258)
[0.000001]
aMDs0.054828(0.000068)
[–0.000001] 0.053582(0.000025)
[0.000000]
afDs0.430966(0.000116)
[–0.000004] 0.422041(0.000037)
[0.000000]
hQ2iens/hQ2icPT
Tiny, and sometimes significant.
Strong Coupling and Charm-Quark Mass
Charmonium Correlator
• Charmonium (in general, quarkonium) correlator [hep-lat/9505025]: are sensitive to αs and mQ.
• The Gn have a continuum limit and have been computed to high orders in continuum perturbative QCD [arXiv:0805.2999].
• Chetyrkin, Kühn, Sturm: moments to αs3 [hep-ph/0604234].
• HPQCD HISQ on asqtad [arXiv:0805.2999] & on HISQ [arXiv:1004.4285].
22
G(t) = a6 Âx
(am0h)2h0| j5(x, t) j5(0,0)|0i
Gn = Ân(t/a)nC(t)
23
charmonium analysis
Setup A. Veernala, talk at Lattice 2017
• This work: charm, but not “heavier-than-charm.”
• Extract ηh mass for 0.9mc and mc, interpolate to find mc. yielding ηc.
• Form reduced moments:where denominator is the moment in free field theory: cancels tree-level discretization effects.
Rn =
8>><
>>:
Gn/G(0)n , n = 4,
1m0c
⇣Gn/G(0)
n
⌘1/(n�4), n � 6,
24
Continuum-PT-Tuning Fit
where
25
Rn = rn�as(µ),µ
�⇥
(1 (n = 4)mc (µ)�1 (n � 6)
)
⇥✓
1+dnhasG2/pi(mhh)
4
◆
⇥✓
1+hnm2
0h �m020c
m20h
◆
⇥
1+gs1dmsea
udsm0s
+gs2dmsea
udsm0s
⇣am0c
p
⌘2+gc
dmseac
m0c
�
+⇣am0h
2
⌘2 N
Âi=0
c(n)i
⇣am0h
2
⌘2i"
1+b(n)i
✓2Lmhh
◆2#
rn(as(µ),µ) = 1+ Âj=1
rn j(µ)a js (µ).
PT, with priors for unknown terms
bare quark-mass tuning
condensate (OPE)
discretization
Continuum-PT-Tuning Fit
26
PRELIMINARY
Stability
27
PRELIMINARY
Error Budget
28
PRELIMINARY (entries in %) as(mZ) mc(mc)Monte-Carlo statistics 0.01 0.07
Perturbation theory 0.31 0.32
Discretization effects 0.35 0.32
Light sea-quark mass mistuning 0.21 0.23
Charm sea-quark mass mistuning 0.17 0.19
Valence heavy-quark tuning 0.07 0.10
as(5 GeV) prior 0.12 0.11
mc(5 GeV) prior 0.03 0.06
Gluon condensate correction 0.10 0.07
Total 0.57 0.58
Error Budget
28
PRELIMINARY (entries in %) as(mZ) mc(mc)Monte-Carlo statistics 0.01 0.07
Perturbation theory 0.31 0.32
Discretization effects 0.35 0.32
Light sea-quark mass mistuning 0.21 0.23
Charm sea-quark mass mistuning 0.17 0.19
Valence heavy-quark tuning 0.07 0.10
as(5 GeV) prior 0.12 0.11
mc(5 GeV) prior 0.03 0.06
Gluon condensate correction 0.10 0.07
Total 0.57 0.58
Comparisons
0.115 0.120 0.125
u, d, s, c sea
u, d, s sea
Fermilab/MILC 2017 (cc correlators)
HPQCD 2014 (cc correlators)
ETM 2013 (ghost-gluon vertex)
ALPHA 2017 (Schrodinger functional)
Bazavov et al. 2014 (static potential)
HPQCD 2010 (cc correlators)
HPQCD 2010 (Wilson loops)
PACS-CS 2009 (Schrodinger functional)
Maltman et al. 2008 (Wilson loops)
αs(Mz)dummymc comparison below
PRELIMINARY
Decay Constants and Heavy-Quark Masses
31
heavy-light analysis uses them all
Heavier-than-Charm cf. arXiv:1611.07411
• Extend previous work on D mesons [arXiv:1407.3772].
• Light valence ml ≤ mv ≤ ms.
• Heavy valence:
• mc ≤ mh ≤ mb;
• amh ≤ 0.9.
• Total 532 data; final base fit omits a ≈ 0.15 fm ensembles:
• 492 data points.
32
HQ-Chiral-Continuum Interp- & Extrapolation
analytic terms in NnLO χPT:
base fit n = 3
nonanalytic terms from NLO HMrASχPT
aka “chiral logs”
heavy-quark mass dependence
cutoff effects à la Symanzik
fine tune c-quark sea
33
fHvM1/2Hv
= (1+HMrAScPT)(1+HQET)(1+SymET)✓
m0c
mc
◆3/27CNLOF0
match static-chiral H0
to QCDF0
HQ-Chiral-Continuum Fit
15 20 25 30 35 40
MHs/Fp4s
4
5
6
7
8
9
10�
Hu/F
3/2
p4s
�H
s/F
3/2
p4s
D
B
a ⇡ 0.09 fma ⇡ 0.06 fma ⇡ 0.042 fmcontinuum
χ2/dof = 500/(532–60), p = 0.2
34
PRELIMINARY
Fit Stability (subset)
4.8054.815
�D+/F 3/2p4s
central
with 0.15 fm
no 0.03 fm
(2+1)
5.795 5.805
�Ds/F3/2p4s
7.18 7.24
�B+/F 3/2p4s
8.84 8.90
�Bs/F3/2p4s
1.10 1.15
�2/d.o.f
(final) base
two-points w/ (2,1)
not (3,2)
35
PRELIMINARY
Preliminary Results J. Komijani, talk at Lattice 2017
• Preliminary results from Lattice 2017: where “stat” includes fit error, and “syst” includes EM & FV but (not yet) that from two-points (so final “syst” for B mesons will be larger).
• Main other changes: exclude a ≈ 0.15 fm data from base fit.
• No dramatic changes.
fD+ = 212.7±0.3stat ±0.3syst ±0.2PDG fp MeVfDs = 250.0±0.3stat ±0.2syst ±0.2PDG fp MeVfB+ = 189.8±0.8stat ±0.3syst ±0.2PDG fp MeVfBs = 231.2±0.7stat ±0.3syst ±0.2PDG fp MeV
36
Comparison
205 215 225 235 245 255 265 275
Fermilab/MILC 17
ETM 14
Fermilab/MILC 14
χQCD 14
HPQCD 12
Fermilab/MILC 11 (Clover c)
HPQCD 10
fDs(MeV)fD+ (MeV)
u, d, s, c sea
u, d, s sea
37
PRELIMINARY
Comparison
175 185 195 205 215 225 235 245 255
Fermilab/MILC 17
ETM 13
HPQCD 13 (NRQCD b)
RBC/UKQCD 14
HPQCD 12 (NRQCD b)
HPQCD 11 (HISQ b)
Fermilab/MILC 11 (Clover b)
fBs(MeV)fB+ (MeV)
u, d, s, c sea
u, d, s sea
37
PRELIMINARY
Heavy Quark Masses from Heavy-Light Meson Masses
• Heavy-light meson masses can be written where J is spin, d0 = –1 & d1 = 1/3, and Z is a renormalization factor.
• In lattice QCD, the quark mass can be varied at will (as above).
• Determine mQ, Λ, and μπ2 from M0 + 3M1, and μG2 from M1 – M0.
• First attempt: quenched QCD, pole mass, lattice PT [hep-ph/0006345].
• Here: 2+1+1 QCD, continuum limit & PT, but which mass?
38
MJ = mQ + L+µ2
p2mQ
+dJZµ2
G2mQ
L
What Quark Mass?
• Pole mass is natural but suffers from renormalon ambiguity.
• Dim reg masses do not, but would put amount of order αsmQ into Λ.
• Potential subtracted and 1S masses brings in quarkonium.
• Kinetic & renormalon-subtracted masses subtract at scale νf.
• Here: a “minimal renormalon-subtracted” mass, inspired by Komijani’s recursion relation for the mass renormalon [arXiv:1701.00347]:
• removes only “ambigous” part of order Λ ;
• convertible to, e.g., RS scheme and, thence, to any other.
39
L
LMS
Fits
• Augment HQET formula with terms to describe discretization effects and light-mass dependence (χPT):
• Fit curves go through data with amh > 0.9 (not shown here).
• Intercept is Λ; slope is (μπ2 – μG2).
• Alas, data for the vector-meson masses not available.
40
0.2 0.3 0.4 0.5 0.6 0.7 0.8
1/mMRSh [GeV�1]
1.1
1.2
1.3
1.4
1.5
MH
s/m
MR
Sh
a ⇡ 0.12fma ⇡ 0.09fma ⇡ 0.06fma ⇡ 0.042fmContinuum
LPRELIMINARY
Fits
• Augment HQET formula with terms to describe discretization effects and light-mass dependence (χPT):
• Fit curves go through data with amh > 0.9 (not shown here).
• Intercept is Λ; slope is (μπ2 – μG2).
• Alas, data for the vector-meson masses not available.
40
0.2 0.3 0.4 0.5 0.6 0.7 0.8
1/mMRSh [GeV�1]
0.60
0.62
0.64
0.66
0.68
0.70
MH
s�
mM
RS
h[G
eV]
a ⇡ 0.12fma ⇡ 0.09fma ⇡ 0.06fma ⇡ 0.042fmContinuum
LPRELIMINARY
Preliminary Results J. Komijani, talk at Lattice 2017
• Preliminary results from Lattice 2017: where “stat” includes fit error, and “syst” includes EM, FV, αs but (not yet) that from two-points (so final “syst” for B mesons will be larger).
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ms(2 GeV) = 92.4(4)stat(5)syst MeVmc(mc) = 1270(04)stat(10)syst MeVmb(mb) = 4198(11)stat(09)syst MeV
mc/ms = 11.755(13)stat(34)syst MeVmb/ms = 53.91(08)stat(11)syst MeVmb/mc = 4.586(05)stat(10)syst MeV
Comparison for Charm Mass
1.2 1.25 1.3 1.35 1.4
u, d, s, c sea
u, d, s sea
u, d sea
Fermilab/MILC 2017
HPQCD 2014
ETM 2014
HPQCD 2010
ETM 2010
mc(mc)
42
PRELIMINARY
Comparison for Charm Mass
1.2 1.25 1.3 1.35 1.4
u, d, s, c sea
u, d, s sea
u, d sea
Fermilab/MILC 2017
HPQCD 2014
ETM 2014
HPQCD 2010
ETM 2010
mc(mc)
heavy-light meson masses charmonium moments
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PRELIMINARY
Remarks & Outlook
Precision of Decay Constants
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0 2 4 6 8 10 12 14 16 18
t
150
200
250
300
MeV
BKDs
2017
years since 2000
Precision of Decay Constants
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2017
0 2 4 6 8 10 12 14 16 18
t
150
200
250
300
MeV
BKDs
years since 2000
What’s Next?
• Further precision on D and B decay constants academic, for now.
• But the “step” improvement will apply to other processes:
• semileptonic decays for |Vcb|, |Vub|, and FCNC;
• neutral meson mixing (experiment has always been sub-%).
• QED and mu ≠ md effects will be necessary [cf., Dürr talk]:
• 1+1+1+1 HISQ ensembles are underway, QCD+QED too;
• QED effects interesting—FV effects, structure vs. universal radiative effects—harder for D and B than for K [cf., arXiv:1611.08497].
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Scale-Setting; Providing Correlations
• Stop using fπ to set absolute scale (depends on |Vud| ⇐ nuclear physics).
• Fermilab/MILC have started to provide correlations among
• semileptonic heavy-to-light form factors;
• B- and Bs-meson mixing;
• D-meson mixing.
• Is the next step a correlation matrix across a whole suite of calculations?
• Can we finish a dozen calculations at the same time?
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Collaborators
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Jon Bailey, Alexei Bazavov, Claude Bernard, Chris Bouchard, Nathan Brown, Jason Chang, Carleton DeTar, Daping Du,
Aida El-Khadra, Todd Evans, Elizabeth Freeland, Elvira Gámiz, Steve Gottlieb, Urs Heller, Jeongjeong Kim, Javad Komijani,
A.S.K., Jack Laiho, Ludmila Levkova, Yuzhi Liu, Ruizi Li, Enrico Lunghi, Yannick Meurice, Paul Mackenzie,
Ethan Neil, Bugra Oktay, Thom Primer, Si-Wei Qiu, Jim Simone, Bob Sugar, Doug Toussaint, Ruth Van de Water,
Alejandro Vaquero, Aarti Veernala, Ran Zhou
Danke schön!