Puttin’ on the HISQ

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).

41

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

42

PRELIMINARY

Remarks & Outlook

Precision of Decay Constants

44

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

44

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].

45

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?

46

Collaborators

47

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!