heavy flavour precision physics from nf=2+1+1 lattice ... · etmc { n f = 2 +1 +1 action glue :...

Heavy flavour precision physics fromNf = 2 + 1 + 1 lattice simulations

Petros Dimopoulos

Centro Fermi& University of Rome “Tor Vergata”

July 2 - 9, 2014“37th International Conference on High Energy Physics”

Valencia, Spain

In collaboration with:A. Bussone, N. Carrasco, R. Frezzotti, P. Lami, V. Lubicz,

F. Nazzaro, E. Picca, L. Riggio, G.C. Rossi, S. Simula, C. Tarantino

Valencia - ICHEP 2014, July 2-9 Petros Dimopoulos Heavy flavour precision physics from Nf = 2 + 1 + 1 simulations

Outline

• tmLQCD with 2 + 1 + 1 dynamical flavours

• charm sector

Determination of mc and mc/ms

Accurate determination of pseudoscalar meson decay constantsfDs , fDs/fD and fD

• bottom sector: Ratio Method + tmLQCD (relativistic quarks)

computation of mb with heavy quark systematic uncertaintiesunder controlnon-perturbative determination of the quark mass ratio mb/mc

On going analysis for fB(s), B-bag parameters and ξ(for B-physics computations with Nf = 2 tmLQCD seeETMC, Carrasco et al. JHEP 03(2014)016.)

• Lattice ME are required for CKM unitarity tests.

• Higgs decays sensitive to mb (less to mc ):Γ(H → qq) ∝ mHm

2q(mH ), q ≡ b, c


ETMC – Nf = 2 + 1 + 1 action

• Glue : Iwasaki [Iwasaki NPB 1985]

• Nf = 2 - light MtmQCD Dirac operator

D` = DW + mcrit + iµ`γ5τ3

[Frezzotti, Rossi, JHEP 2004]

? µ` bare light twisted mass; τ3 acts on flavour doublet

• Nf = 1 + 1 twisted mass strange/charm doublet

Dh = DW + mcrit + iµστ1 + µδτ3

[Frezzotti, Rossi, NP Proc Suppl 2004]

Only O(a2) discretisation errors on physical quantities

• Multiplicative light quark mass renormalization

• mc,s =1

ZP(µσ ±

ZP

ZSµδ)

• No need for RC in pseudoscalar decay constant (PCAC)

• Breaking of parity and isospin – recovered as a→ 0

• (Nf = 1 + 1) – mixing of strange and charm in the unitary setup


ETMC – Nf = 2 + 1 + 1 action

• Osterwalder-Seiler (flavour diagonal) action in the valence sector –

multiplicative quark mass renormalisation - no s/c mixing.

• Mixed action setup – unitary up to O(a2) [Frezzotti, Rossi, JHEP 2004]

3 latt. spacings, a ∈ [0.06, 0.09] fm

Mps ∈ [210, 440] MeV

Mps L ∈ [3.1, 5.4]

L ∈ [2, 3] fm

scale setting determination from fπ

non-perturbative computation of RCs (RI-MOM)


Simulation details for Nf = 2 + 1 + 1 ensembles

β V /a4 aµsea = aµ` aµσ aµδ Ncfg aµs aµc − aµh

1.90 323 × 64 0.0030 0.15 0.19 150 0.0180, 0.21256, 0.25000,0.0040 150 0.0220, 0.29404, 0.34583,0.0050 150 0.0260 0.40675, 0.47840,

0.56267, 0.66178,0.77836,

1.90 243 × 48 0.0040 0.15 0.19 1500.0060 1500.0080 1500.0100 150

1.95 323 × 64 0.0025 0.135 0.170 150 0.0155, 0.18705, 0.22000,0.0035 150 0.0190, 0.25875, 0.30433,0.0055 150 0.0225 0.35794, 0.42099,0.0075 150 0.49515, 0.58237

0.68495,1.95 243 × 48 0.0085 0.135 0.170 150

2.10 483 × 96 0.0015 0.12 0.1385 90 0.0123, 0.14454, 0.17000,0.0020 90 0.0150, 0.19995, 0.23517,0.0030 90 0.0177 0.27659, 0.32531,

0.38262, 0.45001,0.52928,

β L(fm) Mπ(MeV) MπL

1.90 2.84 245 3.53

282 4.06

314 4.53

1.90 2.13 282 3.05

344 3.71

396 4.27

443 4.78

1.95 2.61 239 3.16

281 3.72

350 4.64

408 5.41

1.95 1.96 435 4.32

2.10 2.97 211 3.19

243 3.66

296 4.46

ETMC, Baron et al. JHEP 2010ETMC, Baron et al. Comp.Phys.Com. 2011ETMC, Carrasco et al. 2014


charm sector


mc

• Determine mc using either MexptD = (MD± + MD0 )expt/2 or Mexpt

Ds as input

• mud (MS, 2 GeV) = 3.70(17) MeV, ms (MS, 2 GeV) = 99.6(4.1) MeV[ETMC, Carrasco et al. 1403.4504]

using inputs Mexpt

π0 = 134.98 MeV, MexptK = 494.2(4) MeV, respectively

(pure QCD corrected MexptK for leading strong and EM isospin breaking effects - FLAG 2013).

• Use scaling variables either r0/a or (fictitious ps-mass) Mc′s′ computed at fixed valuesof strange- and charm-like quark masses → control of discretisation effects.

• fit ansatz: Mh`/s = P0 + P1m` (+P2m2`) + P3a2

• tune mh → mc such as after CL & phys. pion mass extrapolation Mh`/s → MexptD(s)

.

• mc (MS,mc ) = 1.348(13)stat+fit (2)ch(6)discr (34)scale (20)RC−syst GeV = 1.348(42) GeV

0 10 20 30 40 50m

l(MeV)

4,4

4,6

4,8

5

5,2

5,4

MD

sr 0

β=1.90 V/a4=32

3x64

β=1.90 V/a4=24

3x48

β=1.95 V/a4=32

3x64

β=1.95 V/a4=24

3x48

β=2.10 V/a4=48

3x96

Continuum Limit

[ETMC, Carrasco et al. 1403.4504]

Nf = 2 + 1 + 1

Nf = 2

Nf = 2 + 1

ETMC ’10

ALPHA ’13

HPQCD ’10

ETMC ’14 (this work)

PDG

mc(MS, mc) [GeV]

1.51.41.31.21.1


mc/ms

• Control systematics of mc/ms using

• R(mc ,ms ,ml , a2) =ms

mc

(Mηc −MDs )(2MDs −Mηc )

2M2K −M2

π

(→ leading term independent of mc and ms )

• Mηc ≡ (cc) PS-meson; on the lattice compute (fermionic) connected diagrams;disconnected contribution negligible [HPQCD, Davies et al. PRL (2010)].

• Extrapolate to CL & phys. point → Rextrap

• mc/ms =[ (Mηc −MDs )(2MDs −Mηc )

2M2K −M2

π

]expt 1

Rextrap = 11.62(16) [error ∼ 1.4%]

10 20 30 40 50m

l (MeV)

0,16

0,165

0,17

0,175

0,18

R

β=1.90 V=323x64

β=1.90 V=243x48

β=1.95 V=323x64

β=1.95 V=243x48

β=2.10 V=483x96

Continuum limit

[ETMC, Carrasco et al. 1403.4504]

Nf = 2 + 1 + 1

Nf = 2

Nf = 2 + 1

ETMC ’10

Durr-Koutsou ‘12

HPQCD ’10

HPQCD ’14


mc/ms

12.51211.511


fD(s)

• Leptonic Decays : D(s) −→ `ν

• Γ(D(s) → `ν) =G 2

F

8πm2`MD(s)

(1−

m2`

M2D(s)

)2f 2D(s)|Vcd(s)|2

• Knowledge of fD(s) =⇒ necessary to extract |Vcd(s)| [Ds → µν, τν: CLEO-c, Belle, BaBar ][D→ µν, τν: CLEO-c, BES ]

• ETMC computation:

? smeared-smeared and smeared-local correlators → plateau at earlier time separation

? determination of ps-meson decay constant (PCAC)

fD(s) =µc + µd(s)

MD(s) sinh(MD(s))〈0|P5|D(s)〉

? sinh(MD(s)) from discretised axial current derivative → reduces discretisation errors


fDs

• Interpolation at s and c quark mass

• Scaling analysis for fcs/Mcs

• Simultaneous CL & chiral fit

(fcs/Mcs )×MexptDs = c0 + c1µ` (+c2µ

2`) + Da2

• In CL & physical point

(fcs/Mcs )×MexptDs −→ fDs

CL-phys. point

β = 2.10

β = 1.95

β = 1.90

µℓ (GeV)

(fcs/M

cs)×(M

Ds)expt(G

eV)

0.050.040.030.020.010.00

0.275

0.270

0.265

0.260

0.255

0.250

0.245

0.240

=⇒ No scale setting uncertainty

=⇒ small discretisation effects

fDs = 248.5 (1.0)stat (2.9)(mc ,ms ) (1.2)ch (1.8)discr (0.2)V (0.3)MDs−exptMeV

fDs = 248.5 (3.8) MeV [error ∼ 1.5%] [Preliminary !]

(From scaling analysis in terms of r0 we get fully compatible result: fDs = 251(9) MeV)


fDs: lattice results

ALPHA ’13

ETMC ’13

FNAL/MILC ’11

HPQCD ’10

HPQCD ’12

FNAL/MILC ’13


PDG (expt + phen)

Nf = 2

Nf = 2 + 1

Nf = 2 + 1 + 1

fDs [MeV]

280270260250240230

? Lattice results obtained in the CL.

? Weak dependence on the number of dynamical flavours within the present accuracy.

? PDG estimate makes use of |Vcs | ' |Vud | − |Vcb|2/2,|Vud | = 0.97425(22), |Vcb| = 0.04.


fDs/fD

• SU(3) breaking ratio: cancellation of many systematics; sensitive to chiral extrapolation

• Interpolation at s and c

• Define [(fcs/fc`)(f``/fs`)] (fK/fπ)phen −→ large cancellation of SU(2) (HM)ChPT logs[Becirevic et al., Phys.Lett.B 2003]

• fit ansatze:

? a(1) + b(1)µ` + D(1)a2

? a(2)[

1 + b(2)µ` +[

3(1+3g2)4 − 5

4

]2B0µ`(4πf0)2 log

(2B0µ`(4πf0)2

)]+ D(2)a2

• (fK/fπ)FLAG = 1.194(5)(aver. over Nf =2+1 and 2+1+1 results) [FLAG 2013]

• B0, f0 from [ETMC Carrasco et al. 2014]

=⇒ @ CL & phys. point, fit results are compatible

within one σstat+fit

=⇒ small discretisation effects

CL-phys. pointCL-phys. point

Lin. FitHMChPT Fit

β = 2.10β = 1.95β = 1.90

µℓ (GeV)

[(f c

s/f

cℓ)(f

ℓℓ/f

sℓ)](f

K/f

π)p

hen

0.050.040.030.020.010.00

1.35

1.30

1.25

1.20

1.15

fDs/fD = 1.186 (9)stat+fit (6)ch (8)disc (5)V (5)fK/fπ

fDs/fD = 1.186 (15) [error ∼ 1.3%] [Preliminary !]


fDs/fD: lattice results

Nf = 2 + 1 + 1

Nf = 2 + 1

Nf = 2

PDG (expt + phen)


FNAL/MILC ’13

HPQCD ’12

FNAL/MILC ’11

ETMC ’13

ALPHA ’13

fDs/fD

1.41.31.21.11

? Lattice results obtained in the CL.? PDG estimate for fD makes use of |Vcd | ' |Vus | (− tiny correction)


fD

• fD = fDs/(fDs/fD )

= 209.5(1.9)stat+fit (2.7)mc (1.5)ch (2.0)disc (0.8)V (0.8)(fK/fπ,MDs ) MeV

fD = 209.5(4.3) MeV [error ∼ 2.1%] [Preliminary!]

ALPHA ’13

ETMC ’13

FNAL/MILC ’11

HPQCD ’10

HPQCD ’12

FNAL/MILC ’13


PDG (expt + phen)

Nf = 2

Nf = 2 + 1

Nf = 2 + 1 + 1

fD [MeV]

240230220210200190

? Lattice results obtained in the CL.? PDG estimate for fD makes use of |Vcd | ' |Vus | (− tiny correction)


bottom sector


ETMC - Ratio Method: B-physics latticecomputations

• We use correlators with relativistic quarks

• We consider ratios of heavy-light (h, `/s) observables that have anexact and known static limit

• HQET-inspired interpolation of (h, `/s) ratios to the bottom-regionfrom the charm region and the static limit

• charm region computations have small discretisation errors

• Ratios computed for pairs of nearby heavy quark masses showsmooth chiral and continuum limit behaviour. Heavy quarksystematics are suppressed

• Determine b-observables through well-controlled ratio chain

[ETMC, JHEP 2010, 2012, 2014]


Ratio Method

• For any observable Qh `/s ≡ Mh`/s , fh`/s , . . . consider the HQET scaling

quantity ΦQ = Qh `/s × (µpoleh )α

• observing that limµpoleh→∞

(Qh `/s × (µpoleh )α

)= constant

e.g. α = −1, 1/2 for Mh`/s , fh`/s , respectively

• construct ratios at nearby µh (µ(n)h = λµ

(n−1)h )

yQ (µ(n)h , λ;µ`/s , a) =

ΦQ (µ(n)h ;µ`/s , a)

ΦQ (µ(n−1)h ;µ`/s , a)

CQ (µ(n)h )

CQ (µ(n−1)h )

? CQ (µ(n)h ) are relevant in the “1/µh” interpolation and include possible

anomalous dimension in HQET and ρ factors, µpoleh = ρ(µh, µ∗)µh(µ∗)

(with µh ← MS scheme )

• yQ (µh, λ;µ`/s , a = 0)µh→∞−→ 1 + O(1/logµh) (residual and small)


b-mass computation

• Consider Qh =Mhs

(Mh`)γ

• HQET asymptotic behaviour limµpoleh→∞

(Mhs/(Mh`)

γ

(µpoleh )(1−γ)

)= const.

• For a sequence of heavy quark masses (µ(1)h , µ

(2)h , · · · , µ(N)

h ) with fixed ratio

µ(n)h = λµ

(n−1)h

• Form ratios

yQ (µ(n)h , λ;µ`, µs , a) ≡

Qh(µ(n)h ;µ`, µs , a)

Qh(µ(n−1)h ;µ`, µs , a)

·(

µ(n)h ρ(µ

(n)h , µ∗)

µ(n−1)h ρ(µ

(n−1)h , µ∗)

)(γ−1)

= λ(γ−1) Qh(µ(n)h ;µ`, µs , a)

Qh(µ(n)h /λ;µ`, µs , a)

(ρ(µ

(n)h , µ∗)

ρ(µ(n)h /λ, µ∗)

)(γ−1)

• For each n = 2, . . . ,N, extrapolate yQ to the CL and phys. pion mass


b-mass computation• Cutoff effects increase (naturally) with n, still under control;

simultaneous chiral and CL fits are smooth (χ2 . 1)

CL - phys. point

β = 2.10

β = 1.95

β = 1.90

µℓ (GeV)

y(2)

Q

0.050.040.030.020.010.00

1.004

1.002

1.000

0.998

0.996

CL - phys. point

β = 2.10

β = 1.95

β = 1.90

µℓ (GeV)

y(8)

Q

0.050.040.030.020.010.00

1.004

1.002

1.000

0.998

0.996

0.994

0.992

0.990

0.988

µ−1b

1/µh (GeV−1)

y Q(µ

h)

0.80.70.60.50.40.30.20.10.0

1.004

1.002

1.000

0.998

0.996

0.994

exactly known static value

fit ansatz yQ (µh) = 1 +η1µh

+η2µ2

h(inspired by HQET)

curvature denotes a large 1/µ2h

contribution to ratios yQ


b-mass computation

• use the chain equation

yQ (µ(2)h ) yQ (µ

(3)h ) . . . yQ (µ

(K+1)h ) = λK(γ−1) Qh(µ

(K+1)h )

Qh(µ(1)h )

·(ρ(µ

(K+1)h , µ∗)

ρ(µ(1)h , µ∗)

)γ−1

• Evaluate the (lhs) with yQ (µ(n)h ) set to the best fit values

• Qh(µ(1)h ) accurately computable in the charm region.

• Adjust (λ, µ(1)h ) such that K integer and Qh(µ

(K+1)h ) ≡ Qexpt

B

→ Obtain b-quark mass: µb = λKµ(1)h

• strong cancellations of perturbative factors ρ’s in the ratios:→ subpercent dependence on ρ’s PT-order

• No need to tune exponent γ. A large range of choices γ ∈ [0, 1) provides fullycompatible final results, while allowing control on(a) discretisation effects(b) HQET-inspired fit of ratios vs. 1/µh


b-mass results

• mb(MS,mb) = 4.26(7)stat+fit (4)ratios (2)ch (3)discr (3)ρ−PT (11)scale (6)RC−syst GeV = 4.26(16) GeV

• Dominant sources of ETMC uncertainty fromscale setting and quark mass RC systematics.

Nf = 2 + 1 + 1

Nf = 2

Nf = 2 + 1

ETMC ’13

ALPHA ’13

HPQCD ’10

HPQCD ’13


PDG

mb(MS, mb) [GeV]4.64.44.24

• We use ratio method and set the triggering quark

mass µ(1)h = mc , we get full non-perturbative

determination of (scheme and scale independent)quark mass ratio

mb/mc = 4.40(8)

(mb/mc = 4.40(6)stat+fit (3)ratios (2)ch(3)discr )

Nf = 2 + 1 + 1

Nf = 2 + 1

HPQCD ’10


mb/mc

4.64.44.2


Other B-observables

• Use scaling analysis and employ ratio method on observables(fhs/Mhs)×Mexpt

Bs

−→ small discr. effects and no scale setting uncertainty.

• Ongoing analysis for computation of fBs , fBs/fB , fB and ξ.

• ETMC 2013 results (preliminary) from Nf = 2 + 1 + 1 simulations:

fBs = 235(9) MeV

fB = 196(9) MeV

fBs/fB = 1.201(25)

[ETMC, Carrasco et al. PoS LAT2013]


Summary

• ETMC has a rich program of precision computations in the charm and bottomsector using simulations with Nf = 2 + 1 + 1 dynamical flavours.

• Accurate determinations for quark mass ratios mc/ms and mb/mc (totaluncertainty ∼ 1.5− 1.8%).

• Accurate calculation for mb using the Ratio Method. Total uncertainty on mcand mb results mainly due to scale setting uncertainty.Heavy quark systematics in mb calculation well under control.

• Precision computation for D-sector pseudoscalar decay constants (uncertainties∼ 1.3− 2.1%).

• On going analysis for improving precision of B-sector pseudoscalar decayconstants. Determination of ξ.

Lattice QCD has definitely entered the era of precision results aiming atsystematically improving control of systematic uncertainties.

The consistency among heavy flavour lattice results obtained from muchdifferent lattice QCD formulations and methods (by a few groups) is veryreassuring.


Summary of (preliminary) Results from ETMC

mc(MS,mc) (GeV) mc/ms fDs (MeV) fD (MeV) fDs/fD

1.348(42) 11.62(16) 248.5(3.8) 209.5(4.3) 1.186(15)

mb(MS,mb) (GeV) mb/mc fBs (MeV) fB (MeV) fBs/fB4.26(16) 4.40(8) 235(9) 196(9) 1.201(25)

Thank you for your attention!


extra slides


Mh` scaling analysis

0 10 20 30 40 50m

l(MeV)

4,2

4,4

4,6

4,8

5

MD

r 0

β=1.90 V/a4=32

3x64

β=1.90 V/a4=24

3x48

β=1.95 V/a4=32

3x64

β=1.95 V/a4=24

3x48

β=2.10 V/a4=48

3x96

Continuum Limit

using fit ansatz: Mh` = P0 + P1m` + P2m2` + P3a2


fDs analysis using scale r0

CL-phys. pointβ = 2.10β = 1.95β = 1.90

µℓ (GeV)

f cs(G

eV)

0.050.040.030.020.010.00

0.320

0.310

0.300

0.290

0.280

0.270

0.260

0.250

0.240

0.230

fDs = 251(9) MeV


Improved plateaux

GEVPSmeared-Local

β = 2.10

x0/a

M(ℓh)

eff(x

0)

40353025201510

0.70

0.69

0.68

0.67

0.66

0.65

0.64

0.63


heavy flavour precision physics from nf=2+1+1 lattice ... · etmc { n f = 2 +1 +1 action glue :...

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