Intro FLAG activities Aims/Criteria Examples Outlook

The FLAG working group: making lattice
results accessible to phenomenologists
Gilberto Colangelo(on behalf of the FLAG)

Tsukuba, June 10. 2009

Intro FLAG activities Aims/Criteria Examples Outlook

OutlineIntroduction
FLAG activities
Aims and criteria
Examplesf+ (0) and fK /fπ
Low energy constants
OutlookIntro FLAG activities Aims/Criteria Examples Outlook

What/Who is FLAG?
FLAG =FLAVIAnet Lattice Averaging Group

European network
on Flavour Physics
Start: 1.10.2006
End: 30.09.2010“Entering the high-precision era of flavour physics through thealliance of lattice simulations, effective field theories and experiment”

Intro FLAG activities Aims/Criteria Examples Outlook

What/Who is FLAG?
FLAG =FLAVIAnet Lattice Averaging Group

Members:
Gilberto Colangelo (Bern)
Stephan Dürr (Jülich, BMW)
Andreas Jüttner (Mainz, RBC/UKQCD)
Laurent Lellouch (Marseille, BMW)
Heiri Leutwyler (Bern)
Vittorio Lubicz (Rome 3, ETM)
Silvia Necco (CERN, Alpha)
Chris Sachrajda (Southampton, RBC/UKQCD)
Silvano Simula (Rome 3, ETM)
Tassos Vladikas (Rome 2, Alpha and ETM)
Urs Wenger (Bern, ETM)
Hartmut Wittig (Mainz, Alpha)Intro FLAG activities Aims/Criteria Examples Outlook

What/Who is FLAG?
FLAG =FLAVIAnet Lattice Averaging Group

History and status:◮ FLAG start: Orsay, November 2007
◮ Meetings: Bern, March 2008 and April 2009
◮ draft and webpage are being finalized◮ will be made public in summer 2009∗∗ Statements and numbers in the present talk are preliminary

Intro FLAG activities Aims/Criteria Examples Outlook

What exactly will FLAG offer?
An answer to the questions◮ what is the best lattice value for quantity X ?
◮ what is a reliable estimate of the uncertainty?

in a way easily accessible to non-experts
Quantities considered in the first edition:◮ light quark masses◮ LEC’s◮ decay constants◮ form factors◮ BK

Intro FLAG activities Aims/Criteria Examples Outlook

What exactly will FLAG offer?
For each quantity we provide:◮ complete list of references◮ summary of relevant formulae and notation◮ summary of the essential aspects of each calculation:

lattice action
number of dynamical quarks (Nf )◮ minimal value and range of quark masses◮ minimal value and range of lattice spacing◮ maximal value and range of lattice volumes◮ renormalization method (where applicable)◮◮

in a unified and easy to read (color coding) manner◮ averages (if sensible)◮ and a “lattice dictionary” for non-experts(details of lattice actions, etc.)

Intro FLAG activities Aims/Criteria Examples Outlook

Color coding – our present definition◮ chiral extrapolation⋆

Mπ,min < 250 MeV• 250 MeV ≤ Mπ,min ≤ 400 MeV¥ Mπ,min > 400 MeV

Intro FLAG activities Aims/Criteria Examples Outlook

Color coding – our present definition◮ chiral extrapolation⋆

Mπ,min < 250 MeV• 250 MeV ≤ Mπ,min ≤ 400 MeV¥ Mπ,min > 400 MeV◮ continuum extrapolation⋆

3 or more lattice spacings, at least 2 points below 0.1 fm• 2 or more lattice spacings, at least 1 point below 0.1 fm¥ otherwise

Intro FLAG activities Aims/Criteria Examples Outlook

Color coding – our present definition◮ chiral extrapolation⋆

Mπ,min < 250 MeV• 250 MeV ≤ Mπ,min ≤ 400 MeV¥ Mπ,min > 400 MeV◮ continuum extrapolation⋆

3 or more lattice spacings, at least 2 points below 0.1 fm• 2 or more lattice spacings, at least 1 point below 0.1 fm¥ otherwise◮ finite volume effects⋆(Mπ L)min > 4 or at least 3 volumes• (Mπ L)min > 3 and at least 2 volumes¥ otherwise

Intro FLAG activities Aims/Criteria Examples Outlook

Color coding – our present definition◮ chiral extrapolation⋆

Mπ,min < 250 MeV• 250 MeV ≤ Mπ,min ≤ 400 MeV¥ Mπ,min > 400 MeV◮ continuum extrapolation⋆

3 or more lattice spacings, at least 2 points below 0.1 fm• 2 or more lattice spacings, at least 1 point below 0.1 fm¥ otherwise◮ finite volume effects⋆(Mπ L)min > 4 or at least 3 volumes• (Mπ L)min > 3 and at least 2 volumes¥ otherwise◮ renormalization (where applicable)⋆

non-perturbative• 2-loop perturbation theory (converging series)¥ otherwise

Intro FLAG activities Aims/Criteria Examples Outlook

Averages
Different lattice results will be averaged if◮ published[lattice proceedings not enough]◮ no red tags
◮ same Nf[no average of Nf = 2 and Nf = 3 calculations]Final FLAG number:◮ average or single no-red-tag Nf = 3 number (if available)◮ average or single no-red-tag Nf = 2 number (if available)

If both Nf = 3 and Nf = 2 numbers available:
agreement ⇒ more confidence in the final number

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Experiment + unitarity
Unitarity + experiment:

PDG (08)|Vud |2 + |Vus |2 + |Vub |2 = 1
Experiment:[|Vub | = 3.39(36) · 10−3 ]FLAVIAnet Kaon WG (08)

|Vus f+ (0)| = 0.21661(47)¯¯¯ Vus fK ¯¯¯¯ V fπ ¯ = 0.27599(59)ud3 relations and 4 unknowns
determine anyone of Vud , Vus , f+ (0) or fK /fπ⇒ get the other threeIntro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπ

LECs

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Lattice calculations of f+ (0) and fK /fπNf0.9644(33)(34)(14) 2+1
20.956(3)(5)
20.9647(15)stat0.968(9)(6)
220.967(6)RBC/UKQCD 08
ETM 08QCDSF 07
RBC 06JLQCD 05

Legenda publication status:

A = published article
P = preprint
C = conference proceedingsACCACaction• ⋆• •¥
¥¥⋆
⋆
⋆¥•

¥
¥
¥

DWFmax. tmQCD
clover (NP)DWF
clover (NP)Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Nf
22+12+12+122+12+12+122+12+1pu

fK /fπ1.210(6)(15)(9)+61.197(3)(−13)
1.191(16)(16)
1.189(20)
1.227(9)(24)
1.18(1)(1)
1.189(2)(7)1.205(18)(62)
1.21(3)
1.218(2)(+11−24 )1.210(4)(13)

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Lattice calculations of f+ (0) and fK /fπ

ETM 09MILC 09
AUBIN 08
PACS-CS 08
ETM 08A
BMW 08HPQCD/UKQCD 08
RBC/UKQCD 07
QCDSF/UKQCD 07
NPLQCD 07
MILC 04

PAC
PA
CA
A
CAA•⋆⋆⋆•⋆⋆•••⋆••¥¥•⋆•⋆⋆¥•⋆⋆•¥¥⋆⋆¥•¥•action
max. tmQCD
KSMILCMILCKSMILC /DWF
clover (NP)max. tmQCD
impr. Wilson
KSHISQMILC
DWF
clover (NP)KS MILC /DWFKSMILCMILCIntro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπ

LECs

Lattice calculations
f+(0) of f+ (0) and fK /fπ
0.95

0.96

0.97

0.98

0.99
SPQcdR 05
JLQCD 05
RBC 06QCDSF 07
ETM 08
RBC/UKQCD 08
our estimate

nuclear β decay
semi-inclusive τ decay
KN 08
CEEKPP 05
JOP 04
BT 03
LR 84
0.95

0.96

0.97

0.980.99

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Lattice calculations
fK/fπof f+ (0) and fK /fπ
1.14

1.16

1.18

1.20

1.22

1.24

1.26
QCDSF/UKQCD 07
ETM 08A
ETM 09MILC 04
NPLQCD 07
RBC/UKQCD 07
HPQCD/UKQCD 08
BMW 08
PACS-CS 08
ALVdW 08
MILC 09
our estimate
nuclear β decay
semi-inclusive τ decay

1.14

1.16

1.18

1.20

1.22

1.24

1.26

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπ

LECs

Lattice calculations of f+ (0) and fK /fπAccording to our policy only three results are relevant
f+ (0) = 0.964(3)(4)
fK /fπ =+61.197(3)(−13 )fK /fπ = 1.189(2)(7)

RBC/UKQCD 08
MILC 09
HPQCD/UKQCD 08

all three can be translated into a value for Vus :|Vus | = 0.2246(9)(9)+23

RBC/UKQCD 08|Vus | = 0.2247(7)(−11 )MILC 09|Vus | = 0.2261(6)(13)

HPQCD/UKQCD 08— and averaged —|Vus | = 0.2253(4)(9)

our average

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Lattice calculations of f+ (0) and fK /fπAccording to our policy only three results are relevant
f+ (0) = 0.964(3)(4)
fK /fπ =+61.197(3)(−13 )fK /fπ = 1.189(2)(7)

RBC/UKQCD 08
MILC 09
HPQCD/UKQCD 08

or of any other of the four unknowns|Vud | = 0.97427(9)(20)

our averagef+ (0) = 0.9620(20)(37)

our averagefK /fπ = 1.1919(16)(48)

our average

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Other sources of information on Vud and Vus
Super-allowed nuclear β decays|Vud | = 0.97425(22)⇒ |Vus | = 0.22544(95)Hardy & Towner 08

f+ (0) = 0.9608(46)fK /fπ = 1.1927(59)τ → [hadrons(S = 1)] + ν decays|Vus | = 0.2165(26)exp (5)th⇒ |Vud | = 0.9763(6)Problematic data:Pf+ (0) = 1.001(12)exclusive channels 6= inclusive

Gamiz et al. 07

fK /fπ = 1.245(16)Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Comparison between lattice and other determinations
0.21

0.220.23

0.972

0.974

0.976

0.978

0.972

0.974

0.976

0.978

ETM 09MILC 09
AUBIN 08
PACS-CS 08
RBC/UKQCD 08
ETM 08
ETM 08A
BMW 08HPQCD/UKQCD 08
RBC/UKQCD 07
QCDSF/UKQCD 07
NPLQCD 07
QCDSF 07
RBC 06JLQCD 05
SPQCDR 05
MILC 04
our estimate
nuclear β decay
semi-inclusive τ decay
0.21

0.22

0.23

|Vus|

|Vud|

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

SU(3) low-energy constants

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Determination based on masses and decay constants

Nfaction(a) RBC/UKQCD 08 2+1 A• ⋆ ¥ ⋆ DW⋆¥¥¥
clover(b) PACS-CS 08
2+1 P(c) MILC 09
2+1 P ⋆ ∗ ⋆⋆• KS∗
Based on value of lowest pion mass. Average of tastes would be more appropriate, but cannot be reconstructed from the paper.
1/3

F0 [MeV] Σ0 [MeV]F /F0(a) 66.1(5.2)
1.229(59)(b) 83.8(6.4) 290(15)1.078(44)+5+13(c)242(9)(−17 )(4) 1.15(5)( −3 )B/B0Σ/Σ01.03(05) 1.55(21)1.089(15) 1.245(10)+38
1.52(17)(−15 )Fπ /F
1.062(8)+61.052(2)(−3 )Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

SU(3) low-energy constants

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Determination based on masses and decay constants

Nfaction(a) RBC/UKQCD 08 2+1 A• ⋆ ¥ ⋆ DW⋆¥¥¥clover(b) PACS-CS 082+1 P(c) MILC 092+1 P ⋆ ∗ ⋆⋆• KS∗
Based on value of lowest pion mass. Average of tastes would be more appropriate, but cannot be reconstructed from the paper.

(a)
(b)
(c)

103 L4103 L5103 L6103 L8103 (2L6 −L4 ) 103 (2L8 −L5 )0.14(8)(-) 0.87(10)(-) 0.07(6)(-) 0.56(4)(-) 0.00(4)(-)
0.24(4)(-)-0.06(10)(-) 1.45(7)(-) 0.02(5)(-) 0.62(4)(-) 0.10(2)(-)-0.21(3)(-)+3+2+2+20.1(3)(−1 ) 1.4(2)(−1 ) 0.2(2)(−1 ) 0.8(1)(1) 0.3(1)(−3 )0.3(1)(1)

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

SU(3) low-energy constants
Determination based on masses and decay constants

3MILC 09
PACS-CS 08
RBC/UKQCD 08
NPLQCD 07
Bijnens 09
GL 85

310 L

232

1

100-1-1

L4-2

L5L6L8

2L6-L4 2L8-L5-2

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECsNf
JLQCD/TWQCD 08 2
RBC/UKQCD 08
2+1
PACS-CS 08
2+1
ETM 08A2JLQCD/TWQCD 08 2A. Hasenfratz et al 08 2
DeGrand-Schaefer 07 2pubch licat
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SU(2) low-energy constantsA • ¥¥ ⋆A • ¥⋆ ⋆A ⋆ ¥¥ ¥A • ••AAAobs.

F [MeV]M π , FπM π , FπM π , Fπ",hrπ2 iV , cπV
CPP,AA (ǫ)
CPP,AA (ǫ)
RTM (ǫ)79.0(2.5)(0.7)
81.2(2.9)(5.7)
89.4(3.3)
86.6(7)(7)
87.3(5.6)
90(4)
84(5)

` +4.2 ´−0.0

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

Nf
CERN-TOV 07
2ETM 082
JLQCD/TWQCD 08 2RBC/UKQCD 08 2+1
PACS-CS 08
2+1
ETM 08A2pubch licat
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SU(2) low-energy constantsA • •¥ ⋆A • •• ⋆A • ¥¥ ⋆A • ¥⋆ ⋆A ⋆ ¥¥ ¥A • ••obs.

ℓ̄3M π , FπMπ , F π
M π , FπM π , FπM π , Fπ",hrπ2 iV , cπV

3.0(5)(1)
3.42(8)(10)(27)` ´
3.38(40)(24) +31−0
3.13(33)(24)
3.14(23)
3.2(8)(2)

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECsNf
ETM 082JLQCD/TWQCD 08 2RBC/UKQCD 08 2+1
PACS-CS 08
2+1
ETM 08A
2JLQCD/TWQCD 09 2pubch licatira ionco l ext stafinntinu rapo tus
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SU(2) low-energy constantsA • •• ⋆A • ¥¥ ⋆A • ¥⋆ ⋆A ⋆ ¥¥ ¥A • ••P • ¥¥obs.

ℓ̄4Mπ , F π
M π , FπM π , FπM π , Fπ",hrπ2 iV , cπV
hr π2 iV , hrπ2 iS , cπV

4.59(4)(2)(13)` ´
4.12(35)(30) +31−04.43(14)(77)
4.04(19)
4.4(2)(1)
4.09(50)(52)

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

ETM 082JLQCD/TWQCD 09 2RBC/UKQCD 08 2+1Bijnens et al 98puNfblica ti
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eSU(2) low-energy constants

APAobs.

• • •• ¥ ¥• ¥ ⋆ℓ̄6Mπ ,Fπ ,hrπ2 iV , cπV 14.9(1.2)(0.7)
hr π2 iV , hrπ2 iS , cπV 11.9(0.7)(1.0)
FVπ (q 2 )12.2(9)16.0(5)(7)

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπLECs

SU(2) low-energy constants
F65707580859095100JLQCD/TWQCD 08
ETM 08JLQCD/TWQCD 08
HHS 08
DGS 07

RBC/UKQCD 08
PACS-CS 08

our estimate

CD 04
6570758085
MeV9095100

f+ (0) and fK /fπ

Intro FLAG activities Aims/Criteria Examples Outlook

LECs

SU(2) low-energy constants
l30123456
CERN-TOV 07
ETM 08JLQCD/TWQCD 08
ETM 08A

RBC/UKQCD 08
PACS-CS 08

our estimate

GL 840123456

f+ (0) and fK /fπ

Intro FLAG activities Aims/Criteria Examples Outlook

LECs

SU(2) low-energy constants
l4
2.533.544.55ETM 08
JLQCD/TWQCD 08
ETM 08AJLQCD/TWQCD 09

RBC/UKQCD 08
PACS-CS 08

our estimate

CGH 012.533.544.55

Intro FLAG activities Aims/Criteria Examples Outlook

f+ (0) and fK /fπ

LECs

SU(2) low-energy constants
l681012141618

ETM 08JLQCD/TWQCD 08

RBC/UKQCD 08

our estimate

BCT 9881012141618

Intro FLAG activities Aims/Criteria Examples Outlook

Outlook◮ FLAG aims to provide a summary of lattice results relevant

for the phenomenology accessible to non-experts◮ paper and webpage will become public this summer◮ we plan to have yearly updates◮ for the future we are open to and encourage contributions

from outside Europe◮ if you are interested and/or have suggestions or criticisms

you are most welcome