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Review on results by the FLAG working group Hadron 2011 K - - PowerPoint PPT Presentation

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Review on results by the FLAG working group Hadron 2011 K unstlerhaus, M unchen 13.-17.06.2011 Andreas J uttner for Theory Division Review on results by the FLAG working group Andreas J uttner 0 Strong claims were recently made

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SLIDE 1

Review on results by the FLAG working group Hadron 2011 K¨ unstlerhaus, M¨ unchen

13.-17.06.2011 Andreas J¨ uttner for Theory Division

Review on results by the FLAG working group Andreas J¨ uttner

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SLIDE 2

Strong claims were recently made based on lattice QCD results: “We find a (2-3)σ tension in the unitarity triangle”

Laiho, Lunghi, Van de Water, PRD 81 (2010) 034503

“. . . confirming CKM unitarity at the permille level”

FLAG arXiv:1011.4408

“. . . we find evidence of new physics in both Bd and Bs systems . . . ”

CKMfitter Group PRD 83 (2011) 036004

“Possible evidence for the breakdown of the CKM-paradigm of CP-violation”

Lunghi, Soni, PLB 697, 323-328 (2011) Review on results by the FLAG working group Andreas J¨ uttner 1

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SLIDE 3

Strong claims were recently made based on lattice QCD results: “We find a (2-3)σ tension in the unitarity triangle”

Laiho, Lunghi, Van de Water, PRD 81 (2010) 034503

“. . . confirming CKM unitarity at the permille level”

FLAG arXiv:1011.4408

“. . . we find evidence of new physics in both Bd and Bs systems . . . ”

CKMfitter Group PRD 83 (2011) 036004

“Possible evidence for the breakdown of the CKM-paradigm of CP-violation”

Lunghi, Soni, PLB 697, 323-328 (2011)

such statements require a precise screening of lattice results and therefore a good understanding of lattice QCD

Review on results by the FLAG working group Andreas J¨ uttner 1

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SLIDE 4

FLAG

→ Flavia Net Lattice Averaging Group (FLAG) was founded to allow also to an outsider to judge the quality and ’state-of-the-art’-fulness of lattice results People: G. Colangelo, S. D¨ urr, A. J., L. Lellouch, H. Leutwyler, V. Lubicz, S. Necco,

  • C. Sachrajda, S. Simula, A. Vladikas, U. Wenger, H. Wittig

Review on results by the FLAG working group Andreas J¨ uttner 2

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SLIDE 5

FLAG

→ Flavia Net Lattice Averaging Group (FLAG) was founded to allow also to an outsider to judge the quality and ’state-of-the-art’-fulness of lattice results People: G. Colangelo, S. D¨ urr, A. J., L. Lellouch, H. Leutwyler, V. Lubicz, S. Necco,

  • C. Sachrajda, S. Simula, A. Vladikas, U. Wenger, H. Wittig

→ quantities we consider: mu, md, ms, f Kπ

+ (0), fK/fπ, BK, NLO LEC’s,

potentially more in the future → What is the current lattice value? Is the quoted uncertainty reliable? → provides:

relevant formulae and notation detailed quality assessment average/recommended range in those cases where quality of lattice results considered very high lattice dictionary for non-experts details of every single lattice simulation (appendix)

→ planned periodic updates of arXiv:1011.4408, http://itpwiki.unibe.ch/flag

Review on results by the FLAG working group Andreas J¨ uttner 2

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SLIDE 6

FLAG

→ Flavia Net Lattice Averaging Group (FLAG) was founded to allow also to an outsider to judge the quality and ’state-of-the-art’-fulness of lattice results People: G. Colangelo, S. D¨ urr, A. J., L. Lellouch, H. Leutwyler, V. Lubicz, S. Necco,

  • C. Sachrajda, S. Simula, A. Vladikas, U. Wenger, H. Wittig

→ quantities we consider: mu, md, ms, f Kπ

+ (0), fK/fπ, BK, NLO LEC’s,

potentially more in the future → What is the current lattice value? Is the quoted uncertainty reliable? → provides:

relevant formulae and notation detailed quality assessment average/recommended range in those cases where quality of lattice results considered very high lattice dictionary for non-experts details of every single lattice simulation (appendix)

→ planned periodic updates of arXiv:1011.4408, http://itpwiki.unibe.ch/flag Other efforts: Laiho, Lunghi, Van de Water: Nf = 2 + 1 light and heavy-light meson observables for CKM-triangle analysis

Lattice QCD inputs to the CKM unitarity triangle analysis, Phys.Rev. D81 (2010) 034503 http://www.latticeaverages.org

Review on results by the FLAG working group Andreas J¨ uttner 2

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SLIDE 7

Why lattice QCD?

perturbation theory works well for weak coupling bound state observables like the proton mass or the B-decay constant for example cannot be predicted by perturbation theory

Review on results by the FLAG working group Andreas J¨ uttner 3

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SLIDE 8

Why lattice QCD?

perturbation theory works well for weak coupling bound state observables like the proton mass or the B-decay constant for example cannot be predicted by perturbation theory but simulations of lattice QCD can do this:

BMW Collaboration, Science 322 (2008) 1224-1227

NOTE: only three input-parameters!!!

Review on results by the FLAG working group Andreas J¨ uttner 3

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SLIDE 9

Lattice QCD

What is . . . ? QCD Nc 3 Nf, fundamental 1+1+1+1+1+1 SU(2) iso-spin brk.

"

mπ 135MeV V ∞ a

Review on results by the FLAG working group Andreas J¨ uttner 4

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SLIDE 10

Lattice QCD

What is . . . ? QCD Lattice QCD Nc 3 3 Nf, fundamental 1+1+1+1+1+1 0, 2, 2+1, 2+1+1 SU(2) iso-spin brk.

" %

mπ 135MeV m sim

π

V ∞ 2-3fm a 0.05-0.1fm

Review on results by the FLAG working group Andreas J¨ uttner 4

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SLIDE 11

Systematics

most results systematics-dominated extrapolation of lattice data to the physical point very often tricky

Review on results by the FLAG working group Andreas J¨ uttner 5

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SLIDE 12

Systematics

most results systematics-dominated extrapolation of lattice data to the physical point very often tricky a → 0 Symanzik eff. th.

0.01 0.02 0.03 0.5 0.55 0.6 (a/r0)2 r0fDs A.J., J. Heitger, JHEP 0905 (2009) 101 Review on results by the FLAG working group Andreas J¨ uttner 5

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SLIDE 13

Systematics

most results systematics-dominated extrapolation of lattice data to the physical point very often tricky a → 0 Symanzik eff. th.

0.01 0.02 0.03 0.5 0.55 0.6 (a/r0)2 r0fDs A.J., J. Heitger, JHEP 0905 (2009) 101 Review on results by the FLAG working group Andreas J¨ uttner 5

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SLIDE 14

Systematics

most results systematics-dominated extrapolation of lattice data to the physical point very often tricky a → 0 Symanzik eff. th.

0.01 0.02 0.03 0.5 0.55 0.6 (a/r0)2 r0fDs A.J., J. Heitger, JHEP 0905 (2009) 101

mq → mphys

q

chiral eff. th.

also talks by Brandt, Zanotti Brandt’s talk yesterday Review on results by the FLAG working group Andreas J¨ uttner 5

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SLIDE 15

Systematics continued

renormalisation, e.g. quark masses and BK although techniques for full non-perturbative renormalisation and running

Martinelli et al., Nucl. Phys. B445 (1995) 81-108, L¨ uscher et al., Nulc. Phys. B384 (1992) 168-228

are standard by now some collaborations still employ perturbation theory

Review on results by the FLAG working group Andreas J¨ uttner 6

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SLIDE 16

Systematics continued

renormalisation, e.g. quark masses and BK although techniques for full non-perturbative renormalisation and running

Martinelli et al., Nucl. Phys. B445 (1995) 81-108, L¨ uscher et al., Nulc. Phys. B384 (1992) 168-228

are standard by now some collaborations still employ perturbation theory scale setting finite size errors chosen discretisation . . .

Review on results by the FLAG working group Andreas J¨ uttner 6

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SLIDE 17

FLAG criteria

chiral extrapolation continuum extrapolation finite volume errors renormalisation renormalisation scale running publication status

Review on results by the FLAG working group Andreas J¨ uttner 7

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FLAG criteria

chiral extrapolation continuum extrapolation finite volume errors renormalisation renormalisation scale running publication status FLAG’s colour coding: ⋆ when the systematic error has been estimated in a satisfactory manner and convincingly shown to be under control

  • when a reasonable attempt at estimating the systematic error has been

made, although this could be improved;

  • when no or a clearly unsatisfactory attempt at

Review on results by the FLAG working group Andreas J¨ uttner 7

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SLIDE 19

Current color coding

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
  • therwise

Finite-volume effects: ⋆ Mπ,minL > 4 or at least 3 volumes

  • Mπ,minL > 3 and at least 2 volumes
  • therwise

Review on results by the FLAG working group Andreas J¨ uttner 8

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Current colour coding

Renormalisation (where applicable): ⋆ non-perturbative

  • 2-loop perturbation theory
  • therwise

Publication status:

A published or plain update of published results P preprint C conference contribution

Only published results enter averages (where applicable) results with different number of dynamical quark flavours considered separately

Review on results by the FLAG working group Andreas J¨ uttner 9

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SLIDE 21

A FLAG example - the kaon sector

K leptonic decay |Vus| s u Aµ K(pK) K → π semi-leptonic decay |Vus| u s d Vµ π+(pπ) K 0(pK) Γ(K → µ¯ νµ(γ)) Γ(π → µ¯ νµ(γ)) = mK (1 − m2

µ/m2 K )

mπ(1 − m2

µ/m2 π) 0.9930(35) × |Vus|2

|Vud|2

  • fK

fπ 2

(Marciano, Phys.Rev.Lett. 2004)

ΓK→πlν = C2

K

G2

Fm5 K

192π2 I SEW[1 + ∆SU(2) + ∆EM] × |Vus|2|f Kπ

+ (0)|2

Review on results by the FLAG working group Andreas J¨ uttner 10

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SLIDE 22

A FLAG example - the kaon sector

1.14 1.14 1.16 1.16 1.18 1.18 1.20 1.20 1.22 1.22 1.24 1.24 1.26 1.26

fK/fπ

ETM 09 ETM 07 QCDSF/UKQCD 07 NPLQCD 06 RBC/UKQCD 08 HPQCD/UKQCD 07 PACS-CS 08, 08A Aubin 08 MILC 09

  • ur estimate for Nf = 2+1

Nf=2+1 Nf=2 MILC 09A JLQCD/TWQCD 09A BMW 10 MILC 04

  • ur estimate for Nf = 2

ETM 10D RBC/UKQCD 10A MILC 10 ETM 10E Nf=2+1+1

0.95 0.95 0.96 0.96 0.97 0.97 0.98 0.98 0.99 0.99 1.00 1.00

f+(0)

LR 84 Bijnens 03 Jamin 04 Cirigliano 05 Kastner 08 RBC/UKQCD 07 ETM 09A QCDSF 07 RBC 06 JLQCD 05

  • ur estimate for Nf = 2

Nf=2 Nf=2+1

K 08 C 05 J 04 B 03 L 84

RBC/UKQCD 10

  • ur estimate for Nf = 2+1

ETM 10D

agreement amongst independent lattice determinations current level of precision does not reveal dependence on flavour content

  • f simulation

Review on results by the FLAG working group Andreas J¨ uttner 10

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SLIDE 23

A FLAG example - the kaon sector

Collaboration Nf p u b l i c a t i

  • n

s t a t u s c h i r a l e x t r a p

  • l

a t i

  • n

c

  • n

t i n u u m e x t r a p

  • l

a t i

  • n

fi n i t e v

  • l

u m e e r r

  • r

s fK /fπ ETM 10E 2+1+1

C

  • 1.224(13)stat

MILC 10 2+1

C

  • ⋆

⋆ 1.197(2)(+3

−7 )

RBC/UKQCD 10A 2+1

P

  • ⋆

1.204(7)(25) BMW 10 2+1

A

⋆ ⋆ ⋆ 1.192(7)(6) JLQCD/TWQCD 09A 2+1

C

  • 1.210(12)stat

MILC 09A 2+1

C

  • ⋆

⋆ 1.198(2)(+6

−8 )

MILC 09 2+1

A

  • ⋆

⋆ 1.197(3)( +6

−13)

Aubin 08 2+1

C

  • 1.191(16)(17)

PACS-CS 08, 08A 2+1

A

⋆

  • 1.189(20)

RBC/UKQCD 08 2+1

A

  • ⋆

1.205(18)(62) HPQCD/UKQCD 07 2+1

A

  • ⋆
  • 1.189(2)(7)

NPLQCD 06 2+1

A

  • 1.218(2)(+11

−24 )

ETM 10D 2

C

  • ⋆
  • 1.190(8)stat

ETM 09 2

A

  • ⋆
  • 1.210(6)(15)(9)

QCDSF/UKQCD 07 2

C

  • ⋆

1.21(3)

FLAG arXiv:1011.4408 Review on results by the FLAG working group Andreas J¨ uttner 11

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SLIDE 24

A FLAG example - the kaon sector

For both Nf = 2 + 1 and N + f = 2 FLAG identified high quality lattice results and provides averages: FLAG averages FLAG arXiv:1011.4408: Nf f Kπ

+ (0)

fK /fπ 2+1 0.9599(34)(41) 1.193(5) 2 0.9560(57)(62) 1.210(6)(17)

Review on results by the FLAG working group Andreas J¨ uttner 12

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SLIDE 25

A FLAG example - the kaon sector

For both Nf = 2 + 1 and N + f = 2 FLAG identified high quality lattice results and provides averages: FLAG averages FLAG arXiv:1011.4408: Nf f Kπ

+ (0)

fK /fπ 2+1 0.9599(34)(41) 1.193(5) 2 0.9560(57)(62) 1.210(6)(17) Together with experimental input |Vusf Kπ

+ (0)|

= 0.2163(5)

  • fK Vus

fπVud

  • =

0.2758(5) |Vud| = 0.97425(22)

FLAVIA KAON WG Eur.Phys.J. C69 (2010) 399-424 Hardy, Towner, Phys. Rev., C79, 2009,05550 Review on results by the FLAG working group Andreas J¨ uttner 12

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SLIDE 26

A FLAG example - the kaon sector

For both Nf = 2 + 1 and N + f = 2 FLAG identified high quality lattice results and provides averages: FLAG averages FLAG arXiv:1011.4408: Nf f Kπ

+ (0)

fK /fπ 2+1 0.9599(34)(41) 1.193(5) 2 0.9560(57)(62) 1.210(6)(17) Together with experimental input |Vusf Kπ

+ (0)|

= 0.2163(5)

  • fK Vus

fπVud

  • =

0.2758(5) |Vud| = 0.97425(22)

FLAVIA KAON WG Eur.Phys.J. C69 (2010) 399-424 Hardy, Towner, Phys. Rev., C79, 2009,05550

FLAG did two kind of analysis: a) test the SM: |Vud|2 + |Vus|2 + |Vub|2

?

= 1 b) using SM-correlations

Review on results by the FLAG working group Andreas J¨ uttner 12

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SLIDE 27

FLAG tests the SM: |Vu|2 ≡ |Vud|2 + |Vus|2 + |Vub|2 = 1

0.96 0.97 0.98 0.99 1 1.01

Vud

0.220 0.225 0.230

Vus

Review on results by the FLAG working group Andreas J¨ uttner 13

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SLIDE 28

FLAG tests the SM: |Vu|2 ≡ |Vud|2 + |Vus|2 + |Vub|2 = 1

0.96 0.97 0.98 0.99 1 1.01

Vud

0.220 0.225 0.230

Vus

Review on results by the FLAG working group Andreas J¨ uttner 13

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SLIDE 29

FLAG tests the SM: |Vu|2 ≡ |Vud|2 + |Vus|2 + |Vub|2 = 1

0.96 0.97 0.98 0.99 1 1.01

Vud

0.220 0.225 0.230

Vus

Review on results by the FLAG working group Andreas J¨ uttner 13

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SLIDE 30

FLAG tests the SM: |Vu|2 ≡ |Vud|2 + |Vus|2 + |Vub|2 = 1

0.96 0.97 0.98 0.99 1 1.01

Vud

0.220 0.225 0.230

Vus

Results: Nf |Vu|2|no|Vud | |Vu|2||Vud | from f Kπ

+ (0)

|Vu|2||Vud | from fK/fπ 2+1 1.002(15) 1.0000(7) 0.9999(6) 2 1.037(36) 1.0004(10) 0.9985(16) CKM-unitarity confirmed at the per-mil level

Review on results by the FLAG working group Andreas J¨ uttner 13

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SLIDE 31

FLAG tests the SM: |Vu|2 ≡ |Vud|2 + |Vus|2 + |Vub|2 = 1

0.96 0.97 0.98 0.99 1 1.01

Vud

0.220 0.225 0.230

Vus

lattice result for f+(0), Nf = 2+1 lattice result for fK/fπ, Nf = 2+1 lattice results for Nf = 2+1 combined lattice result for f+(0), Nf = 2 lattice result for fK/fπ, Nf = 2 lattice results for Nf = 2 combined unitarity nuclear β decay

Results: Nf |Vu|2|no|Vud | |Vu|2||Vud | from f Kπ

+ (0)

|Vu|2||Vud | from fK/fπ 2+1 1.002(15) 1.0000(7) 0.9999(6) 2 1.037(36) 1.0004(10) 0.9985(16) CKM-unitarity confirmed at the per-mil level

Review on results by the FLAG working group Andreas J¨ uttner 13

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SLIDE 32

If FLAG assumes first row unitarity

0.21 0.21 0.22 0.22 0.23 0.23

Nf = 2+1 Nf = 2 τ−decay τ−decay and e

+e

  • Vus

Nf=2+1+1

0.972 0.972 0.974 0.974 0.976 0.976 0.978 0.978 ETM 09 ETM 07 QCDSF/UKQCD 07 ETM 09A QCDSF 07

x

RBC 06 JLQCD 05 MILC 09 Aubin 08 PACS-CS 08, 08A BMW 10 RBC/UKQCD 07 RBC/UKQCD 08 NPLQCD 06 MILC 04

  • ur estimate for Nf = 2+1

y

nuclear β-decay Gamiz 08 Maltman 09

G 08 M 09

MILC 09A JLQCD/TWQCD 09A

x

RBC/UKQCD 10

H 09

  • ur estimate for Nf = 2

y

Vud

HPQCD/UKQCD 07 ETM 10D

x

RBC/UKQCD 10A MILC 10 ETM 10E

x

ETM 10D

x

Nice result: Assuming first row unitarity lattice QCD makes prediction for |Vud| with same precision as super-allowed nuclear beta decays and fully compatible with it

Review on results by the FLAG working group Andreas J¨ uttner 14

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SLIDE 33

BK - neutral kaon mixing

ǫK ∝ BK - hyperbola in the ¯ η − ¯ ρ-plane ǫK = exp(iφǫ) sin(φǫ) ℑ[ ¯ K 0|H∆S=2

eff

|K 0] ∆MK + ℑ(A0) ℜ(A0)

  • Review on results by the FLAG working group

Andreas J¨ uttner 15

slide-34
SLIDE 34

BK - neutral kaon mixing

ǫK ∝ BK - hyperbola in the ¯ η − ¯ ρ-plane ǫK = exp(iφǫ) sin(φǫ) ℑ[ ¯ K 0|H∆S=2

eff

|K 0] ∆MK + ℑ(A0) ℜ(A0)

  • tremendous progress in the last 5 years or so:

cheaper lattice actions break chiral symmetry → lattice 4-fermion operator mixing under renormalisation becomes complicated task use of chiral symmetry respecting fermion formulations have allowed for breakthrough in predictions for BK

Review on results by the FLAG working group Andreas J¨ uttner 15

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SLIDE 35

BK - neutral kaon mixing

ǫK ∝ BK - hyperbola in the ¯ η − ¯ ρ-plane ǫK = exp(iφǫ) sin(φǫ) ℑ[ ¯ K 0|H∆S=2

eff

|K 0] ∆MK + ℑ(A0) ℜ(A0)

  • tremendous progress in the last 5 years or so:

cheaper lattice actions break chiral symmetry → lattice 4-fermion operator mixing under renormalisation becomes complicated task use of chiral symmetry respecting fermion formulations have allowed for breakthrough in predictions for BK BK naively in lattice scheme, matching to MS done in perturbation theory alternative: cite Renormalisation Group Invariant BK: ˆ BK ˆ BK = ¯ g(µ)2 4π −γ0/(2β0) exp ¯

g(µ)

dg γ(g) β(g) + γ0 β0g

  • BK (µ)

lattice can in principle provide ˆ BK in a fully non-perturbative way

Review on results by the FLAG working group Andreas J¨ uttner 15

slide-36
SLIDE 36

BK - neutral kaon mixing

Collaboration Nf p u b l i c a t i

  • n

s t a t u s c

  • n

t i n u u m e x t r a p

  • l

a t i

  • n

c h i r a l e x t r a p

  • l

a t i

  • n

fi n i t e v

  • l

u m e r e n

  • r

m a l i s a t i

  • n

r u n n i n g BK ˆ BK SWME 11 2+1

P

⋆

  • 0.523(7)(26)

0.716(10)(35) RBC/UKQCD 10B 2+1

P

  • ⋆

⋆

  • 0.549(5)(26)

0.749(7)(26) SWME 10 2+1

A

⋆

  • 0.529(9)(32)

0.724(12)(43) Aubin 09 2+1

A

  • ⋆
  • ⋆
  • 0.527(6)(21)

0.724(8)(29) RBC/UKQCD 07A, 08 2+1

A

  • ⋆

⋆

  • 0.524(10)(28)

0.720(13)(37) HPQCD/UKQCD 06 2+1

A

  • ∗

⋆

  • 0.618(18)(135)

0.83(18) ETM 10A 2

A

⋆

  • ⋆
  • 0.516(18)(12)

0.729(25)(17) JLQCD 08 2

A

  • ⋆
  • 0.537(4)(40)

0.758(6)(71) RBC 04 2

A

  • †

⋆

  • 0.495(18)

0.699(25) UKQCD 04 2

A

  • †
  • 0.49(13)

0.69(18)

Review on results by the FLAG working group Andreas J¨ uttner 16

slide-37
SLIDE 37

BK - neutral kaon mixing

0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 ETM 10A JLQCD 08 RBC 04 UKQCD 04 SWME 10 SWME 11 RBC/UKQCD 10B Aubin 09 RBC/UKQCD 09 RBC/UKQCD 07A, 08 HPQCD/UKQCD 06

  • ur estimate for Nf=2+1

BK

Nf=2 Nf=2+1 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 ETM 09D JLQCD 08 RBC 04 UKQCD 04 SWME 10 SWME 11 Aubin 09 RBC/UKQCD 09 RBC/UKQCD 10B RBC/UKQCD 07A, 08 HPQCD/UKQCD 06

  • ur estimate for Nf=2+1

BK

〉

Nf=2 Nf=2+1

Results: Nf = 2 BMS

K (2GeV) = 0.516(18)(12)

ˆ BK = 0.729(25)(17)

Aubin 09 RBC/UKQCD 10B

Nf = 2 + 1 BMS

K (2GeV) = 0.536(17)

ˆ BK = 0.738(20)

ETM 09D Review on results by the FLAG working group Andreas J¨ uttner 17

slide-38
SLIDE 38

Light quark masses mu, md, ms

quark masses cannot be measured directly in experiment procedure:

compute three experimentally measurable quantities to tune bare parameters mud = 1

2(mu + md), ms and ΛQCD

renormalisation of bare parameters

lattice QCD calculations in the iso-spin limit mu = md

Review on results by the FLAG working group Andreas J¨ uttner 18

slide-39
SLIDE 39

Light quark masses mu, md, ms

quark masses cannot be measured directly in experiment procedure:

compute three experimentally measurable quantities to tune bare parameters mud = 1

2(mu + md), ms and ΛQCD

renormalisation of bare parameters

lattice QCD calculations in the iso-spin limit mu = md electro-magnetic corrections have to be taken into account

Review on results by the FLAG working group Andreas J¨ uttner 18

slide-40
SLIDE 40

FLAG summary for quark masses

Collaboration p u b l i c a t i

  • n

s t a t u s c h i r a l e x t r a p

  • l

a t i

  • n

c

  • n

t i n u u m e x t r a p

  • l

a t i

  • n

fi n i t e v

  • l

u m e r e n

  • r

m a l i s a t i

  • n

r u n n i n g mud ms PACS-CS 10

P

⋆

  • ⋆

a 2.78(27) 86.7(2.3) MILC 10A

C

  • ⋆

⋆

  • −

3.19(4)(5)(16) – HPQCD 10

A

  • ⋆

⋆ ⋆ − 3.39(6)∗ 92.2(1.3) BMW 10A, 10B+

P

⋆ ⋆ ⋆ ⋆ b 3.469(47)(48) 95.5(1.1)(1.5) RBC/UKQCD 10A

P

  • ⋆

⋆ c 3.59(13)(14)(8) 96.2(1.6)(0.2)(2.1) Blum 10†

P

  • ⋆

− 3.44(12)(22) 97.6(2.9)(5.5) PACS-CS 09

A

⋆

  • ⋆

a 2.97(28)(3) 92.75(58)(95) HPQCD 09

A

  • ⋆

⋆ ⋆ − 3.40(7) 92.4(1.5) MILC 09A

C

  • ⋆

⋆

  • −

3.25 (1)(7)(16)(0) 89.0(0.2)(1.6)(4.5)(0.1) MILC 09

A

  • ⋆

⋆

  • −

3.2(0)(1)(2)(0) 88(0)(3)(4)(0) PACS-CS 08

A

⋆

  • −

2.527(47) 72.72(78) RBC/UKQCD 08

A

  • ⋆

⋆ − 3.72(16)(33)(18) 107.3(4.4)(9.7)(4.9) CP-PACS/ JLQCD 07

A

  • ⋆

⋆

  • −

3.55(19)(+56

−20 )

90.1(4.3)(+16.7

−4.3 )

HPQCD 05

A

  • −

3.2(0)(2)(2)(0)‡ 87(0)(4)(4)(0)‡ MILC 04, HPQCD/ MILC/UKQCD 04

A

  • −

2.8(0)(1)(3)(0) 76(0)(3)(7)(0)

table shows Nf = 2 + 1 flavour results only Review on results by the FLAG working group Andreas J¨ uttner 19

slide-41
SLIDE 41

FLAG summary for quark masses

2 2 3 3 4 4 5 5 6 6 MeV

CP-PACS 01 JLQCD 02 SPQcdR 05 QCDSF/UKQCD 04 QCDSF/UKQCD 06 ETM 07 RBC 07 MILC 04, HPQCD/MILC/UKQCD 04 HPQCD 05 MILC 07 CP-PACS/JLQCD 07 RBC/UKQCD 08 PACS-CS 08

  • ur estimate for Nf = 2

Dominguez 09

mud

Nf=2+1 Nf=2

Narison 06 Maltman 01 PDG 10 MILC 09 MILC 09A HPQCD 09 PACS-CS 09 Blum 10 JLQCD/TWQCD 08A

  • ur estimate for Nf = 2+1

BMW 10A RBC/UKQCD 10A ETM 10B MILC 10A PACS-CS 10

D 09 N 06 M 01 P 10

HPQCD 10

70 70 80 80 90 90 100 100 110 110 120 120 MeV

CP-PACS 01 JLQCD 02 ALPHA 05 SPQcdR 05 QCDSF/UKQCD 04 QCDSF/UKQCD 06 ETM 07 RBC 07 MILC 04, HPQCD/MILC/UKQCD 04 HPQCD 05 MILC 07 CP-PACS/JLQCD 07 RBC/UKQCD 08 PACS-CS 08

  • ur estimate for Nf = 2

PDG 10

ms

Nf=2+1 Nf=2

Dominguez 09 Chetyrkin 06 Jamin 06 Narison 06 Vainshtein 78 MILC 09 MILC 09A HPQCD 09 PACS-CS 09 Blum 10

  • ur estimate for Nf = 2+1

BMW 10A RBC/UKQCD 10A ETM 10B PACS-CS 10

D 09 C 06 J 06 N 06 V 78 P 10

HPQCD 10

Review on results by the FLAG working group Andreas J¨ uttner 20

slide-42
SLIDE 42

FLAG summary for quark masses

FLAG Results: Nf = 2 mud(2GeV) = 3.6(1)(2)MeV ms(2GeV) = 95(2)(6)MeV

ETM 10N

Nf = 2 + 1 mud(2GeV) = 3.43(11)MeV ms(2GeV) = 94(3)MeV

MILC 09A, RBC/UKQCD 10A, HPQCD 10 Review on results by the FLAG working group Andreas J¨ uttner 21

slide-43
SLIDE 43

FLAG summary for quark masses

FLAG Results: Nf = 2 mud(2GeV) = 3.6(1)(2)MeV ms(2GeV) = 95(2)(6)MeV

ETM 10N

Nf = 2 + 1 mud(2GeV) = 3.43(11)MeV ms(2GeV) = 94(3)MeV

MILC 09A, RBC/UKQCD 10A, HPQCD 10

PDG Result: ms(2GeV) = 101(+29

−21)MeV

Review on results by the FLAG working group Andreas J¨ uttner 21

slide-44
SLIDE 44

FLAG summary for quark masses

FLAG Results: Nf = 2 mud(2GeV) = 3.6(1)(2)MeV ms(2GeV) = 95(2)(6)MeV

ETM 10N

Nf = 2 + 1 mud(2GeV) = 3.43(11)MeV ms(2GeV) = 94(3)MeV

MILC 09A, RBC/UKQCD 10A, HPQCD 10

PDG Result: ms(2GeV) = 101(+29

−21)MeV

Note: Nf = 2 + 1 naive average would yield mud = 3.38(6) MeV and ms = 92.8(1.3)MeV

  • ur estimate leaves room for potential charm quark contributions

Review on results by the FLAG working group Andreas J¨ uttner 21

slide-45
SLIDE 45

FLAG: is the up-quark massless?

FLAG Results: Nf = 2 + 1 mu(2GeV) = 2.19(15)MeV md(2GeV) = 4.67(20)MeV

MILC + FLAG Review on results by the FLAG working group Andreas J¨ uttner 22

slide-46
SLIDE 46

FLAG: is the up-quark massless?

FLAG Results: Nf = 2 + 1 mu(2GeV) = 2.19(15)MeV md(2GeV) = 4.67(20)MeV

MILC + FLAG

determined from K + − K 0-splitting (in QCD, i.e. elm. effects subtracted) mu different from zero by 15 standard deviations error dominated by QED corrections QED contributions need to be taken into account in future lattice simulations

Review on results by the FLAG working group Andreas J¨ uttner 22

slide-47
SLIDE 47

FLAG: is the up-quark massless?

FLAG Results: Nf = 2 + 1 mu(2GeV) = 2.19(15)MeV md(2GeV) = 4.67(20)MeV

MILC + FLAG

determined from K + − K 0-splitting (in QCD, i.e. elm. effects subtracted) mu different from zero by 15 standard deviations error dominated by QED corrections QED contributions need to be taken into account in future lattice simulations PDG Result: mu(2GeV) = 1.7 − 3.3MeV md(2GeV) = 4.1 − 5.8MeV

Review on results by the FLAG working group Andreas J¨ uttner 22

slide-48
SLIDE 48

Low energy constants

NLO SU(2) constants: Σ, F, ¯ l3,4, ¯ l6, cV , ¯ l1 −¯ l2 NLO SU(3) constants: Σ0, F0, ¯ L4,5,6,8,9,10, results not always coherent yet

Review on results by the FLAG working group Andreas J¨ uttner 23

slide-49
SLIDE 49

Low energy constants

NLO SU(2) constants: Σ, F, ¯ l3,4, ¯ l6, cV , ¯ l1 −¯ l2 NLO SU(3) constants: Σ0, F0, ¯ L4,5,6,8,9,10, results not always coherent yet example: ¯ l3 = 3.2 ± 0.8, Fπ/F = 1.073 ± 0.015

1 1 2 2 3 3 4 4 5 5 6 6 CERN-TOV 06 ETM 08 JLQCD/TWQCD 08A ETM 09C RBC/UKQCD 08 PACS-CS 08 GL 84

lbar3

Nf=2+1 Nf=2 MILC 09A MILC 09A [SU(2) fit] [SU(3) fit] PACS-CS 08 [SU(3) fit] [SU(2) fit] Nf=2+1+1 ETM 10

  • ur estimate

[SU(3) fit] MILC 10 RBC/UKQCD 10A MILC 10A [SU(2) fit] 1.04 1.04 1.08 1.08 1.12 1.12 1.00 1.00

Fπ /F

ETM 08 ETM 09C PACS-CS 08 CD 03 Nf=2+1 Nf=2 MILC 09A MILC 09 RBC/UKQCD 08 JLQCD/TWQCD 08A JLQCD/TWQCD 07 HHS 08 ETM 09B Nf=2+1+1 ETM 10

  • ur estimate

MILC 10 MILC 10A

Review on results by the FLAG working group Andreas J¨ uttner 23

slide-50
SLIDE 50

Outlook

in most of the considered quantities the results are mutually compatible per cent level precision (and below) possible lattice QCD is a continously evolving, so will FLAG’s criteria

Review on results by the FLAG working group Andreas J¨ uttner 24

slide-51
SLIDE 51

Outlook

in most of the considered quantities the results are mutually compatible per cent level precision (and below) possible lattice QCD is a continously evolving, so will FLAG’s criteria the FLAG document provides a thorough analysis of state-of-the art lattice results and averages or recommended intervals where appropriate FLAG’s appendix: detailed information on the characteristics of each simulation (lattice discretisation, simulation parameters, fitting model, . . . )

Review on results by the FLAG working group Andreas J¨ uttner 24

slide-52
SLIDE 52

Outlook

in most of the considered quantities the results are mutually compatible per cent level precision (and below) possible lattice QCD is a continously evolving, so will FLAG’s criteria the FLAG document provides a thorough analysis of state-of-the art lattice results and averages or recommended intervals where appropriate FLAG’s appendix: detailed information on the characteristics of each simulation (lattice discretisation, simulation parameters, fitting model, . . . ) periodic updates are planned extension to larger set of quantities FLAG is a service for the larger community; the hard work has been done by lattice collaborations and we kindly ask users of FLAG-results to quote also the original work along with FLAG-averages

Review on results by the FLAG working group Andreas J¨ uttner 24