Flavour Physics from Mixed-Action Lattice QCD Carlos Pena...Carlos Pena III Jornada de usuarios de...

Flavour Physics from Mixed-Action Lattice QCD

Carlos Pena

III Jornada de usuarios de la RES --- Zaragoza, 01/07/10

... or:Disentangling New Fundamental Physics from Old Strong Interactions

Carlos Pena

III Jornada de usuarios de la RES --- Zaragoza, 01/07/10

Team leader: Pilar HernándezUniv Valencia / IFIC

The team

Eric EndressUAM and IFT-UAM/CSIC

Nicolas GarronUniv Edinburgh

Silvia NeccoCERN

Carlos PenaUAM and IFT-UAM/CSIC

Hartmut WittigUniv Mainz

Fabio BernardoniUniv Valencia / IFIC

Coordinated Lattice Simulations

CERN

DESY

Humboldt

Madrid

Mainz

Rome

Valencia

Wuppertal

Fundamental interactions and length scales



Gravity1 A.U. Size of the Universe

General Relativity, no quantum effects


Electromagnetism Weak and Strong nuclear interactions


10 keV/c 100 MeV/c � 1 GeV/c

λ =h

p←→ length ∼ 1

energyQuantum World

Quantum ChromoDynamics

QFT describing the strong interaction at a fundamental level

QCD describes strong interactions via gluon exchanges between quarks, pretty much the same as electromagnetism is described via photon exchanges between charged particles (QED).

Distinctive feature: interaction force grows stronger with the distance, quarks and gluons are confined into bound states (hadrons).


Asymptotic freedom: strong interaction grows weak at short distances (high energies), strong at long distances (low energies).



Analytical computations can be carried out for high-energy contributions (perturbation theory).

Low-energy regime (hadrons) requires numerical techniques.



Binding energies for hadronic states much larger than rest mass of constituent particles.

Ebind(proton)3mqc2

≈ 50

Ebind(H)(me + mp)c2

≈ 1.4× 10−5electromagnetism:

strong interaction:



Binding energies for hadronic states much larger than rest mass of constituent particles.

99.9% of the mass of ordinary matter is generated by strong interaction binding energy of quarks into protons and neutrons.

Lattice Quantum ChromoDynamics

Only known first-principles approach to the formulation of QCD as a strongly coupled quantum field theory, main computational tool for low-energy regime.

Lattice sizes, quark masses, . . .

Systematic limitations

Lattice-spacing and finite-volumeeffects

The light-quark mass m is largerthan the physical one

a

L

Available range of a, L,m must be such that the results can beextrapolated to a→ 0, L→∞ and m→ 0

Niels Bohr Institute, 16.–18. August 2006 Lattice sizes, quark masses, ... 6/31

Spacetime discretised to 4-dimensional lattice.

Quark fields live in sites, interact via gluon field with close neighbours.

Physics scales to fit between a and L.

Wilson 1974







a

L





Path integral: �φ(x1) . . . φ(xn)� =1Z

�[dφ(x)] e−S[φ] φ(x1) . . . φ(xn)

Computed numerically, involves reiterated inversion of sparse complex matrices of size 12(L/a)4 × 12(L/a)4. Tipically (L/a) ∼ 32 ⎯ 128.

Wilson 1974








a

L





Computations naturally involve two phases:

Generation of set of fields that sample integration space (configurations).

Computation of observables on configuration ensemble (physics).

Wilson 1974



The DD-HMC algorithm

Uses of domain-decomposition ideasin lattice QCD

� Computation of D−1w φ using a

“Schwarz preconditioner”

� Simulation algorithm including adoublet of light sea quarks

ML CPC 156 (2004) 209; CPC 165 (2005) 199

Domain decompositions provide an opportunity to separate low- andhigh-frequency modes

Niels Bohr Institute, 16.–18. August 2006 The DD-HMC algorithm 20/31

Ideal problem for large-scale parallelisation: lattice divided into weakly connected blocks.







ML CPC 156 (2004) 209; CPC 165 (2005) 199










ML CPC 156 (2004) 209; CPC 165 (2005) 199




Matrices are very ill-conditioned: cost of simulating QCD in the physical regime increases dramatically for small quark masses.

Dark ages of LQCD (1980-2005): simulations hindered by uncontrolled approximations.







ML CPC 156 (2004) 209; CPC 165 (2005) 199




Mid-00’s breakthrough: teach hadronic physics to algorithms.

Physical QCD simulations feasible with machines at an above the Tflops scale.

Sexton-Weingarten, Hasenbusch, Lüscher

cost ≈ 40�

10 MeVm

�3 �L

3 fm

�5 � a

0.1 fm

�7Tflops × year







ML CPC 156 (2004) 209; CPC 165 (2005) 199




Physical QCD simulations feasible with machines at an above the Tflops scale.

cost ≈ 0.1�

10 MeVm

�1 �L

3 fm

�5 � a

0.1 fm

�6Tflops × year

Mid-00’s breakthrough: teach hadronic physics to algorithms.

Sexton-Weingarten, Hasenbusch, Lüscher

cost ≈ 40�

10 MeVm

�3 �L

3 fm

�5 � a

0.1 fm

�7Tflops × year


Dürr et al, Science 322 (2008) 1224

Lattice Quantum ChromoDynamicsdynamical simulations : parameters landscape

• number of flavours : Nf

• lattice spacing : a

• lattice size : L

• pion masses : mPS

0.20

0.15

0.10

0.05

0.00

1/1.25

1/2.5

1/5

0

600500

400300

200100

a [fm]

1L

[fm−1]mπ [MeV]

exptJLQCD/CP-PACS (2001) Nf = 2

ETMC Nf = 2 + 1 + 1MILC Nf = 2 + 1 + 1MILC Nf = 2+ 1

RBC-UKQCD Nf = 2+ 1JLQCD Nf = 2+ 1QCDSF Nf = 2+ 1

PACS-CS Nf = 2+ 1BMW Nf = 2+ 1

TWQCD(Iwa) Nf = 2TWQCD(plaq) Nf = 2

JLQCD Nf = 2BGR Nf = 2

QCDSF Nf = 2ETMC Nf = 2

CLS Nf = 2a[fm]

mπ [MeV]

0.20

0.15

0.10

0.05

0.00600500400300200100

1L [fm−1]

mπ [MeV]

1/1.25

1/2.5

1/5

0600500400300200100

oblique dotted line : mπL = 3.5Caveat in plots : no information on systematic effects (scale setting, cut-off effects, . . . ), ms , mc , . . .

review talk by Christian Hoelbling

Extremely competitive landscape in LQCD: several collaborations from Europe/US/Japan provide essential input for High Energy Physics experiments in LHC era.

Herdoiza, Lattice 2010

Lattice Quantum ChromoDynamicsdynamical simulations : parameters landscape

• number of flavours : Nf

• lattice spacing : a

• lattice size : L

• pion masses : mPS

0.20

0.15

0.10

0.05

0.00

1/1.25

1/2.5

1/5

0

600500

400300

200100

a [fm]

1L

[fm−1]mπ [MeV]

exptJLQCD/CP-PACS (2001) Nf = 2

ETMC Nf = 2 + 1 + 1MILC Nf = 2 + 1 + 1MILC Nf = 2+ 1

RBC-UKQCD Nf = 2+ 1JLQCD Nf = 2+ 1QCDSF Nf = 2+ 1

PACS-CS Nf = 2+ 1BMW Nf = 2+ 1

TWQCD(Iwa) Nf = 2TWQCD(plaq) Nf = 2

JLQCD Nf = 2BGR Nf = 2

QCDSF Nf = 2ETMC Nf = 2

CLS Nf = 2a[fm]

mπ [MeV]

0.20

0.15

0.10

0.05

0.00600500400300200100

1L [fm−1]

mπ [MeV]

1/1.25

1/2.5

1/5

0600500400300200100

oblique dotted line : mπL = 3.5Caveat in plots : no information on systematic effects (scale setting, cut-off effects, . . . ), ms , mc , . . .

review talk by Christian Hoelbling

Extremely competitive landscape in LQCD: several collaborations from Europe/US/Japan provide essential input for High Energy Physics experiments in LHC era.

Herdoiza, Lattice 2010


CERN

DESY

Humboldt

Madrid

Mainz

Valencia

Wuppertal


Common effort to produce dynamical lattice QCD gauge configurations.

Different teams join to set up independent physics projects that use the common configuration pool.

Distinctive feature: “radical” first-principles approach, work closest to continuum limit.

CLS machines

Code

Custom code written in ANSI C with core arithmetic routines in assembler.

Optimised use of system architecture: extremely balanced throughput inside/outside computational node.

Typical runs use 72 ⎯ 512 processors, almost perfect scaling in parallelisation.

Core part of the code performing between 2.4 Gflops/cpu (block inversions) and 0.7 Gglops/cpu (preconditioning). Average sustained in the 1 Gflops/cpu ballpark.

Timing of Qhat_blk------------------

64x32x32x32 lattice, 8x4x2x2 process grid, 8x8x16x16 local lattice

bs = 8 8 4 4

Time per lattice point: 0.768 micro sec (2469 Mflops [32 bit arithmetic])

Our project: light hadron effects in Flavour Physics

LQCD computations are essential to understand the flavour problem and check the Standard Model / uncover new Physics.


decay amplitude = short distance (electroweak + high-energy QCD) x long distance (low-energy QCD)



decay amplitude = short distance (electroweak + high-energy QCD) x long distance (low-energy QCD)


s e n s i t i v i t y t o S M consistency / new physics



Need excellent control of symmetry properties of external particles, less accurate for vacuum virtual excitations mixed actions.

Control low-energy contributions to kaon physics.



3

am aMP R+, bare R!, bare

!-regime0.002 - 0.569(44) 2.43(15)0.003 - 0.572(43) 2.41(14)

p-regime0.020 0.1960(28) 0.636(40) 2.20(12)0.030 0.2302(25) 0.691(33) 1.93(9)0.040 0.2598(24) 0.723(31) 1.75(8)0.060 0.3110(24) 0.772(30) 1.51(7)

TABLE I: Results for aMP and R±,bare

for a smooth extrapolation to the chiral limit. It is alsoimportant to notice that at this volume and for thesemasses finite volume corrections are visible and takeninto account in the formulas (10) and (11)...

FITTING STRATEGY

At the kaon mass or heavier, where finite volume correc-tions can be safely neglected, the continuum-limit renor-malization group-invariant (RGI) ratios R±,RGI can beextracted from Refs. [35, 36]. By defining the referencevalues

R±,RGIref ! R±,RGI

!!!r20M2

P =r20M2

K

(13)

at the pseudoscalar mass r20M

2K = 1.573, we obtain

R+,RGIref = 0.954(52) and R!,RGI

ref = 0.910(76). SinceWilson coe!cients are computed in a mass independentrenormalization scheme

R±,RGI = R±,bare"R±,bare

!!!r20M2

K

#!1R±,RGI

ref (14)

for any value of the quark mass.

IV. PHYSICS DISCUSSION

We can now combine our results for R±,RGI with theWilson coe!cients in Eq. (3) to obtain

g+1 = 0.50(?) , g!1 = 2.9(?) ,

g!1g+1

= 5.8(??) , (15)

where errors take into account uncertainties on k±1 ,

R±,RGIref and statistical errors on R±,bare. A solid esti-

mate of discretization e"ects would require simulationsat several lattice spacing, which is beyond the scope

0 0.02 0.04 0.06 0.08

am

0

0.5

1

1.5

2

2.5

3

R

ms/2

R+

R-

FIG. 1: Dependence of R±,bare on am

of this exploratory study. However, computations ofR± at di"erent lattice spacings and for masses closeto ms/2 [5, 34, 38] indicate that discretization e"ectsmay be already comparable or smaller than our statis-tical errors. In this respect it is interesting to noticethat quenched computations of various physical quan-tities carried out with Neuberger fermions show smalldiscretization uncertainties at this lattice spacing [37].

Our values of g±1 in Eq.(15) reveal a clear hierarchyamong the low-energy constants, g!1 " g+

1 , which in turnimplies the presence of a #I = 1/2 rule in this corner ofthe parameter space of (quenched) QCD.

Assuming that QCD reproduces the experimental am-plitudes, the LECs of the #S = 1 e"ective Hamiltoniancan be extracted from a combination of LO ChPT andexperimental results [39]

g+, exp1 # 0.50 , g!, exp

1 # 10.4 ,g!, exp1

g+, exp1

# 20.8 . (16)

Apart for quenching e"ects, these LECs di"er from theones we have computed due to higher order e"ects inChPT and/or due to contributions arising when thecharm mass is heavier. A comparison of the values inEqs. (15) and (16) suggests the presence of a large con-tribution to the #I = 1/2 rule from physics at the intrin-sic QCD scale. Barring accidental cancellations amongquenching e"ects and higher order ChPT corrections, ourvalue of g+

1 points to the fact that higher order ChPT cor-rections in |A2| may be relatively small. In this case, infact, the charm mass dependence is expected to be mild(only via the determinant). On the contrary our value forg!1 is o" by more than a factor three with respect to theexperimental value. Apart from possible large quench-ing artifacts, this suggests that the charm mass depen-dence and/or higher order e"ects in ChPT are large for|A0|. These two contributions can be disentangled by im-plementing the second step of the strategy proposed inRef. [5].

All the above speculations are, of course, invalidatedif it turns out that quenching a"ects these correlationfunctions in a significant way. In this respect it is im-

W (K → (ππ)I=0)W (K → (ππ)I=2)

≈ 5 × 100

Need excellent control of symmetry properties of external particles, less accurate for vacuum virtual excitations mixed actions.

Control low-energy contributions to kaon physics.

Giusti et al., Phys Rev Lett 98 (2003) 2007

Scientific production with MN resources

13(+3) publications from continued activity.

9 pre-CLS publications include benchmark works for the determination of strong low-energy constants, understanding of enhancement of zero isospin kaon decays.

Work by the team regularly features in plenary talks at major field conferences, high impact in terms of community recognition.

Upcoming papers provide first fully successful implementation of mixed-action strategy. Crucial step for phenomenological applications in Flavour Physics.

Scientific production with MN resources

13(+3) publications from continued activity.

9 pre-CLS publications include benchmark works for the determination of strong low-energy constants, understanding of enhancement of zero isospin kaon decays.

Work by the team regularly features in plenary talks at major field conferences, high impact in terms of community recognition.

Upcoming papers provide first fully successful implementation of mixed-action strategy. Crucial step for phenomenological applications in Flavour Physics.

Thanks to BSC/RES staff for continuing support and superb reliability of the machine during several periods.

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Flavour Physics from Mixed-Action Lattice QCD Carlos Pena...Carlos Pena III Jornada de usuarios de...

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