Non-perturbative Inputs for Flavour PhysicsNon-perturbative Inputs for Flavour Physics

Federico MesciaINFN-Frascati

OUTLINE

Theoretical inputs from Lattice QCD

Method and Systematics

Tour on a few observables

Conclusions

OUTLINE

Theoretical inputs from Lattice QCD

Method and Systematics

Tour on a few observables

Conclusions

IFAE ‘06, Pavia, April 19 - 21

Flavour Physics & Lattice QCD Flavour Physics & Lattice QCD

Physics of b, c, s, d, u flavored hadrons can be consistently treated by a series of effective theories below the W scale:

• matrix elements: Lattice QCD

• CKM-couplings and loop functions

( )= × ×H

MH W

CKVA f CO

For some quantities, Lattice QCD remains the only tool that can unlock the complete potential of exp. measurements

• Lattice QCD is Quantum Field Theory on a Finite and Discrete Box;

Lattice QCDLattice QCD

lattice size L

• However, although no ``ab initio’’ limitations on the approach, limitations in computing resources introduce some approximations:

source of systematic errors.

V

gauge field

quark field• Physical Quantities are computable from first principles, by tuning only the parameters appearing in the QCD Lagrangian, namely mq and αs lattice spacing a

Numerical limit: light quark massesNumerical limit: light quark masses

Simulation costs for light masses are very expensive:

• The Wilson formulation of the lattice QCD action (standard up to 2002) did not allowto get mπ< 500 MeV [mq/ms<0.5 ]**(JLQCD/MILC/CP-PACS/SPQcdR studies)

•Technical issues: exceptional configurations, algorithm slow down

**(physical mπ= 137 MeV [mq/ms=0.04 ])

Recent developments in both algorithms and new lattice actions aRecent developments in both algorithms and new lattice actions are solving this issue:re solving this issue:

• Staggered: MILC-2002, mπ~240 MeV (mq/ms~0.1) ( NF=2+1 advanced studies)cheap but 4 tastes (fourth root trick): unknown systematics!!

• Wilson: Luscher-2005, mπ~280 MeV (mq/ms~0.16) (feasibility studies: NF=2)good physical properties but more expensive

• Twisted-mass: Jansen-2006, mπ~300 MeV (mq/ms~0.2) (feasibility studies : NF=2)easy to implement, but isospin and parity broken at O(a)

)seaqmSystematic Errors: UnquenchingSystematic Errors: Unquenching

• Only Staggered fermions successful so far. Realistic world but some doubts:Effects from unphysical tastes require peculiar contrivances:

• Det1/4: no proof that this is correct nor wrong• Fit with tenths of free parameters• Perturbative subtraction/renormalisation

• Is the continuum Limit QCD? Locality, unitarity?Is the continuum Limit QCD? Locality, unitarity? unknown systematics!!

NF=2+1 QCD mu=md + ms

→ ∞seacm

Studies with dynamical quarks are becoming availableStudies with dynamical quarks are becoming available

QUENCHED QCD NF=0

→ ∞seaqm

• widely investigated: accurate studies agree among many groups and procedures.

NF=2 QCD mu=md , → ∞sea

s cm• Effort to unravel the complete QCD dynamics: Wilson fermions where systematicscan be all estimated and hopefully reduced. But, less appealing for phenomenology!!

Strange Quark Mass?: Wilson (NF =0 & NF =2) vs Staggered Strange Quark Mass?: Wilson (NF =0 & NF =2) vs Staggered

80 - 90 MeVNF =2+1

100 - 120 MeV(NF =0 - NF =2)

100(10) MeV(NF =0)

Systematic accuracy not well under control in the unquenched case yet (non-pert. vs pert

renormalisation.... )

Systematic accuracy not well under control in the unquenched case yet (non-pert. vs pert

renormalisation.... )

Other Systematic Errors:Other Systematic Errors:

To simulate a physical system on the lattice, the minimal condition is:

Computer power limits us at

•At finite a (~2-4 GeV) and 1/L (~80 -200 MeV), mud and mb inaccessible: effective theories helpful [ChPT, HQET, NRQCD] dominant source of present/future uncertainties

•Residual discretisation errors and finite Volume effects:simulations with several lattice spacings and volumes

To simulate a physical system on the lattice, the minimal condition is:

Computer power limits us at

•At finite a (~2-4 GeV) and 1/L (~80 -200 MeV), mud and mb inaccessible: effective theories helpful [ChPT, HQET, NRQCD] dominant source of present/future uncertainties

•Residual discretisation errors and finite Volume effects:simulations with several lattice spacings and volumes

L 1/ , 1/P qM a m

/ 50≤L a

Hot Topics: Hot Topics: ∆∆mmss (D0/CDF)(D0/CDF) & & BB→→τντν (Belle)(Belle)

2 2

2

2222

2

22

02

2

6

( ) 18

( )

ττ

π

τνπ

η∆ = ⋅

⎛ ⎞Γ → = −⎜ ⎟

⎝ ⎠

Bq Bq

Bq

q

F Wq B

F

tb tq

ubB

B

B tG mm m

mG

B

mB mm

f

V

x

f

SV V

―― Lattice QCD inputs:Lattice QCD inputs: ffBBdd , , ffBsBs && BBBB

• sea quark effects seem at O(10%-15%):• But continuum scaling or other systematic

(NP-Ren., FV effects, Different h.q. formulations …) not completely investigated 230 30 MeV

sBf = ±

50ss Bs B i fb pµ µγ γ =

High level of accuracy;

Good agreement among different approaches;Continuum extrapolation; (De Divitiis et al.

(2003), ALPHA (2003))

Quenched SimulationsQuenched Simulations

• NF=2: JLQCD (03), high statisticsJLQCD (03), high statistics and O(O(aa))--improved action;improved action;• NF=2+1: HPQCD HPQCD ‘‘0303--’’05, staggered action:05, staggered action:lighter sea quarks.lighter sea quarks.

Unquenched SimulationsUnquenched Simulations

With the present accuracy

NRQCD

FNAL

RELAT.

FNAL

NRQCD

LATTICE 2005:LATTICE 2005:

NRQCD

s s

d d

B B

B B

f m

f m

2 2 2

2 2

2

3(1 3 )1 log4 (4 )

(1 3 ) 1.8

s s

d d

B B

B B

f m g m mff m

g

π π

π µ+

∝ +

+ ∼

1.20(4)=sB

B

ff

50dd BB ip fb dµ µγ γ =

• Pion Loops could be significant [Kronfeld-Ryan (02)]

Delicate Issue: Chiral Extrapolation Delicate Issue: Chiral Extrapolation

LATTICE 2005:LATTICE 2005:

• Chiral Log Effects roughly estimated(JLQCDJLQCD (NF=2, mq/ms>0.5)+HPQCDHPQCD (NF=2+1, mq/ms>0.13))

With the present accuracy:With the present accuracy:

Still more statistics and “lighter” quark masses is needed

Still more statistics and “lighter” quark masses is needed Final Chiral Loop Effects: O(5%)

86 5695 171.287(42)( ), 1.017(16)( )s

d

d

BB

B

BBB

+ +− −= =

JLQCD(03), NJLQCD(03), NFF=2=2

( ) ( ) 2 283 BqBqBq

q L L qb b fqB B mq Bµ µγ γ =

•• No sea quark effects!!No sea quark effects!!•• Consistent with diagnosis deduced Consistent with diagnosis deduced

from from QChPTQChPT versus versus ChPTChPT: : Booth95,Sharpe,Zhang96

With the present accuracy:With the present accuracy:

JLQCD(03): NJLQCD(03): NFF=2, clover light & NRQCD heavy=2, clover light & NRQCD heavy

( ) ( ) 2 283 BqBqBq

q L L qb b fqB B mq Bµ µγ γ =

Lattice data are consistent with a constant.

Chiral Loops not a issue for

They are expected small from ChPT

Chiral Loops not a issue for

They are expected small from ChPTB d

B

B mixing from Lattice QCD

Lellouch, ICHEP ‘02

Hashimoto-OkamotoICHEP ‘04 -Lat ’05

203(27)(+0-20) 216(27)

238(31) 230(30)

276(38) 262(35)

1.18(4)(+12-0) 1.20(5)

1.18(4)(+12-0) 1.21(5)

(MeV)Bf

(MeV)sBf

ˆ (MeV)s sB Bf B

/sB Bf f

ξ

Now averages include rough “estimates” of chiral log (mq/ms>0.13) and unquenched effects (NF=2+1)Now averages include rough “estimates” of chiral log (mq/ms>0.13) and unquenched effects (NF=2+1)

Mind: still coarse setupMind: still coarse setup:: (1/a~2 (1/a~2 GeVGeV, 1/L~80 , 1/L~80 MeVMeV))

What can we expect?What can we expect?3, 5 years3, 5 years

We can not expect to work with We can not expect to work with b, ub, u close to their physical close to their physical masses in unquenched QCD masses in unquenched QCD → irreducible uncertaintyirreducible uncertainty::

promising prospectives for u/d extrapolation: improve algorithms in the range 200 MeV< mπ< 300 MeV;use ChPT functional form in this range with FV effects under control;

relevant development for b:

Non-perturbative renormalization of HQET solved and signal improved: • Interpolate to B, improved HQET (mb→∞) results with QCD above the charm region. Errors expected to reduce!!

No expectation from alternative effective theories:• NRQCD: Difficulties with higher orders 1/(amH) : renormalon shadow, no continuum limit• FNAL: renormalisation procedure unclear!!

What about BWhat about B--physics in 3, 5 years?physics in 3, 5 years?

Charm physics: Charm physics: semisemi-- and and leptonicleptonic decaysdecays(Cleo(Cleo--cc) )

2

2

222 2

2

22( ) 1

8

( ) (0)

νπ

ν +

⎛ ⎞Γ → = −⎜ ⎟

⎝ ⎠

Γ → ∝

Dq

lF Dq l

Dc

cq

q

q

mG mD l mm

D P fVl

fV

―― Lattice QCD inputs:Lattice QCD inputs: ffDD , , ffDsDs && ff++(0)(0)• charm and strange quarks directly accessible on lattice simulations:

best tests

• light content enlarges uncertainties

→sD lv ϕ→sD lv

50 µ µγ γ =qq Dq D ip fd

High control of systematic errors, 5% accuracy:De Divitiis et al. (2003), ALPHA (2003)

continuum limit & non-pert. ren.

Quenched SimulationsQuenched Simulations (MeV)sDf

• NF=2: CPCP--PACS (05): PACS (05): O(O(aa))--improved action improved action for light/charm quarks;for light/charm quarks;

• NF=2+1: MILC/FNAL 05:MILC/FNAL 05: staggered action staggered action for light quarks for light quarks & & ““FNALFNAL”” effeff. . thth. for charm . for charm

Unquenched Simulations: 2005Unquenched Simulations: 2005

error dominated by discretisation error (done on a single lattice spacing) (223 17 3)MeV= ± ±DfCLEOCLEO--c:c:

2 0 22 2 2 2

2 2( ) ( ) ( ) ( )µ

µ µ+ ⎡ ⎤− −= + − +⎢ ⎥

⎣ ⎦D K D K

K D D Km mf q f m mK p V D p p

q qqp q

• Unquenched agrees well with quenched;

• Good agreement with Cleo-c/Belle, for both normalisation and f.f. shape

dominant syst. error from heavy quark discretisation (~9%)

Experimental error can be reduced by current factories Belle/Babar/Cleo-c

1. Indirect 1. Indirect CPCP--Violation Violation in the in the KaonKaon systemsystem

―― εεΚΚ and and ΒΒΚΚ

CP-Violation in K – K Mixing: εK and BK

K εεKK → indirect CP-violation

The Effective ∆S=2

Hamiltonian

QQ((µµ))

High level of accuracy, ~6%: continuum limit & non-pert. ren.DimopoulosDimopoulos `05, B`05, BKK(MS,2GeV)=0.57(3)(MS,2GeV)=0.57(3)

Benchmark calculation for years was JLQCD ’97, BBKK(MS,2GeV)=0.63(4); (MS,2GeV)=0.63(4); pert. pert. renren. and large . and large discretizationsdiscretizations errorserrors

Quenched average (ICHEP’04-LAT’05):

Current Lattice results for BKCurrent Lattice results for BK

Quenched SimulationsQuenched Simulations

• Dynamical computations of BK are underway by a number of collaborations, but so far the results are very preliminary.• “Guesstimate” from comparison of unquenched & quenched results at similar masses and lattice spacings

UnquenchingUnquenching

KKll33: : VVusus and and UnitarityUnitarity

UnitarityThe most accurate test of CKM unitarity|Vud|2 + |Vus|2 + |Vub|2 = 1

The most accurate test of CKM unitarity|Vud|2 + |Vus|2 + |Vub|2 = 1

|Vus| → possibly responsible!!Relies on old experimental and theoretical results of Kl3

|Vus| → possibly responsible!!Relies on old experimental and theoretical results of Kl3

PDG04 0.2200(26)usV = ~2.4 σ discrepancy

2 20.9739(3 0.22 11 3)) 69(Uud ud ub

NIusV V VV =+ −== ⇒

CKM05

Rate

..

2 52 2 2 2

(2)3( ) | | (1 )192

( (0) |) |Vπ ν δ δπ

γ +Γ → = ⋅ + +K KlF KK K ew SU emus

G MK l C I Sf

Vus from K 3 decaysVus from K 3 decays

2 2 2 2

2 22 2

0

0

( ) ( )

(0) (

| | ( )

0)

K KKf q f q

f f

M M M MK p p q qq q

s u µ µ µπ πµππ γ

+

+⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

− −⟨

=

⟩ = + − +

Using exp. inputs from Br, IK and δ the quantity

can be measured at 0.2%

Using exp. inputs from Br, IUsing exp. inputs from Br, IKK and and δ δ the quantitythe quantity

can be measured at 0.2%( )0 -

(0)V Kus f π

+⋅

To attack Vus :A PRECISION OF O(1%) MUST BE REACHED ON THE LATTICE !!

Succeful strategy in D.Becirevic et al,NPB 705(2005) 339

8 8 111.2384(24) 10 , 5.15(4) 10 , 8.935(8) 10PDG PDG PDGL SK

s s sτ τ τ+− − −= ⋅ = ⋅ = ⋅

0 -V Kus f π

+⋅ -CKM 2005

••CKMCKM--Unitarity recovered:Unitarity recovered:

f+ (0) = 0.960 ± 0.005stat ± 0.007syst K0π-

|Vus|2 +|Vud|2 +|Vub|2=0.9993(11)

-

0.2179(24)

0.2215(26)

VV

us

us

ff

+

+

⎫= ⎪⋅ = ⎭

⋅⎬⎪

our-LR

Bijnens Jamin

uni

uniTheory

2 higherσ −

( )0 -

0.2165(5)V Kus f π

+⋅ =Exp

|V|Vusus||KKl3 =(0.2253=(0.2253±±0.0020) 0.0020) δδ|V|Vusus| ~ 1% | ~ 1%

(dominated by the f(dominated by the f++(0) theoretical uncertainty)(0) theoretical uncertainty)

2006 Summary of f+(0) lattice estimates2006 Summary of f+(0) lattice estimates

0=FN

2 1= +FN

2=FN

All these new lattice numbers should be considered as preliminaryfor the following reasons

ConclusionsConclusions

• So far, no significant deviations from the SM observed!

• Then, New physics is hidden in the error bars!!

• Mind: Susy is affected by hadronic quantities as much as the SM

Future Favour Physics Programme:

refining estimates of hadronic uncertainties by Lattice QCD:

Realistic unquenched studies with finer lattices and lighter quark masses.

not at all easy!! neither fast!!

Meanwhile, do not throw away higher-precision quenched values

BACKUP

To get B-physics on the lattice, 2 main routes

First of all, to avoid large discretization errors (amH, aΛQCD)O(a) improved actions and operators Working at several ``a’’ and go to a→0

a) Relativistic Approach: [rather large errors]

• Compute QCD for the accessible heavy quarks,

• Extrapolate to 1/mB with heavy quark scaling law (APE,UKQCD)recent improvement: combine data simulated from HQET (mb→∞) (SPQcdR),

: Non-perturbatively renormalised in HQET devised (ALPHA)

b) Effective Theory Approach (NRQCD and FNAL): [unknown uncertainties]

• Some of the coefficients, in the action and the operators, are known only in free theory

• Difficulties with higher orders 1/(amH) : ``renormalon shadow’’, cancellation of power divergences, ``no continuum limit’’

FINAL ERROR: COMPARE RESULTS OR COMBINEDIFFERENT APPROACHES