federico mesciaifae2006/talks/fisicasapore/...flavour physics & lattice qcd flavour physics...
TRANSCRIPT
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