<<  Laternenumzug Le Plan de vente  >>
Lattice QCD and precision flavour physics at a SuperB factory
Lattice QCD and precision flavour physics at a SuperB factory
Prepared for:
Prepared for:
The goal of a SuperB factory: Precision flavour physics for indirect
The goal of a SuperB factory: Precision flavour physics for indirect
Can we calculate hadronic parameters with a comparable (~1%) level of
Can we calculate hadronic parameters with a comparable (~1%) level of
Why Lattice QCD
Why Lattice QCD
Present theoretical accuracy
Present theoretical accuracy
History of lattice errors
History of lattice errors
Sharpe Latt96
Sharpe Latt96
Estimates of Lattice QCD uncertainties in the SuperB factory era:
Estimates of Lattice QCD uncertainties in the SuperB factory era:
A previous estimate
A previous estimate
Assumptions:
Assumptions:
Strategy:
Strategy:
Estimate of computational power
Estimate of computational power
Sources of errors in lattice calculations
Sources of errors in lattice calculations
Minimum lattice spacing
Minimum lattice spacing
Minimum lattice spacing (cont
Minimum lattice spacing (cont
Minimum quark mass
Minimum quark mass
Minimum box size
Minimum box size
? If we require
? If we require
Heavy quark extrapolation
Heavy quark extrapolation
? Besides the static point, lattice HQET also allows a
? Besides the static point, lattice HQET also allows a
Target simulations to aim at the 1% level precision
Target simulations to aim at the 1% level precision
Estimates of CPU costs
Estimates of CPU costs
Empirical formulae for CPU cost
Empirical formulae for CPU cost
Cost of the target simulations:
Cost of the target simulations:
Estimates of error for 2015
Estimates of error for 2015
Precision flavour physics at the SuperB
Precision flavour physics at the SuperB
UTA in the SM: 2007 vs 2015
UTA in the SM: 2007 vs 2015
Sin2? = 0.690  0.023
Sin2? = 0.690 0.023
SM prediction for
SM prediction for
New Physics discovery
New Physics discovery
Minimal Flavor Violation
Minimal Flavor Violation
Today
Today
Lets work on that
Lets work on that
Backup slides
Backup slides
Expectations for LHCb
Expectations for LHCb
The agreement is spectacular
The agreement is spectacular

: Lattice QCD and precision flavour physics at a SuperB factory. : Vittorio Lubicz. : Lattice QCD and precision flavour physics at a SuperB factory.ppt. zip-: 2309 .

Lattice QCD and precision flavour physics at a SuperB factory

Lattice QCD and precision flavour physics at a SuperB factory.ppt
1 Lattice QCD and precision flavour physics at a SuperB factory

Lattice QCD and precision flavour physics at a SuperB factory

V. Lubicz

Outline Estimates of uncertainties of Lattice QCD calculations in the SuperB factory era Precision studies of flavor physics at the SuperB: impact of experimental and theoretical constraints

Padova, 23 ottobre 2007

2 Prepared for:

Prepared for:

3 The goal of a SuperB factory: Precision flavour physics for indirect

The goal of a SuperB factory: Precision flavour physics for indirect

New Physics searches

An important example: - Test the CKM paradigm at the 1% level

Today

With a SuperB in 2015

4 Can we calculate hadronic parameters with a comparable (~1%) level of

Can we calculate hadronic parameters with a comparable (~1%) level of

precision ?

The EXPERIMENTAL ACCURACY at a SuperB factory will reach the level of 1% or better for most of the relevant physical quantities

?

?

?md (ps-1)

?ms (ps-1)

BR(B???) (10-4)

Central Value

Current error

SuperB (75 ab-1)

sin2?

0.680

0.026 (4%)

0.005 (0.7%)

105o

7o (7%)

1-2o (1-2%)

54o

20o (37%)

1-2o (2-4%)

|Vcb| (10-3)

41.7

2.2 (5%)

0.2 (0.5%)

|Vub| (10-4)

36.4

2.0 (5%)

0.7 (2%)

0.507

0.005 (1%)

0.002 (0.4%)

18.06

0.12 (0.7%)

0.05 (0.2%)

0.83

0.48 (64%)

0.03 (4%)

ASL(Bd) [10-3]

- 0.7

5

0.1

5 Why Lattice QCD

Why Lattice QCD

Lattice QCD is the theoretical tool of choice to compute hadronic quantities

It is only based on first principles

It does not introduce additional free parameters besides the fundamental couplings of QCD

All systematic uncertainties can be systematically reduced in time, with the continuously increasing availability of computing power and the development of new theoretical techniques

6 Present theoretical accuracy

Present theoretical accuracy

7 History of lattice errors

History of lattice errors

Uncertainties have been dominated for many years by the quenched approximation. Unquenched calculations still have relatively large errors.

8 Sharpe Latt96

Sharpe Latt96

0.90(3)(15) 17%

Lellouch Latt00

0.86(5)(14) 17%

Hashimoto Ichep04

0.73(5)(5) 10%

Tantalo CKM06

0.78(2)(9) 12%

the quenched uncertainty reduced by a factor 1.5 in the last years

F.Mescia HEP2007

9 Estimates of Lattice QCD uncertainties in the SuperB factory era:

Estimates of Lattice QCD uncertainties in the SuperB factory era:

WARNING

? Uncertainties in Lattice QCD calculations are dominated by systematic errors. The accuracy does not improve according to simple scaling laws

Predictions on the 10 years scale are not easy. Estimates are approximate

In many cases, experiments have been more successful than expectations/predictions Is that also true for theoretical results ?

? I have tried to be conservative

10 A previous estimate

A previous estimate

S.Sharpe @ Lattice QCD: Present and Future, Orsay, 2004 and report of the U.S. Lattice QCD Executive Committee

11 Assumptions:

Assumptions:

I assume that non hadronic uncertainties, e.g. N2LO calculations, will be reduced at a level ? 1%

12 Strategy:

Strategy:

Determine the parameters of a target lattice simulation (i.e. lattice spacing, lattice size, quark masses) aiming at the 1% accuracy on the physical predictions Evaluate the computational cost of the target simulation Compare this cost with the computational power presumably available to lattice QCD collaborations in 2015

13 Estimate of computational power

Estimate of computational power

Today ~ 1 10 TFlops 2015 ~ 1 10 PFlops

For Lattice QCD:

2007

2015

The Moores Law

14 Sources of errors in lattice calculations

Sources of errors in lattice calculations

? Statistical - O(100) independent configurations are typically required to keep these errors at the percent level

? Discretization errors and continuum extrapolation: a?0 [Now a ? 0.1 fm]

? Chiral extrapolation: [Now mu,d ? ms/6]

? Finite volume [Now L ? 2-2.5 fm]

? Renormalization constants: Ocont(?) = Z(a?,g) Olatt(a) - In most of the cases Z can be calculated non-perturbatively: accuracy can be better than 1%

15 Minimum lattice spacing

Minimum lattice spacing

Rough estimate:

- For light quarks: ?2 ~ ?n ~ ?QCD. For heavy quarks: ?2 ~ ?n ~ mH

[From S.Sharpe @ Lattice QCD: Present and Future, Orsay, 2004]

? Assume O(a) improved action:

- Improved Wilson: n=3. Staggered, maximally twisted, GW: n=4

16 Minimum lattice spacing (cont

Minimum lattice spacing (cont

Today: a ~ 0.06 - 0.10 fm ( cost ~ a-6 )

17 Minimum quark mass

Minimum quark mass

? If we require ? = 0.01 then (assuming c2=1):

- c1 ~ c2 ~ O(1)

? Assume simulations at two values of m?/m?. The resulting error is

(m?/m?)min ? 0.27

? Chiral perturbation theory (schematic):

Physical value:

Today:

18 Minimum box size

Minimum box size

Finite volume effects are important when aiming for 1% precision. The dominant effects come from pion loops and can be calculated using ChPT. E.g:

[Becirevic, Villadoro, hep-lat/0311028]

19 ? If we require

? If we require

= 0.01 then (assuming c=1):

with c ~ O(1)

m? L ? 4.5

L ? 4.5 fm

Today the typical size is: 323 ? 64 More than 300 times smaller

V ? 1363 ? 270

? For matrix elements with at most one particle in the initial and final states finite volume effects are exponentially suppressed:

? With a = 0.033 fm the number of lattice sites is

20 Heavy quark extrapolation

Heavy quark extrapolation

? A relativistic b quark cannot be simulated directly on the lattice. It would require a mb<< 1. Typically that means:

This lattice is too fine, even for PFlop computers.

? Two approaches to treat the b quark:

- HQET

1) Use an effective theory on the lattice:

- NRQCD (no continuum limit)

- Fermilab

2) Simulate relativistic heavy quark in the charm mass region and extrapolate to the b quark mass

? The most accurate results can be obtained by combining the two approaches

21 ? Besides the static point, lattice HQET also allows a

? Besides the static point, lattice HQET also allows a

non-perturbative determination of (?/M)n corrections [Heitger, Sommer, hep-lat/0310035]

The point interpolated to the B meson mass has an accuracy comparable to the one obtained in the relativistic and HQET calculations

[Becirevic et al., hep-lat/0110091]

22 Target simulations to aim at the 1% level precision

Target simulations to aim at the 1% level precision

23 Estimates of CPU costs

Estimates of CPU costs

? The cost depends on the lattice action:

Wilson - Standard - O(a)-improved - Twisted mass

Staggered

Ginsparg-Wilson - Domain wall - Overlap

Tremendous progress of the algorithms in the last years. The Berlin wall has been disrupted

Berlin plot [Ukawa, Latt01]

Cheap, but affected by uncontrolled systematic uncertainty [det1/4]. Not a choice for the PFlop era.

Good chiral properties, 10-30 times more expensive than Wilson

24 Empirical formulae for CPU cost

Empirical formulae for CPU cost

For Nf=2 Wilson fermions:

? Comparison with Ukawa 2001 (the Berlin wall):

[Del Debbio et al. 06]

25 Cost of the target simulations:

Cost of the target simulations:

Affordable with 1-10 PFlops !!

Overhead for Nf=2+1 and lattices at larger a and m is about 3

26 Estimates of error for 2015

Estimates of error for 2015

27 Precision flavour physics at the SuperB

Precision flavour physics at the SuperB

?K

?

?

?

?md (ps-1)

?ms (ps-1)

?

BR(B???) (10-4)

Central Value

Current error

Error in 2015

sin2?

0.680

0.026 (4%)

0.005 (0.7%)

105o

7o (7%)

1o (1%)

54o

20o (37%)

1o (2%)

0.2258

0.0014 (0.6%)

0.0008 (0.4%)

|Vcb| (10-3)

41.7

2.2 (5%)

0.2 (0.5%)

|Vub| (10-4)

36.4

2.0 (5%)

0.7 (2%)

0.507

0.005 (1%)

0.002 (0.4%)

18.06

0.12 (0.7%)

0.05 (0.2%)

mt (GeV)

163.8

3.2 (2%)

1.5 (1%)

fBs?Bs (MeV)

262

35 (13%)

2.5 (1%)

1.13

0.06 (5%)

0.006 (0.5%)

fB (MeV)

189

27 (14%)

1.9 (1%)

0.83

0.48 (64%)

0.03 (4%)

BK

0.90

0.09 (11%)

0.009 (1%)

2.280

0.013 (0.6%)

0.013 (0.6%)

ASL(Bd) [10-3]

- 0.7

5

0.1

28 UTA in the SM: 2007 vs 2015

UTA in the SM: 2007 vs 2015

29 Sin2? = 0.690  0.023

Sin2? = 0.690 0.023

? = (91.2 5.4)o

? = (66.7 6.4)o

Sin2? = 0.6749 0.0043

? = (104.55 0.45)o

? = (54.28 0.38 )o

30 SM prediction for

SM prediction for

ms

?ms = (17.5 ? 2.1) ps-1

?ms = (17.93 ? 0.25) ps-1

?ms = (XX.XX ? 0.05) ps-1

Experimental error in 2015:

31 New Physics discovery

New Physics discovery

CBd = 1.04 0.34

?Bd = (-4.1 2.1)o

With present central values, given the Vub vs sin2? tension, the Standard Model would be excluded at > 5?

?Bd = (0.02 0.51)o

CBd = 0.997 0.031

32 Minimal Flavor Violation

Minimal Flavor Violation

The most pessimistic scenario for indirect NP searches in flavour physics

No new sources of flavour and CP violation

NP contributions controlled by the SM Yukawa couplings

Ex: Constrained MSSM (MSUGRA), .

1HDM / 2HDM at small tan? Same operator as in the SM NP only modifies the top contribution to FCNC and CPV NP in K and B correlated

2HDM at large tan? New operator wrt the SM Also the bottom Yukawa coupling can be relevant NP in K and B uncorrelated

33 Today

Today

With a SuperB

Remember: this is the most pessimistic scenario!!

?S0 = 0.004 0.059 ? > 6 ?0 @ 95% NP masses > 600 GeV

?S0 = -0.16 0.32 ? > 2.3 ?0 @ 95% NP masses > 200 GeV

[DAmbrosio et al., NPB 645]

34 Lets work on that

Lets work on that

Conclusions

? The performance of supercomputers is expected to increase by 3 orders of magnitude in the next 10 years (TFlop ? PFlop)

? Even without accounting for the development of new theoretical tools and of improved algorithms, the increased computational power should by itself allow lattice QCD calculations to reach the percent level precision in the next 10 years

? If this expectation is correct, the accuracy of the theoretical predictions will be on phase with the experimental progress at the Super B factory.

? The physics case for a SuperB factory is exciting

35 Backup slides

Backup slides

36 Expectations for LHCb

Expectations for LHCb

from V. Vagnoni at CKM 2006

37 The agreement is spectacular

The agreement is spectacular

2% !

UTA

Lattice [Dawson]

fBs?BBs = 261 6 MeV

UTA

Lattice [Hashimoto]

fBs?BBs = 262 35 MeV

UTA

? = 1.24 0.08

Lattice [Hashimoto]

? = 1.23 0.06

Lattice QCD and precision flavour physics at a SuperB factory
http://900igr.net/prezentacija/anglijskij-jazyk/lattice-qcd-and-precision-flavour-physics-at-a-superb-factory-135811.html
c

29
900igr.net > > > Lattice QCD and precision flavour physics at a SuperB factory