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Diapositiva 1

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Minimum quark mass. Chiral perturbation theory (schematic) ... to treat the b quark: 1) Use an effective theory ... Heavy quarks phys. 0.9 PFlop-years Wilson ... – PowerPoint PPT presentation

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Title: Diapositiva 1


1
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
3
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
The EXPERIMENTAL ACCURACY at a SuperB factory
will reach the level of 1 or better for most of
the relevant physical quantities
Can we calculate hadronic parameters with a
comparable (1) level of precision ?
5
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
7
History of lattice errors
Uncertainties have been dominated for many years
by the quenched approximation. Unquenched
calculations still have relatively large errors.
8
F.Mescia HEP2007
the quenched uncertainty reduced by a
factor 1.5 in the last years
9
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
S.Sharpe _at_ Lattice QCD Present and Future,
Orsay, 2004 and report of the U.S. Lattice QCD
Executive Committee
11
Assumptions
  • I assume that non hadronic uncertainties, e.g.
    N2LO calculations, will be reduced at a level ? 1

12
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
2007
2015
The Moores Law
Today 1 10 TFlops 2015 1 10 PFlops
For Lattice QCD
14
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(µ) Z(aµ,g)
Olatt(a) - In most of the cases Z can be
calculated non-perturbatively accuracy can
be better than 1
15
Minimum lattice spacing
From S.Sharpe _at_ Lattice QCD Present and Future,
Orsay, 2004
Rough estimate
? Assume O(a) improved action
- Improved Wilson n3. Staggered, maximally
twisted, GW n4
- For light quarks ?2 ?n ?QCD. For heavy
quarks ?2 ?n mH
16
Minimum lattice spacing (cont.)
Today a 0.06 - 0.10 fm ( cost a-6 )
17
Minimum quark mass
? Chiral perturbation theory (schematic)
- c1 c2 O(1)
? Assume simulations at two values of mp/m?. The
resulting error is
? If we require e 0.01 then (assuming c21)
(mp/m?)min ? 0.27
Physical value
Today
18
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
? For matrix elements with at most one particle
in the initial and final states finite volume
effects are exponentially suppressed
with c O(1)
? If we require e 0.01 then (assuming c1)
mp L ? 4.5
L ? 4.5 fm
? With a 0.033 fm the number of lattice sites
is
Today the typical size is 323 ? 64 More than
300 times smaller
V ? 1363 ? 270
20
Heavy quark extrapolation
? A relativistic b quark cannot be simulated
directly on the lattice. It would require a mbltlt
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 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
23
Estimates of CPU costs
? The cost depends on the lattice action
Wilson - Standard - O(a)-improved - Twisted mass
Staggered
Ginsparg-Wilson - Domain wall - Overlap
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
  • Tremendous progress of the algorithms in the
    last years.
  • The Berlin wall has been disrupted

Berlin plot Ukawa, Latt01
24
Empirical formulae for CPU cost
For Nf2 Wilson fermions
Del Debbio et al. 06
? Comparison with Ukawa 2001 (the Berlin wall)
25
Cost of the target simulations
Overhead for Nf21 and lattices at larger a and
m is about 3
Affordable with 1-10 PFlops !!
26
Estimates of error for 2015
27
Precision flavour physics at the SuperB
28
UTA in the SM 2007 vs 2015
29
Sin2ß 0.690 0.023
a (91.2 5.4)o
? (66.7 6.4)o
Sin2ß 0.6749 0.0043
a (104.55 0.45)o
? (54.28 0.38 )o
30
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
CBd 1.04 0.34
fBd (-4.1 2.1)o
With present central values, given the Vub vs
sin2ß tension, the Standard Model would
be excluded at gt 5s
CBd 0.997 0.031
fBd (0.02 0.51)o
32
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 tanß 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 tanß New operator wrt the SM Also
the bottom Yukawa coupling can be relevant NP in
K and B uncorrelated
33
DAmbrosio et al., NPB 645
Today
With a SuperB
Remember this is the most pessimistic scenario!!
dS0 0.004 0.059 ? gt 6 ?0 _at_ 95 NP masses gt
600 GeV
dS0 -0.16 0.32 ? gt 2.3 ?0 _at_ 95 NP masses gt
200 GeV
34
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
Lets work on that !!
35
Backup slides
36
Expectations for LHCb
from V. Vagnoni at CKM 2006
37
UTA
Lattice Dawson
2 !
fBsvBBs 261 6 MeV
UTA
Lattice Hashimoto
fBsvBBs 262 35 MeV
UTA
? 1.24 0.08
Lattice Hashimoto
? 1.23 0.06
The agreement is spectacular!
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