Baum Izhak Prof. Guido Martinelli Prof. Lubicz Vittorio ... · Co-Supervisors: Prof. Lubicz...
Transcript of Baum Izhak Prof. Guido Martinelli Prof. Lubicz Vittorio ... · Co-Supervisors: Prof. Lubicz...
Candidate: Baum Izhak (XXIII ciclo)
Supervisor: Prof. Guido Martinelli
Co-Supervisors: Prof. Lubicz Vittorio (Roma3)
Prof. Simula Silvano (Roma3)
Hadronic Matrix Elements for Weak Transitions
Beyond the Standard Model
PhD Research Project
Dip. di Fisica, Università di Roma “La Sapienza”
June 4, 2009
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Outline
● Motivation: Why calculate Weak matrix elements?
● Introduction to lattice theory and methodology● A few details of our calculations
● Our results so far: the K→ ElectroMagnetic and ChromoMagnetic matrix elements
● Conclusions
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The Standard Model (SM) describes extremely well all physical phenomena at current energies [Mele 2008; Martin 2008]
but there are still signs of new physics.
● Hierarchy problem –divergence of higgs mass
● Dark matter: no candidate !
● Baryogenesis ↔ CP violation: too small !
● Flavor problem: mt=170 GeV, m
u=5 MeV
and others...
Why calculate Weak matrix elements?The Standard Model – notable problems, solutions (SUSY)
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Why calculate Weak matrix elements?The Standard Model – notable problems, solutions (SUSY)
The Standard Model (SM) describes extremely well all physical phenomena at current energies
but there are still signs of new physics.
● Large hierarchy problem – divergence of higgs mass
● Dark matter: no candidate!
● Baryogenesis ↔ CP violation: too small!● Small hierarchy = Flavor problem: m
t=170 GeV, m
u=5 MeV
and others...
Most studied theory beyond the SM: SuperSymmetry (SUSY), solves many of the problems of the SM, but not all
Among the most popular theories beyond the SM is SUperSYmmetry (SUSY), which solves many of the problems of the SM, but not all
✔ Hierarchy problem – Higgs mass not diverging with cutoff
✔ Dark matter: neutralino 0
✔ Baryogenesis ↔ CP violation: easily accomodated
✗ Flavor problem: remains unexplained in SUSY
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Why calculate Weak matrix elements?
BR( KL
0 → ℓ∓ℓ ) = 67.55 0.17%
BR( K → ℓℓ ) = 8.30 0.09%
These BR's in the SM depend on the vector form factor:
(K→ ℓℓ) f
+(0)2
Which is calculated from the lattice matrix element:*t->q^2
Kaon Kℓ3
semileptonic decays as precision tests of the SM
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Why calculate Weak matrix elements?
● Rare Kaon decays have not been detected yet:
BR( KL
0 → ℓℓ∓ )exp < 6.6·10-10
● In the SM are estimated to be:
BR( K→e e )SM ~1.5·10-12
BR( K→)SM ~3·10-10
● New physics can be the leading contribution,
with Electromagnetic and ChromoMagnetic operators:
Kaon rare semileptonic decays as new physics probes
My work so far has been concentrated on these operators.
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Lattice theory [Montvay 94 ; Martinelli 88]
Explicitly calculate the path integral in discrete Euclidean space-time:
The lattice acts as a regulator:
● UV regulator – lattice step 1/a
● IR regulator – finite size 1/L
finite a and L contribute to systematic errors
aL
T
L
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Lattice theoryIn early days: ● cost of dynamic fermions too high → quenched approximation
● Light fermion masses: ● expensive ● Mesons too large with respect to L
Today:● Unquenched calculations are feasible
● light (u,d) fermions are still out of reach (but getting closer).
→ calculate at higher masses and extrapolate to physical mass → another systematical error
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Lattice methodologyexample: 2-point pion propagator
Calculate correlation functions of the operator
at large times at p=0, we can calculate the pion mass:
0 5 10 15 20 251E-3
1E-2
1E-1
1E+0 C_2ptsfitm
= (306 2) MeV
Z = (2.33 0.03)·10- 2
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Details of our calculations
● Lattice step: a~0.09 fm
● Lattice size: L=24, T=48
● Dynamical flavors: nf=2
● Our pion mass range: 300 < mπ < 600 MeV
● (mπphysical = 140 MeV)
● Twisted boundary conditions: Ψ (L)=ei2πθ Ψ (0)
→ smallest momentum: pmin
=θ ·2π /L
● Improved Symanzik gauge action
● Maximally twisted mass fermion action
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<EM>plateuax = 0.01465(35)
Results so farThe EM operator matrix element
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Results so farEM operator tensor form factor
fT
q2a2
fT (0) = 0.393(8)
= 0.59(6)pole fit
The EM operator definition:
Parametrize to get tensor form factor:
Pole fit in momentum:
m = 306(2) GeV, mK = 536(2) GeV
And overall renormalization constant, calculated non-perturbatively:Z
T=0.75
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Results so farEM operator, extrapolation to physical mass
EM operator extrapolated: m → mphys
ffT T (0) = 0.345(11)(0) = 0.345(11)Previous result [becirevic 2001]
fT (0) = 0.77(6)
Our result is smaller by a factor~2 (but with better statistical accuracy), work in progress
m2a2
fT (0)
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Results so farCM operator matrix element
<C
M>
q2a2
<CM(0)> = 0.0168(27) = 2.41.1
pole fit
The CM operator definition:
Requires an additive renormalization,because of mixing with scalar current:
m = 377(2) GeV, mK = 558(2) GeV
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Results so far
MK
2a2 = m2a2
<CM(0)>bare
<QS(0)>
c/a = -0.020(4)
CM operator renormalization
Impose renormalization condition: in the chiral limit for zero momentum,
m=mK=0, p=0
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Results so far
CM operator extrapolated: m → mphys
<CM(0)><CM(0)>renormrenorm = 0.0017 = 0.0017 0.00160.0016
● Up to an overall renormalization constant, to be calculated
● Imposes an upper bound on the CM operator matrix element
● No previous lattice calculations, this constitutes a good result !
m2a2
<C
M(0
)>ren
orm
CM operator renormalized
Extrapolation to physical mass
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Conclusions● The lattice approach enables calculation of new
theoretical results based on first principles.
● For <|QEM
|K> Better accuracy than previously achieved can be obtained for phenomenologically interesting quantities, with the ETMC results.
● Our calculation of <|QCM
|K> provides the first lattice estimate of this matrix element. In this case, even an upper bound on the matrix element would represents an information of relevant phenomological intrerest.
● More work is needed in checking the results and estimating errors.
I wish to thank my supervisors for a lot of help and
many enlightening discussions
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[1] B. Mele, PhD course lecture notes (2008) ; S. P. Martin,”A Supersymmetry Primer,'' arXiv:hep-ph/9709356 (v5 2008)
[2] I. Montvay and G. Munster, ”Quantum fields on a lattice”, Cambridge, UK: Univ. Pr. (1994) ; G. Martinelli, ”Phenomenology From Lattice QCD,'' GIFT Seminar 1988:146-198
[3] D. Becirevic, V. Lubicz, G. Martinelli and F. Mescia, Phys. Lett. B501, 98 (2001) [arXiv:hep-ph/0010349]
References