Intro QCD Isospin breaking Weak interactions

KAON09: Standard Model
Gilberto Colangelo

KAON09 – Tsukuba, June 12. 2009

Intro QCD Isospin breaking Weak interactions

The Standard Model @ E ∼ MK
(u=d,s)

LSM = LQCD

(u=d,s)

LQCD+ LQED + L[mu −md ] + Lnonren≡ QCD with three flavoursd
mu = md = mu +m≡ m̂2◮ dominant term
◮ only two parameters (m̂, ms )◮ very rich phenomenology(spectrum, scattering, nuclear physics)◮ ⇒ ideal playground for a theorist!

Intro QCD Isospin breaking Weak interactions

The Standard Model @ E ∼ MK(u=d,s)

LSM = LQCD

+ LQED + L[mu −md ] + Lnonren

LQED + L[mu −md ] =isospin-breaking part◮ small correction◮ one more free parameter (mu − md )◮ mostly ignored by theorists⇒ until experiments become precise enoughIntro QCD Isospin breaking Weak interactions

The Standard Model @ E ∼ MK
(u=d,s)

LSM = LQCD
Lnonren =+ LQED + L[mu −md ] + Lnonren

1 P (d) (d)d=5 M d−4i ci OiP∞WExamples:(5)= µ̄σµν F µν µ(6)= ūL γ µ sL ēL γµ νLOaµOKℓn◮ tiny nonrenormalizable corrections◮ breaks several symmetries(P, CP, flavour)◮ makes kaons most interesting

through them we glimpse into the physics at the electroweak scale

Intro QCD Isospin breaking Weak interactions

QCD @ low energy
Problem: calculate the path integral of QCD nonperturbatively
Approaches:◮ lattice◮ chiral perturbation theory◮ dispersion relations

Topics @ this conference:◮ determination of LECs
◮ convergence of SU(3) χPT(role of the strange quark?)◮ ππ scattering lengths(brute force, first principles)(symmetry)(causality≡analyticity, unitarity)

Intro QCD Isospin breaking Weak interactions

Convergence of [SU(3)] χPT
Lattice talks by:Boyle, Christ, Izubuchi, Mescia, Noaki

Observed quark mass dependence described by χPT?

Intro QCD Isospin breaking Weak interactions

Convergence of [SU(3)] χPT

Intro QCD Isospin breaking Weak interactions

Convergence of [SU(3)] χPTtalk by P. BoyleIntro QCD Isospin breaking Weak interactions

Convergence of [SU(3)] χPT

Intro QCD Isospin breaking Weak interactions

Convergence of [SU(3)] χPT◮ NLO SU(3) χPT

works as expected in phenomenology◮ NNLO analyses show that fits may be delicate(many-parameter fits may end up in a region where the χPT serieslooks not convergent)◮ ms is not small◮ lattice may teach us something new about the role of thestrange quark in QCD◮ need to wait for lattice data at lower ms

Intro QCD Isospin breaking Weak interactions

ππ scattering lengths
-0.02

-0.03

2a0 -0.04

1996

1983

1966

-0.05

Universal Bandtree, one loop, two loops__l4=4.4±0.2, l3 free__l3=2.9±2.4, l4 free-0.06

Colangelo, Gasser & Leutwyler 2001
0.16

0.18

0.2

0.22

0a00.240.26

Intro QCD Isospin breaking Weak interactions

ππ scattering lengths-0.03-0.0352universal bandscalar radius
CGL
MILC
NPLQCD
CERN
ETM
RBC/UKQCD
JLQCD
PACS-CSa0-0.04-0.045

0.20

0.21

0.22

0a00.230.24

Intro QCD Isospin breaking Weak interactions

ππ scattering lengths

Figure by B. Bloch-Devaux, talks also by D. Madighozin and E. Blucher

Intro QCD Isospin breaking Weak interactions

πK scattering lengths?

Figure courtesy of J. Gasser

Intro QCD Isospin breaking Weak interactions

πK scattering lengths?

Intro QCD Isospin breaking Weak interactions

On the measurement of the ππ scattering lengths◮ measurement done in three different ways

1. π + π − lifetime
2. cusp in K → 3π
3. Ke4 decays

DIRAC
NA48 (cf. also first results by KTeV)
Geneva-Saclay, E865, NA48

◮ for the first two: measurement at all possible thanks to

isospin breaking◮ for the third: isospin breaking corrections necessary toproperly interpret the resultcf. talk by B. Bloch-Devaux

Intro QCD Isospin breaking Weak interactions

Isospin breaking effects
At the present level of experimental precision, isospin breaking
effects have to be understood in detail:⇒ lattice for QCD+QED and with mu 6= md
talk by T. Izubuchi◮ very interesting exploratory study◮ new theoretical issues (finite volume effects)◮ long term goal (light-by-light) worth the efforts

Intro QCD Isospin breaking Weak interactions

Isospin breaking effects
At the present level of experimental precision, isospin breaking
effects have to be understood in detail:⇒ lattice for QCD+QED and with mu 6= md
talk by T. Izubuchi⇒ χPT for QCD+QED and with mu 6= md◮ Kℓ2 and Kℓ3 decays

th: E. Passemar
exp: E. Goudzovski, M. Palutan, B. Sciascia◮ for rare decays◮ study of radiative decays

th: C. Smith
exp: V. Duk, M. Moulson, R. Wanke

The very sensitive tests of lepton universality, or of CKM unitarity, or the SM test in K → πν̄ν need a thorough control of isospin
breaking corrections

Intro QCD Isospin breaking Weak interactions

Experimental study of non-renormalizable interactions
In contrast to new-physics searches, in the SM one can explicitly◮ integrate out the heavy degrees of freedom in the SMtalk by C.S. Lim◮ run the effective Hamiltonian down to lower scales
talk by M. Gorbahn◮ obtain the Wilson coefficients of the non-renormalizable

operators at low-energy as functions ofthe CKM matrix elements
the masses of the heavy degrees of freedom◮ the gauge couplings◮◮

cf. reviews by A. Buras

Intro QCD Isospin breaking Weak interactions

Experimental study of non-renormalizable interactions
In contrast to new-physics searches, in the SM one can explicitly◮ integrate out the heavy degrees of freedom in the SMtalk by C.S. Lim◮ run the effective Hamiltonian down to lower scales
talk by M. Gorbahn◮ obtain the Wilson coefficients of the non-renormalizable

operators at low-energy as functions ofthe CKM matrix elements
the masses of the heavy degrees of freedom◮ the gauge couplings◮◮

cf. reviews by A. Buras

to obtain predictions ⇒ evaluate the hadronic matrix elements

Intro QCD Isospin breaking Weak interactions

Semileptonic decays
If leptons are involved, the hadronic matrix elements can beevaluated with good accuracy
talks by P. Boyle, F. Mescia, E. Passemar, C. Smith
Lepton universality test:
RK= (2.498 ± 0.014) · 10−5 (WA)RK= (2.477 ± 0.001) · 10−5 (SM)talks by E. Goudzovski, B. Sciascia

CKM unitarity

Cirigliano, Rosell 07

talk by M. Palutan|Vud |2 + |Vus |2 − 1 = −0.0004(7)Intro QCD Isospin breaking Weak interactions

Semileptonic decaystalk by E. Goudzovski

Intro QCD Isospin breaking Weak interactions

Semileptonic decays

talk by M. Palutan

Intro QCD Isospin breaking Weak interactions

Nonleptonic decays
If only light quarks are involved, the hadronic matrix element
evaluation becomes very hard:talk by N. Christ◮ K → ππ a major RBC/UKQCD project:

L = 4.5 fm, 1/a = 1.4 GeV, Mπ = 240, 180 MeV◮ “Expect 20% result for ∆I = 1/2 rule and ǫ′ /ǫ in ∼ 3 years!”◮ First lattice calculation of the ππ a0 as a by-product?
0Until then, the beautiful results of NA48 and KTeV:
by E. Blucher and M. Pepeµ ′¶ǫ
Re= (16.8 ± 1.4) · 10−4ǫ(WA)and measurements of K lifetimes and K → 3π BR’s talk by S. Bocchetta
do not provide a test of the SM

Intro QCD Isospin breaking Weak interactions

Photon and Z penguins...
...offer an interesting situation in which short and long distancegive competing contributions
using χPT and dispersion relations ⇒ long-distance physics
talk by C. SmithIntro QCD Isospin breaking Weak interactions

Photon and Z penguins...
...offer an interesting situation in which short and long distancegive competing contributions
using χPT and dispersion relations ⇒ long-distance physics
talk by C. SmithIntro QCD Isospin breaking Weak interactions

Photon and Z penguins...

talk by M. Gorbahn

Intro QCD Isospin breaking Weak interactions

Photon and Z penguins...

talk by D. Bryman

Intro QCD Isospin breaking Weak interactions

OutlookIn a few years from now...

talks by D. Bryman, H. Morii, H. Nanjo and G. RuggieroFig. from the talk by M. Gorbahn