THEORY OF (SOME) KAON DECAYShome.thep.lu.se/~bijnens/talks/jparc16kaon.pdfTREK at J-PARC OKA at...
48
Theory of Kaon decays Johan Bijnens What is kaon History Introduction K → ππ K → π‘ν or πνν Other decays Summary 1/45 THEORY OF (SOME) KAON DECAYS Johan Bijnens Lund University [email protected] http://www.thep.lu.se/~bijnens The international workshop on future potential of high intensity accelerators for particle and nuclear physics (HINT2016) – J-PARC, Japan 5-8 December 2016
Transcript of THEORY OF (SOME) KAON DECAYShome.thep.lu.se/~bijnens/talks/jparc16kaon.pdfTREK at J-PARC OKA at...
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
1/45
THEORY OF (SOME) KAON DECAYS
Johan Bijnens
Lund University
http://www.thep.lu.se/~bijnens
The international workshop on future potential of high intensity accelerators for particle and nuclearphysics (HINT2016) – J-PARC, Japan 5-8 December 2016
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
2/45
Overview
1 What is kaon
2 HistoryFirst kaonsMain kaon contributions
3 Introduction
4 K → ππ∆I = 1/2 rule: an old problemε′/ε
5 K → π`ν and K → πννKπ form-factorsK → πνν
6 Other decaysLepton UniversalityKaons, ChPT and hadron physics
7 Summary
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
3/45
Google Kaon
http://www.tech-ex.com/article images1/
324984/DSC02855.JPG
http://tiranaxxl.com/place/
kaon-brewhouse/
Tirana, Albania
http://kaon.com
Wikipedia
Theory ofKaon decays
Johan Bijnens
What is kaon
History
First kaons
Main kaoncontributions
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
4/45
The first kaons
a V particle
Theory ofKaon decays
Johan Bijnens
What is kaon
History
First kaons
Main kaoncontributions
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
5/45
The first kaons
a τ+ → π+π+π− decay
Theory ofKaon decays
Johan Bijnens
What is kaon
History
First kaons
Main kaoncontributions
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
6/45
Kaon main contributions
Produced with strong interaction rates, decay weakly:Introduction of strangeness: Gell-Mann–Pais
θ, τ , κ, . . . : All the same massThe θ-τ puzzle
τ → 3π =⇒ negative parity,θ → 2π =⇒ positive parity,Two particles or parity broken
K 0-K0: Two states with very different lifetimes
KL and KS are the CP even and odd statesCP-violation
∆I = 1/2 rule: Γ(KS → π0π0) ≫ Γ(K+ → π+π0)
Direct CP-violation ε′/ε
Determination of Vus
ππ scattering lengths
· · ·
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
7/45
Experiments (Theory needs it for comparison)
New data from old Kaon experimentsE949 at BNLNA48(/2) at CERNKTeVKLOE at Frascati
From some unexpected placesLHCb at CERN
From current and under construction experimentsNA62 at CERNTREK at J-PARCOKA at IHEP, ProtvinoKOTO at J-PARCKLOE-2 at Frascati
ProposalsKLEVER at CERN (KL → π0νν), KOTO stage 2
And all those I forgot
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
8/45
Flavour Physics
Experiments in flavour physics often very precise
New effects start competing with the weak scale: can bevery visible
If it changes flavour: limits often very goods d
u, c
t
W
γ, g ,Z
Heavy particles cancontribute in loop
Sometimes need a precise prediction for the standardmodel effect
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
9/45
Reviews, recent talks, what do we do
Kaon 2016 http://www.ep.ph.bham.ac.uk/KAON2016/
V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles,“Kaon Decays in the Standard Model,”Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001 [hep-ph]]
A.J. Buras (recent talks):“The Revival of Kaon Flavour Physics,” arXiv:1609.05711 [hep-ph]“Kaon Flavour Physics Strikes Back,” arXiv:1611.06206 [hep-ph]“The Renaissance of Kaon Flavour Physics,” [arXiv:1606.06735 [hep-ph]]
testing CPT (i.e. QFT) and Quantum mechanics (notcovered here)
determining standard model parameters precisely
looking for deviations from SM in all possible corners
Needs precise theory predictions for SM and BSM
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
10/45
The overall framework
SCALE FIELDS (remove) Effective Theory
� MW squarks, lepto-quarks,. . . SM + BSM
⇓ use OPE if new heavy, otherwise loop-diagrams
MW W ,Z ,H, t, (b, c)Standard Model +dim ≥ 5 operators
⇓ using OPE, step at mb, mc
. mc g , τ , s, d , uQCD,QED, +dim ≥ 5 operators
⇓ ??? The difficult one
MK γ, µ, e, ν`, π, K , η, hadronsChPT, lattice,sum rules, models
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
11/45
Last step pictorially
A weak decay:
Hadron:1 fmW -boson:10−3 fm
su
du
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
11/45
Last step pictorially
A weak decay:
Hadron:1 fmW -boson:10−3 fm
su
du
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
12/45
Why Kaon?
Same arguments for B, Bs , D, K so why Kaon?
L = LSM + 1Λ2O∆F=2
G. Isidori kaon 2016
We need to test all transitions in and between generationsKaon physics: main probe of second to first generation
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
13/45
Some recurring themes
Precision experiments must be matched by precision theory
The very high energy part is (except for speculations onwhich BSM) under control
The QCD and QED running to a low scale is now typicallydone at NNLO or even N3LO.
EW for many now at NLO
So precision is needed in the last steps
Recurring themes:
Radiative corrections (photons in experiment)Other electro-magnetic corrections (photons in theory)In ChPT and sum rules: determine all parametersIn Lattice QCD: proper matching to continuum quantitiesLong distance contributions: (∆S = 1)2 vs ∆S = 2Isospin breaking
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
14/45
K → ππ and the ∆I = 1/2 Rule
K+ −→ π+π0 :K+
π0
W+
π+
+K+ W+
π0
π+
K 0 −→ π0π0 :K 0
π0
W+
?
? π0
: IMPOSSIBLE
Experimentally:
Γ(K 0 −→ π0π0) =1
2Γ(KS −→ π0π0) = 2.3 10−12 MeV
Γ(K+ −→ π+π0) = = 1.1 10−14 MeV
So the zero one is the largest !!!
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
14/45
K → ππ and the ∆I = 1/2 Rule
K+ −→ π+π0 :K+
π0
W+
π+
+K+ W+
π0
π+
K 0 −→ π0π0 :K 0
π0
W+
?
? π0
: IMPOSSIBLE
Experimentally:
Γ(K 0 −→ π0π0) =1
2Γ(KS −→ π0π0) = 2.3 10−12 MeV
Γ(K+ −→ π+π0) = = 1.1 10−14 MeV
So the zero one is the largest !!!
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
15/45
Isospin amplitudes
A[K 0 → π0π0] ≡√
1
3A0 −
√2
3A2
A[K 0 → π+π−] ≡√
1
3A0 +
1√6A2
A[K+ → π+π0] ≡√
3
2A2
∣∣∣∣A0
A2
∣∣∣∣ = 22.4 and the naive gives√
2∣∣∣∣A0
A2
∣∣∣∣ = 18 (p2 part) fit to K → 2π, 3π up to order p4, JB, Borg 2005
For later use: AI = −iaI e iδI
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
16/45
δ0 − δ2
Recent analysis a0, a2 and δ0 − δ2
Cirigilano, Ecker, Pich, 0907.1451
Older (full ChPT fits):Cirigliano, Ecker, Neufeld, Pich, hep-ph/0310351
JB, Borg, hep-ph/0405025, hep-ph/0410333, hep-ph/0501163
δ0 − δ2 = (60.8± 2.2± 3.1)o = (57.9± 1.5±?)o
(NLO ChPT fit for all)
Now fit to data but only use NLO ChPT for the isospinbreaking partsδ0 − δ2 = (52.84± 0.83)o
Change 3o from experiment and 5o from theory.
δ0 − δ2 = (47.7± 1.5)o ππ Colangelo, Gasser, Leutwyler
Isospin breaking is enhanced by the ∆I = 1/2 rule: ±3o
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
17/45
A0/A2: analytical
Short distance enhancement from gluon exchange (early70s), now known at three loop level
Large Nc : factorization exact
Corrections can be included Bardeen-Buras-Gerard 88-91
A. J. Buras, J. M. Gerard and W. A. Bardeen, “Large N Approach to KaonDecays and Mixing 28 Years Later: ∆I = 1/2 Rule, BK and ∆MK ,”
Eur. Phys. J. C 74 (2014) 2871 [arXiv:1401.1385 [hep-ph]].
Almost all analytical work builds on the 1/Nc approach
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
18/45
A0/A2: analytical
T. Hambye et al. BBG approach hep-ph/9802300, hep-ph/9906434
JB,Prades: matching to QCD-models via fictitious X -bosonexchange so match currents, not four-quark operators.Low Q2: ChPT, Intermediate: ENJL plus for BK and Q8
better models and data. Still lacking: beyond chiral limitand improving intermediate Q2. hep-ph/9811472,
hep-ph/9911392, hep-ph/0005189, hep-ph/0108240, hep-ph/0304222,
hep-ph/0601197
Peris, de Rafael Use a MHA approach for each needed Greenfunction, i.e. single resonance saturation per channelhep-ph/9805442, hep-ph/9812471, hep-ph/0006146, hep-ph/0305104
Hambye et al. AdS/QCD . Essentially MHA but with a towerof (axial-)vector mesons hep-ph/0512089, hep-ph/0612010
Pallante, Pich Large Nc plus FSI hep-ph/0007208, hep-ph/0105011
Earlier: Bertolini, Fabbrichesi, Eeg Chiral Quark Modelhep-ph/9511255, hep-ph/9705244, hep-ph/0002234
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
19/45
A0/A2: analytical
0
2
4
6
8
10
0.5 0.6 0.7 0.8 0.9 1
Re
G8
µ [GeV]
II
I
muladd
0
0.1
0.2
0.3
0.4
0.5
0.5 0.6 0.7 0.8 0.9 1
G
27
µ [GeV]
I
II
I quadratic
muladd
Parameters from the NLO ChPT fit to A0,A2:
G8 = 5.39
G27 = 0.36
Can get a reasonable agreement but still errors/problems
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
20/45
A0,A2: lattice
Taku Izubuchi this afternoon
Technique worked out by Lellouch-Luscher long ago
A2 relatively easy, OK since several years, several groupsReA2 = 1.381(46)stat(258)syst 10−8 GeVRBC/UKQCD 1206.5142
ReA2 = 1.479(4) 10−8 GeV (exp)
A0 much more difficult (disconnected graphs),but there is progressReA0 = 4.66(1.00)stat(1.26)syst 10−7 GeVRBC/UKQCD 1505.07863
ReA0 = 3.3201(18) 10−7 GeV (exp)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
21/45
CP-violation
K 0-K0
mixing: box-diagrams
Direct CP-violation in K → ππ: Penguin diagrams
s d
u, c
t
W
γ, g ,Z
1
Many effects but ε′/ε Gilman, Wise 79: Gluonic Penguins
Electroweak Penguins can be important JB, Wise, 1984
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
22/45
ε′/ε
η00 =A(KL → π0π0)
A(KS → π0π0)η00 =
A(KL → π+π−)
A(KS → π+π−)
Re ε′
ε ≈16
(1−
∣∣∣ η00η+−
∣∣∣2)Measured CERN (NA31/NA48) and FNAL (KTeV) 1999
Re ε′
ε = 16.6(2.3) 10−4
CP-violation must be produced at the weak scale
ε′ =i√2e i(δ2−δ0)Rea2
Rea0
(Ima2
Rea2− Ima0
Rea0
)So need (at least) to calculate Ima0, Ima2
More difficult: sizable cancellations between gluonic vselectroweak penguins
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
23/45
ε′/ε
Same methods as for real part can be used, uncertaintyenhanced because of the cancelation
large Nc
Upper bounds on the gluonic Penguin A. J. Buras and
J. M. Gerard, JHEP 1512 (2015) 008 [arXiv:1507.06326 [hep-ph]]
ε′/ε ≤ (8.6± 3.2) 10−4 vector mesons onlyJ. Bijnens and J. Prades, JHEP 0006 (2000) 035 [hep-ph/0005189]
ε′/ε = (6± 3) 10−3 chiral limitDiscrepancy needs to be understood
Lattice
RBC/UKQCD 1505.07863
ε′/ε = (1.4± 5.2± 4.4) 10−4
For the electroweak Penguin everyone agrees essentially
Possible discrepancy with experiment tantalizing (ε′ and ε)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
∆I = 1/2
ε′/ε
K →π`ν or πνν
Other decays
Summary
24/45
εK
εK measures the CP-violation in K 0-K0
transitionss du, c , t
d su, c , t
W W gives (sLγµd)(sLγµd)
Main uncertainty: determination of Vcb
(FLAG 2016)
εK = 1.69(17) 10−3 Vcb Exclusive, lattice QCDεK = 2.10(21) 10−3 Vcb Inclusive, QCD sum rules
ExperimentεK = 2.228(11) 10−3
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
25/45
Overview of K → π
The CKM element Vus : two main sources:s u
ν `
WGives operator (sLγµuL)(¯γµνL)K → µν =⇒ FK |Vus |: need FK
K → π`ν =⇒ f+(0)|Vus |: need f+(0)
K → πνν: Penguin and box diagrams also lead to a(hadronic) vector operator (sLγ
µdL)(νLγµνL)
s d
νν
u, c , t
W
Z
s du, c, t
ν νe, µ, τ
W W
BSM: replace red/green by your favourite BSM particles
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
26/45
Definition of Kπ form-factors
Needed for K+`3, K 0
`3, K+,0 → π+,0ννWe have four transitions:
〈π0(p′)|sγµu|K+(p)〉 = 1√2
[(p + p′)f K
+π0
+ + (p − p′)f K+π0
−
]〈π−(p′)|sγµu|K 0(p)〉 =
[(p + p′)f K
0π−+ + (p − p′)f K
0π−−
]〈π+(p′)|sγµd |K+(p)〉 =
[(p + p′)f K
+π+
+ + (p − p′)f K+π+
−
]〈π0(p′)|sγµd |K 0(p)〉 = −1√
2
[(p + p′)f K
0π0
+ + (p − p′)f K0π0
−
]Scalar formfactor: f K
iπi
0 = f Kiπi
+ + (p−p′)2
m2Ki−m
2πif K
iπi
−
In the isospin limit: all cases have the same form-factors
Behrends-Sirlin-Ademollo-Gatto:f+,0 = 1 + a(ms − m)2 + · · ·
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
27/45
Measurements
Both neutral and charged decay
f+ and f0
f+(t) = f+(0)(1 + λ+t + λ′+t
2 + · · ·)
f0(t) = f+(0) (1 + λ0t + · · · )Alternatively use dispersive parametrizations
KLOE,NA48,ISTRA,KTeV: large number of recentmeasurements
Correlations in the form-factor measurements veryimportant
f+: VMD and SU(3) breaking
f0: Scalar meson dominance? (or dispersive better?)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
28/45
Isospin breaking: general results
To first order: insert 12 (mu −md)
(uu − dd
)once
JB, Ghorbani, 0711.0148
f K+π0
k =f Ak (t) + δf Bk (t) + · · ·
f K0π−
k =f Ak (t)− δf Dk (t) + · · ·
f K+π+
k =f Ak (t) + δf Dk (t) + · · ·
f K0π0
k =f Ak (t)− δf Bk (t) + · · ·
δ = mu −md , t = (p − p′)2
Valid for k = +,−, 0 and for scalar current matrix elements
f K+π0
k (t)− f K0π−
k (t)− f K+π+
k (t) + f K0π0
k (t) = O(δ2)
r(t) =f K
+π0
k (t)f K0π0
k (t)
f K0π−
k (t)f K+π+
k (t)= 1 +O(δ2)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
29/45
Chiral Perturbation Theory
p2: f+ = 1, f− = 0 (current algebra)(corrections at q2 = 0: (ms −mq)2)Berends-Sirlin-Ademollo-Gatto
p4 : f+(0) Leutwyler-Roos 1984
p4: Gasser-Leutwyler 1985
and isospin corrections for the weak decays
Radiative corrections: Cirigliano, Knecht, Neufeld, Talavera,. . .
p4 and radiative corrections for rare decays:Mescia-Smith, arXiv:0705.2025
p6 isospin limit: paperJB, Talavera, hep-ph/0303103 (seealso Post, Schilcher, hep-ph/0112352)
p6 isospin breaking: JB, Ghorbani, arXiv:0711.0148
Numbers for K`3: see Kastner, Neufeld, arXiv:0805.2222
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
30/45
f0(t) and f+(0)
JB, Talavera, hep-ph/0303103 Main Result:
f0(t) = 1−8
F 4π
(C r12 + C r
34)(m2
K −m2π
)2
+8t
F 4π
(2C r12 + C r
34)(m2
K + m2π
)+
t
m2K −m2
π
(FK/Fπ − 1)
−8
F 4π
t2C r12 + ∆(t) + ∆(0) .
∆(t) and ∆(0) contain NO C ri and only depend on the Lri at order p6
=⇒All needed parameters can be determined experimentally
Now update input with the new results:
∆(0) = −0.02276 (p4) + 0.01140 (p6 pure loop) + 0.0504 (p6Lri )
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
31/45
Update on K`3
Take Bijnens-Talavera 2003 result but update for BE14parameters
f K0π−
+ (0) = 1− 0.02276− 0.00754 = 0.970± 0.008
in good agreement with the latest lattice numbers (FLAG2016)2+1: 0.9677(27)2+1+1: 0.9704(32)
Note original JB-Talavera: 0.976(10)
FLAG1: 0.956(08)
Jamin, Oller, Pich, hep-ph/0401080: 0.978(09)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
32/45
r0−
1.023
1.024
1.025
1.026
1.027
1.028
1.029
1.03
1.031
-0.05 0 0.05 0.1 0.15 0.2 0.25
r 0-
t [GeV2]
p2
p4
p6
r0− = f K+π0
+ /f K0π−
+
Isospin breaking is needed when comparing the different decays
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
33/45
Universality in K`3
Data Moulson CKM2014: KLOE, ISTRA, NA48, KTeV(Flavianet kaon WG)
|Vus f+(0)|KLe3 0.2163(6) 0.26%KLµ3 0.2166(6) 0.28%KSe3 0.2155(13) 0.61%K±e3 0.2172(8) 0.36%K±µ3 0.2170(11) 0.51%
Note the good agreement(after all isospin breaking corrections)
|Vus f+(0)| = 0.2165(4)
Interpret as µ-e universality: 0.4%
Can be improved from both theory and experiment side
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
34/45
Update on CKM unitarity
FK/Fπ and f+(0) from latticeFK/Fπ & K , π → µν =⇒ |Vus/Vud |f+(0) & K → π`ν =⇒ Vus
CKM first row unitary to about 1σ
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
35/45
Prediction for K → πνν in the SM
QCD corrections: NNLO: Buras, Gorbahn, Haisch, Nierste, 2005
NLO EW: Brod, Gorbahn, Stamou, 2008, 2001
Isospin breaking: Mescia, Smith, 2007, JB, Ghorbani, 2007
Long distance effects (Main theory uncertainty)Isidori, Mescia, Smith, 2005
K
ν
π
νe, µ, τ
K , π, η
Further progress lattice QCD
Theory uncertainties about 2% in BR
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
36/45
Prediction for K → πνν in the SM
Theory uncertainties about 2% in BR
BR(K+ → π+νν) = (9.11± 0.72) 10−11
BR(KL → π0νν) = (3.00± 0.30) 10−11 Buras et al
1503.02693
largest error: CKM elements
We are eagerly awaiting the experimental results:NA62, KOTO,. . .
10% accuracy: test the predictions
few % accuracy: improve on CKM elements(and BSM tests)
Effective Zsd vertices 10-20% from SM are allowed evenin ‘nice’ BSM models Giudice,Isidori,Paradisi,12
Kaon physics: also lepton third generation via K → πντ ντRelated to all the hints in B-decays with µ and τ?
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Kπ form-factors
K → πνν
Other decays
Summary
36/45
Prediction for K → πνν in the SM
Theory uncertainties about 2% in BR
BR(K+ → π+νν) = (9.11± 0.72) 10−11
BR(KL → π0νν) = (3.00± 0.30) 10−11 Buras et al
1503.02693
largest error: CKM elements
We are eagerly awaiting the experimental results:NA62, KOTO,. . .
10% accuracy: test the predictions
few % accuracy: improve on CKM elements(and BSM tests)
Effective Zsd vertices 10-20% from SM are allowed evenin ‘nice’ BSM models Giudice,Isidori,Paradisi,12
Kaon physics: also lepton third generation via K → πντ ντRelated to all the hints in B-decays with µ and τ?
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
37/45
Lepton Universality
World’s best lepton universality test
RK =Γ(K+ → e+ν)
Γ(K+ → µ+ν)Very precise theoryCirigliano, Rosell, 2007
RK = 2.477(1) 10−5
KLOE 2009RK = 2.493(31) 10−5
NA62 2013RK = 2.488(10) 10−5
World RK = 2.488(9) 10−5
(0.4%)
TREK (E36)RK = x .xxx(6) 10−5
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
38/45
Other lepton universality and flavour violation tests
K → πeν vs K → πµν (see earlier)
K → e+e− vs K → µ+µ−
KL → π0µe (≤ 7.6 10−11)
K+ → π+µe (≤ 1.3 10−11)
K+ → π−µ+µ+ (≤ 8.6 10−11)
K+ → π+µe (≤ 4.7 10−12)
KL → µ±e∓ (≤ 5 10−12)
Strong tests in both neutral and charged kaons
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
39/45
KS → γγ
Well predicted by CHPT at order p4 Goity, D’Ambrosio, Espriu, 1986
KS
π+,K+
KS
π+,K+
KS
π+,K+
Prediction was: BR = 2.1 · 10−6
NA48 & KLOE: 2.63(17) · 10−6 (PDG 2016)
No full p6 calculation exists
FSI effects estimated, enough to get agreement
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
40/45
KL → γγ
Needs more work: main contribution is full of cancellations:difficult
KL π0, η, η′
NA31, NA48, KLOE: BR = 5.47(4) 10−4
can be explained with reasonable values of η, η′ parameters
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
41/45
KL → π0γγ
Predicted at p4 by ChPT: BR: 6.8 10−7
Espriu, D’Ambrosio 1988, Ecker, Pich, de Rafael 1987
NA48, KTeV: 1.2733(33) 10−6
ChPT prediction: events must be at high mγγ
Rate within expectation from higher order corrections
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
42/45
ππ scattering lengths
ππ-scattering is the simplest hadronic interaction
Good theory prediction: two-loop ChPT JB et al 95,97 andRoy equations Ananthanarayan et al 2000 togethera0
0 = 0.220± 0.005 Colangelo, Gasser, Leutwyler 2001
a20 = −0.0444± 0.0010
can be measured in K+ → π+π−e+ν from interferencebetween two formfactors
Isospin breaking, especially electromagnetic very important
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
43/45
ππ scattering lengths from K → ππ`ν
a00 = 0.2220± 0.0128± 0.0050± 0.0037 a0
0 = 0.220(5)a2
0 = −0.0432± 0.0086± 0.0034± 0.0028 a20 = −0.0444(10)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
LeptonUniversality
Kaons, ChPTand hadronphysics
Summary
44/45
ππ scattering lengths from K → πππ
interference near thecusp =⇒ scatteringlength
Full NR EFTanalysis:Bisegger et al 2009
Done by NA48/2
a00 − a2
0 =0.2571(48)(25)(14)
a00 − a2
0 = 0.264(4)
Theory ofKaon decays
Johan Bijnens
What is kaon
History
Introduction
K → ππ
K →π`ν or πνν
Other decays
Summary
45/45
Summary
A bit of history
K → ππ
K → πνν and K`3
Some other examples
For all these results a very strong interplay between theoryand experiment was needed
Looking forward to continue doing this and many newresults
