WG1: KAON PHYSICS. Johan Bijnens Lund University. bijnens

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1 lavi net WG1: KAON PHYSICS Johan Bijnens Lund University bijnens Various ChPT: bijnens/chpt.html Euroflavour07 WG1:Kaon physics Johan Bijnens p.1/27

2 Overview Conveners: Johan Bijnens and Gino Isidori Flavianet average for e.g. V us WG session talks I. Rosell: Improving the theoretical status of π(k) e ν e [γ] B. Sciascia: KLOE perspectives on Kaon decays J. Bijnens: Isospin violation at NNLO for K l3 and rare decays D. Greynat: Progress on analytical expression of K l3 form factors at two loop order R. Wanke: NA48/NA62 Status and Prospects of Semileptonic and Leptonic Kaon Decays Euroflavour07 WG1:Kaon physics Johan Bijnens p.2/27

3 Overview Plenary talks (well planned at least): H. Neufeld, E. Passemar, A. Fuhrer, F. Mescia, B. Moussallam Many other talks relevant for Kaons Thanks to B. Sciascia for getting talks to work (and thanks to Microsoft for updating my laptop automatically into not working) Euroflavour07 WG1:Kaon physics Johan Bijnens p.3/27

4 I. Rosell Improving the theoretical status of Ignasi Rosell Universidad CEU Cardenal Herrera EuroFlavour 07 In collaboration with: V. Cirigliano (Los Alamos) JHEP 0710 (2007) 005 [ [hep-ph]] To appear in PRL [ [hep-ph]] Euroflavour07 WG1:Kaon physics Johan Bijnens p.4/27

5 I. Rosell 1. Motivation i) helicity suppressed sensitive probe af SM extensions attention in SUSY ii) Effects from weak-scale new physics iii) Ongoing experimental searches iv) Strong dynamics cancels out partially in the ratio SM can reach this precision Required corrections present predictions: * ** ** * Marciano and Sirlin 93 ** Finkemeier 96 Euroflavour07 WG1:Kaon physics Johan Bijnens p.5/27

6 I. Rosell Phenomenology (continuation) Marciano et al. Finkemeier Discrepancy at 0.2% level NA48/3 plans to reach an uncertainty of 0.3% Euroflavour07 WG1:Kaon physics Johan Bijnens p.6/27

7 I. Rosell 7. The individual modes LO result Universal short-distance EW correction Kinoshita 59 Studied at : Given in Knecht et al. 00 Estimated in Descotes- Genon et al. 05 This work The only remaining task: at Future work Euroflavour07 WG1:Kaon physics Johan Bijnens p.7/27

8 J. Bijnens lavi net ISOSPIN VIOLATION AT NNLO FOR K l3 AND RARE DECAYS Johan Bijnens Lund University bijnens@thep.lu.se bijnens Various ChPT: bijnens/chpt.html Euroflavour07 Isospin violation at NNLO for K l3 and rare decays Johan Bijnens p.1/24 Euroflavour07 WG1:Kaon physics Johan Bijnens p.8/27

9 J. Bijnens Formfactor relations r(t) = 1 + δ 2 is always true, also for r (t) and r 0 (t) Vector operator is I=1/2 (m u m d )(ūu dd) is I =1 f K+ π 0 l (t) = f A l (t) + δfb l (t) + O(δ2 ), f K0 π l (t) = f A l (t) δfd l (t) + O(δ2 ), f K+ π + l (t) = f A l (t) + δfd l (t) + O(δ2 ), f K0 π 0 l (t) = f A l (t) δfb l (t) + O(δ2 ), Photon exchange has I = 0, 1, 2, I = 2 part breaks relation Relation also true for scalar currents su, sd Euroflavour07 Isospin violation at NNLO for K l3 and rare decays Johan Bijnens p.8/24 Euroflavour07 WG1:Kaon physics Johan Bijnens p.9/27

10 J. Bijnens f + (0) Palutan: KAON07 r 0 (0) = = , r 0 exp = 1 + SU(2) = ± As we see, we obtain a reasonable agreement. Euroflavour07 Isospin violation at NNLO for K l3 and rare decays Johan Bijnens p.16/24 Euroflavour07 WG1:Kaon physics Johan Bijnens p.10/27

11 J. Bijnens Callan-Treiman point Callan-Treiman: f 0 ( m 2 K m 2 π) = F K Fπ + O(m u,m d ). CT f 0 ( m 2 K m 2 π) F K Fπ = (GL, iso) CT = NNLO using BT formulas With δp 4 Calculated with F K /F π = 1.22 K+ π 0 CT = , K0 π CT = , K+ π + CT = , K0 π 0 CT = Euroflavour07 Isospin violation at NNLO for K l3 and rare decays Johan Bijnens p.23/24 Euroflavour07 WG1:Kaon physics Johan Bijnens p.11/27

12 D. Greynat Progress on analytical expression of Kl 3 form factors at two loop order David Greynat a In collaboration with Roberto Bonciani a, Christoph Haefeli a, Roland Kaiser b, Antonio Pich a and Eduardo de Rafael b a Institut de Física Corpuscular Valencia b Centre de Physique Théorique Marseilles FlaviaNet Meeting Orsay 14 th - 16 th November Euroflavour07 WG1:Kaon physics Johan Bijnens p.12/27

13 D. Greynat Introduction First step : Laporta s Algorithm Second step : Multi-dimensional Converse Mapping theorem An example of calculation J. Bijnens web page http :// bijnens/chpt.html The chiral expansion of f Kπ is given by f = f (2) }{{}.=1 + f (4) + f (6) (3) From now, we are taking the two loops expression for f Kπ provided by J. Bijnens. It involves scalar two loop D-dimensional integrals V. = ˆ d D k 1 (2π) D d D k 2 (2π) D Num. [ ] [ ] [ (4) k 2 1 m1 2 (k1 q) 2 m2 2 (k1 + k 2 p) 2 m4] 2 at the end 396 scalars integrals! Necessity of a method to obtain a complete analytical expression. Progress on analytical expression of Kl 3 form factors at two loop order David Greynat Euroflavour07 WG1:Kaon physics Johan Bijnens p.13/27

14 D. Greynat Introduction First step : Laporta s Algorithm Second step : Multi-dimensional Converse Mapping theorem An example of calculation Laporta s Algorithm S.Laporta, Int. J. Mod. Phys. A 15 (2000) 5087 T. Gehrmann and E. Remiddi, Nucl. Phys. B 580 (2000) 485 R. Bonciani, P. Mastrolia and E. Remiddi, Nucl. Phys. B 661 (2003) 289 Every two loops amplitudes obey to the following form I = ˆ d D k 1 (2π) D d D k 2 (2π) D for S scalar products and D denominators. S n1 1 Sn N N D l 1 1 Dl L L 1. Use the Integrate by parts relation (Stokes theorem) ˆ [ ] d D k 1 d D k 2 (2π) D (2π) D k µ v µ S n 1 1 Sn N N j D l 1 1 Dl L L = 0 for v = k 1, k 2, p, q. 2. Use Lorentz invariance and discrete symmetries Progress on analytical expression of Kl 3 form factors at two loop order David Greynat Euroflavour07 WG1:Kaon physics Johan Bijnens p.14/27

15 D. Greynat Introduction First step : Laporta s Algorithm Second step : Multi-dimensional Converse Mapping theorem An example of calculation Obtaining then the following representation ˆ ω 1 = n=0 k=0 (4ρ 1 ) n n! [ + ρ 1 ǫ 2 2 Γ ( [ ρ k 2 Γ k! 2 ǫ n, 1 ǫ 2 k, 1 ǫ 2 n n k ǫ+2, ǫ n k, 3 2 ǫ 2 n k 1+ ǫ 2, 2 ǫ n, 1 ǫ 2 n 3 2 ǫ 2 n, 2 ǫ n k, 1 ǫ 2 n k ] ] [ + 4ρ 1 Γ ] ) 1 ǫ 2 k, 1 ǫ 2 n, 1+ ǫ 2 n 1 2 n, 2 ǫ k n, 1 ǫ 2 k n We doing the same processus for all 6 2-forms ω j... To obtain finally the following behaviour after an ǫ-expansion H(m 2 η, m 2 K,m 2 K,m 2 π) 1 ǫ 2 [ 1 8 ( 2m 2 K + m 2 η) ] + in agreement with literature Of course the epsilon-expansion and the cut of the infinite series are not obligatory and in this sense, we have an analytic expansion of the Master Integrals. M. Caffo et al., Nuovo Cimmento Vol. III, A, N 4 (1998) Progress on analytical expression of Kl 3 form factors at two loop order David Greynat Euroflavour07 WG1:Kaon physics Johan Bijnens p.15/27

16 KLOE and NA48/NA62 B. Sciascia gave a summary of (some of) the KLOE kaon results R. Wanke gave a summary of (some of) the NA48/NA62 kaon results No 20 minute summary can give tribute to all the Kaon results from these experiments So summary of summaries???????? Euroflavour07 WG1:Kaon physics Johan Bijnens p.16/27

17 B. Sciascia ± ± µ B. Sciascia, LNF INFN for the KLOE collaboration FlaviaNet meeting - Orsay, 14 November 2007 Euroflavour07 WG1:Kaon physics Johan Bijnens p.17/27

18 B. Sciascia from data 07 Euroflavour07 WG1:Kaon physics Johan Bijnens p.18/27

19 ) ( 0 B. Sciascia ± BR and lifetime measurements K ± e3 K ± µ3 K ± µ ± ν K ± π ± π 0 : (K ± e ) τ ± (K ± / τ ± /τ µ ) ± Κ ± τ ± τ ± γ ± π ± π 0 τ ± τ ± τ ± ρ τ τ K ± π + π 0 K + π + π 0 K µ ν (K π ) Euroflavour07 WG1:Kaon physics Johan Bijnens p.19/27

20 B. Sciascia FFe3 and FFµ3 using K ± π µ µ π π µ µ Euroflavour07 WG1:Kaon physics Johan Bijnens p.20/27

21 B. Sciascia Conclusions f (χ ± π ± π + π ± Euroflavour07 WG1:Kaon physics Johan Bijnens p.21/27

22 R. Wanke NA48/NA62 Status and Prospects of Semileptonic and Leptonic Kaon Decays Rainer Wanke Institut für Physik, Universität Mainz EuroFlavour 07 Orsay, November 14, 2007 Rainer Wanke EuroFlavour 07, Orsay, November 14, 2007 p.1/18 Euroflavour07 WG1:Kaon physics Johan Bijnens p.22/27

23 R. Wanke Overview NA48/NA62 K l3 and K l2 : 1999 K L running (NA48): K L e3 branching ratio and form factors, K L µ3 form factors, K L e3γ 2003 and 2004 K ± running (NA48/2): K e3 ±, K± µ3 branching ratios, K± l3 form factors, Γ(K e2 )/Γ(K µ2 ) 2007 K + running (NA62): High statistics Γ(K e2 )/Γ(K µ2 ). Possibility for K ± l3, K L l3 All NA48 Semileptonic and Leptonic Analyses: Minimum-bias data for precision measurements = High trigger efficiencies, small systematics K High 2000 K only S L Intensity NO Spectrometer ε /ε run ε /ε run ε /ε run K + K L S ε /ε run K + K L S K High Intensity S 2003 K + High Intensity 2004 K + High Intensity K + K L S K + K L S 2007 K + Minimum Bias K S Hi. Int. K S High Int. Rainer Wanke EuroFlavour 07, Orsay, November 14, 2007 p.2/18 Euroflavour07 WG1:Kaon physics Johan Bijnens p.23/27

24 R. Wanke K e2 /K µ2 Two preliminary NA48 measurements from 2003/2004 data: NA48/2 (2003 data), presented in 2005: About 4000 signal events from normal running period. Systematics dominated by trigger efficiencies. Γ(K e2 )/Γ(K µ2 ) = (2.416 ± ± 0.024) 10 5 NA48/2 (2004 data), presented in 2007: About 4000 signal events from special minimum bias trigger. Small systematics, except background. (measured from data large statistical uncertainty in syst. error.) Completely uncorrelated with 2003 measurement. Γ(K e2 )/Γ(K µ2 ) = (2.455 ± ± 0.041) 10 5 Both results in agreement with each other, PDG, KLOE and SM theory. Rainer Wanke EuroFlavour 07, Orsay, November 14, 2007 p.9/18 Euroflavour07 WG1:Kaon physics Johan Bijnens p.24/27

25 R. Wanke K e2 /K µ2 Expectations from 2007 Expected precision on K e2 /K µ2 : Statistical: ±0.3% Systematic: ±0.2% In total expected: P-326, 2008? 4 NA48/2 (2003), prel. 3 NA48/2 (2004), prel. 2 KLOE, prelim σ(r K )/R K ±0.35% -5 Γ(K e2 ) / Γ(K µ2 ) [10 ] SM tanβ : Next year?! tanβ 13 < < 5x same R K central value % CL limits < < % CL limits charged higgs mass (GeV/c 2 ) < 5x < charged higgs mass (GeV/c 2 ) Rainer Wanke EuroFlavour 07, Orsay, November 14, 2007 p.14/18 Euroflavour07 WG1:Kaon physics Johan Bijnens p.25/27

26 R. Wanke First Measurement of K ± π ± e + e γ In whole 2003/2004 K ± data: (CERN-PH-EP/ ) 120 K ± π ± e + e γ signal candidates (Bkg: 7.3 ± 1.7 events) = 4 the published K ± π ± γγ statistics! Model-independent branching fraction: Br(K ± π ± e + e γ,m eeγ > 260 MeV) = (1.19 ± 0.12 stat ± 0.04 sys ) 10 8 ĉ extraction: ĉ = 0.90 ± 0.45 Entries / (5 MeV/c 2 ) Data MC K + π + π 0 πd 0 MC K + π + πd 0γ MC K + π + π 0 e + e - MC K + π + e + e - MC K + π 0 D e+ ν Entries / (5 MeV/c 2 ) Data MC K + π + πd 0γ MC K + π + π 0 e + e - MC K + π + e + e - MC K + π + πd 0 MC K + π + π 0 π 0 D Invariant π ± e + e - + γ mass [GeV/c ] 2 Invariant e e - γ mass [GeV/c ] Rainer Wanke EuroFlavour 07, Orsay, November 14, 2007 p.17/18 Euroflavour07 WG1:Kaon physics Johan Bijnens p.26/27

27 Conclusions Expect more Kaon results in theory and experiment in EUROFLAVOUR08 Euroflavour07 WG1:Kaon physics Johan Bijnens p.27/27