Rare Kaon Decays and CP, TCP Violation

1. Rare Kaon Decays and CP, TCP Violation Vincenzo Patera* LNF/INFN *From KLOE collaboration

2. Foreword and outline Foreword: kaons again? In spite of a long history the K system is still a laboratory for the flavour physics, an interferometry system, a repository of all kinds of CP violation and can be a sensitive probe for NP.. Then: YES, kaons again! • CP Violation and SM tests • TCP Violation tests • Detour to Vus • Outlook & Conclusions Blind analysis everywhere Notice: all the limits are at 90% C.L. The talk focuses on the experimental results of the last 2 years Caveat: from an experimentalist point of view…!

3. MIXING or INDIRECT DIRECT CP violation in the decay amplitute CP eigenstates ≠ mass eigenstates INTERFERENCE CP violation from interference of “DIRECT and MIXING” DIRECT CP firmly established after more than 30 years Re(e’/e) = (16.7±2.3)x10-4 Ceccucci LP03 Kaon and CP: classification eK Re(e’/e)

4. Kaons, Unitarity Triangle(s) & CP The CP violation found its niche in the CKM mixing matrix and in its Wolfenstain parametrization. Up to O(l4) the CKM is given by: If V*tdVts is complex CP is violated.. In shorthand: • A Unitarity Triangle stems from any complex unitarity costraint, but the unique measure of the CP in the CKM = 2xarea of any UT JCP = Im(Vud*VusVts*Vtd) ~ VusVud Im lt • Unique CP parameter lt probed by K or B sector differently: SM test and/or NP sensitivity

5. K+→p+nn- a KL→p0nn h g b KS→p0e+e- KS→p0m+m- KL→p0gg r KL→m+m-g KL→gg KLeemm KL→m+m- Im lt = A2l3 h Re lt= A2l3 r The Unitarity Triangle and K rare decays The rare Kaon decays BR directly measure the UT, someone by itself, someone by the aid of ancillary K decays measurement. KL→p0e+e- KL→p0m+m- Unfortunately BR ranges from 10-8 to 10-11

6. Rare Kaon decays and SM test • Yet, in spite of the experimental difficulty, the rare K system: • Is theoretically clean (almost..) • Is highly sensitive to NP • Has different sensivity to NP wrt the B sector SM test: sin2b(J/YKS) vs sin2b(Kpnn) Not only Kpnn ! NP sensitivity of KLp0ll system : Buras,Fleisher,Recksiegel, Schwab : hep-ph/0402112 b

7. Im lt = A2l3 h Re lt= A2l3 r lt and K+p+nn GOOD from a theorist point of view!! K+→p+nn a • Negligible long distance effects  10-13 • Hadronic matrix element via isospin rotation K+e+p0n • Reliable th. estimate from SM g b Charm loop contribution = r0  1.4 *Isidori hep-ph/0307014

8. side view end view K+p+nn : E787/E949@BNL • E949 wrt E787 improvement: • Photon veto hermeticity • Tracking & energy resolution • DAQ and trigger • Protons/sec from AGS • Not optimal in 2002 run: • Spill duty factor • Proton momentum • K/p electrostatic separators

9. p+ momentum in K+ frame (MeV) K+p+nn @E949: detectionstrategy Signal: a p+ from K+. No kinematic closure and overwhelming bck. • 700 MeV/c K+ stopped  decay • Detect pion from pm e decay chain • Measure everithing you can: range, momentum , energy, time 12 weeks of data taking. Bck shapes modeled on data. Each bck rejected by at least 2 independent cuts.

10. E949 E787 K+p+nn @E949:the signal Opening the box a new event is found Background check: compare events predicted vs observed loosening one cut vs the other. Acceptance from MC verified on K+p+p0

11. K+p+nn @E949:results E949 result (12 weeks of run) E949 & E787 combined result • Analysis of the low momentum region (PNN2) in progress • Efforts to achieve on PNN2 a S/N 1 and sensitivitysimilar to PNN1 • E949 was approved for 60 weeks of data taking  more stat?? (bad news…) E949(02) = combined E787&E949. E949 projection with full running

12. Im lt = A2l3 h a h KL→p0nn g b CP: Imlt and KLp0nn • Direct measure of ImltJCP • No long distance effects • Only top loop contribution • Very small theoretical error on SM prediction • Grossmann-Nir bound : BR(KLp0vv) < 4.4 x BR(K+p+nn) < 1.4 x 10-9 A dream for a theorist, a nightmare for an experimentalist. All neutral, 2/3 invisible final state: “Nothing to nothing” *Isidori hep-ph/0307014

13. KLp0e+e-(m+m-): KTeV @ Tevatron • Charged particle momentum • resolution < 1% for p>8 GeV/c; • Momentum scale known to 0.01% from K. • CsI energy resolution < 1% for E> 3 GeV; energy scale known to 0.1% from Ke. • TRD system pion/electron ID • K0p0D with 0De+e-gused to normalize flux and acceptance. KTeV More than 20 years history..

14. Data MC BG Sum Lnp0MC XLp0 MC Signal MC KLp0nn@KTeV: the limit • 1997 e’/e Data. • Analysis of events with Dalitz p0 decay. • Bck limited • 4 order of magnitude higher wrt SM prediction BR (KLp0nn)< 5.9x 10-7 (p0eeg) PRD61(2000)

15. KLp0nn: E391a@KEK-PS Firs detector designed for KLp0nn: veto, veto, veto.. • Pencil beam • Detector with complete veto system • 4p coverage with thick calorimeter • Wide acceptance • Double decay chamber • Operation in high vacuum • High PTg + nothing selection • Step by step approach • KEK-PS E391a • JPARC Pencil Beam Detector system

16. KLp0nn : E391a detector Detector integration: Jan 22, 2004 Start of Run I data taking : Feb 18 2004 End Run I data taking Jun 30 2004

17. KLp0p0 KLp0p0p0 6-g invariant mass (GeV/c2) 4-g invariant mass (GeV/c2) KLp0nn@E391a:Run I (2004) Expected sensitivity by Run I: 4÷9x10-10 Results from Run I in fall 2004 Requesting Run II in 2005

18. Im lt = A2l3 h a h KL→p0e+e- KL→p0m+m- g b KS→p0e+e- KS→p0m+m- KL→p0gg CP : Im lt from KLp0e+e-(m+m-) The connection of the KLp0e+e-(m+m-) decays to lt is not straightforward, but substantial improvement of theory and experimental results have been in the last 2-3 years, expecially related to ancillary modes

19. 2) Indirect CP term due to KL-KS mixing 1) Direct CP term Im lt , dominated by short distance dynamics e+(m+) e-(m-) e+(m+) e-(m-) • Amplitude 2) can be extracted viaefromKSp0e+e-(m+m-)decay while 3) can be derived fromKLp0ggdata • Direct and Indirect CP amplitudes can interfere. • In the past 2 years both precise calculation for 1)* and new data for KS p0e+e-(m+m) and KLp0ggappeared on the market e+(m+) e-(m-) CP : Im lt from KLp0e+e-(m+m-) KLp0e+e-(m+m-)phenomenology:the decay amplitude has 3 ingredients: 3) CP conserving term via gg intermediate state *Isidori,Smith,Underdorfer hep-ph/0404127 Buchalla, D’Ambrosio,Isidori Nucl.Phys.B672(2003)

20. e+(m+) e-(m-) From KLp0l+l- to Imlt : KSp0l+l- KLp0l+l- CP mixing contribution ( and interference) can be evaluated via e and the corresponding KSp0l+l-amplitude*. BR(KSp0e+e-)  5 x10-9 BR(KSp0m+m-)  1 x10-9 Assuming the VMD the KS BR can be predicted of the order: *Buchalla,D’Ambrosio,Isidori Nucl.Phys. B(2003)

21. KSp0e+e-(m+m-): NA48/1 @CERN KS beam : 2000 (only gs) and 2002 run LKr Calorimeter: (E)/E  3.2%/√E  9%/E  0.42% s(t)  265 ps for 50 GeV e Spectrometer: pT kick ~250 MeV/c (P)/P  0.48%  0.009 P[GeV/c]% Muon system: s(t)  350 ps M(00) ~ M(+-) ~ 2.5 MeV More than 20 years history..

22. From KLp0l+l-to Imlt : KSp0l+l- Dataset: 3.51 x1010 KS decays with t< 2.5tS and 40<EK<240 GeV Main Backgrounds • For e channel: KSp0p0D with a g lost:rejected by mee> 0.165 GeV/c2cut • timeaccidentals , mainly from plv + p0p0(p0): studied from time side bands • KL,Se+e-gg Greenlee background due to double g radiation: estimated from 2001 KL run (statistics x10). Negligible for the m channel KSp0e+e- KSp0m+m-

23. 7 signal events 6 signal events MK(GeV) Mgg(GeV) Mgg(GeV) Mmmp(GeV) From KLp0e+e-to Imlt : KSp0l+l- KSp0m+m- KSp0e+e- Assuming vector interaction and unity form factor for electron channel to recover the mee>0.165 GeV/c2 BR(KSp 0 e+e-) = BR(KS p 0 m +m -) = [PLB576 (2003)] CERN-PH-EP/2004-025

24. e+(m+) e-(m-) 0++,2++ KLp0e+e-(m+m-) : SM prediction The last ingredient is the CP conserving amplitude of KLp0l+l- . It can be parametrized in term of : BR(KLp0gg) =(1.36±0.03stat±0.03sys±0.03nor)x10-6 * =(1.68±0.07stat±0.08sys)x10-6 ** Finally: BR(KLp0gg) BR(KSp0ll) theory • The lt parameter dependence is embedded also in the interference term. • The positive sign of the interference term seems to be theoretically preferred*,** *Isidori,Smith,Unterdorfer hep-ph/0404127 **Friot,Greynat,de Raphael hep-ph/0404136 *NA48 PLB2002 **KTeV PRL1999

25. KLp0e+e-(m+m-) : SM prediction Taking Im(lt) = (1.36±0.12)x10-4 a prediction can be done for BRs: Contribution to BR BR(KLp0 e+ e-)SM x 1011= (3.1 or 1.3) ±1.0 BR(KLp0 m+ m-)SM x 1011= (1.8 or 1.2) ±0.3 x10-12 BRs vs Imlt Interf (-) Interf (+) Main uncertainties come from experimental inputs and (less) from CPC contribution theoretical evaluation (mm channel)

26. Mgg (GeV/c2) Meegg (GeV/c2) KLp0e+e- @KTeV: backgrounds Background due to KLp+p-p0,KLp0Dp0(p0) , KLpev is removed using TRD and cut on charged momenta and event pt2 1999 data • Irriducible background with same final state of the signal from Greenlee double radiation: KLe+e-gg with a BR=(6.31 ± 0.14 ± 0.42)x10-7 • The background has radiative gs collimated with e±. Discrimination via minimum angle between g and e • The signal has almost isotropic gs in the p0 frame. Discrimination via angle between g and KL in p0 frame Signal: two gs and two opposite tracks with e IDs 1997+1999 dataset: 6.7x1011 KL

27. 1999 data Mgg (GeV/c2) Meegg (GeV/c2) KLp0e+e- @KTeV:results Opening the box after these cuts 1 events is found out of 1 ±1/3background events expected. The limit obtained is: BR(KL → p0 ee ) < 2.8 × 10-10 @90%CL Phys. Rev. Lett. 93, 021805 (2004) 1997+1999 data 2 order of magnitude lower than the previous limit but 1 order of magnitude higher then the SM prediction. Future measurement will need improvement both in KL statistic and in background rejection

28. Pt2 (GeV/c)2 M (GeV/c2) KLp0m+m- @KTeV: backgrounds A similar analysis has been made for KLp0m+m- on the 1997 dataset: 2.7x1011 KL Signal: two gs and two opposite tracks with m IDs Background mainly due to KLp+p-p0,KLpmv +2gacc and to double radiative KLm+m-gg. the Greenlee bck is less severe than for e+e- case ( the m radiates less): BR(KLm+m-gg) = (10.4+7.5-5.9 ±0.7)x10-9 Kinematic costraint on inv. mass and pt of total event single out the signal

29. Events/1MeV M (GeV/c2) KLp0m+m- @KTeV: results Opening the box 2 events were found in the signal region with 0.87 expected The limit obtained is: BR(KL→ p0mm) < 3.8 × 10-10 @90%CL Also theKLp0m+m-exp. limit has been pushed down by orders of magnitude but is still ~1 order of magnitude above SM Phys. Rev. Lett. 84, 5279-5282 (2000) 1997 data

30. Relt= A2l3 r r KL→gg KL→gee(mm) KLeeee(mm) KL→gg KL→gee(mm) KLeeee(mm) KL→m+m- Kaon rare decays and Re(lt) • The BR(KLmm) is almost saturated by the absortive amplitude, computed from measured BR(KLgg) with small error. • The (tiny) short distance contribution of dispersive amplitude is related to r : a g b The long distance contribution to dispersive amplitude, via KLgg*, KLg*g*, must be extracted from KLgl+l- and KLe+e-l+l-data

31. signal Straw Chamber 1 & 2 bck Neutral Beam Dump Drift Chamber 3 & 4 Drift Chamber 5 & 6 Trigger Scintillator Cerenkov Lead Glass Calorimeter Muon hodoscope E871 Re(lt):KLmm and E871@BNL BR(KLmm) = (7.18 ±0.17)x10-9 Accuracy limited by the error (th. & exp.) on dispersive amplitude evaluation r < 0.33 @90% C.L. PRL84(2000)

32. UT and CP from K: status summary • K+p+nn : BR twice of SM prediction but within statistical error. (new run?) • KLp0nn : exp. limit far away from SM, but E391a is getting closer. • KLp0ll : experimental limits a factor 10 above SM. New exp. needed (may be KLp0mm easier?) • KLmm : sensitivity to r limited both by theory and by exp. error on KL→gg f.f. Courtesy of G.Isidori New generation of dedicated experiments (& beams)needed.

33. Outline • CP Violation and SM tests • TCP Violation • Detour to Vus • Outlook & Conclusions

34. Rare Kaon decays and TCP A TCP test typical of the Kaon system can be derived from the KL,S amplitudes imposing unitarity via the Bell-Steinberger relation: Main uncertainty on CPT violating parameterd is due to the error on A(KS3p0) and on |h000|=A(KS3p0)/A(KL3p0) contribution to d: The experimental limit on BR and d in literature are: BR(KS3p0) < 1.4x10-5 (SND, PL B459 1999) Im  = (2.4 ± 5.0) × 10-5 CPLEAR ’99

35. KL tag ByTOF KSe KS3p0 : KLOE@DAFNE m =1019.4 MeV The KS→3p0 is a CP violating decay, with a BR in the SM ~1.9x10-9. The F-factory provides an abundant pure KS beam KLKS 106/pb-1 p* = 110 MeV/c S = 6 mmL= 3.4 m K+K- 1.5 106/pb-1 p* = 127 MeV/c ±= 95 cm • The  decay at rest provides pure, monochromatic, back to back kaon beams in 1-- quantum state • Tagging: observation of KS,L signals presence of KL,S • KL,S beams in the same detector at the same time KLOE run 2001-2002 0.45 fb-1  1.4x109f decays Foreseen 2 fb-1 2005

36. KS3p0 : KLOE@DAFNE Drift chamber (4 m  3.3 m) 90% He + 10% IsoB, CF frame 12582 stereo sense wires p/p=0.4 %(tracks with  > 45°) vertex ~ 1 mm (M) ~ 1 MeV Electromagnetic calorimeter Lead/scintillating fibers 4880 PMT’s E/E=5.7% /E(GeV) t=54 ps /E(GeV)  50 ps (relative time between clusters) L() = 2 cm( from KL) Superconducting coil (5 m bore) B = 0.52 T ( B dl = 2 T· m)

37. 22 • Data • MC 2 23 KS3p0 @KLOE: results • KS tagged by KL which interacts on EMC (e~30%). • The KL interaction are identified by energy and b. • KS signal selected by 6 gs • Main bck from KS2p0 + acc. • Event fitted in 3p0 and 2p0 hyphothesis • 4 candidates in signal box with 3.2±1.4±0.2 expected by bck (MC) • BR(KS3p0) < 2.1x10-7@90% CL(KLOE04 PRELIMINARY)* • BR(KS3p0) < 7.4×10-7 @90%C.L. (NA48 ’04 hep-ex/0408053) Im(d) = (-0.2±2.0)x10-5 Accuracy limited by A(KL,S→p+p-) *This conference

38. Outline • CP Violation and SM tests • TCP Violation • Detour to Vus • Outlook & Conclusions

39. Detour: a look at the Vus saga No theory ! No t’s ! No hyperons ! Only K measurements ! 2002: after a huge revision of the Vud determination (th. & exp.) according to PDG: |Vud|2+|Vus|2+|Vub|2  |Vud|2+|Vus|2 = 1-2.4s The preferencial source of Vus being Kl3 decay (Ko & K+): theory From experiment: BRs, lifetimes and form factors to compute G and IlK • BUT (in 2002) ... • BRs obtained from fit to ratios of BRs. Errors and central values to be checked • m3/e3 disagreement with measured ff slopes, 4% or 3s • Unknown inclusion of radiative processes

40. |Vus| ** KLOE NA48 KTeV E865 KSe3 KLm3 KLe3 KLe3 KLe3 K+e3 K+e3 Vus after 2002: new measurements *this conference 2003– E865: BR(K+ p0e+n) 2004– KTeV: main 6 KL BRs and Kl3 f.f. 2004*– NA48: BR(KLpen), BR(K±p0e±n) and f.f. 2004*– KLOE: BR(KSpev) , BR(KLpln) and t(KL) fully inclusive measurements:Kpen(g), pmn(g) The new Vus seem to amazingly agree with unitarity in spite of a bit of “entropy”.. For example in the KLpnm(e) case: **Czarnecki,Marciano,Sirlin hep-ph/0406324

41. Vus saga: BRs vs form factors BUT agreement of new Vuss gets even better if the same ingredients (but the BRs) are used for Vus*→BRs seem ok! Less agreement on new measured form factors. Notice: linear vs quadratic f.f. can account as much as 1% on Vus. t from PDG04 f.f. by KTeV. Vus x f+(0) • PDG02 2004 results *F.Mescia,A.Antonelli, this conference **2l”ISTRA=l”KTeV

42. exp lattice theory ♦ fK/fp-1=0.210(4)(13)|Vus| =(0.2219±0.0026) (MILC hep-lat/0407028) (Marciano hep-ph/0406324) Vus and Kaons: something new Alternative method to extract Vus from K±m±n: given fK/fp computed on lattice, then: G(Km2) is from a 1972 measurement and PDG fit. It is not known what radiative contribution is retained. Adding contribution of radiation |Vus| goes up! New measure? (KLOE,NA48,ISTRA)

43. Outline • CP Violation and SM tests • TCP Violation • Detour to Vus • Outlook & Conclusions

44. Outlook: KOPIO@BNL Aim to collect 60 KL→p0nn events with S/B~2 (Im lt to 15%) KL→p0nn Approved & funded Advanced R&D Construction start 2005 (?) • Microbunched flat beam: measure velocity (momentum 800 MeV/c) of KL • Hermetic high efficiency veto • Measure g time, position and energy • High vacuum decay region

45. Outlook: E391@JPARK KLp0nn • Evolution of the E391a@KEK • Pencil beam concept • Target sensitivity well beyond SM prediction for KLp0nn • Start in 2009(?) JPARK

46. Outlook: NA48/3@CERN K+p+nn • Based on upgrade of NA48/2 detector • Unseparated, positive beam of 75 GeV/c with P/P~1% • Upstream detector to identify kaons and measure K momentum • Hermetic photon vetoes • Finely segmented Hadron Calorimeter/Muon veto Goal: About 50 Events with a S/B of 10:1 in 2 years of data taking • EoI exists • Intense R&D activity in 2004 • time schedule  Villars Workshop in fall 2004

47. Outlook: further initiatives/projects K+ physics at the JPARK charged beam (2009) Four LOI presented addressing K+p+nn , T violation in K+m3 , rare K+ decays , K+e3 BR with high statistic Pure KS beam – F factories (schedule?) Clean environment to study KS decay: CP, TCP violation and KSp0l+l- . DAFNE-2 (?) project, dedicated workshop in Alghero in 2003 OKA@Protvino: RF-separated K± beam project (schedule?) Rare K± decays physics, direct CP violation in K±p±pp± and K±p0p0p±

48. Conclusions • The field of rare kaon decays is quite active. A generation of detectors is now mature (e’/e, LFV, T violation) and a new round of initiatives is approaching. • Projects are addressing both neutral and charged Kpnn. Despite of the experimental difficulty this item will be on the spot in the next years. • New (coherently on KS & KL) projects/ideas are needed to explore the KL,Sp0ll system. Interference with mixing CP amplitude enhance both direct CP signal and sensitivity to NP. Mostly exp. limited..Why not? (expecially the m mode..) • The Vussaga seems to have an happy end. New results in better agreement with unitarity. Focus now on f.f. and K0, K+ lifetimes

49. Further results on rare K decays and T T violation: E246@KEK-PS. Final results (2004) from K+m+p0n: PT = (- 1.7 ± 2.3stat ± 1.1syst)x10-3 TCP violation: KS semileptonic asymmetries @KLOE AS = (2 ± 9stat± 6syst) x 10-3 KLOE2004 (preliminary) Lepton Flavor Violation: KLme E871@BNL. BR(KL→ me) < 4.7  10-12 90% CL Lepton Flavor Violation: K+p+m+e- E865@BNL BR(K+p+m+e- ) < 1.2 x 10-11 Dalitz decay @ KTeV : BR(KL→eemm)= (2.69± 0.24± 0.12) x 10-9 BR(KL→eeee)= (4.16 ± 0.13 ± 0.13 ± 0.17) x 10-8 And many more……..

50. Spare materials