The Well-tempered kaon

1. The Well-tempered kaon For the Use and Profit of the Physical Youth Desirous of Learning as well as for the Pastime of those Already Skilled in this Study drawn up and written by Marco S. Sozziof the University of Pisa and INFN Anno 2008 or Searching for very rare kaon decays

2. Program M.Sozzi – The Well-tempered kaon

3. Praeludium Introduction Kaons: lightest kind of flavoured matter A large and significant part of particle physics… The minimal flavour laboratory:• All the features of flavour physics are present • Very simple (minimal) system • Very nicely accessible experimentally (large rates, large BRs, small backgrounds, …) • Usually pretty hard for theorists… Is there still something to be learned by using kaons? M.Sozzi – The Well-tempered kaon

4. Toccata LF Violation? Already done Several dedicated efforts BNL AGS experiments (E865) set very high standards Flux and backgroundsare now limiting further progress Sensitivity to NP up to ~ 100 TeV Impressive reach. No new LFV projects.Background limitations M.Sozzi – The Well-tempered kaon

5. Toccata New KTeV LFV limit KTeV Byproduct of ε’/ε experiment: KTeV exploited its large KL sample and PID capability to search for LFV as a s→dμe transition, on the full dataset: 4.21 exp, 5 found 0.66 exp, 0 found M.Sozzi – The Well-tempered kaon

6. Toccata Loop-induced: K+→π+ℓ+ℓ– Long-distance (γ*) dominated (S,T contributions negligible) Model-dependent predictions for individual BR. BR ratio: in agreement with theory (>0.23). +e+e–: BR at 3%, form factor slope at 6%. ++–: BR at 17%, form factor slope at 50%. Limited fundamental physics to be learned from very precise measurement (unless way off !). M.Sozzi – The Well-tempered kaon

7. PDG average: BR = (2.88±0.13)∙10–7Top sample: E865 (10K events)New measurement in flight by NA48/2:Kaon flux: 1.7x10117146 candidates (0.6% background)Normalization to K+→π+π0D Toccata New NA48/2K+→π+e+e– FF fits do notdiscriminatebetweenmodels NA48/2 preliminary: 1.4  from E865 (10K evts): (2.94 ± 0.05 ± 0.13 ± 0.05)∙10–7 M.Sozzi – The Well-tempered kaon

8. Toccata K+→π+μ+μ– Poor agreement in PDG BR data(scale factor 2.7) PDG-average: BR = (8.1±1.4)∙10–8 World sample < 800 evts.Top sample: E865 (400 events) Severe background from K→3π (E865: 6.5% bkg) Most recent measurement by HyperCP @ FNAL (4% K in secondary beam), 110 events in 20% of statistics Linear FF fit agrees with πee NA48/2 NA48/2 analysis ongoing (few thousand events, O(1%) bkg) M.Sozzi – The Well-tempered kaon

9. Toccata CP violation in Kdecays So far the most straightforward manifestation of CP violation (/) was not seen. K±→ ±ℓ+ℓ–: width asymmetry O(10–5) in SM, can be larger with SUSY. Useful handle from mℓℓ dependence.First measurements available, insufficient statistics: HyperCP (2002): A(K ) = 0.02  0.11  0.04 New NA48/2 (2008) preliminary: A(K ee) = 0.021  0.015  0.013 “Small SM effect, good NP probe”. M.Sozzi – The Well-tempered kaon

10. The re-tuning issue Kaons have been very successful indeed in uncovering most of the qualitative features of the flavour sector in the SM BUT they are often ill-behaved: troubles with low-energy (mK~O()) quark processes cannot be evaded when dealing with light hadrons (until our theory colleagues will solve QCD…). Can often relate observable kaon properties to one another (χPT), but usually lack solid (unfailing) predictive approaches. That is: RE-TUNING is often required for each “piece” M.Sozzi – The Well-tempered kaon

11. K  ℓℓ decays The Well-Tempered kaon Some very rare FCNC decays are largely SD-dominated and can be computed to exceptionally high (few percent) parametric precision, unmatched by any other FCNC quark process This usually goes together with other SD-effects (very high mass-scale sensitivity, CP violation) Kaon decays thus switch to quantitative testing of the SM (behaving properly in any key!) M.Sozzi – The Well-tempered kaon

12. SD K  ℓℓ decays Praeludium A single hadronic current with well-measured (K-π) matrix element (isospin), strong suppression of LD effects and few effective operators: this gives theoretical HEAVEN (and experimental hell) M.Sozzi – The Well-tempered kaon

13. Divertimento KL0ℓ+ℓ- : not only and Three contributions: (1) The computable SD CPV part (2) An indirect (ε) CPV part(known from εif KS decays measured) (3) A LD (γ*γ*) CP-conserving part(related to its on-shell counterpart KS→π0γγ) M.Sozzi – The Well-tempered kaon

14. Divertimento (2) CPV ind: KS→ π0ℓ+ℓ– NA48/1 2003-2004 KS 0e+e– KS 0μ+μ– NA48/1 NA48/1 6 events 7 events Would still profit from improvements… M.Sozzi – The Well-tempered kaon

15. Divertimento (3) CPC: KL → π0γγ Interesting by itself in χPT: no free parameters at O(p4) New KTeV result on full dataset 1982 eventsNormalization to KL→π0π030% background (KL→3π0) Supersedes previous KTeV result (half dataset)BR=(1.55±0.07±0.08)∙10–6 Relevant for CPC KL→π0e+e– Agrees with NA48 2002 result:BR=(1.27±0.04±0.01)∙10–6 M.Sozzi – The Well-tempered kaon

16. CPV dir 8% CPV int 25% CPV ind (KS→π0e+e–)50% CPC (th. + KL→π0γγ) CPC (th. 30% + KL→π0γγ) CPV ind (KS→π0μ+μ–)50% CPV dir 10% CPV int 25% Divertimento KL0ℓ+ℓ- Isidori et al. EPJ C36 (2004) 57 CONSTR. INT. (2) KS measurements: indirect CP-violating term dominates.(3) KL measurements: CP-allowed contribution small.Sensitivity of BR to CKM phase depends on (unmeasurable) relative signof the two CP-violating terms.Theoretical predictions: constructive interference.Interesting correlations w. K→π DESTR. INT. (NA48/1) M.Sozzi – The Well-tempered kaon

17. KL0ℓ+ℓ- Divertimento With the ancillary measurements done these decays are now re-admitted into the SD exclusive club (paying membership) KL 0μ+μ– KL 0e+e– KTeV Bkg limited, excellent EM calorimetry Smaller SD part,larger CPC, smaller bkg Irreducible “Greenlee” (QED) background: BR(KL→γγe+e–) ≈ 6·10–7Dalitz plot analysis, time-dependent analysis, μ polarization: require a further experimental step in intensity/rate capability M.Sozzi – The Well-tempered kaon

18. K  : the “holy grail” Praeludium c,u contributionK+ only (37%) The best measurement of |Vtd|?Rather a highly-sensitive search for NPComparison of the two can discriminate by itself the flavour structure of NP Theoretically clean also BSM ! M.Sozzi – The Well-tempered kaon

19. Searching for the holy grail Praeludium The theorist The experimentalist “Just look for a decay of a short-lived particle with 109 background, with a poor signature and no kinematic closure.” “Normal science: when the processes which can be easily handled by theorists are experimental nightmares (and vice versa)”. (Apologies to T. Kuhn) High fluxes, high vacuum, high ermeticity, excellent vetoing, excellent resolutions… An interesting challenge M.Sozzi – The Well-tempered kaon

20. To the faithful departed Praeludium b. Batavia, 1997 - d. Batavia, 200142 people from USA, Brasil, Greece, Russia>50M$ to measure 100 KL→π0νν and KL→π0μ+μ– in flight KAMI b. Brookhaven, 1999 - d. Washington, 2002 in infancy68 people from USA, Canada, Russia, Japan~2M$ to measure ~10 K+→π+νν w. stopped K b. Batavia, 2001 - d. (twice) Washington, 200364 people from USA, Russia100M$ to measure 100 K+→π+νν in flight (sep. beam) b. Brookhaven, 2000 - d. Washington, 200589 people from USA, Russia, China, Japan, Switzerland150M$ to measure 60 KL→π0νν in flight M.Sozzi – The Well-tempered kaon

21. Fuga K+ + BR(SM) = (8.5 ± 0.7)∙10–11Non-parametric theoretical uncertainty ~5% (11% overall) Background from K decays: μ+ν (0.63), and +0 (0.21), beam scattering, charge-exchange + Kℓ3 and pion nuclear interactions. No kinematic constraints. VETO !!!Background suppression 1011: redundancy is a must. Stopped K: separated beam, high effective decay rate, kinematics. Measured @ BNL (3+4 events).In-flight K: high veto efficiency, high acceptance. The long march First search: 1969 (10-4) Observation: 1997 (10-10) NA62 M.Sozzi – The Well-tempered kaon

22. Fuga K+ +: BNL E787-E949 Study of region 2 below +0 peak: higher background (nuclear π int.): S/B = many times worse Region 1 between two 2-body peaks (“smaller” background): E787+E949: 3 events E787+E949: 4 eventsBkg: 2.15±0.43 BR = (1.47+1.30-0.89) ·10-10 Bkg: 0.30±0.03 (P=0.001) M.Sozzi – The Well-tempered kaon

23. K+ + science (or) fiction Fuga (“4.4” events)BR(exp) = 2 x BR(SM) Today ? ? Tomorrow(2012?) 100 events Mean=SM 100 events Mean=E787/949 M.Sozzi – The Well-tempered kaon

24. In Europe: CERN NA62 Fuga NA62 Proposal 2005: CERN-SPSC-2005-013, SPSC-P-326 Bern, Birmingham, CERN, Dubna, Ferrara, Fairfax, Firenze, Frascati, IHEP, INR, Louvain, Mainz, Merced, Napoli, Perugia, Pisa, Roma I+II, Saclay, San Luis Potosi, SLAC, Sofia, Triumf, Torino • New approach: decay in flight75 GeV/c unseparated K+ beam (K ≈ 6.6%) • Reuse parts of NA48 apparatusand existing SPS protons (3.3·1012 ppp ≈ 1/20)Sensitivity not limited by beam flux • Acceptance 14% Expect ≈ O(100) eventswith S/B≈10 in 2 years (2012+) M.Sozzi – The Well-tempered kaon

25. NA62 Fuga Background rejection:- γ vetoing: high-performance LKr calorimeter, lead-glass rings; low-E π = low γinefficiency- Kinematics: vacuum (straw) spectrometer, Si K+ tracking in 1 GHz- PID(π/μ): Ne RICH and μ veto/hadron calorimeter- Positive Kaon ID: beam RICH Several challenges:•200 ps 1 GHz Si beam tracker, 0.5% X0/station •Vacuum spectrometer •Vetoing • Triggering and fully efficient DAQ M.Sozzi – The Well-tempered kaon

26. Fuga 24MCHF NA62 92% kinematically constrained bkg. 8% not-constrained bkg. Acc.3.5% Acc.10.9% • Scientific approval from CERN and INFN • R&D towards completion • Strenghtening the collaboration M.Sozzi – The Well-tempered kaon

27. KL 0 Ricercar BR(SM) = (2.5 ± 0.4)∙10–11Non-parametric theoretical uncertainty ~1% (16% overall)No CPC part, indirect CPV tiny: pure SD “interference” CPV (dominant operator, if no LFV) Background from K decays: 00 (8.7·10–4, CPV), 000(19.5%),+–0 (12.5%),halo neutron inelastic interactions. Unmeasurable parent particle.No kinematic constraints.VETO !!! Grossman-Nir bound:BR(KL) < 4.4 BR (K+)from isospin E391a E17 Low-energy approach:KL TOF for kinematics, large prod. angle, large beam emittance, γ tracking High-energy approach:excellent vetoing, “pencil” beam for kinematics, high pT M.Sozzi – The Well-tempered kaon

28. KL 0 Ricercar m(γγ) constraintBetter pT resolution π0→γe+e– (1.2%) π0→γγ (98.8%) Old KTeV limits(high-energy) BR < 1.5 ∙10–61 event (3.7±1 bkg) n interactions BR < 5.9 ∙10–70 events (0.12±0.05 bkg) n interactions, 3π0D • Dalitz approach cannot reach SM level • Beam halo neutron interactions very challenging M.Sozzi – The Well-tempered kaon

29. At a new US machine? Praeludium b. Batavia 2002, d. Batavia 2006, reborn Batavia 2007 with: Most recent US proposals: a KL→π0νν and a stopped K+→π+νν experiment at the (improved) 8 GeV FNAL booster, in the perspective of a future MW proton driver (Project-X): Booster: 16kW, 22.5·1012 ppp/1.4s (60% of BNL AGS): 2011-2018 Project-X: 200 kW, 10-60 x booster: 2018-2020(100% duty factor assumed) FNAL Project-X M.Sozzi – The Well-tempered kaon

30. Unfortunately, unlikely Kaons at FNAL? KL→π0νν: low-energy, small emittance beam, detector in vacuum, high(er) acceptance 30 ev/year @ booster, 300-900 ev/year @ Project-XK+→π+νν: stopped, low-energy (500 MeV/c, higher stop probability) separated beam, finely-segmented compact detector w. high magnetic field40 ev/year @ booster,250-1500 ev/year @ Project-XAlso discussed high-energy, in-flight, RF-separated beam exp. (200 ev/year) FNAL PAC – June 2008 May 2008 - P5: only possible in a “HEP fund doubling” scenario M.Sozzi – The Well-tempered kaon

31. Ricercar In Japan: E391a (KEK) KEK 12 GeV/c PS (2·1012 ppp). Pilot project for J-PARC experiment“Pencil” beam (kinematics, vetoing): ‹pK› ≈ 2 GeV/c, n/K ≈ 60Photon vetoes at 1 MeV level, high acceptanceHigh vacuum, hadronic background MCLarge pT (>120 MeV/c) and decay vertex cutsDouble veto region (3π0 w. back γ) M.Sozzi – The Well-tempered kaon

32. Ricercar E391a new limit Run I partial analysis (10% of data): Run II:Solved problem of matter on beamand DAQ inefficiency, reduced n flux Control bkg: 1.9±0.2, obs. 3, 0.39±0.08, obs. 2Background: exp. 0.41±0.11, obs. 0 (0.11 π0π0, 0.30 halo n)Acceptance: 0.67%, 5.1∙109 k Single-event sensitivity: 2.89∙10–8Still above Grossman-Nir bound Comparable Run III M.Sozzi – The Well-tempered kaon

33. Ricercar J-PARC J-PARC complex Beam to experimentsin second half of 2008 50 GeV, 3.3∙1014 ppp, 20-50% DC, 750 kW Hadron hall M.Sozzi – The Well-tempered kaon

34. Ricercar In Japan: J-PARC E14 Improved beamline (reduced halo, n/K ≈ 7, lower background, veto)Step 1: re-use E391a barrelThicker and more fine-grained CsI calorimeter (KTeV)Waveform digitizationUpgraded vetos (KOPIO-like beam hole γ veto) Flux x10, Time x10, Performance x10 Goal: 2.7 events (S/N ≈ 1.6) in 3 yearsConstruction 2009, first physics run 2011 ?Step 2: 100 SM events (S/N ≈ 4.8), new dedicated target ? M.Sozzi – The Well-tempered kaon

35. More ideas/plans… K+→π+νν @ J-PARC: E949-like stopped experiment KL→π0νν @ Protvino: KLOD @ U70: E391a-like, 10 GeV, γtracking KL→π0νν @ CERN: at improved LHC proton injector (SPS+), high-energy, long hermetic vetoing decay region KL→π0νν @ a super-intense phi-factory: KL of known momentum and direction (some orders of magnitude away from any presently conceivable project) A high-intensity (MW) proton driver (30-100 GeV/c) is the best source of K (synergy with  program but high DC required). High yield: better experiments and access to more powerful analysis approaches M.Sozzi – The Well-tempered kaon

36. So why kaons? Coda New Physics (if it exists) is small, and not too weird concerning flavour: If Nature is not MFV it is almost MFV(remember superweak?) Large suppressions (VtsVtd) make K attractive:• Rare decay (small SM contribution) can see NP in large effect• Well-controlled decaycan see NP in a not-so-large effect Or maybe there is NO new physics at the TeV-scale (interesting in a way, provided the SM Higgs is not there…):Experimentally K SES and high-energy scale reach are unrivaled F=1 processes are different from those constraining the CKM matrix M.Sozzi – The Well-tempered kaon

37. Kaons, once again. Nature rewards perseverance. Now just go and measure it. “There's nothing remarkable about it. All one has to do is hit the right keys at the right time and the instrument plays itself ”.J.S. Bach M.Sozzi – The Well-tempered kaon

38. Spare slides M.Sozzi – The Well-tempered kaon

39. Future machines? A high intensity p driver (>1014 ppp) would be very valuable for “ultimate” K measurements. Sinergies with neutrino physics? With LHC injectors upgrade? Energy in the tens of GeV range, slow extraction (high DC) Intense K+ beam: K± CP asymmetriesIntense K+ RF-separated beam: K+ + Tertiary K0 beam: CPT tests at Planck scale (K   phases) Intense KL beam: KL 0, KL 0e+e-, KL 0μ+μ- (with several handles), diverse program M.Sozzi – The Well-tempered kaon

40. Divertimento KL0ℓ+ℓ- Isidori et al. EPJ C36 (2004) 57 (2) KS measurements: indirect CP-violating term dominates. (3) KL measurements: CP-allowed contribution small. Sensitivity of BR to CKM phase depends on (unmeasurable) relative signof the two CP-violating terms.Theoretical predictions: constructive interference. CONSTR. INT. DESTR. INT. BR(KL 0e+e-)CPV ×1012≈ 17 (ind) ±9 (interf) + 4 (dir) BR(KL 0μ+μ-)CPV × 1012 ≈ 8 (ind) ± 3 (interf) + 2 (dir) Interesting correlations w. K→π M.Sozzi – The Well-tempered kaon

41. Return to 2007-level funding (1) μ→e conversion (2) Participation to super-B factory abroad No K physics in this scenario M.Sozzi – The Well-tempered kaon

42. Toccata LFV with K+ BNL E865 Impressive reach. No new LFV projects.Better background suppression would be required M.Sozzi – The Well-tempered kaon

43. KTeV (1996-1999) FNAL Main Injector (120 GeV) pDouble KL beam (<p>=70 GeV/c)Regenerated KSPure CsI calorimeterData taking in 1997 and 1999100 physicists, 12 USA/Japan institutions M.Sozzi – The Well-tempered kaon

44. 54 60 66 PK spectra, 603GeV/c BM z 10 cm 200 250 m 1cm 50 100 NA48/2 (2003-2004) CERN SPS (450 GeV) p, twin simultaneous K± beams130 physicists, 16 European institutions 2 ÷ 3 M K/spill (π/K ~ 12)π decay products stay in pipe magnet K+ K+ ~11012 ppp focusing beams K K− 0º prod.angle • Cleaning • Beam spectrometer (0.7%) Beams coincide within ~1mm all along 114m decay volume,always in vacuum • Momentum • selection • Focusing •  sweeping 1011 K decays per year collected vacuum tank He tank + spectrometer M.Sozzi – The Well-tempered kaon not to scale

45. Toccata K+→π+e+e–: Form Factor Different models for F(z):χPT @ O(p6) + unitarity, VMD z<0.08 experimentally not accessible (Dalitz background) Basically 1-parameter sensitivityResults quite agree among experimentsThey disfavour naïve VMD model NA48/2 preliminary M.Sozzi – The Well-tempered kaon

46. Fuga BNL E787-E949: K+ + E787: 1989-1998K+ 800 MeV/c DC-separated (K/π ≈ 3), 5·105 K/1012 pKaon ID: Č, MWPC, dE/dx Decay at rest, redundancy, e decay chain. Acceptance 0.2% Final result: 2 events (0.15 bkg) E949: upgrade (K/ ≈ 4), vetos, beam counters, range stack, calorimeter, trigger, DAQ. Goal: 10 SM events in 60 weeks 11 week run in 2002 (1/5): sensitivity ~ E787. +1 event. Miss the other 4/5 of data… M.Sozzi – The Well-tempered kaon

47. E391a backgrounds π0π0 0.11 ± 0.09halo n in CC02 0.16 ± 0.05halo n in CV 0.08 ± 0.04halo n in CV () 0.06 ± 0.02-------------------------------------------Total 0.41 ± 0.11 Al window run M.Sozzi – The Well-tempered kaon

48. J-PARC E14 schedule M.Sozzi – The Well-tempered kaon