Summary on CP Violation with Kaons Patrizia Cenci INFN Sezione di Perugia XX Workshop on Weak Interaction and Neutrinos Delphi, June 7th 2005 On behalf of the NA48 Collaboration Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Vienna

Overview   Introduction   CP Violation with Kaons   Experiments: KLOE, KTeV, NA48   Results:  Direct CP Violation with neutral Kaons  Charge Asymmetry in K 0 e3  K S → 3π 0  K S,L → π 0 l + l -  Direct CP Violation in K ± 3 π decays   Prospects and conclusions

Introduction   Why Kaons  crucial for the present definition of Standard Model  search for explicit violation of SM: key element to understand flavour structure of physics beyond SM   Motivation for Kaons experiments  Test of fundamental symmetries  CP Violation: charge asymmetry, T violating observables  CPT test: tigher contraints from Bell-Steinberger rule, K S /K L semileptonic decays  Sharpen theoretical tools  Study low energy hadron dynamics: χ PT tests and parameter determination, form factors  Probe flavour structure of Standard Model and search for explicit violation (e.g. Lepton Flavour Violation)  Rare decays suppressed (FCNC: 2nd order weak interactions) or not allowed by SM  Sensitivity to physics BSM

CP Violation with Kaons Brief History of CP Violation   1964: CP violation in K 0 (Cronin, Christenson, Fitch, Turlay)   : Direct CP violation in K 0 (NA31, NA48, KTeV)   2001: CP violation in B 0 decay with oscillation (Babar, Belle)   2004: Direct CP violation in B 0 (Belle, Babar) CP Violation: a window to physics beyond SM  CP Violation in Kaon decays can occur either in  K 0 -K 0 mixing or in the decay amplitudes  Only Direct CP Violation occurs in K ± decays (no mixing)  Complementary observables to measure Direct CP Violation in Kaons: ε’/ε, rare decays, A g

Experiments with Kaons Fermilab KTeV: 1997,1999 K L,K S Frascati - DaФne KLOE > 2000 K S,K L,K  Active Experiments CERN NA K L,K S NA48/1 2000,2002 K S NA48/ K 

FNAL - KTeV Experiment  Parallel K beams: 2 proton lines (~ ppp) K S K L K S from K L on Regenerator (scintillator plates), K S identification K S identification via x-y position switches beam line once per cycle   +  - :   +  - : Magnetic Spectrometer  (p)/p  0.17%  p[GeV/c]%   0  0 :   0  0 : CsI calorimeter  (E)/E  2.0%/√E  0.45%  M (  0  0 ) ~  M (  +  - ) ~ 1.5 MeV  Photon veto and muon veto  M (  0  0 ) ~  M (  +  -) ~ 1.5 MeV Experimental Program KTeV: 1997,1999 K L,K S

CERN - NA48 Experiment  Simultaneous K beams: split same proton beam (~10 12 ppp) convergent K L -K S beams K S K S from protons on near target K S identification K S identification via proton tagging   +  - : Magnetic Spectrometer Δp/p = 1.0% 0.044% x p [GeV/c] Δp/p = 1.0%  0.044% x p [GeV/c]   0  0 : LKr Calorimeter ΔE/E = 3.2%/√E 9%/E 0.42% [GeV] ΔE/E = 3.2%/√E  9%/E  0.42% [GeV]  Photon and muon veto Beam pipe  (  ) ~  (  +  -) ~ 2.5 MeV  M (  0  0 ) ~  M (  +  -) ~ 2.5 MeV Experimental Program NA K L,K S NA48/1 2000,2002 K S NA48/ K 

LNF DaФne: the Ф Factory Ф Factory: e + e -  s = MeV = M Ф Ф Decays: BR(Ф → K L K S )=34.3%; BR(Ф → K + K - )=49.31% tagged K decays from Ф →  KK  pure K beams clean investigation of K decays and precision measurements KLOE data taking: /pb May 2005 Integrated Luminosity 920×10 6  decays New KLOE run in progress L peak = 1.4 × cm -2 s -1 Goal: collect 2 fb -1 by end ×10 6  decays (Recent results from KLOE: S. Dell’Agnello – LNF SC Open Meeting, may ’05 and M. Martini – Krare may ‘05)

LNF: the KLOE detector EM Calorimeter: Lead and scintillating fibres Drift Chamber: Stereo geometry

Direct CP Violation: experimental results on ε’/ε Re(  /  )  Final Result ( )  Half Statistics ( ( )  Direct CPV established in K 0 → ππ by NA48 and KTeV  more results expected (KTeV, KLOE)  no third generation experiments  Result (roughly) compatible with SM  Exclude alternative to CKM mechanism (superweak models and approximate-CP)  Despite huge efforts, ε’/ε not yet computed reliably due to large hadronic uncertainties  Improvement of the calculation expected with lattice  New physics may contribute as a correction to SM predictions (16.7  2.6)  10 -4

K 0 e3 Charge Asymmetry  K 0 e3  Charge Asymmetry in K 0 e3 is due to  K 0 -K 0 mixing (Indirect CPV)   Limits on CPT and ΔS=ΔQ   Il CPT is conserved and ΔS=ΔQ:  8 e3 8 e3  Results in NA48 (~2x10 8 K e3 ) and KTeV (~3x10 8 K e3 )  2  Re(ε) NA48: δ L (e)=(3.317  stat  syst ) x KTeV: δ L (e) = (3.322  stat  syst ) x PDG2004: δ L (e) = (3.27  0.12) x 10 -3

Semileptonic K S decays   KLOE: first measurement (2002), update in progress   New preliminary result:   CPT Test: new measurement of the charge asymmetry in K S : (δ L (e) = 3.32  0.07)  )   40   Data — MC sig + bkg  Method: K S tagged by opposite K L ( Ф →  KK ) Identify  e pairs using TOF Event counting by fitting the [E(  e)-P] distribution (test for ν ) Independent measurement of the two charge modes  Selected ~10 4 signal events per charge in the data (0.5 fb -1 ) E miss – P miss (MeV) BR( K S   e ) = (7.09  0.07 stat  0.08 syst ) δ S (e)= (-2  9  6)  10 -3

| η 000 | = CP Violation in K S   0  0  0   K S  3  0  is CP violating [ CP(K S ) = +1, CP(3  0 ) =- 1]   Allowed by SM, but never observed   According to SM:   Last limit from direct search: BR(K S  3  0 ) < 1.4x10 -5 (SND, 1999)  amplitude ratio η 000  Can be parametrized with the amplitude ratio η 000   The uncertainty on K S  3  0 amplitude limits the precision on CPT test (Bell-Steinberger relation) CPTCP If CPT is conserved: η 000 Re(η 000 ): CPV in mixing η 000 Im(η 000 ): direct CPV 

BR(K S   ) ≤ 1.2 x 10 CL  Best limit KLOE search for K S  0  0  0  Direct search, new result  Rarest decay studied by KLOE so far  Data sample: 0.5 fb -1 ( run)  37.8 x 10 6 (K L -crash tag + K S   )  Require 6 prompt photons  large background ~40K events  Kinematic fit, 2  0, 3  0 estimators (  2,  3 )  After all analysis cuts (  3  = 24.4%)  2 candidate events found  expected background: 3.13 ± 0.82 ± 0.37 Submitted to Phys. Lett. hep-ex/ Prospects with 2 fb -1 : if background ~ negligible level UL will improve by factor ~ 10 (down to few )

NA48/1: K S  0  0  0  and η 000  Measurement in NA48  Sensitivity to η 000 from K S -K L interference superimposed on a huge flat K L   0  0  0 component  Aim: O(1%) error on Re(η 000 ) and Im(η 000 )  Method: measure K S -K L interference near the production target 3  0 η 000 use 3  0 events from near-target run for η 000 K L  3  0 normalize to K L  3  0 from far-target run use MC to correct for residuals acceptance difference and Dalitz decays  :  Time evolution of K L,S  3  0  :

NA48/1 results on K S  0  0  0  Data samples (run 2000): K L,S  3  0 K L  3  0  Near-target run: 4.9  10 6 K L,S  3  0 data 90  10 6 K L  3  0 MC K L  3  0 K L  3  0  Far-target (K L ) run: 109  10 6 K L  3  0 data 90  10 6 K L  3  0 MC  Fit method: fit double ratio Final Results Final Results (2004) :  Re(η 000 ) = ± stat. ± syst  Im(η 000 ) = ± stat. ± syst  |η| < % CL K S  3  0  Br(K S  3  0 ) < 7.4  % CL If Re(η 000 ) = Re(ε) = 1.66  (CPT): If Re(η 000 ) = Re(ε) = 1.66  (CPT):  Im(η 000 ) CPT = ± stat. ± syst  |η| CPT < % CL K S  3  0  Br(K S  3  0 ) CPT < 2.3  % CL Ratio of near-target and far-target data corrected for acceptance (3 Energy intervals)

K ± → 3  matrix element |M(u,v)| 2 ~ 1 + gu + hu 2 + kv 2 Direct CP Violation in K ± 3  K + -K - asymmetry in g  Direct CP violation if Dalitz variables i=3 is the odd pion K  π + π - π ± : g = K  π 0 π 0 π ± : g = |h|, |k| << |g|  2even  1even  3odd K±K± Kπ+π-π±Kπ+π-π± NA48/2: search for Direct CPV by comparing the linear slopes g ± for K ± BR(K ±  ±  +   )=5.57% BR(K ±  ±  0  0 )=1.73% i=1,2,3

Experimental and theoretical status |A g | Experimental results Ford et al. (1970) HyperCP prelim. (2000) TNF prelim. (2002) - “neutral” mode NA48/2 proposal SM estimates of A g vary within an order of magnitude (few to 8x10 -5 ). “charged” “neutral” CPV asymmetry in decay width is much smaller than in Dalitz-plot slopes A g (SM: ~10 -7 …10 -6 ) SM SUSY Newphysics Models beyond SM predict substantial enhancements partially within the reach of NA48/2. (theoretical analyses are by far not exhaustive by now) Theory

NA48/2 goal and method  Primary NA48/2 goal:  Measure slope asymmetries in “charged” and “neutral” modes with precisions δA g < 2.2x10 -4, and δA g 0 < 3.5x10 -4, respectively  Statistics required for this measurement: > 2x10 9 in “charged” mode and > 10 8 in “neutral” mode  NA48/2 method:  Two simultaneous K + and K – beams, superimposed in space, with narrow momentum spectra  Detect asymmetry exclusively considering slopes of ratios of normalized u distributions  Equalise K + and K – acceptances by frequently alternating polarities of relevant magnets

NA48/2 experimental set-up P K spectra, 60  3 GeV/c cm cm m He tank + spectrometer ~7  ppp K+K+ KK +/- beams overlap within ~1mm all along 114m decay volume focusing beams BM z magnet vacuum tank not to scale K+K+ KK beam pipe Front-end Achromat Split +/- Select momentum Recombine +/- Quadrupole quadruplet  Focusing  μ swapping Second Achromat Cleaning Beam spectrometer

NA48/2 Data Taking Data taking finished 2003 run: ~ 50 days 2004 run: ~ 60 days Total statistics in 2 years: K      +   : ~ 4x10 9 K    0  0   : ~ 2x10 8 ~ 200 TB of data recorded This presentation: first result based on 2003 K ±       + sample

K ± 3  statistics U |V| even pion in beam pipe Data taking x10 9 K ±  1.61x10 9 K ±       + events Accepted statistics K + : 1.03 x10 9 events K  : 0.58 x10 9 events K + /K – ≈ 1.8  odd pion in beam pipe  M =1.7 MeV/c 2 Events Invariant  mass

 Use only the slopes of ratios of normalized u-distribution  Build u-distributions of K + and K - events: N + (u), N - (u)  Make a ratio of these distributions: R(u)  Fit a linear function to this ratio: normalised slope ≈  g e.g. uncertainty δAg < 2.2∙10 -4 corresponds to δ  g < 0.9∙10 -4  Compensate unavoidable detector asymmetry inverting periodically the polarity of the relevant magnets:  Every day: magnetic field B in the spectrometer (up/down: B+/B-)  Every week: magnetic field A of the achromat (up/down: A+/A-) A g measurement strategy - 1

A g measurement strategy - 2 Z X Y Jura (left) Saleve (right) beam line: K + Up beam line: K + Down B+ BB UD beam line polarity (U/D) SJ direction of kaon deviation in the spectrometer (S/J)  “Supersample” data taking strategy:  achromat polarity (A) was reversed on weekly basis  spectrometer magnet polarity (B) was reversed on daily basis  1 Supersample ~ 2 weeks  2003 data: 4 Supersamples Four ratios are used to cancel acceptances: Achromat Spectrometerfield

R = R US  R UJ  R DS  R DJ ~   g  u  Cancellation of systematic biases: 1)Beam rate effects: global time-variable biases (K + and K - simultaneously recorded) 2)Beam geometry difference effects: beam line biases (K + beam up / K - beam up etc) 3)Detector asymmetries effects (K + and K - illuminating the same detector region)  Acceptance is defined respecting azimuthal symmetry: 4)Effects of permanent stray fields (earth, vacuum tank magnetisation) cancels onlytime variationasymmetries The result is sensitive only to time variation of asymmetries in experimental conditions (beam+detector) with a characteristic time smaller than the corresponding field-alternation period (e.g. the supersample time scale: beam-week, detector-day) A g measurement strategy - 3 Quadruple ratio is used for further cancellation:

Beam systematics  T  Time variations of beam geometry  Acceptance largely defined by central beam hole edge (R~10 cm)  Acceptance cut defined by a (larger) “virtual pipe” - centered on averaged beam positions - as a function of charge, time and K momentum Beam widths: ~ 5 mm Y, cm X, cm 5mm Sample beam profile at DCH1 2 mm Beam movements: ~ 2 mm

Spectrometer systematics  Time variations of spectrometer geometry  DCH drifts by O(100 μ m) in a 3 month run: asymmetry in p measurement  alignment is fine tuned by forcing the average value of the reconstructed invariant 3  masses to be equal for K + and K - Maximum equivalent horizontal shift: ~200  or ~120  or ~280   Momentum scale  due to variations of the magnet current (10 -3 )  sensitivity to a 10 −3 error on field integral: ΔM ≈ 100 keV  mostly cancels due to simultaneous beams  in addition, it is adjusted by forcing the average value of reconstructed invariant 3  masses to the PDG value of M K+  M 

Trigger systematics  Measure inefficiencies using control data from low bias triggers  Assume rate-dependent trigger inefficiencies symmetric L2 inefficiency L2 trigger (online vertex reconstruction): time-varying inefficienciy (≈ 0.2% to 1.8%) flat in u within measurement precision: u-dependent correction applied 3x10 -3 cut L1 trigger (2 hodoscope hits) stable and small inefficiency ( ≈ 0.7·10 -3 ): no correction cut

Fit linearity: 4 Supersamples  2 =39.7/38 SS0:  g=(0.6±2.4)x10 -4  2 =38.1/38 SS1:  g=(2.3±2.2)x10 -4  2 =29.5/38 SS2:  g=(-3.1±2.5)x10 -4  2 =32.9/38 SS3:  g=(-2.9±3.9)x10 -4 U U U U

Systematics summary and results Conservative estimation of systematic uncertainties Effect on Δgx10 4 Acceptance and beam geometry 0.5 Spectrometer alignment0.1 Analyzing magnet field0.1  ±  decay0.4 U calculation and fitting0.5 Pile-up0.3 Systematic errors of statistical nature Trigger efficiency: L20.8 Trigger efficiency: L10.4 Total systematic error1.3 RawCorrected for L2 eff SS00.0±1.50.5±2.4 SS10.9±2.02.2±2.2 SS2-2.8± ±2.5 SS32.0± ±3.9 Total-0.2± ±1.3 22 2.2/33.2/3 Combined result in Δg x 10 4 units (3 independent analyses) L2 trigger correction included

Stability of the result Quadruple ratio with K(right)/K(left)K(up)/K(down) K(+)/K(-) 4 supersamples give consistent results control of detector asymmetry control of beam line asymmetry ΔgΔg MC reproduces these apparatus asymmetries Δg =(-0.2±1.0 stat. ±0.9 stat.(trig.) ±0.9 syst. )x10 -4 Δg =(-0.2 ± 1.7) x ΔgΔg ΔgΔg E K (GeV) z vertex (cm)

Preliminary result on A g NA48/ SM SUSY HyperCP prelim. (2000) (“C”) TNF (2004) (“N”) Ford et al. (1970) (“C”) Smith et al. (1975) (“N”) |A g | C N  This is a preliminary result, with conservative estimate of the systematic errors  The extrapolated statistical error is  A g =1.6×10 -4  2004 data: expected smaller systematic effects (more frequent polarity inversion, better beam steering) A g = (0.5±2.4 stat. ±2.1 stat.(trig.) ±2.1 syst. )x10 -4 A g = (0.5±3.8) x NA48/ data Newphysics

Search for K S  0 e + e    BR(SM)=3-10x10 -12, BR(  e + e  )≈6  10 −7  χ PT  3 contribution to this decay ( χ PT): K L  0   A 1 (CPC): not predicted, derived from K L  0  (K 2  0  *  *  0 e + e , NA48, KTeV)  A 2 (CPV Ind ): not predicted, measured by K S →  0 e + e - (NA48/1)  A 3 (CPV Dir ): predicted in terms of CKM phase (electroweak penguins and W boxes with top) Motivation: determination of the indirect CP violating amplitude of the decay K L  0 e + e  Motivation: determination of the indirect CP violating amplitude of the decay K L  0 e + e  K L  0 e + e  Indirect CPV e+e+e+e+ e-e-e-e- KTeV limits (90%CL) BR(  0 ee) < 2.8x BR(  0  ) < 3.8x10 -10

NA48/1: K 0 S →  0 l  l  NA48/1: K 0 S →  0 l  l  K S →  0 ee K S →  0  First measurement BR(  0 ee) = (stat) ± 0.8(syst)  |a s |= (stat) ± 0.07 (syst) PLB 576 (2003) 7 events, bkg First measurement BR(  0  ) = (stat) ± 0.2(syst)  |a s |= (stat) ± 0.05 (syst) PLB 599 (2004) 6 events, bkg Main motivation for the NA48/1 proposal

SM prediction for K 0 L →  0 l  l  SM prediction for K 0 L →  0 l  l   From K L measurement: small CPC contribution  From K S measurement: indirect CPV contribution dominates  Sensitivity of BR to CKM phase depends on the (unmeasurable) relative sign of the two CPV terms  Theory: constructive interference favored *  Sensitivity to new physics: enhanced electroweak penguins would enhance the BR Isidori et al. EPJC36 (2004 ) DestructiveConstructive J. Buras et al. hep-ph/ NP B697 (2004) * Two indeopendent analysis: G. Buchalla, G. D’Ambrosio, G. Isidori, Nucl.Phys.B672,387 (2003) - S. Friot, D. Greynat, E. de Rafael, hep-ph/ , PL B 595

Prospects and conclusions  Kaon was central in the definition of SM  Quantitative tests of CKM mechanism and search for new physics beyond SM are possible with rare Kaon decay mesurements  High level of precision is attainable  Constraints to CKM variables and further test of CPV from FCNC processes (“golden decays”):  K L  0 e + e  decays  K   decays

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The “golden” K   l l decays Motivation  FCNC processes, no tree level, proceed via loop diagrams  access to quark level physics with small theoretical uncertanties : v dominant short distance contributions v long distance only for charged lepton modes v matrix elements of quark operators related to K e3 decays v CPV K L decays  Charged leptons final states: easier lepton identification but high levels of radiative background  Best change: K   decays: v no long distance contributions v clean theoretical predictions  no radiative background v K L decay dominated by direct CPV

Why Kaon again?      (1,0)(0,0) K L →  +  - K L   K L  e + e -  K L  e + e - e + e - K L  e + e -  +  - K L   0  K S   0 e + e - K L   0 e + e - K L   0  K L  e + e -  K +   +  Unitarity Triangle: V ud V* ub + V cd V* cb + V td V* tb = 0 ρ and η precise measurements: important as precision test of the CMK formalism - used to describe CP and quark mixing - and search for new physics (,)(,) The study of K mesons allows quantitative tests of the SM independent and complementary to B physics (1.4,0)

Experimental prospects  K 0 L     K 0 L     Large window of opportunity exists.  Upper limit is 4 order of magnitude from the SM prediction  Expect results from data collected by E391a (proposed SES~ )  Next experiment  Future: JPARC and  K 0 L    ee(  )  Long distance contributions under better control  Measurement of K S modes has allowed SM prediction  K S rates to be better measured (KLOE?)  Background limited (study time dep. Interference?)  100-fold increase in kaon flux to be envisaged  K +     K +     The situation is different: 3 clean events are published  Experiment in agreement with SM  Next round of exp. need to collect O(100) events to be useful: P326 at CERN  Move from stopped to in flight experiments

KAon BEam Spectrometer (KABES) 3 MICROMEGA gas chamber stations measure beam particle charge (prob. mis-ID~10 -2 ); momentum (  p/p=0.7%); position in the 2nd achromat (  x,y  100  m). Not used yet for K ±  3  ± analysis Measurement of kaon momentum: Reconstruct K 3 π with a lost pion; Redundancy in K 3 π analysis; Resolve K e4 reconstruction ambiguity. E. Goudzovski / CERN, 1 March 2005

Neutral mode asymmetry K ±  ±  0  0  28 x 10 6 events (1 month of 2003)  Statistics analyzed: 28 x 10 6 events (1 month of 2003)   Statistical error with analyzed data:  A g = 2.2 ×   Extrapolation to data:  A g = 1.3 ×   Similar statistical precision as in “charged” mode   Possibly larger systematics errors

KLOE search for K S  +  -  0  Motivation:  Present status:  BR(CPC) ~ 3x10 -7, BR(CPV) ~ 1.2x10 -9  Direct measurement of CPC part possible with ultimate 2fb -1  Measurement tests of prediction (untested) of χ PT  Data sample: 740 pb-1  373 pb-1 (2001/2 data) (2004 data)  Assuming BR=3x10 -7 : ~230 signal events produced  Prospect with 2 fb -1 :  ~16 events, of which ~9 background  ~60% statistical accuracy on BR(K S  +  -  0 )  BR with accuracy below 50% : competitive with other measurements, and the only direct search E621 (1996) (stat) ± 1.1(syst)  CPLEAR (1997) (stat) (syst)  PDG2004 (average)  χ PT 2.4 ± 0.7  10 -7

K L,S      e  e  : why? CPV inner bremsstrahlung CPC direct emission CPV direct emissionCharge radius For K L : interference gives indirect CP-violating asymmetry in the orientation of     and e  e  decay planes Easier access to polarization asymmetry in K   Large (  14%) asymmetries predicted

K L,S      e  e  KTeV: K L NA48: K S,K L 1.5K events BR = (3.63  0.18)  No asymmetry: A  = (  1.1  4.1)% BR = (4.69  0.30)  [NA48: BR = (3.08  0.2)  ] A  = (13.3  1.7)% [NA48: A  = (14.2  3.6)%]

KTeV: | η + - | measurement Direct CPV:, the result is: Assuming Γ(K S  πeν)=Γ(K L  πeν), the result is:  2.7 σ discrepancy with PDG average (hep-ex/ )