Precision measurements of Charged Kaon radiative decays in NA48/2 WIN'11 23rd International Workshop on WEAK INTERACTIONS AND NEUTRINOS Cape Town, South Africa, 31 January - 5 February 2011 Monica Pepe INFN Perugia on behalf of the NA48/2 Collaboration (Cambridge, CERN, Chicago, Dubna, Edimburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Vienna )

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 2  NA48/2 CERN SPS  Study of the K ± →  ±    decay [Eur. Phys. J. C68 (2010), 75]  Measurement of DE and INT term fractions  Limit on CPV parameters (A N, A W )  Measurement of the K ± →  ±  decay (preliminary)  Measurement of the K ± →  ± e + e -  decay [Phys. Lett. B659 (2008), 493]  Conclusions OUTLINE

The SPS at CERN produces 400 GeV/c protons using either a fast or slow extraction system The SPS is used as well as injector for the LHC accelerator SPS LHC NA48/NA62: at the heart of the LHC ! N Jura mountains Geneva airport France Switzerland LHC NA48  NA62 The CERN Accelerator Complex Note: NAYY ≡ YYth experiment installed in the North Area on a beam extracted from the SPS accelerator NA48 A fixed target experiment at the CERN SPS dedicated to the study of CP violation and rare decays in the Kaon sector 3 Monica Pepe - INFN Perugia The NA48 CERN WIN'11, Cape Town, 31/1 - 5/2 2011

2007/8 K  e2 /K   2 run NA62 NA48 ( ) : Direct CP-Violation in neutral K (not presented here...) Re(ε’/ε) = (14.7 ± 2.2) · NA48/1 (2002) : Rare K S decays and hyperons (not presented here...) BR (K S →  0 e + e - ) = ( ± 0.8) · BR (K S →  0  +  - ) = ( ± 0.2) · NA48/2 ( ) : Direct CP-Violation in charged K (not presented here...) A g ch = (-1.5 ± 2.2)  A g 0 = (1.8 ± 1.8) x NA62 (phase 1: phase 2: ) R (K e2 /K  2 ), and new experiment K +   + 4 KTeV (2008) (19.2 ± 2.1) · The NA48 experiment: history WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia NA48/1

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 5 P K = 60±3 GeV/c ~ 7  p/spill 400 GeV/c Simultaneous K + and K - beams: Flux ratio: K + /K – ~ 1.8 large charge symmetrization of experimental conditions Width ~ 5 mm K + /K - ~ 1 mm 5-6% K ± (2003 – 2004) Simultaneous K ± Beam in NA48/2

The NA48 detector WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 6 Beam pipe => PT KICK = 120 MeV  Magnetic spectrometer (4 DCHs): Δp/p = 1.02%  0.044%*p [GeV/c]  Hodoscope Fast trigger Precise time measurement (150 ps )  Liquid Krypton EM calorimeter (LKr) Quasi-homogeneous High granularity (~13000 cells), 27 X 0 ΔE/E = 3.2%/√E  9%/E  0.42% [GeV]  x =  y =0.42/E 1/2 0.06cm  x =  y =0.42/E 1/2  0.06cm  Hadron calorimeter, muon veto counters, photon vetoes LV1 trigger: hodoscope, DCH multiplicity, LKr E deposition LV2 trigger: software algorithm on fast on-line data processing (~1MHz  ~10kHz)

Unprecedented statistics in many channels Two years of data taking: 2003 (~50 days) and 2004 (~60 days) Main purpose was to measure direct CP violation in charged kaon decays, through asymmetry in Dalitz plot distribution New limits on CP violation in charged kaon decays WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 7 NA48/2 Data taking Before NA48/2 NA48/2  ±      ±      e   ±     e   ± e + e -  ±   ±      ± e + e -  A g ch = (-1.5 ± 2.2)  A g 0 = (1.8 ± 1.8) x Statistics: K      +   : ~ 4 x 10 9 K      0  0 : ~ 1 x 10 8 Sensitivity to K ± decays with branching ratios down to 10 –9 More than 200 TBytes recorded ! NA48 Experimental hall

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 8 K  →      rare decay [Eur. Phys. J. C68 (2010), 75] Test for low energy QCD (ChPT theory)

Theoretical framework WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 9 DEIB INT DE P * K = 4-mom of the K ± P *  = 4-mom of the  ± P *  = 4-mom of the radiative  Differential rate: Lorentz invariant  IB can be predicted from BR(     ) + QED corrections  DE O(p 4 ) contribution terms (cannot be predicted in model independent way in ChPT) X M magnetic: two amplitudes by chiral anomaly Reducible: calculated using WZW functional (X M ~270 GeV -4 ) Direct: small contribution, not model independent X E electric: no prediction in ChPT (depends on unknown constants)  INT arises from interference between IB and DE X E (possible CPV contributions)

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 10 W distributions for IB, DE, INT IB30xDE30xINT Inner Bremsstrahlung(IB): BR = (2.75 ± 0.15) ·10 -4 PDG (55<T * π <90 MeV) Direct Emission (DE): BR = (4.3 ± 0.7) ·10 -6 PDG (55<T * π <90 MeV) Interference (INT): not yet measured T ∗ π : kinetic energy of the charged Pion in the Kaon cms Very different distributions!

T *   T *   DE  T *   INT  Standard region The use of standard region 55 < T *  < 90 MeV as safe choice for BG rejection But…. region <55 MeV is the most interesting to measure DE and INT This measurement is performed in the region 0 < T *  < 80 MeV to improve statistics and sensitivity to DE WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia Enlarged T *  region

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 12 NA48/2 measurement of K ± → π ± π 0 γ decay  Simultaneous K + and K - beams: possibility to study CP violating effects  Larger T * π region in the low energy part (0 < T* π < 80 MeV)  Background contribution <1% wrt DE mainly K ± → π ± π 0 π 0 (accidentals < 5x10 -3 wrt DE)  Order <‰ γ mistagging probability for IB, DE and INT  W resolution better than 1%  Fit performed with both likelihood and polynomial techniques

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 13 NA48/2 Measurement technique HIGH STATISTICS  ~ 1 Million reconstructed events (the full number is used for the CPV measurements)  after a cut on W [0.2, 0.9] and on E γ > 5 GeV, still 600 k events left in the region M K ± 10 MeV for the measurement of DE and INT fractions FIT TECHNIQUE  Fitting conditions 0.2 < W < 0.9 & T *  < 80 MeV E  min > 5 GeV 14 bins in the fit to enhance sensitivity to INT  Extended maximum Likelihood main method corrected for different acceptances using MC  Polynomial fit used only as a cross-check assumes equal IB, DE, INT acceptance

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 14 Fit results  Extended maximum Likelihood Data(i) = N 0 [(1  )·MC IB (i) +  ·MC INT (i) +  ·MC DE (i)]  The algorithm assigns weights to MC W distributions of the 3 components to reproduce data  The method relies on the very different W distributions  2 = 14.4/13 prob = 0.35 NA48/2 Likelihood residuals Final result ( data): Frac(DE) T * π(0-80)MeV = BR(DE) / BR(IB) = (3.32 ± 0.15 stat ± 0.14 sys ) · Frac(INT) T * π(0-80)MeV = BR(INT) / BR(IB) = (-2.35 ± 0.35 stat ± 0.39 sys ) · 10 -2

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 15  Polynomial fit Fit results (cross-check)  Fit the ratio W(Data)/W(MC IB )  Assume equal acceptances  Use proper integrals of DE/IB & INT/IB  Frac(DE) = b · 2.27·10 -2 Frac(INT)= a · Final result : cross-check ( data): Frac(DE) T * π(0-80)MeV = BR(DE) / BR(IB) = (3.19 ± 0.16 stat )·10 -2 Frac(INT) T * π(0-80)MeV = BR(INT) / BR(IB) = (-2.21 ± 0.41 stat ) · F = c · (1+ (a ± e) W 2 +bW 4 ) ×

DE and INT fraction: final results WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 16 Final result ( data): Frac(DE) T * π(0-80)MeV = (3.32 ± 0.15 stat ± 0.14 sys )·10 -2 Frac(INT) T * π(0-80)MeV = (-2.35 ± 0.35 stat ± 0.39 sys )·10 -2 INT has never been observed before! K ± →π ± π 0 γ : first extraction of X E and X M  = Under the approximations: SystematicsDE (x )INT (x ) Acceptance L1trigger L2 trigger LKr Energy scale < < Total  = 0 and cos( δ 1 1 -δ 0 2 ) = cos(6.5°) ~ 1 X E and X M can be extracted using the formulae: Electric and Magnetic components X E =(-24 ± 4 stat ± 4 sys ) GeV -4 X M = (254 ± 6 stat ± 6 sys ) GeV -4 (WZW reducible anomaly prediction for X M ~ 270 Gev -4 )

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 17 Fit to data with INT=0 (T *  in 55 – 90 MeV) Bad  2 =51/13 prob=2·10 -6 NA48/2 Likelihood residuals (INT=0) BR(DE) INT=0, T*  (55-90)MeV = (2.32 ± 0.05 stat ± 0.08 sys )·10 -6 Measured in 0<T *  <80 MeV extrap. to 55< T *  < 90 MeV by MC. BR(IB) =2.61·10 -4 [D’Ambrosio et al] Clear disagreement with INT=0 hypothesis! Need a fit with non vanishing interference

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 18 CPV in K ± → π ± π 0 γ K ± →  ±    with direct photon emission is not suppressed by ΔI = 1/2 rule good channel to search for direct CP violation (NA48/2 sample ~1 M events) Asymmetry in the decay rate : R = N beam (K + )/N beam (K − ) = ± , δR/R ~ 2·10 −4 from K ± →  ±      decay used as normalization. |A N | < 1.5 × 10 90% CL First limit on sinΦ = ± 0.43 |sin Φ| < 90% CL A W = e ʃ INT / IB = (−0.6 ± 1.0 stat ) × 10 −3 NO CP asymmetry observed in K ± → π ± π 0 γ Asymmetry in the Dalitz plot: Theoretical range 2· ·10 -5 (50 < E γ < 170 MeV) but Susy contribution can push A~10 -4 PDG08 value : (0.9 ± 3.3)% A N = (N + - RN – ) / (N + + RN – ) = (0.0 ± 1.0 stat ± 0.6 sys ) × 10 −3 N + = 695k K + N - = 386k K -   /ndf =9.4/18 NA48/2

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 19 K  →    rare decay

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 20 K ± → π ± γγ theory relevant only at low m  In the ChPT framework the differential rate of the K ± (p) → π ± (p 3 ) γ(q 1 ) γ (q 2 ) process (no O (p 2 ) contribution) is: O (p 4 ) O (p 6 ) [G. Ecker, A. Pich and E. de Rafael, Nucl., Phys. B303 (1988), 665] [G. D’Ambrosio and J. Portoles, Nucl., Phys. B386 (1996), 403 ] A(z, ĉ)  dominant loop diagram contribution responsible for a cusp at m γγ = m 2π C  contains poles and tadpoles diagrams [J.M. Gerard, C. Smith, S. Trine, Nucl. Phys. B 730 (2005) 1] B = D = 0 Model dependent. Unitarity corrections effects can increase the BR by % (only z is dynamically relevant)

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 21 K ± → π ± γγ theory: dependence on ĉ  Both BR and M  spectrum shape strongly depend on the ĉ parameter ( O (1))  The M  spectrum has a pronounced cusp-like behaviour at 2  threshold. O (p 4 ) m 2π M  spectra for ĉ=–2.3, ĉ=0 The spectrum dependence will be used to extract the ĉ value BR(K ± → π ± γγ) = ( ·ĉ ·ĉ )·10 -7 ≥ 4·10 -7 BR(K     ) vs ĉ unitarity corrections

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 22 K ± → π ± γγ : NA48/2 result m  m  First observation of the cusp at 2  threshold! m 2π Previous measurement by E787 based on 31 events (5 BG events) [PRL79 (1997) 4079] : BR(π ± γγ) = (1.10  0.32)·10 –6 Data sample K      0 used as normalization 1164 events in 40% of the full data (~40 times previous world sample) Background: mainly from    0  (IB) (3.3%) Systematic: mainly from trigger efficiency Shape analysis Assume MC O (p 6 ) and ĉ = 2 for comparison Data shape follows ChPT description Possibility for precise ĉ measurement, but not quantitative result yet NA48/2 measurement BR(K ± → π ± γγ) = (1.07  0.04 stat  0.08 sys )·10 –6 Our model dependent BR determination is model independent BR and ĉ extraction in preparation NA48/2 PRELIMINARY

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 23 K  →   e + e –  First Observation [Phys. Lett. B659 (2008), 493]

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 24 K     e + e -  : BR measurement K    e + e –  similar to K      with internal  -conversion O (p 6 ) ChPT prediction BR(   e + e -  ) = (0.9÷1.7)·10 -8 Never observed before! K      0 D    e + e –  as normalization ( 18.7M events,  K =(1.48 ± 0.04)·10 11 ) Background mainly from    0 D  IB  (7.3%) Systematic mainly from Normalization and Background BR computed in bins of m ee  no assumption on m ee  (model independent measurement) cut on m ee  > 260 MeV/c 2 [F. Gabbiani, Phys. Rev. Lett. D59 (1999), ] BR(K ± →   e + e -  ) mee  >260 MeV = (1.19 ± 0.12 stat ± 0.04 syst )·10 -8 Model-independent BR (m ee  > 260 MeV/c 2 ) Data sample (NA48/2 full statistics) 120 candidate events

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 25 K     e + e -  : shape analysis The ĉ value is extracted by fitting data to the absolute O (p 6 ) ChPT prediction [F. Gabbiani, Phys. Rev. Lett. D59 (1999), ] ĉ = (0.90 ± 0.45)  2 /ndf=8.1/17; prob=96.4% 1.2  away from BNL E787 value in K + → π + γγ : ĉ =1.8 ± 0.6 Using NA48/2 measured ĉ and O (p 6 ) ChPT prediction we compute BR (m ee  < 260 MeV/c 2 ) to obtain the total model dependent BR: BR(K ± →   e + e -  ) = (1.29 ± 0.13 exp ± 0.03 ĉ )·10 -8 [Batley et al. Phys.Lett.B659:493, 2008]

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 26 CONCLUSIONS NA48-2 exp: K ± → π ± π 0 γ  Precise measurement of DE contribution and first measurement of INT term Frac(DE) T * π(0-80)MeV = BR(DE) / BR(IB) = (3.32 ± 0.15 stat ± 0.14 sys ) · 10 –2 Frac(INT) T * π(0-80)MeV = BR(INT) / BR(IB) = (-2.35 ± 0.35 stat ± 0.39 sys ) · 10 –2  Incompatibility of data with INT=0 hypotesis established  Extraction of Magnetic and Electric components X E =(-24 ± 4 stat ± 4 sys ) GeV –4 X M = (254 ± 6 stat ± 6 sys ) GeV –4  No evidence for CPV asymmetry in both rates and Dalitz plot NA48-2 exp: K ± → π ± γ γ  Preliminary measurement of BR at O (p 6 ) and ĉ = 2 BR(K ± → π ± γγ) = (1.07  0.04 stat  0.08 sys )·10 –6  Model independent measurement and ĉ extraction in preparation NA48-2 exp: K ± → π ± e + e - γ  First observation and measurement of BR and shape BR(K ± →   e + e -  ) = (1.19 ± 0.12 stat ± 0.04 syst )·10 –8 ĉ = (0.90 ± 0.45)

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 27 Spare Slides

Experimental status of BR(DE) DE±errstat E787 (4.7±0.9) · K E470 (3.8 ± 1) · K ISTRA + (3.7 ± 4) · PDG 08 (4.3±0.7) · // Assumption INT=0 in the DE measurement Measurements performed in the range 55MeV<T *  < 90MeV No Interference and no CPV observed INT(E787) = (-0.4 ± 1.6)% T *  (55-90) MeV 28 Rare Kaon Decay K ± →  ±    WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia

WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia 29 K ± → π ± π 0 γ EVENT SELECTION 1 charged track, P > 10 GeV at least 3 em clusters, E > 3 GeV, clust-clust distance > 10 cm no hits in muon detector |Zcha – Zneu| 400 cm for all other pairs)  20% sample reduction BUT radiated photon mis-ID < 0.1% 54 < E K < 66 GeV M K within 10 MeV/c 2 from PDG value E  > 5 GeV (to exclude region with L1 trigger efficiency < 99%) 0 < T* < 80 MeV (upper cut due to effective L2 trigger cut at 90 MeV)

Reconstruction and backgrounds Data sample: 600K events in the region M K ± 10MeV Fitting conditions: GeV BG <1% of DE due to       Accidentals <5·10 -3 wrt DE  mistagged events <10 -3  2 radiative   1  3  0 decay  ’s Reconstruction aims to identify the radiative  30 Rare Kaon Decay K ± →  ±    WIN'11, Cape Town, 31/1 - 5/2 2011

Mistagging self background to DE Wrong  in W Generated W distribution IB Reconstruction Reconstructed IB events using a  from the  0 look like DE!!! Mistagging lead to overestimated DE Mistag(IB) =(0.52±0.06)·10 -3 Mistag(DE) =(0.48±0.23)·10 -3 Mistag(INT)=(0.49±0.24)·10 -3 NA48/2 mistag 31 Rare Kaon Decay K ± →  ±    WIN'11, Cape Town, 31/1 - 5/2 2011

Fitting techniques and fit results - Extended Maximum Likelihood Fit (main method) An algorithm assigns weights to MC W distributions of the 3 components to reproduce data This algorithm relies on the very different W distributions - Polynominal Fit (used as cross-check) The ratio W(Data)/W(IBMC) is fitted with polynomial function: F = c · (1 + aW 2 + bW 4 ) Final result ( ): Frac(DE) T* π (0-80)MeV = %DE / %IB = (3.32 ± 0.15 stat ± 0.14 sys )*10 -2 Frac(INT) T* π (0-80)MeV = %INT / %IB =(-2.35 ± 0.35 stat ± 0.39 sys )*10 -2 SystematicsDE x INT x Acceptance L1trigger L2 trigger Energy scale < < Total INT has never been observed before! IB BG INT DE Rare Kaon Decay K ± →  ±    WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia

CPV table of systematic EffectValue P K distribution correction3· Acceptance difference< 4·10 -5 LVL1 trigger3·10 -4 LVL2 trigger4·10 -4     cross section difference~ 4·10 -5 R max variation3.5·10 -4 Total Systematic6.1· CPV in K ± →  ±    WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia

Backgrounds to K ± →  ± e  e   Bkg sourceB.R.Exp. evts K ± →  ±  0 D  (IB) 3.3 ∙ ±0.5 K ± →  ±  0 D  (DE) 5.3 ∙ ±0.03 K ± →  ±  0 e  e   (IB) ~1.7 ∙ ±0.9 K ± →  ±  0 e  e   (DE) ~2.6 ∙ ±0.01 K ± →  ± e  e   (  radiative) 2.9 ∙ ±0.5 K ± →  ±  0  0 D 2.1 ∙ ±0.7 Accidentals ±1.0 Total Bkg events7.3± K ± →  ±e  e  WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia

Systematic on BR(K ± →  ± e  e   ) EffectΔBR ·10 -8 Background subtraction±0.107 Electron/Pion ID±0.005 Detector acceptance±0.005 Trigger efficiency±0.007 MC statistics±0.011 Normalization±0.032 Total Systematic±0.04 Total Statistical uncertainty± K ± →  ±e  e  WIN'11, Cape Town, 31/1 - 5/ Monica Pepe - INFN Perugia