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Stefano Venditti University of Pisa & INFN

Recent results from NA48/2 on pion scattering lengths using Ke4 decay and cusp in K ± -> π ± π 0 π 0. Stefano Venditti University of Pisa & INFN. On behalf of the NA48/2 collaboration:

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Stefano Venditti University of Pisa & INFN

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  1. Recent results from NA48/2 on pion scattering lengths using Ke4 decay and cusp in K±->π±π0π0 Stefano Venditti University of Pisa & INFN On behalf of the NA48/2 collaboration: Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa Saclay, Siegen, Torino, Wien QCD@WORK 2007

  2. Outline • The NA48/2 experiment; • Ke4: theory and NA48/2 analysis; • Ke4: results for form factors and interpretation in terms of pion scattering lengths (a0,a2); • Cusp: K3pi theory and analysis; • Cusp: fit procedure and extraction of (a0-a2); • Conclusions. Stefano Venditti QCD@WORK 2007 17/06/2007

  3. NA48/2 beam line Width ~ 5mm K+/K-~ 1mm K+ 54 60 66 PK spectra, 603GeV/c K− Beams coincide within 1 cm over 114 m of decay volume Detectors Incoming SPS 400 GeV protons K+/K- flux~1.8 Stefano Venditti QCD@WORK 2007 17/06/2007

  4. NA48 DETECTORS • Spectrometer: • 4 DCHs -> redundancy. • σp/p=1.0%+0.044%× p(p in GeV); • Liquid Krypton EM calorimeter: • 16000 cells -> high granularity. • σE/E=3.2%/√E+ 9%/E+0.42%; • Hodoscopes (charged, neutral): • Trigger, time measurement. • Muon veto, Hadronic calo, Kabes, photon vetoes. Stefano Venditti QCD@WORK 2007 17/06/2007

  5. NA48/2 DATA: 2003 run: ~ 50 days 2004 run: ~ 60 days EVENTS SELECTED FOR K±->π±π±e±ν AND K±->π±π0π0: K3pi: ~ 108 events (greatest K3pi sample ever collected) Ke4: 0.68 M events (from 2003 data only) Stefano Venditti QCD@WORK 2007 17/06/2007

  6. Ke4:Theory 4 body decay->5 independent variables UsingCabibbo-Maksymowicz variables: Sπ(Mππ2),Se(Meν2),cosθπ,cosθe,Φ π+ Φ e+ θe θπ K π- ν Hadronic ME:<π+π-|Aλ+Vλ|K>=(1/MK)[FPλ+GQλ+R(K-P)λ+(H/M2)ελμνσKμPνQσ] (Pλ=dipion 4V; Qλ=dilepton 4V; Kλ=kaon 4V) F,G,R: axial form factors f.f. expansion wrt Se, q2: Fs=fs+f’sq2+f’’sq4+fe(Se/4mπ2)+… Fp=fp+f’pq2+… Gp=gp+g’pq2+… Hp=hp+h’pq2+… H: vector form factor Partial wave expansion of amplitude: F = Fseiδs + Fpeiδp cosθπ +d-wave terms G = Gpeiδg + d-wave terms H = Hpeiδh + d-wave terms q2=(Sπ/4mπ2)-1 R negligible (relevant in Kμ4) Fit parameters: Fs, Fp, Gp, Hp, δ=δs-δp Stefano Venditti QCD@WORK 2007 17/06/2007

  7. Ke4 Analysis: selection and BG rejection e± Ke4-> 3 charged tracks (2 opposite sign pions),1 ν. BR ~ 4 · 10-5 • Spectrometer for momenta measurement; • LKR info used to tag electron and pions (E/p); • Missing energy and Pt (because of neutrino). ν K± π- π+ BG checked with data: wrong sign events have same total charge but wrong electron charge (es:e+π-π- for K- decay):their contribution to total BG is the same or is to be rescaled by a factor 2 wrt “real” BG, depending on the process. • Background, main sources: • π±π+π-, with π->eν in-flight decay or π misidentified as e; • π±π0,π±π0π0,with π0->e+e-γ Dalitz decay and,e misidentified and γ(s) undetected. Mke4 Pk Stefano Venditti QCD@WORK 2007 17/06/2007

  8. Data/MC comparison Mππ Meν GeV GeV cosθπ cosθe Stefano Venditti QCD@WORK 2007 17/06/2007

  9. Ke4 analysis: fitting procedure Iso-populated 10(Mππ)x5(Meν)x5(cosθe)x5(cosθπ)x12(Φ)=15000 bins in the C-M variables used. Form factor values used to minimize a log-likehood estimator well-suited for small numbers. Ten independent fits in Mππ bins, assuming constant f.f. over single bins. K+: Data: 435654 events,29 evts/box MC: 10.0 M events,~667 evts/box K-: Data: 241856 events,16 evts/box MC: 5.6 M events,~373 evts/box • no normalization->only relative f.f. and their variation wrt kinematical variables; • residual variation (linear slope) observed wrt Mev for Fs: 2-dim fit performed; • Fs from bin/bin normalization after fit. K+/K-~1.8 (both data and MC) MC/Data~23 (both K+ and K-) Fs2~(1+f’s q2 + f’’s q4 +f’e Se/4mπ2)2 Stefano Venditti QCD@WORK 2007 17/06/2007

  10. fp,hp≠0, no q2 dependence gp linear wrt q2 Correlation: g’p gp -0.914 Stefano Venditti QCD@WORK 2007 17/06/2007

  11. Ke4: form factors results All f.f. parameters measured within 5% to 15% relative precision • Relative form factors: f.f./Fs(0); • measured separatedly for K+,K- and then combined; • Fs obtained from bin/bin normalization,Fp,Gp,Hp deconvoluted from observed Fs(q2,Se) variation. value±stat.±syst. f’s/fs=0.165±0.011±0.006 f’’s/fs=-0.092±0.011±0.007 f’e/fs=0.081±0.011±0.008 fp/fs=-0.048±0.004±0.004 gp/fs=0.873±0.013±0.012 g’p/fs=0.081±0.022±0.014 hp/fs=-0.411±0.019±0.007 • SYSTEMATIC CHECKS • Two independent analyses; • Acceptance control; • BG level and shape control; • Radiative correction included; • Possible bin-to-bin correlation considered. Stefano Venditti QCD@WORK 2007 17/06/2007

  12. Ke4:δphase shift and a0,a2 extraction • Extraction of pion scattering lengths fromδ=(δ00-δ11) phase shift can be done through external experimental and theoretical (e.g. Roy equation) inputs, which relate δand (a0,a2); • The Universal Band parameterization corresponds to a 1-dimensional fit of δ with a fixed relation between a0 and a2. Stefano Venditti QCD@WORK 2007 17/06/2007

  13. Ke4: comparison with other experiments • Thanks to the independent bin analysis, the scattering length extraction can be performed on old data even if the collaboration doesn’t exist anymore; • E865 quotes values ranging from a0=0.203 to a0=0.237, NA48 seems to obtain slightly higher values; • Further checks are ongoing to understand the two different results, expecially in the last Mππ bin. a0=0.25 a0=0.20 Stefano Venditti QCD@WORK 2007 17/06/2007

  14. Plane (a0,a2): theory and experiments • Several equations relating a0 and a2 exist (ACGL,DFGS,…) • A 2-dimensional fit (on a0and a2) can also be performed (dotted lines in figure,centered on best χ2 and including 68% of events); • E865 and NA48/2 point at slightly different regions of the universal band; removing the last E865 bin brings the two results closer and decreases χ2. Isospin breaking corrections neglected so far. This contribution was considered negligible until short time ago. Calculations to apply this correction are ongoing. Stefano Venditti QCD@WORK 2007 17/06/2007

  15. MKPDG ± 6 MeV cut Resolution: 0.9 MeV/c2 pm contribution 59.3M K+ 32M K- p+p0p0 invariant mass, GeV/c2 K3pi:selection m0: pion mass Ei,Ej: γenergies Zik:π0 vertex distance from LKR • For each photon pair (e.g. i,j) a decay vertex reconstructed along beam axis assuming π0 mass: • m02=2EiEk(1-cosβ)~EiEk(Dik)2/(Zik)2 Zik; • Pair of photons minimizingΔZ=Zjl-Zik chosen; • Compatibility within ± 6 MeV wrt PDG kaon • mass requested. γ LKR γ Dik γ Zij Zkl K Djl ΔZ γ ππ invariant mass Excellent at low Mππ values Stefano Venditti QCD@WORK 2007 17/06/2007

  16. v u K±→±00 dalitz plot Primary goal: asymmetry measurement Dalitz variables: u=(s3-s0)/π2 v=(s2-s0)/π2 Comparison between Dalitz plot distribution for K+ and K- to look for direct CP violation. Matrix element: |M(u,v)|2~1+gu+hu2+kv2+... 3s0=Mk2+Mπ2+2Mπ02 si=(Pk-Pi)2 (i=1,2,3;3=odd pion) Ag≠0->direct CP violation π+(even) π-(odd) K+ π+(even) • SM Ag predictions in range 10-6-10-5; • Beyond SM models enhance the prediction; Stefano Venditti QCD@WORK 2007 17/06/2007

  17. Acceptance equalization N(A+B+K+) RUS= N(A+B-K-) N(A+B-K+) RUJ= N(A+B+K-) N(A-B+K+) RDS= N(A-B-K-) N(A-B-K+) RDJ= N(A-B+K-) Y X Achromats: K+ Up Jura B+ K+K- B Saleve • In each ratio the charged pions are deflected towards the same side of the detector (left-right asymmetry cancels out) • In each ratio the event at the numerator and denominator are collected in subsequent period of data taking(global time variations) • The whole data taking is subdivided periods in which all the field configurations are present. 4-ple ratio: R4=RUS*RUJ*RDS*RDJ≈ n(1+Dg/f(u))4 • 3-fold cancellation: • L-R asymmetry; • Beam shape asimmetry; • Global time variations. RESULTS: Slope difference: Δg=(2.2±2.1stat±0.7syst)·10-4 Charge asymmetry: Ag=(1.8±1.7stat±0.5syst)·10-4 Stefano Venditti QCD@WORK 2007 17/06/2007

  18. “Bonus” goal: cusp in M2π0π0 distribution 2003: 16.0 mln events 2004 (80%): 43.6 mln events 80k • Cusp analysis not foreseen at the beginning of the experiment; • First cusp observation on 2003 data, 2004 data now included (~80% of the whole statistics); • A cusp can be seen in M2(π0π0) distribution at 4Mπ+ value and is the effect of the interference of (at least) two amplitudes. 200k 60k 160k 120k 40k 80k 20k 40k 0 M2(00), (GeV2) M2(00), (GeV2) 45k 120k 110k 40k 100k 35k 90k 30k 80k +– threshold +– threshold 25k 70k 0.079 0.080 0.078 0.078 0.076 0.077 0.076 0.077 0.079 M2(00), (GeV2) M2(00), (GeV2) Stefano Venditti QCD@WORK 2007 17/06/2007

  19. Cusp theory: final state rescattering N. Cabibbo, PRL 93 (2004) 121801 M(K± π±π0π0)=M1+M2 M0=direct emission amplitude = A0(1+g0u/2+h’u2/2+k’v2/2) π± Not the same parameterization used for asymmetry! Amplitude parameterized (rather than matrix element) K± π0 π0 M1=rescattering amplitude = -2/3(a0-a2)m+M+√1-(M00/2m+)2 K->3π± amplitude at threshold Negative interference under 2m+ : no rescattering S-wave ππ scattering lengths : 1-loop rescattering π± π+ π0 K± M2=4m2π+ π0 π- Stefano Venditti QCD@WORK 2007 17/06/2007 M2π0π0(GeV2)

  20. Cusp theory: higher order diagrams N. Cabibbo and G. Isidori, JHEP 503 (2005) 21 • 1 and 2-loop processes included; • Five S-vawe scattering lengths (ax, a++, a+-, a+0, a00), expressed as linear combinations of a0 and a2; • Isospin symmetry breaking (~2%) considered; • Radiative corrections missing -> a0-a2 precision >= 5 %. Examples of 2-loop diagrams: π± π0 π* K± π* π0 π± Two loop effect on cusp π* π0 No cusp π* π* K± Cusp (2-loop correction) Cusp Arbitrary scale π0 No rescattering π* π* Imaginary amplitude π± π* K± π0 Negative amplitude π* π* π0 π* 0.076 0.078 0.080 0.074 Stefano Venditti QCD@WORK 2007 17/06/2007 M2π0π0(GeV2)

  21. Cusp: fit procedure • Detector response computed with a full GEANT MC; resolution matrix (computed on s3 variable) applied on MC-generated data; • Five free parameters (g0, h’,m+(a0-a2),m+a2,N) in MC data. Use of MINUIT to minimize χ2 based on difference data-MC. Resolution smears MC bins: FiMC=∑ RijGj Reconstructed s3 generated MC bin: G=G(M00,g0,h’,m+(a0-a2),m+a2) Generated s3=M2(00)(GeV2) (Fdata-NFMC)2 χ2(g0, h’,m+(a0-a2),m+a2,N)=∑ δF2data+δ2N2F2MC bins Stefano Venditti QCD@WORK 2007 17/06/2007

  22. Cusp: dealing with pionium • Pionium created when relative velocity between two opposite-sign pions is ~0. It is created by EM interaction, decays (~10-16 sec) by strong interaction; • No Coulomb corrections -> Pionium cannot be accounted for in this model -> 7 bins (±3.5 resolution σ’s around dipion mass) excluded from Data/MC comparison. 7 bins excluded (0.0775-0.0785 GeV2) If excess in data all interpreted as pionium, one gets: R=(K+A2)/(K+–) = (1.820.21)10–5 Theoretical prediction:R=0.810–5 [Z.K. Silagadze, JETP Lett. 60 (1994) 689] Stefano Venditti QCD@WORK 2007 17/06/2007

  23. Geometric acceptance; • MC sample; • LKR showers • V-dependence of amplitude. • Analysis technique; • Trigger inefficiency; • Resolution; • LKR non-linearity; Systematic checks Cusp: results (2003+2004 data, 80% of statistics) (a0–a2)m+ = 0.261  0.006stat.  0.003syst.  0.013ext. a2m+= –0.037  0.013stat.  0.009syst.  0.018ext. Using a chiral symmetry constraint [Colangelo et al., PRL 86 (2001) 5008]: a2 = –0.0444 + 0.236(a0–0.22) – 0.61(a0–0.22)2 – 9.9(a0–0.22)3 (a0–a2)m+ = 0.263  0.003stat.  0.0014syst.  0.013ext. Stefano Venditti QCD@WORK 2007 17/06/2007

  24. Conclusions • The NA48 results for a0 and a2 following two different paths (ke4 and cusp) are consistent; • Agreement is also found with DIRAC result, which computes a0 and a2 measuring pionium lifetime; • Both analyses are still ongoing, room for improvements. Stefano Venditti QCD@WORK 2007 17/06/2007

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