Measurement of pp scattering lengths in Kaon decays by NA48/2

1. Measurement of pp scattering lengths in Kaon decays by NA48/2 EPS-HEP 2007 Manchester 19-25 july 2007 Gianluca Lamanna(Università & INFN di Pisa) on behalf of NA48/2 collaboration

2. Outline • Introduction • Ke4 (K±→ p+p-e±n) • Form factors and pion scattering lengths • Data 2003: Preliminary results • Cusp (in K±→p±p0p0) • A new method to extract pion scattering lengths through the strong rescattering process p+p-→ p0p0 • Data 2003+2004: Preliminary results • Conclusions Gianluca Lamanna – HEP07

3. Width ~ 5mm 54 60 66 K+/K-~ 1mm K+ PK spectra, 603GeV/c BM K− Experimental setup:The Beams SPS protons @ 400 GeV Simultaneus, unseparated, focused beams Gianluca Lamanna – HEP07

4. NA48/2 detector Spectrometer: σp/p = 1.0% + 0.044% p [p in GeV/c] LKR calorimeter: σE/E = 3.2%/√E + 9%/E + 0.42% [E in GeV] CHOD, HAC,MUV, vetos Kabes Beam Monitor Only the spectrometer and LKr are involved in the analysis. The CHOD is used at the trigger level. Gianluca Lamanna – HEP07

5. 2003 run: ~ 50 days 2004 run: ~ 60 days Total statistics 2 years: K±→±00: ~1·108 K±→±+-:~3·109 Greatest amount ofK→3 evercollected v Beam Pipe u NA48/2 data & results • The main goal of NA48/2 was to measure the CP violation in charged kaon decays through the study of the asymmetry in three pion decays • The goal to reach a precision of 10-4 in the CP violation parameters Ag has been obtained after 2 years of data taking (2003 and 2004) • No signal of CP violation outside the SM at our level of precision Ag=(-1.5+1.5stat+0.9trig+1.1syst)·10-4 Ag0=(1.8+1.7stat+0.5syst)·10-4 Phys.Lett.B 634:474-482,2006 Phys.Lett.B 638:22-29,2006 CERN-PH-EP-2007-021 Gianluca Lamanna – HEP07

6. Ke4: formalism • The Ke4 dynamics is fully described by 5 (Cabibbo-Maksymovicz) variables: Mpp2, Men2, cosqp, cosqe and f In the partial wave expansion the amplitude can be written using 2 axial and 1 vector form factors (the axial form factor R is suppressed in Ke4 but accessible in Km4): F=Fseids+Fpeidpcosqp G=Gpeidp H=Hpeidp The form factors can be expansed as a function of Mpp2 and Men2: Fs=fs+fs’q2+fs’’q4+fe’(Men2/4mp2)+... Fp=fp+fp’q2+... Gp=gp+gp’q2+... Hp=hp+hp’q2+... q2=(Mpp2/4mp2)-1 F (Fp,Fs), G, H and d=dp-ds will be used as fit parameters Gianluca Lamanna – HEP07

7. Kaon momentum GeV/c p K p e p n Ke4: selection & background • Selection: • 3 tracks • Missing energy and missing Pt • LKr/DCH energy to electron PID • 677500 decays The background is studied using the electron “wrong” sign events (we assume DQ=DS and total charge ±1) and cross check with MC. The total bkg is at level of 0.5%. Main background sources: ppp + p→en ppp with p misidentified pp0p0 or p0 + p0(Dalitz) +e misidentified and gs outside the LKr Gianluca Lamanna – HEP07

8. ● Data ▬ MC Mpp Ke4: Fitting procedure • The form factors (F,G,H and d) are extracted minimizing a log-likehood estimator in each of 10(Mpp)x5(Men)x5(cosqe)x5(cosqp)x12(f)=15000 equi-populated bins. In each bin the correlation between the 4+1 parameters is taken into account. • The form factors structure is studied in 10 bins of Mpp, assuming constant form factors in each bins • A 2D fit (Mpp, Men) is used to study the Fs expansion • All the results are given wrt to Fs(q=0) constant term, due to the unspecified overall normalization (BR is not measured) Gianluca Lamanna – HEP07

9. Ke4: Fitting procedure and results Fs(q2) Fp(q2) • Fs is quadratic in q2 • First measurement of Fp≠0 Gp(q2) Hp(q2) • Linear in q2 • No linear term (hp’) Gianluca Lamanna – HEP07

10. Ke4: form factors result • Systematics checks: • Acceptance • Background • PID • Radiative corrections • Evaluation of the sensitivity of the form factors on the Men dependence of the normalization Preliminary (2003 data) 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 • All the Form factors are measured relatively to fs • first evidence of fp≠0 and fe’≠0 • The f.f. are measured at level of <5% of precision while the slopes at~15% (factor 2 or 3 improvement wrt previous measurements) • Separately measured on K+ and K- and then combined (different statistical error) Gianluca Lamanna – HEP07

11. Ke4:d dependence • The extraction of the pion scattering lengths from the d=ds-dp phase shift needs external theoretical and experimental data inputs . • The Roy equations, for instance, provide this relation between d and a0,a2 near threshold, extrapolating from the Mpp>0.8 GeV region. The precision of these data defines the width of the Universal Band in the (a0,a2) plane. • The fit of the experimental points using the Roy equations in the universal band allows to extract the a0 and a2 values Gianluca Lamanna – HEP07

12. Ke4: (a0,a2) plane: result and comparison • Minimizing the c2 in the 2D fit it’s possible to identify the favoured solution (and the corresponding ellipse) • The E865 and NA48/2 results agreement is marginal (manly due to the last d point in E865) (work ongoing (see Gasser talk at Kaon07) ) • The correlation between a0 and a2 is ~96% (similar for both experiment) Gianluca Lamanna – HEP07

13. Ke4: “neutral” Selection: one electron track in the DCH , 4 photons in the LKr, p0 mass constraints, missing Pt. 9642 events in 2003 (previous exp. 216 events)~30000 events in 2004 Background: pp0p0 with a misidentified p, ke3g+1 accidental ~ 3% in 2003 (276 events) ~ 2% in 2004 Due to the p0p0 symmetry only the s-wave is present (fs’, fs’’) f’e has been measured consistent with 0 within the present statistics BR(Ke400)prel= (2.587±0.026stat±0.019syst±0.029ext)·10-5 f’s/fs=0.129±0.036±0.020 f’’s/fs=-0.040±0.034±0.020 Preliminary Gianluca Lamanna – HEP07

14. i dij Vertex LKr j Z(i,j) Z(k,l) Dz Cusp: K±→p±p0p0 selection • Offline selection:among all the possiblegpairings, the couple for which c2 is smallest is selected • The K-decay vertex is the average between the two decay vertices • After associating a charged track to the 2p0sthe compatibility with the PDG kaon mass is requested to be ± 6 MeV. MKPDG ± 6 MeV/c2 cut Resolution: 0.9 MeV/c2 pm contribution p+p0p0 invariant mass, GeV/c2 Gianluca Lamanna – HEP07

15. M2pp M2pp Cusp: Dalitz plot distribution • The high statistics and the good resolution allow to see a “cusp” in the U (orM2p0p0) distribution in the position of2mp+ • 16.0 M events in 2003 + 43.6 M events in 2004 data taking • ~65% of the whole statistics Gianluca Lamanna – HEP07

16. p± p± p± K± K± K± p0 p- p0 p0 p0 p0 M p+ M0 M1 p0 + = M00 1– ( )2 M1 = –2/3(a0–a2)m+M+ 2m+ Cusp: one loop rescattering M0 = A0(1+g0u/2+h’u2/2+k’v2/2) • The M1 contribution is real below and immaginary above pp threshold 13% of depletion • Below the threshold the (negative) interference term gives a “depletion” in the p0p0 mass distribution • The cusp is proportional to (a0-a2) pp threshold Cabibbo Phys. Rev. Lett. 93, 121801 (2004) Gianluca Lamanna – HEP07

17. + = + + ... p± p± p± K± K± K± p0 p- p0 p0 p0 p0 M p+ M0 M1 p0 p p p0 p K± p p0 p Cusp: two loops • Including 2-loops diagrams other terms appear in the amplitude • All the S-wave amplitudes (5 terms) can be expressed as linear combination of a0 and a2 • The isosping breaking effect is taking in to account • The radiative correction (most relevant near threshold) are still missing • A deviation from the no rescattering amplitude behaviour appears also above threshold Cusp No rescattering Sub-Leading effect Leading effect 0.076 0.078 0.080 0.074 M2(00), (GeV/c2)2 Cabibbo,Isidori JHEP 0503 (2005) 21 Gianluca Lamanna – HEP07

18. Cusp: fit procedure & result • The detector acceptance correction is obtained with a full GEANT simulation • The 1-D fit is performed excluding 7 bins around the threshold position • The excess of events in this region is interpreted as pionium signature Pionium : R=(K+A2)/(K+–) = (1.820.21)10–5. Prediction:R=0.810–5(Silagadze, 94) (a0–a2)m+= 0.261  0.006stat.  0.003syst.  0.0013ext . a2m+= –0.037  0.013stat.  0.009syst.  0.0018ext. • This result is fully compatible with our previous measurement on partial sample (Phys.Lett. B633:173-283,2006) Preliminary Using ChPt constraints [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.  0.0013ext Gianluca Lamanna – HEP07

19. Cusp: systematics & “neutral” slopes • Standard expansion is not enough to describe the K→3p dynamics • The slopes has been remeasured as (slightly different definition wrt to the PDG definition): • The external error comes from A00/A+-= 1.9750.015 • A theoretical error of 0.013 (in a0-a2) have to applied to take in to account the still missed radiative correction and the high order terms Preliminary g= (64.9 0.3stat. 0.4syst. )% h’= (–4.7 0.7stat 0.5syst.)% k’= (0.970.03stat.0.08syst.)% First evidence of k≠0 Gianluca Lamanna – HEP07

20. NA48/2 Ke4 NA48/2 Cusp DIRAC band (prel. 2007) Conclusions • NA48/2 exploited two different procedure to measure the pp scattering lengths. • Ke4: the pp phase shift can be related to the a0 and a2 using theoretical input (e.g. Roy equations) • K→pp0p0: the pp scattering lengths are extracted from the study of pp rescattering contribution in the mp0p0 mass distribution (the error is dominated by the theoretical error) • Applying the isosping breaking corrections the two results are fully compatible • The results are compatible with the DIRAC experiment results • Isospin breaking corrections applied both in Cusp and in Ke4 (work ongoing (see Gasser talk at Kaon07) ) Gianluca Lamanna – HEP07

21. Spares Gianluca Lamanna – HEP07

22. Men slope: 2D fit f’’s f’s f’s -0.96 0.03 f’’s -0.06 • In the 1D fit a residual variation is observed with respect to Men • 2D in (Mpp2, Men2) performed • Linear depence with Men2 Fs=fs+fs’q2+fs’’q4+fe’(Men2/4mp2)+... f’e/fs = 0.081±0.011±0.008 Gianluca Lamanna – HEP07

23. Ke4: isospin breaking correction • See Gasser’s talk @ Kaon 2007 • Thanks to the indipendent bin analysis the correction can be applied also to old data coming from previous experiment • The results become compatible with the cusp’s results Gianluca Lamanna – HEP07

24. Fit results K+ K- Gianluca Lamanna – HEP07

25. Standard Dalitz plot parameterization D=(data-fit)/data One loop c2=420/148 Two loops c2=155/146 Pionium c2=149/145 Excluding 7 bins c2=145/139 Cusp fit (in 2003) |M(u,v)|2~1+gu+hu2+kv2+... Gianluca Lamanna – HEP07

26. Dirac experiment • The |a0-a2| quantity can be extracted from the measurement of the lifetime of pionic atoms in a model independent way • The ionized exotic atoms are produced in a fixed target • Lifetime in the order of 3 fs • ChPt predicts with high accuracy this lifetime • p is thep0momentum andd corrections • Physics Letters B 619 (2005) 50 • |a0-a2|=0.264+0.033-0.020 • expected error in 2007: +7.4%, -4.2% Gianluca Lamanna – HEP07

27. Spectrometer alignment • The kaon mass depends from the time variation of the spectrometer alignment • The mis-alignment gives a mis-measurement of the charged pionmomentum • The reconstructed invariant K mass is used to fine tune the spectrometer by imposing (acorrection ) : MK+ =MK- • The non-perfect field alternation is tuned by imposing (b correction): MK+-=MKpdg Eq. Sensitivity (on DCH4): M/x  1.5 keV/m Kaon sign B sign P = P0∙(1+β)∙(1+qbP0) Raw momentum Gianluca Lamanna – HEP07

28. DCH1 (upstream magnet) K K+ X, cm Beam movements • Short time scale movement: the beam moves during the SPS spill • Monitored with an high resolution beam monitor on the beams • The 2 beam movement is “coherent” • No effect in the 4-uple ratio • Large time scale movement: the beam positions change every run • Acceptance largely defined by central beam hole edge (~10 cm radius) • The cut is defined around the actual beam position obtained with the c.o.g. measured run by run, for both charges as a function of the K momentum (“virtual pipe” cut) Gianluca Lamanna – HEP07

29.  10-4 P kick(stray field) P kick(spectrometer) “blue field” The Earth field (Blue Field) was directly measured and used at the vertex recostruction level. The residual systematics isΔ<10-5 Gianluca Lamanna – HEP07