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Фундаментальные параметры  рассеяния в распадах заряженных каонов эксперимент NA48/2

Фундаментальные параметры  рассеяния в распадах заряженных каонов эксперимент NA48/2. содержание. Эксперимент NA48/2 « cusp » эффект и параметры киральной теории сравнение с Ke4 результатами. Эксперимент NA48/2.

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Фундаментальные параметры  рассеяния в распадах заряженных каонов эксперимент NA48/2

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  1. Фундаментальныепараметрырассеяниявраспадахзаряженныхкаоновэксперимент NA48/2 В.Кекелидзе, "Марковские чтения"

  2. содержание • Эксперимент NA48/2 • «cusp» эффект и параметры киральной теории • сравнение с Ke4 результатами В.Кекелидзе, "Марковские чтения"

  3. В.Кекелидзе, "Марковские чтения" Эксперимент NA48/2 Основная задача - Поиск зарядовой асимметрии в распадахK(3) 2003 run: ~ 50 days 2004 run: ~ 60 days Total statistics in 2 years: K+: ~4·109 K00: ~1·108 Rare K± decays: BR’s down to 10–9can be measured > 200 TB of data recorded

  4. Установка NA48 В.Кекелидзе, "Марковские чтения" • High resolution • magnetic spectrometer (+): • 2 + 2 drift chambers; • magnet with • momentum kick 265 MeV/c • electromagnetic cal. (00): liquid krypton (~10m3 at 120 K) 13212 cells granularity 2x2 cm2 Rate ~106 KL decays / spill

  5. В.Кекелидзе, "Марковские чтения" LKr - э-м жидко-криптоновый калориметр

  6. В.Кекелидзе, "Марковские чтения" PK spectra, 603 GeV/c BM z 10 cm NA48/2 beam line Simultaneous K+ and K beams: large charge symmetrization of experimental conditions 2-3M K/spill (/K~10), decay products stay in pipe. Flux ratio: K+/K– 1.8 magnet 54 60 66 K+ K+ beam pipe Be target focusing beams K ~71011ppp, 400 GeV Second achromat K • Cleaning • Beam spectrometer (resolution 0.7%)‏ Front-end achromat Quadrupole quadruplet Beams coincide within ~1mm all along 114m decay volume • Momentum selection • Focusing •  sweeping vacuum tank He tank + spectrometer 1cm not to scale 200 250 m 50 100

  7. В.Кекелидзе, "Марковские чтения" 2003 + 2004: 59.6 mln events +–threshold An anomaly was observed at invariant massM(00) = 2m+ inK00decays never observed in previous experiments «Сusp» - эффект • Cusp - «остриё», • особенность в спектре, • связаннаясизломом; • вотличиеотпика, • достоверноенаблюдение • такойособенности • требует • большойстатистики • и • высокогоразрешения

  8. «Сusp» - эффект и параметры киральной теории длиныпионногорассеяния важнейшим свободным параметром киральной теории (ChPT) является кварковый конденсат <qq>, который определяет относительные размеры масс и импульсов в степенном разложении a0 и a2- длины ppрассеяния (S-волны) соответственно с изоспином I=0 и I=2, также входят в амплитуды pp-рассеяния связь <qq> с a0 и a2 известна из теории с высокой точностью; поэтому измерения a0 и a2 позволяют получить важные ограничения для параметров ChPT Pion scattering lengths can be measured in the study of the cusp-effect in K00decays 2003 result: PLB 633 (2006) 173, Cabibbo-Isidori theoretical framework] N. Cabibbo, PRL 93 (2004) 121801 Анализ был проведен независимо 2-мя группами из Пизы и Дубны В.Кекелидзе, "Марковские чтения"

  9. K00 selection В.Кекелидзе, "Марковские чтения" accidental photon (Dik)2 m02 = 2EiEk(1-cos) ≈ EiEk2 = EiEk (zik)2 Ek LKr z Em Dik K-decay vertex zlm Ei zik z El selected photon 20 mass resolution , MeV/c2 … excellent at low M00! M2(00), (GeV/c2)2 for each photon pair (i,k) a decay vertex is reconstructed along the beam axis under the assumption of 0 decay m0 – mass of 0 Ei, Ek – energy of i, k Dik – distance between iand k on LKr zik – distance from 0 decay vertex to LKr 103 MK-3 mass spectrum(2004 data)‏ Events Background isnegligible

  10. Объяснение «Cusp» - рассеяние в конечном состоянии В.Кекелидзе, "Марковские чтения" + K+ 0 0 1–()2 M00 2m+ No M1 amplitude M1 amplitude present:13% depletionunder the threshold Arbitrary scale N. Cabibbo, PRL 93 (2004) 121801 M(K00)= M0 + M1 Direct emission: Kaon rest frame: u=2mK∙(mK/3Eodd)/m2 v=2mK∙(E1E2)/m2 M0 = A0(1+g0u/2+h0u2/2+k0v2/2)‏ Rescattering amplitude: Negative interferenceunder threshold M1 = –2/3(a0–a2)m+M+ Combination of S-wave  scatteringlengths K3 amplitudeat threshold (isospin symmetryassumed here)‏ M2(00), (GeV/c2)2

  11. В.Кекелидзе, "Марковские чтения" One-loop diagrams: Two-loop diagrams: a) 2 scattering b) irreducible 3 scattering c) reducible 3 scattering Теория: двух-петлевые диаграммы N. Cabibbo and G. Isidori (“CI”), JHEP 503 (2005) 21 • S-wave scattering lengths(ax, a++, a+–, a+0, a00) expressed as linear combinations ofa0anda2 • isospin symmetry breaking - following J. Gasser • for example,ax=(1+/3)(a0–a2)/3,where=(m+2–m02)/m+2=0.065- isospin breaking parameter • all rescattering processes at one- & two-loop level • radiative corrections missing:(a0– a2)precision ~5% Prediction of thetwo-loop theory Arbitrary scale Cusp point No rescatteringamplitude Subleadingeffect Leading effect M2(00), (GeV/c2)2

  12. Theory: effective fields В.Кекелидзе, "Марковские чтения" G. Colangelo, J. Gasser, B. Kubis, A. Rusetsky (Bern-Bonn group: “BB”) Phys.Lett. B638 (2006) 187-194 • Non-relativistic Lagrangian for effective fields; expanding in another small parameters. • Valid in the whole decay region. • Another (in comparison with CI) part of amplitude is absorbed in the polinomial terms (so another correlations). • At two loops, algebraically different formulae for amplitude • FORTRAN code written by authors

  13. процедура фитирования В.Кекелидзе, "Марковские чтения" Log(Rij) 420x420 bins Reconstructeddistribution: FjMC = RijGi Reconstructed s3 (GeV/c2)2 Generated distributionG(M00) = G(g0,h’,a0,a2,M00)‏ fit region MINUIT minimization of 2of data/MC spectra shapes Generated s3=M200, (GeV/c2)2 (FDATA–NFMC)2 2(g0,h0,m+(a0–a2),m+a2,N)= FDATA2+N2FMC2 s3 bins 1-dimensional fit of the M00 projection Detector response matrix Rij obtained with a GEANT-based MC simulation 5 free parameters

  14. В.Кекелидзе, "Марковские чтения" Fit quality & pionium signature Points excluded from the fitdue to absence of EM correctionsin the used model 7 data bins skipped aroundthe M(+–) threshold Combined 2003+2004 sample Excess of events in the excluded interval,if interpreted as due to pionium decaying as A200,gives R=(K+A2)/(K+–) = (1.820.21)10–5. Prediction [Z.K. Silagadze, JETP Lett. 60 (1994) 689]: R=0.810–5.

  15. В.Кекелидзе, "Марковские чтения" atoms and  resonant structure with experimental resolution • Электромагнитные поправки в конечном состоянии(Gevorkian, Tarasov, Voskresenskaya, Phys.Lett. B649 159 (2007)) • Two contributions from K±→ ± decay to the K±→ ±  cusp region: • Pionium formation :  atom →  (negligible width)‏ • Additional  unbound states with resonance structure →   resonant structure (no experimental resolution)‏ In our fit we use a free parameter fatom (relative excess in the bin of width 0.00015 GeV2) to represent Pionium + resonant structure  resonant structure with experimental resolution measured value% (6 1) % is in good agreeemen with the prediction 5.8%

  16. Effect of radiative corrections В.Кекелидзе, "Марковские чтения" Bern — Bonn radiative correction to pion rescattering amplitude for 3pi decays. (Bissegger M., Fuhrer A., Gasser J., Kubis B., Rusetsky A. Nucl. Phys., B806, 2009, 178-223.) • Electromagnetic part is included into Lagrangian and all • the first-order diagrams are taken into account • But the bound states and resonant peak at the very threshold • can not be calculated perturbatively • (a free parameter fatom is used to represent the peak-like contribution) • Could be extracted as a relative effect for amplitude and • Implemented also to Cabibbo-Isidori case

  17. Effect of radiative corrections В.Кекелидзе, "Марковские чтения" 68% - probability ellipses for statistical errors only to illustrate the shift. Corrected Uncorrected

  18. Example of correlation coefficients (CI) В.Кекелидзе, "Марковские чтения"

  19. В.Кекелидзе, "Марковские чтения" Результатпо данным 2003+2004 (окончательный) (a0–a2)m+= 0.2571  0.0048stat. 0.0025syst. 0.0014ext. a2m+= –0.024  0.013stat. 0.009syst. 0.002ext. External uncertainty: due to (A++–/A+00)|threshold = (1.93-1.94)±0.015; (central value depends on fitted matrix element, error comes from PDG data) Additional theoretical uncertainty (higher order terms neglected) is estimated from the difference between results obtained using Bern-Bonn and Cabibbo-Isidori formulae:  (a0–a2)m+= 0.0088; a2m+= 0.015. The relative errors for a2 are essentially larger than (a0-a2) ones, as a2 alone leads to the second-order contribution to the cusp shape

  20. Systematical errors for independent a0, a2 В.Кекелидзе, "Марковские чтения" in units of 10-4

  21. В.Кекелидзе, "Марковские чтения" Результатпо данным 2003+2004 учитывающий ограничение из киральной теории [Colangelo et al., PRL 86 (2001) 5008]: (окончательный) (a0–a2)m+= 0.2633  0.0024stat. 0.0014syst. 0.0019ext. Theory precision uncertainty for this case is estimated by theorists: (a0–a2)m+= 0.0053 (2%). ChPT prediction : 0.2650 +/- 0.0040 Experimental precision is compatible with the theoretical one, the only problem is the theoretical uncertainty of measurement !

  22. Systematical errors with ChPT constraint (a2 is a function of a0) В.Кекелидзе, "Марковские чтения" In units of 10-4

  23.  scattering in K± →e± decay

  24. Ke4 formalism p*(e) p*()  Direction of the total  momentum in the K+ rest frame Direction of the total e+e momentum in the K+ rest frame  e K  e a rare decay [ B.R. = (4.09 ± 0.09) x 105 ] described by five variables Cabibbo – Maksymowicz variables : s≡ M2 se≡ Me2 e   For K K  ee 

  25. Ke4 formalism The form factors can be expanded as a function of M2 and Me2: In the partial wave expansion (only S and P waves) the amplitude can be written using form factors: F=Fseis+Fpeipcos G=Gpeip H=Hpeip Fs=fs+fs’q2+fs’’q4+fe’(Me2/4m2)+... Fp=fp+fp’q2+... Gp=gp+gp’q2+... Hp=hp+hp’q2+... q2=(M2/4m2)-1 F (Fp,Fs), G, H and =p-s will be used as fit parameters

  26. Ke4: selection & background Kaon momentum GeV/c  K  e   • Selection: • 3 tracks • Missing energy & missing Pt • LKr/DCH to electron PID 739500 K+ ; 411000 K- Main background sources: •  (→e The background is studied using the electron “wrong” sign events (we assume DQ=DS & total charge ±1) and cross check with MC. The total bkg is at level of 0.5%. •  with misidentified •  or  +(Dalitz) +e misidentified and s outside the LKr

  27. Ke4: Fitting procedure Data MC K+ evts 739500 49 17.7 M 1180 Evts/bin K- evts 411000 27 9.8 M 650 Evts/bin ● Data ▬ MC M • The form factors (F,G,H and ) are extracted minimizing a log-likehood estimator in each of 10(M)x5(Me)x5(cose)x5(cos)x12()=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 M, assuming constant form factors in each bins • a 2D fit (M, Me) 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)

  28. Ke4: form factors result • Systematics checks: • Acceptance • Background • PID • Radiative corrections • Evaluation of the sensitivity of the form factors on the Medependence of the normalization f’s/fs = 0.158±0.007±0.006 f’’s/fs= -0.078±0.007±0.007 f’e/fs = 0.067±0.006±0.009 fp/fs = -0.049±0.003±0.004 gp/fs = 0.869±0.010±0.012 g’p/fs = 0.087±0.017±0.015 hp/fs = -0.402±0.014±0.008 Preliminay (2003+2004 data) • All the Form factors are measured relatively tofs • first evidence offp≠0andfe’≠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- - then combined (different statistical error)

  29. Ke4 results: а0 = 0.218 ± 0.013(stat) ± 0.007(syst) ± 0.002(theor) a2 = -0.0457 ± 0.0084(stat) ± 0.0041(syst) ± 0.0030(theor) (correlation coefficient 97%) Using ChPT link: a0 = 0.220 ± 0.005(stat) ± 0.002(syst) ± 0.006(theor)

  30. В.Кекелидзе, "Марковские чтения" Измерение длин пионного рассеяния - фундаментальных параметров киральной теории 68% - probability ellipses, full uncertainties

  31. a0=0.2186  0.0065 2% th. uncert. В.Кекелидзе, "Марковские чтения"

  32. заключение физикакаонов, как и 50 лет назад остается актуальной и является потенциальным источником новыхоткрытий В.Кекелидзе, "Марковские чтения"

  33. SPARE В.Кекелидзе, "Марковские чтения"

  34. The Ke4 decay amplitude depends on two complex phases identified with • 0 : the  scattering phase shift in the I = 0 , l= 0 state (s – wave) • 1 : the  scattering phase shift in the I = 1 , l = 1 state (p – wave) ≠ 0 in the Ke4 decay amplitude asymmetric distribution of the charged lepton direction with respect to the plane defined by the two pions ( distribution) (Shabalin 1963) The asymmetry of the distribution increases with M The Ke4 decay rate depends on the phase shift difference  = 0 – 1  is an increasing function of M ; → 0 for M→ 2m ( from scattering theory :(k) ≈ ak at very low centre-of-mass momentum k ; a is the scattering length ; a ≠ 0 for s – waves only )

  35.       NA48 / 2 (Preliminary)  distributions for four M bins 2m+ < M < 0.291 GeV 0.309 < M < 0.318 GeV 0.335 < M < 0.345 GeV 0.373 GeV < M < mK

  36.  versus M (no isospin – breaking corrections) OLD PICTURE !!! Geneva – Saclay : ~ 30,000 events , p K+ = 2.8 GeV/c BNL E865 : 406,103 events (with ~ 4.4% background), p K+ = 6 GeV/c NA48/2 : 677,510 events (with ~0.5% background), p K± = 60 GeV/c NOTE: the isospin – breaking corrections reduce  by 0.01 – 0.012 (J. Gasser)

  37. To extract scattering lengths from d=d0-d1 some external data (I=2 pp scatteringg at higher energies) and theoretical input are needed, for example: Solution of Roy equations - ACGL, Phys.Rep.353(2001), DFGS, EPJ C24 (2002) that relates d and (a0,a2) . The Universal Band centre line parametrisation corresponds to 1-parameter fit with a2=f(a0) ChPT constrain gives another relation between (a0,a2) inside Universal Band. Isospin symmetry breaking is taken into account (new)

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