Bernard Peyaud CEA Saclay, IRFU -SPP

Transcription

1 Measurements of pp scattering lengths from K ± decays Experimental studies of K 3p and K e4 decays with the NA48/2 experiment at CERN Bernard Peyaud CEA Saclay, IRFU -SPP On behalf of the NA48/2 collaboration: Cambridge, CERN, Chicago, Dubna, Edinburgh, Ferrara, Firenze, Mainz, Northwestern, Perugia, Pisa, Saclay, Siegen, Torino, Wien Bernard Peyaud 1

2 Outline what can we learn from pp scattering lengths? the NA48/2 experimental setup measuring a 0, a 2 with: cusp in K ± p ± p 0 p 0 decays phase difference d pp in K ± p ± p - e ± n decays conclusion Bernard Peyaud 2

3 R pp scattering lengths: why interesting? p p angular wave number: k 2mE at low energy kr <<1 S-wave dominates the total cross section Bose statistics isospin I = 0, 2 allowed scattering matrix S pp> = exp(2id) pp> i.e. 2 phases: d 0,2 = a 0,2 k related to scattering lengths a 0, a 2 NA48/2 uses charged kaons to measure scattering lengths a 0, a 2 - cusp-effect in K p p 0 p 0 decays - d pp and form factors in K p p - e + n decays study of pp system near threshold S-wave scattering lengths a 0, a 2 are essential parameters of cpt spontaneous symmetry breaking from <q q> condensate? Bernard Peyaud 3

4 P K spectra, 60 3 GeV/c K ± NA48/2 beam line 2-3M K ± /spill (p/k~10), p decay products stay in pipe. Flux ratio: K + /K 1.8 Simultaneous K + and K - beams: large charge symmetrization of experimental conditions magnet K + Be target K + K - focusing beams beam pipe BM z ~ ppp, 400 GeV K - Second achromat 1cm Front-end achromat Momentum selection Quadrupole quadruplet Focusing sweeping Cleaning Beam spectrometer ( 0.7% (resolution Bernard Peyaud not to scale Beams coincide within ~1mm all along 114m decay volume vacuum tank 200 He tank + spectrometer 250 m 10 cm

5 Main detector components: The NA48 detector Magnetic spectrometer (4 DCHs): 4 views/dch: redundancy efficiency; used in trigger logic; Δp/p = 1.0% %*p [GeV/c]. Hodoscope fast trigger; precise time measurement (150ps). ( LKr ) Liquid Krypton EM calorimeter High granularity, quasi-homogenious; E /E = 3.2%/E 1/2 + 9%/E % [GeV]; x = y =0.42/E 1/ mm (1.5mm@10GeV). Hadron calorimeter, muon veto counters, photon vetoes. Beam pipe Beams Bernard Peyaud 5

6 NA48 data Prime goal of NA48/2: measurement of CP-violating charge asymmetry in K 3 p decays both modes with large BR s of (2-5) 10-2 View of the NA48/2 beam line 2003 run: ~ 50 days 2004 run: ~ 60 days Total statistics in 2 years: K ± p ± p - p + : ~ evts K ± p ± p 0 p 0 : ~ evts Rare K ± decays with BR s down to 10 9 also measured and compared to cpt predictions cusp in K ± p ± p 0 p 0 decays d pp in K e4 decays >200 TB of data recorded Bernard Peyaud 6

7 Evidence of cusp structure in K ± p ± p 0 p 0 decays 2003: ~16x10 6 events 2004: ~44x10 6 events First observation of the cusp made with 2003 data Addition of 2004 data: statistics x M 2 (p 0 p 0 ), (GeV/c 2 ) 2 M 2 (p 0 p 0 ), (GeV/c 2 ) 2 Homogeneous selection conditions + MC/Data statistics allows global analysis of all data p + p - threshold M 2 (p 0 p 0 ), (GeV/c 2 ) 2 M 2 (p 0 p 0 ), (GeV/c 2 ) 2 Bernard Peyaud 7

8 Arbitrary scale Theory: final state rescattering. N. Cabibbo, PRL 93 (2004) Direct emission (k,h << g): M(K ± p ± p 0 p 0 ) = M 0 + M 1 ( 2 / M 0 = A 0 (1+g 0 u/2+h 0 u 2 /2+k 0 v 2 M + ( 2 / = A + (1+g + u/2+h + u 2 /2+k + v 2 Rescattering amplitude: M 1 = 2/3(a 0 a 2 )m + M M ( ) 2 2m + Kaon rest frame: u = 2m K (m K /3-E odd )/m 2 p v = 2m K (E 1 -E 2 )/m 2 p Negative interference under threshold p + K + p 0 p 0 Combination of S-wave pp scattering lenghts K ± 3p ± amplitude at threshold No M 1 amplitude (isospin symmetry M 1 amplitude present: ( here assumed 13% depletion under the threshold Bernard Peyaud 8 M 2 (p O p 0 ), (GeV/c 2 ) 2

9 Arbitrary scale Theory: 2 loops diagrams: N. Cabibbo and G. Isidori (CI), JHEP 503 (2005) 21 S-wave scattering lengths (a x, a ++, a +, a +0, a 00 ) are linear One-loop diagrams: combinations of a 0,a 2 Isospin symmetry breaking following J. Gasser. Radiative corrections missing; (a 0 a 2 ) precision ~5% V-dependent terms ~ (k /2)V 2 introduced recently in unperturbed K ± p ± p + p - and K ± p ± p 0 p 0 amplitudes. Two-loop diagrams: a) 2p scattering Prediction of the two-loop theory Cusp point b) irreducible 3p scattering c) reducible 3p scattering No rescattering amplitude Subleading effect Leading effect Bernard Peyaud 9 M 2 (p 0 p 0 ), (GeV/c 2 ) 2

10 Theory: effective field G. Colangelo, J. Gasser, B. Kubis, A. Rusetsky (CGKR)Phys.Lett. B638 (2006) polynomial parts of amplitudes expressed in terms of (U,V)-slopes g,h,k numerically different from CI ones, and faster integration of the amplitude over V. Non-relativistic Lagrangian for effective fields Validity in the whole decay region. different part of amplitude (wrt CI) absorbed in the polynomial terms ( different correlations). At two loop level different formulae for amplitude FORTRAN code written by authors CI fit uses our recently measured parameters of the K ± 3p ± amplitude M + = A + (1+g + u/2+h + u 2 /2+k + v 2 /2): ( (8 - = + k g + = (15); h + = (26); CGKR has similar parameters but numerically different due to additional rescattering terms in the in M + amplitude. simultaneous fit of the NA48/2 K ± 3p ± and K ± p ± p 0 p 0 Dalitz plots for CGKR fit: g + = ; h + = ; k + = Bernard Peyaud 10

11 Pionium signature 7 Points around p + p - threshold are excluded from the fit due to absence of EM corrections in the model Combined samples Excess of events in the excluded interval (CI fit), if interpreted as due to pionium decaying as A 2p p 0 p 0, gives R G(K ± p ± A 2p )/ R G(K ± p ± p + p - ) = (1.8±0.3)x10 5. Prediction [Z.K. Silagadze, JETP Lett. 60 (1994) 689]: R=0.8x10 5. Bernard Peyaud 11

12 ( 1 ) Uncertainties & results Experimental constants are needed in the amplitude calculation external uncertainty dominated by R = (A ++ /A +00 ) threshold = Using a chiral symmetry constraint [Colangelo et al., PRL 86 (2001) 5008]: a 2 = ( / ) (a ) 0.61(a ) 2 9.9(a ) 3 CI :(a 0 a 2 )m + = stat syst ext. CGKR: (a 0 a 2 )m + = stat syst ext. ( preliminary ) Theory precision uncertainty for CI case: d(a 0 a 2 )m + = Bernard Peyaud 12

13 ( 2 ) Uncertainties and results With both a 0 and a 2 as free parameters in the fit CI case: ( preliminary ) (a 0 a 2 )m + = stat syst ext. a 2 m + = stat syst ext. Theoretical uncertainty: 5%. CGKR case: (a 0 a 2 )m + = stat syst ext. a 2 m + = stat syst ext. Theoretical uncertainty not given. CGKR case has large correlations between a 2 and polynomial terms of amplitude. CIparametersveryclosetoPDG s,a 0,a 2 better disentangled from g and h slopes. Bernard Peyaud 13

14 NA48/2: cusp fit results ( preliminary ) theoretical limits (Universal Band) Universal Band CI cpt band 68.3% prob. CI fit results: -stat. error only -stat. + syst. error -stat. + syst. + external -all including theoretical error a CI fit with cpt constraint CGKR 68.3% prob. CGKR fit results: -statistical only error; -statistical and systematical; -stat., syst. and external; CGKR fits with cpt constraint and lower limit of Universal Band constraint Bernard Peyaud 14

15 K e4 (K -> e n p + p - ) Results from 2003 Data analysis published (EPJC 54 3 (2008) 411) Event selection, reconstruction and FF extraction K e4 decays : kinematic variables and Form Factors Understanding d pp in terms of p p scattering lengths the pp scattering process is described theoretically by dispersion relations (Roy equations) that relate amplitudes with different isospin. As a result d pp depends essentially on two parameters, the scattering lengths a 00 and a 02. at low energy cpt constrains a 00 and a 02 through the size of the quark condensate Bernard Peyaud 15

16 Ke4 decays: event selection and background rejection Topology of p + p - e n signal : 3 charged tracks, 2 opposite sign pions, 1 electron (LKr info E/p ~ 1), some missing energy and p T (neutrino) Background : main sources π π + π - decay followed by π e n (dominant) or π misidentified as e π π 0 (π 0 ) decay + π 0 Dalitz decay (e + e g) + e misidentified as π and g (s) undetected Total background level is kept at ~ 0.5 % relative level Control from data sample : Wrong Sign -total charge (±1) as Right Sign events -electron charge opposite to total charge Log scale P Kaon In RS events: twice the rate if coming from K3p same rate if coming from K2p(p0) GeV/c Bernard Peyaud 16

17 Ke4 charged decays : 4-body decay formalism Five kinematic variables (Cabibbo-Maksymowicz): 2 invariant masses: S p M 2 pp, S e =M 2 en 3 angles : cosq p, cosq e and f. partial wave expansion of the amplitude: F, G = Axial Form Factors F = F s e ids + F p e idp cosq p + d-wave term G = G p e idg + d-wave term H = Vector Form Factor H = H p e idh + d-wave term expansion in powers of q 2, Se/4mp 2 (q 2 (S p /4m p2-1)) F F G s H p p p f f s g p h + p p + + f ' s f g + h q ' p 2 q ' p ' p q 2 q f '' s q 4 + f e ( 4 ) 2 S / m e p +.. In each m pp bin the fit parameters are F s, F p, G p, H p and d = d s - d p Bernard Peyaud 17

18 Ke4 charged decays : Total Data sample ( ) = 1.15x10 6 events! The 5 dimensional space spanned by C.M. variables, (M pp, M en, cosq p, cosq e and f) is binned with 10x5x5x5x12=15000 boxes with equal population The set of Form Factor values is used to minimize a log-likelihood estimator taking into account the statistics of the data and MC in each box. K + sample ( events) K - sample ( events) MC K+ sample (17.7 Millions events) MC K- sample (9.8 Millions events) 49 events/box 27 events/box ~1180 events/box ~653 events/box Ratio K+/K- ~ 1.8 both in Data and MC (run by run basis) Ratio MC/Data ~ 24. both for K+ and K- (run by run basis) Bernard Peyaud 18

19 Ke4 charged decays : the mass and cosq distributions K + and K - samples fitted separately, results combined data (symbols), simulation after fit (hist) and background ( x 10 to be visible) Background flat in cosq p, cosq e, f, concentrated at low M pp and M en = m p Mpp (GeV/c2) Men (GeV/c2) cosqp cosqe Bernard Peyaud 19

20 Ke4 charged decays : the f distributions CP symmetry : [d 5 N(K + )] at q p,q e,f = [d 5 N(K - )] at q p,q e,-f K - K + f (rad) Ratio K+/K- = 1.8 as expected from beam composition Bernard Peyaud 20

21 Ke4 joint distribution (cosqe,f) à la Pais-Treiman Distribution has 9 intensity functions:i i = I i (m pp,m en ) N( cosq e,f) = I 1 +I 2 cos2q e +I 3 sin 2 q e cos2f +I 4 sin2q e cosf +I 5 sinq e cosf +I 6 cosq e +I 7 sinq e sinf + I 8 sin2q e sinf + I 9 sin 2 q e sin2f With I 1 = f s 2 g 2 + f p2 g 2 /3 + g 2 (b 2 +a 2 /3)+ h 2 b 2 g 2 + 2/3 f p g cose f ag I 2 = -f s2 g 2 + g 2 /3 (b 2 -a 2 ) - f p2 /3 g 2 + h 2 /3 b 2 g 2-2/3 f p g cose f ag I 3 = -2/3 g 2 b 2 + 2/3 h 2 b 2 g 2 I 4 = p/2 f s g cos(d) bg I 7 = p f s g sin(d) bg I 5 -p f s h cos(d-e 2 ) bg 2 I 8 -p/2 f s h sin(d-e 2 ) bg 2 I 6-8/3 g h cos(e 2 ) b 2 g I 9-8/3 g h sin(e 2 ) b 2 g Intensity functions d=atan(i 7 /2I 4 ) d-e 2 =atan(2i 8 /I 5 ) e 2 =atan(2i 9 /2I 6 ) Bernard Peyaud 21

22 d pp signature in joint distribution (cosq e,f) m pp bin 1 m pp bin 5 m pp bin 10 COSq e > 0 data fit COSq e < 0 data fit COSq e > 0 data fit COSq e < 0 data fit f COSq e < 0 data fit f COSq e < 0 data fit f -p 0 p d pp 0.03 asym(cosq e ) 0 asym(f) 0 -p 0 p d pp 0.15 asym(cosq e ) > 0 asym(f) > 0 -p 0 p d pp 0.30 asym(cosq e ) >> 0 asym(f) >>0 Bernard Peyaud 22

23 Getting Fp, Gp, Hp fp 0 No q2 dependence Linear with q2 Correlation g p g p (0) Bernard Peyaud 23

24 Ke4 charged decays : d pp and (a 0 0,a 02 ) Extracting a 00 and a 02 from d =d 00 - d 11 variation requires I=2 pp data at m pp > theoretical work numerical solutions of Roy equations (ACGL Phys. Rep.353 (2001), DFGS EPJ C24 (2002) ) to connect d with (a0, a2 ) Universal Band where CL uses a relation a 2 = f(a 0 ) the cpt constrain band (CGL NPB603(2001)): reduced uncertainty(± 0.008) a 2-parameter fit can also be performed with 2 free parameters a 00 and a 0 2 Isospin symetry breaking to be accounted for ( Bern arxiv:hep-ph/ by J. Gasser) 2 free parameters isospin corrections ON Da0 = ± (stat) Da2 = ± (stat) Bernard Peyaud 24

25 Ke4 charged decays : isospin corrections to d Using Bern corrections: 11 to 15 mrad over the fitted Mpp range Uncertainty R ± DR = 37 ± 4 ( R=m s -m ud /(m d -m u )) DR translates into Ddcorr = at most ± GeV/c 2 quoted as theoretical precision (though marginal effect) Well matched to the NA48/2 analysis where radiative and isospin symmetry breaking effects factorize: Gamow factor x PHOTOS generator x Isospin corrections Formula coded from arxiv Fit range [0.285,0.390] Bernard Peyaud 25

26 Ke4 charged decays : isospin corrections to d All Data K+ and K- combined= = Isospin corr OFF = Isospin corr ON Correction (~10mrad) is larger than the statistical error on each point above 0.3 GeV/c 2 (7-8 mrad) 2p fit a 0 0 a 0 2 Isospin corr OFF ± ± Isospin corr ON ± ± Bernard Peyaud 26

27 relative Form Factors = FF/Fs(0) - measured separately for K + and K -, - combined according to stat. errors, - Fs obtained from bin to bin norm. - Fp, Gp, Hp de-convoluted from observed Fs(q2,Se) variation. Scattering length a 0 now measured with ~2% relative precision (cpt 1p fit), Improved precision for a 0 (~6%) and a 2 (~18%) in a 2-free parameter fit Systematic uncertainty as for 2003 (conservative, will be revisited) but~0.5 x (stat) for a 0,a 2 Charged Ke4: results from decays 2003 EPJC 54(2008) preliminary Bernard Peyaud 27 f s /f s f s /f s f e /f s ± ± ± ± ± ± f p /f s ± ± g p /f s g p /f s ± ± ± ± h p /f s ± ±0.014 a 0 ChPT 1p fit a 2 =f(a 0 ) a 0 free a 2 free ±0.006 ( ±0.0015) ± ± value stat ± ( ±0.0011) ± ±0.0084

28 scattering lengths measurements by NA48 Two statistically independent measurements by NA48/2: CI Cusp in K (p ± p 0 p 0 ) : 1p fit within 2 models (CI, CGKR) Ke4 with isospin corrections 2p fit using Roy equations 1p fit with cpt constraint remarkable agreement with cpt CGKR Precise cpt predictions : a 2 = ± and a 0 = ± Bernard Peyaud 28

29 Comparing with other measurements Ke4 : isospin corrections to published d pp of all 3 experiments + 1p cpt fit Note : E865 result dominated by highest energy data point, otherwise compatible Cusp : use 1p cpt fit and 2 models DIRAC : a 0 -a 2 non-symmetric errors from PLB619 (2005), use cpt constraint, still being revisited Yellow band is cpt prediction NA48/2 experimental precision now at the same level as theory! Events a 0 from 1p ChPT fit, isospin corr ON Bernard Peyaud 29

30 Epilogue arxiv hep-ph/ v1 20 Dec K e4 and cusp data from NA48/2 has allowed to measure (a 0,a 2 ) with precision equal to cpt data and theory agree remarkably well and it demonstrates that the pion mass is dominated (94%) by the quark condensate i.e. spontaneous breakdown of cpt (G. Colangelo, Garda workshop Feb. 2008) M 2 p - qq F 2 p ( m u + m d ) + ( m 2 q ) M. Gell-Mann, R. J. Oakes and B. Renner, Phys. Rev. 175 (1968) 2195 Bernard Peyaud 30

31 SPARES Bernard Peyaud 31

32 K e4 amplitudes and phases with T and CP violation f p e f nominal Ke4 parameters <g>=0.92, <g >=0.8, h =-0.37 e 1 =0, e h =p f s e fp h p K + e h g p gf p /a e f d e 2 e 1 g p -e fp CPT /CP /T f s f p -e f e 1 (K - ) = -e 1 (K + ) and e 2 (K - ) = -e 2 (K + ) K - -e 2 h p -e 1 g p d gf p /a Bernard Peyaud 32 g p -e f