Juliet Lee-Franzini. Laboratori Nazionali di Frascati. Cape Cod, June 2003

Transcription

1 σ(e + e hadrons+γ) Juliet Lee-Franzini Laboratori Nazionali di Frascati Cape Cod, June 2003

2 1. Why measure σ(hadrons+γ) 2. σ had (s ) at fixed s 3. Advantages 4. Dadvantages 5. First results from KLOE 6. What next for KLOE th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 2

3 The question: there a dcrepancy between standard model estimates and measurements important enough to warrant any possible check. Radiative return due to initial state radiation, allows the measurement of hadro-production for 2m π < s < s, at fixed collider s. Recall that to calculate of a µ we need the vacuum polarization corrections due to quark loops: th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 3

4 γ µ γ h u, d, s, c, b, t u, d, s... g s p-qcd which cannot be calculated for low s, but th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 4

5 H H H H IΠ(s)/π = sσ(e + e hadr)/(16π 3 α 2 ) δa had,lo µ = 1 4π 3 4m 2 π σ e + e hadr (s)k(s)ds. K(s) 1/s, i.e. enhance low s. Some authors substitute: σ e + e hadr (s) s s σ hadr(s) = R hadr s /(s ) (4π α 2 /3s) the lowest order QED cross section for e + e annihilation into massless muons. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 5

6 Radiative return due to initial state radiation, gives us the possibility of measuring hadro-production for 2m π < s < s, at fixed collider s. To lowest order the ISR ONLY amplitude (W 2 = s): e e s, s' hadr, dσ(hadrons + γ) ds π d cos θ γ = α πs σ hadr(s ) s' [ s 2 + s 2 s (s s ) from which ] 1 sin 2 θ s s 2s Binner, Kühn and Melnikov th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 6

7 Example: hadr=π + π, s = s π = M 2 π + π. dσ(ππγ) ds π d cos θ γ σ(e + e π + π, s π ) σ(e + e γγ, s) Advantages 1. Do not need to operate the collider at different energies 2. The overall energy scale, at least in a detector like KLOE establhed at W=m φ and applies to all values of M(hadr) 3. The luminosity measured at fixed energy, for the entire data set, avoiding painful corrections th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 7

8 e e s, s' Dadvantages I. hadr, s' e e s, s γ = s s γ = s s s hadr, s' FS radiation O(1) background to σ of interest! Cannot dtinguh two processes, need prece estimates. Must also remove - correct for and properly retain th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 8

9 Dadvantages II. One must perform an absolute measurement of a cross section which only a tiny fraction of the total cross section At KLOE, σ(bhabha) 100 µb σ(hadrons) 3 µb σ(π + π γ) 0.01 µb th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 9

10 e + e π + π, γγ, γπ + π M e 2 J µ e A µ 1 s (p p) ν A ν F π (s) e e q' q p' p σ ππ = π α2 3s β3 F π (s) 2 ee M 2 = 2e 4 ( u t + t u ) dσ γγ d cos θ = 2πα2 s 1 + cos 2 θ sin 2 θ e e hard s dσ(ππγ) ds π d cos θ γ = α πs σ ππ(s π ) [ s 2 + s 2 π s π (s s π ) ] 1 sin 2 θ s s π 2s π th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 10

11 Radiative corrections ISR. Th a well understood process and we have the appropriate, tested tools for dealing with it. PHOKHARA = full NLO - calculation to ppg initial state radiation H. Kühn, H. Czyz, G. Rodrigo Full 1 loop 2 nd Photon +1% -1% Comparon KKMC m + m - g KKMC/Phokhara Phokhara / Analyt. Calc. } We have performed together with S. Jadach a comparon between Phokhara and KKMC for radiative muon pair production fi Agreement on few permil level in entire energy range fi Effect of higher order corr. (3 rd photon, ) only vible > ca. 0.9GeV 2 and small Radiative corrections on the level of few per-mil KLOE Results on Hadronic Physics 26 th Meeting LNF Scientific Committee th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 11

12 Vacuum Polarization Th the same for everybody and presumably very well understood, today. The question to apply it, correctly, to data and whatever normalizing process used to get L (usually Bhabha scattering). FSR 1. Hard photon s p m Therefore also + s +... th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 12

13 Ways out? Take only small angle γ, ISR dominates, FSR not important. ddm 1.02 GeV nb/gev ISR+FSR ISR only ISR+FSR ISR only, o o o o All angles M GeV ISR+FSR ISR only, o o o o M GeV But small s had lost th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 13

14 Simultaneously measure 3 form factors, F π, F 1, F 2. Inclusive σ preferred. (F.J.) F ( 0, m) s s' m F ( s) F ( s', m) A truly inclusive measurement, as recommended, never possible. Background channels invalidate the measurement. There are possible compromes, but with poorer statcs. Otherwe try χpt calculations. In any case 3-body processes are suppressed, 1/32π 2. Likewe ρπγ small. It quite reasonable to begin with point like pions and correct the result (G.I.) th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 14

15 FSR 2. Soft photons Th refers to the presence of soft radiation in the final state, together with radiation of a hard photon by the initial electron-positron which allows one to measure σ(s < s). One needs proper modelling to ensure that whatever FSR has been removed by the event selection criteria, reintroduced for a proper measurement to get to the muon anomaly. Not Quite Final Results from KLOE I am reporting now on a precion measurement of the π + π cross section around the ρ region, performed with KLOE, with 2 million π + π γ events I wh to remind you why our first effort concentrated in th energy region by showing the impact of related measurements on a µ. Let us remember that out of a contribution to a µ of , due to the π + π channel, whose best measurement comes from CMD-2 at Novosibirsk with 110,000 events and a combination of τ data, in the π ± π 0 channels, from LEP and CESR, which appear to dagree. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 15

16 KLOE contributions 1. a µ. Comparon of measurement and calculations. HMNT, '02 (ee incl) DEHZ '03 (ee) DEHZ '03 ( ) E821 '02 BNL a The situation somewhat embarrassing: we can t say if there agreement with experiment... there possibly a problem with τ-e + e data. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 16

17 2. e + e data are clearly lower than τ extracted info, around the ρ region F ee F F average prelim CMD-2 CMD OLYA DM s (GeV ) a µ (τ e + e ) = (24.3 ± 7.9 exp ± 3.8 rad ± 2.8 I spin ) σ dcrepancy th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 17

18 The dagreement in fact stronger, when comparing BR: 6% or 4.6σ. 6% a rather large I-spin violation! CLEO OPAL ALEPH prelim. CVC Average BR( th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 18

19 KLOE can th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 19

20 e + e π + π γ simplified To lowest order, but only ISR, Binner, Kühn and Melnikov give: [ dσ(ππγ) = α3 ds π d cos θ γ 3s 2 F π(s π ) 2 βπ 3 s 2 + s 2 ] π 1 s π (s s π ) sin 2 θ s s π 2s π where s π = M 2 ππ and β π = 1 4m 2 π /s π the pion velocity in the ππ system. Integrating over cos θ, from x 1 = cos θ 1 to x 2 = cos θ 2 (θ 1 > θ 2 ) we get: dσ(ππγ) ds π = α3 3ss π F π (s π ) 2 β 3 π [ 1 2 s 2 + s 2 π s(s s π ) ( log 1 + x 2 + log 1 x ) 1 1 x x 1 s s π 2s (x 2 x 1 ) ] th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 20

21 For θ < θ γ < 180 θ, x = cos θ dσ(ππγ) = α3 F π (s π ) 2 βπ 3 ds π 3ss π = α sπ [ s 2 + s 2 π s(s s π ) log 1 + x 1 x s s π s [ s 2 + s 2 π s(s s π ) log 1 + x 1 x s s π 2s ] x σ(ππ, s π ) 2x ] = H σ(ππ, s π ) Definition of H, the radiator function. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 21

22 12 10 b dds nb/gev ; s, GeV 2 th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 22

23 a.u. 1/Hp pp a m K( s) s(pp) ppg ppg s GeV 2 δa µ a µ 1.45 δσ ππγ σ ππγ p th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 23

24 From PHOKARA e e o o 100 ddm nb/gev W=1.02 GeV 0.04 W=10.6 GeV 80 all 0.03 all o o 0.01 o o M GeV M GeV th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 24

25 Magnet SC Coil, B=0.6 T EM Calor. Pb scint fiber 4880 pm Drift Ch sense wires tot wires Al-Be beam pipe r=10 cm, 0.5 mm thick YOKE S.C. COIL Barrel EMC DRIFT CHAMBER Cryostat QCal End Cap EMC Pole Piece Paolo Franzini 7 m 6 m th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 25

26 s E /E /E = 5.7% // E(GeV) s T = ps ps // E(GeV) ps ps (Bunch (Bunch length length contribution contribution subtracted subtracted from from constant constant term) term) Driftchamber Electromagnetic calorimeter s p p /p /p = 0.4% (for tracks) s xy xy ª 150 mm, s z z ª 2 mm th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 26

27 YOKE S.C. COIL Cryostat The photon momentum and angle are obtained from p γ = ( p π + + p π ). Photons with θ < 15 (> 165 ) from the interaction region do not reach the calorimeter. o DRIFT CHAMBER o o o o Barrel EMC o End Cap EMC Pole Piece 7 m Pions are accepted for 40 < θ π < 140. Paolo Franzini 6 m th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 27

28 PHOKHARA for KLOE angular regions ddm (nb/gev 2 ) ISR+FSR 100FSR M (GeV ) FSR FSR+ISR, % M (GeV ) FSR contribution negligible for θ γ < 15 (> 165 ) 40 < θ π + π < 140 th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 28

29 dσ(π + π γ) dm 2 ππ = N obs N bkg M 2 ππ 1 ɛ sel ɛ acc 1 L Signal e + e π + π γ σ 5-25 nb Some background processes e + e φ K S K L, K S π + π, K L does not decay, σ 0.4µb e + e φ ρπ π + π π 0, σ 0.5µb Radiative Bhabha a fraction of µb (large e + e angles) e + e µ + µ γ: for s <600 MeV σ(µµγ) larger than σ(π + π γ). th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 29

30 σ(e + e π + π ) and σ(e + e µ + µ ) 1.4 b Amendolia et al s, GeV th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 30

31 Event candidate, probably π + π π 0 K S th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 31

32 π + π γ events are selected requiring two opposite charged particles in the drift chamber, rather loosely coming from the interaction point. Most background events, such as φ K S π + π +K L not decaying and φ π + π π 0, are removed early in reconstruction by kinematics and cuts on m x, computed from ( M φ p m2 x p 2 + m2 x) 2 ( p+ + p ) 2 = 0, i.e. assuming that a pair of same mass particles are produced according to e + e x + x γ. We do not want to apply restrictive kinematical requirements, or inst on multiple photon detection, to avoid imposing restrictive cuts on soft radiation, to be later corrected. The observed mass, m x, spectrum for the accepted two track events shown below th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 32

33 Particle identification obtained with an estimator that uses time of flight, compared to momentum, and the energy deposit pattern in the EM calorimeter. Its effectiveness apparent. At least one of the two particle must be a pion, 95% of the signal retained. g( m x ) 3000 cnts m x spectrum for candidates e e before PID after PID (MeV) m x th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 33

34 Dtribution in the {M 2, m x } plane m x 200 (MeV) 180 Fiducial region in the {M π + π, m x } plane th M 2 2 (GeV ) Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 34

35 π + π π 0 and µ + µ γ background subtraction 10 4 Entries Mean RMS Backgrounds are estimated from data and subtracted. Monte Carlo simulations are in excellent agreement +5% π + π - π DATA after m trk cut BCKG/TOT µ + µ - γ th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 35

36 Radiative Bhabha, e + e γ, background BCKG/TOT +5% M 2 ππ th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 36

37 Background removed by m x cut. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 37

38 Efficiencies Trigger Includes CR veto Reconstr. Filter filfo Event Classification Track eff, ver eff PID like m x mtrk FILFO MTRK TRG*TRK*VTX*TCLO*LIKE TOTAL EFF. GeV GeV 2 th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 38

39 Measuring the luminosity Acceptance: Comparon DATA MC to understand systematic effect Normalize to same number of events Monte Carlo (BABAYAGA) Data Points (1.1pb -1 ) * Entries Mean RMS Entries Mean RMS Entries Mean RMS Cut Cut Cut Polar Angle [ ] Momentum [MeV] Acoll. [ ] th Only Polar Angle makes an non-negligible effect, the other dtributions are safe what concerns systematics Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 39

40 SUMMARY LUMI SYSTEMATIC ERROR Theory 0.5% Acceptance 0.3% correct by 0.28% Knowledge s 0.1% Background 0.1% correct by 0.53% Tracking 0.1% Clustering 0.1% correct by 0.23% Trigger <0.1 % correct by 0.51% Total 0.5% th., 0.4% exp. = 0.6% th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 40

41 Luminosity comparons BHABHA 1. BABAYAGA (Pavia, Carloni et al.) 2. BHAGEN (Modified Berends) σ(vlab, 1)=428.8±0.3 nb σ(vlab, 1)=428.5±0.3 nb diff. 0.1±0.1 % Large angle γγ. 45 < θ γ < 135, σ=120 nb L(BHABHA)-L(γγ) =0.2 % th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 41

42 σ(π + π γ) th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 42

43 KLOE dipion mass resolution has been unfolded from the spectrum after all corrections d ee /d M nb/gev ,095,095 events KLOE, M L=140.7/ pb or 40 < <140 E> MeV PRELIMINARY (GeV ) th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 43

44 PION FORM FACTOR From σ(π + π, s π ) = 1 H and dσ(ππγ) ds π σ(π + π, s π ) = πα2 3e π β 3 f π 2 we get the pion form factor. H(s π ) obtained from PHOKHARA with F π =1. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 44

45 The KLOE e + e π + π cross section extracted from the measured π + π γ cross section above, compared with CMD-2 results KLOE CMD-2 PRELIMINARY M (GeV ) th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 45

46 A dcrepancy at low mass evident PRELIMINARY! th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 46

47 a µ a µ σ(s π )K(s π )ds our calculation, we use values w/o FSR and VP correc. (like us) KLOE a µ =424.7 a µ =381.4 a µ =240.1 PRELIMINARY 0.30< Mππ 2 <0.95 GeV2 0.37< Mππ 2 <0.93 GeV2 0.50< Mππ 2 <0.93 GeV2 CMD-2 ( a µ =368.1) a µ =376.7 a µ = < Mππ < Mππ 2 <0.93 GeV2 <0.93 GeV2 1/2 % agreement with CMD-2 above 0.5 GeV 2 VP and FSR corrections need checking! th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 47

48 th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 48

49 What s next for KLOE Measure large photon angle region 1. Access The Low Mass Region 1000 Contribution 11 to ( x10 ) a , nb W (MeV) th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 49

50 ee small (nb/gev 2 ) KLOE MC (EVA) ee a( )= 1000x s (GeV ) th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 50

51 There have been no recent measurement of σ(e + e π + π ) at small mass. It worth noting however that the region from threshold to M ππ < 600 MeV (s π <0.36 GeV 2, contributes to the muon anomaly. By choosing small values for θ γ we removed some problems with FSR but lost the pions recoiling against the photon, inside the unaccessible forward and backward cones. By going to the large angle photon region, KLOE will recover th portion of the cross section. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 51

52 2. At large angle we can also study the scalar meson contribution to σ(hadrons) proposed by Naron. Photon tag i.e. photon detected 45 < θ γ < 145 Fit improves if a σ contribtion added th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 52

53 3. Measure pion angular dtribution. d dcos ISR+FSR ISR+FSR, ISR only ISR only o o o o 1.02 GeV cos With more information it will also be possible to clarify the validity of present modelling of FSR or learn how to deal with it better. th Cape Cod, June 2003 Juliet Lee-Franzini - σ(e + e hadrons+γ) 53