Hadronic Decays of the ω Meson. Uppsala University

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1 Hadronic Decays of the ω Meson Lena Heijkenskjöld Uppsala University L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

2 Standard Model Three fundamental forces Strong Weak Electro- Magnetism Quantum Chromo Dynamics Electro-Weak theory Prevailed a multitude of test L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

3 Standard Model Three fundamental forces Strong Weak Electro- Magnetism Quantum Chromo Dynamics Electro-Weak theory Prevailed a multitude of test Hint of physics beyond SM: anomalous magnetic moment of the muon a µ = gµ a exp µ =99()() a SM µ = a QED µ + a EW µ + a Had µ =98()()().σ discrepancy physics beyond the standard model L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

4 Hadron Physics Elementary particles Calculations in the lower energy (Q) regime Q Perturbative QCD applicable α s (Q ). τ decays (N LO) DIS jets (NLO) Heavy Quarkonia (NLO) e + e jets & shapes (res. NNLO) e.w. precision fits (NNLO) ( ) pp > jets (NLO) pp > tt (NNLO) October Hadrons Phenomenological models and Effective Field Theories or Lattice QCD.. QCD αs(mz) =.8 ±. Q [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

5 Hadron Physics Elementary particles Calculations in the lower energy (Q) regime Q Perturbative QCD applicable α s (Q ). τ decays (N LO) DIS jets (NLO) Heavy Quarkonia (NLO) e + e jets & shapes (res. NNLO) e.w. precision fits (NNLO) ( ) pp > jets (NLO) pp > tt (NNLO) October Hadrons Phenomenological models and Effective Field Theories or Lattice QCD.. QCD αs(mz) =.8 ±. Q [GeV] Quark Model Composite objects: Baryons - qqq Mesons - q q J P = K K + η π π η π + J P = Y K K + ω ρ ρ ρ + φ Classification in Y and I K K - K K - I - I L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

6 This thesis The ω meson I G (J PC ) = ( ) m ω= 78.() MeV, Γ ω = 8.9(8) MeV ω Γ i /Γ ω π + π π 89.(7)% π γ 8.8(8)% σ [mb] π + π. +.. % -8 σ(e + e Hadrons) ω φ J /ψ ψ (S) ρ ρ Υ Z s [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

7 This thesis The ω meson I G (J PC ) = ( ) m ω= 78.() MeV, Γ ω = 8.9(8) MeV ω Γ i /Γ ω π + π π 89.(7)% π γ 8.8(8)% π + π. +.. % -8 Part I: ω π + π π Dalitz plot study with WASA-at-COSY Theory, WASA experiment, Analysis, Results σ [mb] Thesis outline ρ ω σ(e + e Hadrons) φ ρ J /ψ ψ (S) Υ s [GeV] Part II: Additional ω studies Search for ω π + π signal with WASA-at-COSY Simulation study of π π interference for ω Dalitz plot measurement using KLOE data Z L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

8 Part I: ω π + π π Dalitz plot study with WASA-at-COSY Z Φ L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

9 Introduction Part I: WASA Dalitz plot Part II: WASA ω π + π signal Part II: KLOE simulation study What is a Dalitz plot? -body decay sij = Pi + Pj.. s [GeV] M given by two independent variables D representation, e.g. M(s, s ) dγ ds ds = s [GeV] M (π) m L. Heijkenskjo ld (Uppsala University).. Hadronic Decays of the ω Meson /

10 Introduction Part I: WASA Dalitz plot Part II: WASA ω π + π signal Part II: KLOE simulation study What is a Dalitz plot? -body decay sij = Pi + Pj.. s [GeV] M given by two independent variables D representation, e.g. M(s, s ) dγ ds ds = s [GeV] M (π) m Common choice of variables when m = m T T X = Q (m + m )T Y = (m Q). Z =X + Y Φ Y Φ = tan - -. X Y X L. Heijkenskjo ld (Uppsala University)...8 Z Hadronic Decays of the ω Meson /

11 ω π + π π dynamics - Dalitz plot density distribution M(s, s ), M = : Phase space Restrictions from quantum numbers ω : I (J P ) = ( ) J π = and J π = P - wave phase space M = P p i p j Y X Z Φ L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 7 /

12 ω π + π π dynamics - π π interactions M / P Intermediate ρ π π rescattering ω ρ π π π Lagrangian approach π ω π ρ π Predictions of d Γ ds ds Dispersion approach πv ππ V πππ C. Terschlüsen, B. Strandberg, S. Leupold, F. Eichstädt Eur.Phys.J. A9 () S.P. Schneider, et al., Eur.Phys.J. C7 () and Danilkin, et al. Phys. Rev. D9 () 99 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 8 /

ω π + π π dynamics - π π interactions M / P Intermediate ρ π π rescattering ω ρ π π π Lagrangian approach π ω π ρ π Predictions of d Γ ds ds Experiment - Theory comparison Parametrisation F (Z, Φ) P

13 ω π + π π dynamics - π π interactions M / P Intermediate ρ π π rescattering ω ρ π π π Lagrangian approach π ω π ρ π Predictions of d Γ ds ds Experiment - Theory comparison Parametrisation F (Z, Φ) P Dispersion approach πv ππ V πππ F (Z, Φ) = + αz + βz / sin(φ) + γz + δz / sin(φ) + O(Z ) Fits are performed on theory predictions. C. Terschlüsen, B. Strandberg, S. Leupold, F. Eichstädt Eur.Phys.J. A9 () S.P. Schneider, et al., Eur.Phys.J. C7 () and Danilkin, et al. Phys. Rev. D9 () 99 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 8 /

14 Introduction Part I: WASA Dalitz plot Part II: WASA ω π + π signal Part II: KLOE simulation study Why study ω π + π π dynamics? Previous measurement Largest previous statistics for study of the dynamics - events. Unable to distinguish ρ onset. L. Heijkenskjo ld (Uppsala University) Hadronic Decays of the ω Meson 9 /

15 Introduction Part II: WASA ω π + π signal Part I: WASA Dalitz plot Part II: KLOE simulation study Why study ω π + π π dynamics? Previous measurement Largest previous statistics for study of the dynamics - events. Unable to distinguish ρ onset. Benchmark for meson transition form factors ω γ π γ a part of ρ γ L. Heijkenskjo ld (Uppsala University) π γ Hadronic Decays of the ω Meson Probe of hadron structure Contribution to HLbL (muon g-) 9 /

16 Experimental setup Wide Angle Shower Apparatus Extraction ANKE RF cavity JESSICA PAX Electron cooler Stochasticcooling TOF JULIC WASA EDDA Quadrupole Barrier bucket cavity Dipole COSY at Forschungszentrum Jülich, Germany L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

Forschungszentrum Jülich, Germany Collected data p + d He + ω π + + π + π π + γ π + + π weeks beam time

17 Experimental setup Wide Angle Shower Apparatus Extraction RF cavity ANKE PAX Electron cooler EDDA WASA Stochasticcooling JESSICA TOF JULIC γ γ π π + He Quadrupole Barrier bucket cavity Dipole COSY at Forschungszentrum Jülich, Germany Collected data p + d He + ω π + + π + π π + γ π + + π weeks beam time in T beam =. GeV h T beam =. GeV h Trigger on He L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

18 Event selection He candidate π He γ γ π + L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

19 Event selection He candidate π He π + π γγ candidates γ γ π + Experiment Fitted background FWHM MeV Mean MeV Charged tracks PID using drift chamber and solenoid T oppositely charged IM(γ γ) [GeV] γ reconstruction in calorimeter neutral L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

chamber and solenoid T oppositely charged.

20 Event selection He candidate π He π + π γγ candidates π candidates γ γ π + Experiment Fitted background FWHM MeV Mean MeV Charged tracks PID using drift chamber and solenoid T oppositely charged IM(γ γ) [GeV] γ reconstruction in calorimeter neutral L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

Event selection He candidate γ γ π π + He π + π γγ candidates π candidates Kinematic fit Constraint: P in = P out, Hypothesis: pd Heπ + π γγ Choose final track candidates Test pd Heπ + π

21 Event selection He candidate γ γ π π + He π + π γγ candidates π candidates Kinematic fit Constraint: P in = P out, Hypothesis: pd Heπ + π γγ Choose final track candidates Test pd Heπ + π hypothesis Cut on P(χ )>. Improve resolution for X Rec = T, θ, φ Reconstructed Kin. fitted IM(π + π π ) [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

22 Event selection Selected sample T beam =. GeV T beam =. GeV () () MM( He) [GeV] MM( He) [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

23 Introduction Part II: WASA ω π + π signal Part I: WASA Dalitz plot Part II: KLOE simulation study Dalitz plot analysis - Creating the Dalitz plots Z bins 7 D-representation for comparison Z L. Heijkenskjo ld (Uppsala University) Hadronic Decays of the ω Meson Φ bins Z [,] and Φ [ π, π] bins Φ Bin size Z bin Φ bin /

24 Introduction Part II: WASA ω π + π signal Part I: WASA Dalitz plot Part II: KLOE simulation study Dalitz plot analysis - Creating the Dalitz plots Φ Bin size Z [,] and Φ [ π, π] bins Z bins 7 D-representation for comparison Φ bins Simulated distributions - Hω π and Hπ F = ΛHω π + {a + a x + a x }Hπ Experiment Exp. signal Fitted background Fitted background + signal Fit range Peak region Z Extracting the ω events Z bin Φ bin χ/d.o.f = 7 / Λ= R Imax Imin λ Hω π λ = # signal events MM( He) [GeV] # events Tbeam =. GeV 79() 8() Residuals Tbeam =. GeV L. Heijkenskjo ld (Uppsala University) Hadronic Decays of the ω Meson /

25 Dalitz plot analysis - Creating the Dalitz plots Using simulated signal data ɛ ij = Nfit ij N ij true Efficiency correction Analysis efficiency T beam =. GeV T beam =. GeV Bin-wise efficiency correction Ñ ij = N ij.7. ɛ ij Z bin Φ bin L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 7 /

26 Dalitz plot analysis - Creating the Dalitz plots Using simulated signal data ɛ ij = Nfit ij N ij true Efficiency correction Analysis efficiency T beam =. GeV T beam =. GeV Bin-wise efficiency correction Ñ ij = N ij.7. ɛ ij Z bin Φ bin Resulting experimental Dalitz plots Efficiency corrected bin content 8 T beam =. GeV T beam =. GeV (scaled) Z bin Φ bin R Z bin Φ bin Compare the distributions: R ij = Ñij M ij σ N ij + σ M ij Unbinned ML fit of Gaussian: µ =. and σ =.9 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 7 /

27 Dalitz plot analysis - Parametrisation Parametrisation F (Z, Φ) P F (Z, Φ) = + αz + βz / sin(φ) + γz + δz / sin(φ) + O(Z ) Fit results Parameters used in fit α β γ χ /d.o.f. N N / N N α () / 9 N N αβ (8) () - 8 / 8 N N αγ (8) - () 8 / 8 Sensitive to α parameter: Onset of ρ state Efficiency corrected bin content 8 T beam =. GeV Fitted function Z bin Φ bin Efficiency corrected bin content 8 T beam =. GeV Fitted function Z bin Φ bin Normalised residuals Normalised residuals L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 8 /

28 Dalitz plot analysis - Systematical checks True data simulated with P-wave Fit with F (Z, Φ) P Test of fit procedure χ / d.o.f. = /9 - - α χ / d.o.f. = /8 - - α β L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 9 /

29 Dalitz plot analysis - Systematical checks True data simulated with P-wave Fit with F (Z, Φ) P Test of fit procedure χ / d.o.f. = /9 α Test of signal extraction method χ / d.o.f. = /9 Simulated dist. - H ω π (P-wave) and H π Generate H Gen H Exp Extract signal events Fill Dalitz plot α χ / d.o.f. = /8 - - α χ / d.o.f. = /8 - - α β β /9 7/9 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 9 /

30 Dalitz plot analysis - Systematical checks True data simulated with P-wave Fit with F (Z, Φ) P Test of fit procedure χ / d.o.f. = /9 α Test of signal extraction method χ / d.o.f. = /9 Simulated dist. - H ω π (P-wave) and H π Generate H Gen H Exp Extract signal events Fill Dalitz plot - - Test of efficiency correction Fit uncorrected Dalitz plots - - α χ / d.o.f. = /8 - - α χ / d.o.f. = /8 - - α β β α (x ) Nominal Eff.Check χ /d.o.f. 9/9 79/9 /9 7/9 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 9 /

31 Dalitz plot analysis - Systematical checks True data simulated with P-wave Fit with F (Z, Φ) P Test of fit procedure χ / d.o.f. = /9 α Test of signal extraction method χ / d.o.f. = /9 Simulated dist. - H ω π (P-wave) and H π Generate H Gen H Exp Extract signal events Fill Dalitz plot - - Test of efficiency correction Fit uncorrected Dalitz plots Test of data set consistency Individual fits to the two Dalitz plots α (x ) - - χ / d.o.f. = /8 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 9 / α - - α χ / d.o.f. = /8 - - Nominal Eff.Check T beam. T beam. χ /d.o.f. 9/9 79/9 α β β /9 7/9

32 ω π + π π Dalitz plot - Summary π He p + d He + ω T beam =. and. GeV γ γ π + () events in the Dalitz plots Fit of parametrisation ( + αz) P α > with. σ Theoretical predictions: α Lagrangian approach (Uppsala) and Dispersive calculations (Bonn,JPAC) This study Uppsala Bonn JPAC L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

33 Part II: Additional ω studies A search for the ω π + π signal in WASA A simulation study of π π interference study with KLOE Φ M ππ [GeV] Z L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

34 Introduction Why search for ω π + π BR(ω π + π ) = (. +.. )% Isospin violating ρ ω mixing assumed Interference pattern in M ππ In WASA data 8() ω π + π π events L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

35 Introduction Why search for ω π + π BR(ω π + π ) = (. +.. )% Isospin violating ρ ω mixing assumed Interference pattern in M ππ In WASA data 8() ω π + π π events Previous observations π + p/d X π + π π p X π + π K p X π + π Nγ Nπ + π e + e π + π dip peak peak/ shoulder shoulder shoulder L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

36 Introduction ρ ω mixing Sources of isospin violation: EM interactions, m u m d,... Common approach: ρ I, and ω I, ρ = ρ I ɛ ω I ω = ω I + ɛ ρ I ω I π + π often neglected L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

37 Introduction ρ ω mixing Sources of isospin violation: EM interactions, m u m d,... Common approach: ρ I, and ω I, ρ = ρ I ɛ ω I ω = ω I + ɛ ρ I ω I π + π often neglected The role of production γ V e + e : known coupling mixing info from e + e hadronic: not known α = α = 9 ρ A ρ + ω A ω + ρ ω A ω = Mπ Mππ [GeV] Mππ [GeV] M π = W s ρ { A ρ + g( + m R(s ω )) A ρ A ω cos(α) g m I(s ) Aρ Aω sin(α)} ω Mππ [GeV] Mππ [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson / α = 8 α = 7

38 - - - Data analysis Event selection Selection of He, π + and π Kinematical fit: choosing final tracks and suppress Heπ + π π Cut on P(χ )>. 7 Experimental data P(χ ) Reduction of non π + π events ) [GeV] Heπ..... ) [GeV] Heπ ( MM ) [GeV] Heπ ( MM ( MM MM ( Heπ + ) [GeV] MM ( Heπ + ) [GeV] MM ( Heπ + ) [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

39 Data analysis The resulting π + π mass distribution MM( He) [GeV] MM( He) [GeV] L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

40 Data analysis The resulting π + π mass distribution Residuals Experiment Fitted background 8 Fit region MM( He) [GeV] MM( He) [GeV] Residuals 8 8 Experiment Fitted background Fit region MM( He) [GeV] MM( He) [GeV] Fit to background using simulated distribution H π F = {a + a x + a x }H π No convincing ρ ω interference L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

41 Data analysis The resulting π + π mass distribution Experiment Experiment 8 Estimated signal Estimated signal MM( He) [GeV] MM( He) [GeV] Estimation of # ω π + π events in final sample With assumption of no interference L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

42 Summary Data collected by WASA, 8() ω π + π π events (BR=89%) Search for ω π + π signal (BR=.%) Observe ρ ω signal in hadronic production 8 8 Experiment Fitted background Fit region MM( He) [GeV] 8 Experiment Fitted background Fit region MM( He) [GeV] Residuals - - Residuals No visible interference Estimated # ω π + π small Size of ρ π + π signal unknown L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

43 Part II: Additional ω studies A search for the ω π + π signal in WASA A simulation study of π π interference study with KLOE Φ M ππ [GeV] Z.9.9 L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 7 /

44 Introduction pb s [,] MeV e + e π ω π π + π π 9() reconstructed events Could be used for Dalitz plot study! Previous study of e + e π ω with KLOE Accumulator DAΦNE LINAC m DEA R F I N U DA KLOE Storage rings Yoke S.C. coil Barrel EMC Drift Chamber QCal m Endcap EMC KLOE 7 m L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 8 /

45 Introduction pb s [,] MeV e + e π ω π π + π π 9() reconstructed events Could be used for Dalitz plot study! Previous study of e + e π ω with KLOE Accumulator DAΦNE LINAC m DEA R F I N U DA KLOE Storage rings Yoke S.C. coil Barrel EMC Drift Chamber QCal m Endcap EMC KLOE 7 m Why care about π π interference? Identify primary π in simulation Effect of π π interference in Dalitz plot Needed for ɛ = Reconstruced True No πprimary/decay in simulation with interference Effect in simulation? Effect in experiment Can simulation without interference be used? L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 8 /

46 Simulation studies The reaction model M = J + ωπ = G ω[t ω(p π, p π, p π +, p π ) t ω(p π, p π +, p π, p π ) t ω(p π, p π, p π +, p π )] + (p π p π ) ω π ρ π π π = J + ωπ + J + ωπ L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 9 /

47 Simulation studies The reaction model M = J + ωπ = G ω[t ω(p π, p π, p π +, p π ) t ω(p π, p π +, p π, p π ) t ω(p π, p π, p π +, p π )] + (p π p π ) ω π ρ π π π = J + ωπ + J + ωπ The simulation procedure Generate π π + π π at s = GeV with GENBOD W PS Calculate M W = M W PS Exclude interference M I = J + ωπ W I = M I W PS L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson 9 /

48 Simulation studies - The results Pion kinematics W I W W I W p (π ) [GeV/c] 8 8 Opening angle (π π ) [deg] I W / W I W / W W I W W I W IM(π. + π ). [GeV] M [GeV] recoil I W / W I W / W No drastic effect on simulation when excluding interference L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

49 Simulation studies - The results Pion kinematics W I W W I W Dalitz plot Select π Decay using mω IM(π+ π π i ) W/W I p (π ) [GeV/c] 8 8 Opening angle (π π ) [deg] Φ.8 I W / W W I W I W / W W I W I W / W IM(π. + π ). [GeV].7 I W / W M [GeV] recoil No drastic effect on simulation when excluding interference Noticeable effect from interference. Take care in analysis strategy Z L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

50 Overall Summary ω π + π π Dalitz plot α ω π + π signal search This study Uppsala Bonn JPAC 8 Experiment Fitted background Experiment Fitted background Fit region Fit region 8 8 π π simulation study MM( He) [GeV] MM( He) [GeV] Φ.8. Residuals Residuals Z.9.9 Thank you for your attention L. Heijkenskjöld (Uppsala University) Hadronic Decays of the ω Meson /

Hadronic decays of the omega meson measured with WASA-at-COSY

Hadronic decays of the omega meson measured with WASA-at-COSY Department of Physics and Astronomy, Uppsala University, Lägerhyddsvägen 1, Uppsala, Sweden E-mail: lena.heijkenskjold@physics.uu.se In this