Measurement of the Dipion Mass Spectrum in the Decay X(3872) J/ψ π + π at the CDF II Experiment

Transcription

1 Measurement of the Dipion Mass Spectrum in the Decay X(387) J/ψ π + π at the CDF II Experiment A. Rakitin June 7, 5 Thesis Defense MIT, Cambridge, Massachusetts rakitin/defense.pdf

2 Introduction New narrow resonance X(387), discovered by Belle, in B + X(387)K + J/ψ π + π K + decay in August 3 [hep-ex/389]: The nature of X(387) is puzzling: new charmonium state c c? so-called hybrid meson c cg? deuteron-like molecule D -D? Are we opening new chapter in heavy flavor spectroscopy? Events/. GeV/c Belle speculated: X(387) J/ψ π + π via J/ψ ρ? isospin-violating for charmonium if ρ found X(387) is molecule? Shape of dipion mass spectrum may help to know this. M(π + π - l + l - ) - M(l + l - ) (GeV/c ) Discovery confirmed by CDF, D and BaBar (in order of appearance) Purpose of our analysis: obtaining the dipion mass spectrum comparing to theoretical predictions understanding X(387) properties/identity A. Rakitin, MIT, Thesis Defense, June 7, 5

3 Tevatron Collider at Fermilab: short overview p p bunches, ( ) p ( p) per bunch bunches collide every 396 ns at CM energy.96 TeV record L inst =.7 3 cm sec total integrated L = fb ( 8 pb on tape, 36 pb used) high energy physics frontier until LHC turn-on A. Rakitin, MIT, Thesis Defense, June 7, 5

4 CDF Experiment: short overview CDF is a multi-purpose detector Silicon Vertex Detector up to 8 layers of silicon layers in r-φ & r-z planes Central Outer Tracker (COT) 96 layer drift wire chamber axial & stereo layers coverage η -ln(tan θ ) < σ(hit) 5 µm σ(p t ) p t.5% p t Time-of-Flight system Calorimeters: central, wall, plug coverage η < 3.6 Muon chambers coverage η <.5 Components important for analysis are highlighted in red A. Rakitin, MIT, Thesis Defense, June 7, 5 3

5 Data sample obtained via J/ψ trigger tracks with matching muon stubs mass of µ + µ around J/ψ mass Luminosity: 36 pb All tracks: + axial & + stereo COT hits, 3+ Si r-φ hits p t > 4 MeV/c Single muons: p t >.5 GeV/c J/ψ selection: p t (J/ψ) > 4 GeV/c Vertex fit χ (µ + µ ) < 5 m(µ+µ ) m(j/ψ) Data Selection < 6 MeV/c Cone around J/ψ π + π momentum with both pions, R Vertex fit χ (J/ψ π + π ) < 5 φ + η <.7 Candidates / 5 MeV/c CDF II Preliminary, 36 pb 35 5 ± (stat.) Ψ(S) M(ππ) > 5 MeV/c > 6 GeV/c, η <.6 J/ψππ: p t ± 3 (stat.) X(387) J/ψππ Mass [GeV/c Upper graph: reconstructed J/ψ π + π Lower graph and inset: m ππ ] additional cut > 5 MeV/c improves signal-tonoise ratio for X(387) peak Fiducial cuts for detector efficiency corrections: p t (J/ψ π + π ) > 6 GeV/c, η(j/ψ π + π ) <.6 A. Rakitin, MIT, Thesis Defense, June 7, 5 4

6 Analysis Strategy: Analysis performed for ψ(s) first and then for X(387) divide J/ψ sample into m ππ slices fit J/ψ π + π mass in m ππ slices get yield in each slice obtain m ππ spectrum correct m ππ spectrum for detector efficiency (from Monte Carlo), to be able to compare to other experiments compare corrected m ππ spectrum to various theoretical predictions Does X (387) J/ψ π + π decay go via J/ψ ρ? What is the X (387)? A. Rakitin, MIT, Thesis Defense, June 7, 5 5

7 J/ψ π + π mass fit in m ππ slice Candidates per.5 MeV/c ψ(s) 5 MeV/c < m ππ < 53 MeV/c Mass of J/ψππ in m(ππ) range (.5,.53) GeV/c J/ψππ Mass [GeV/c ] N = 835 ± 38 N rel =.5 ±. ψ(s) σ m = ±. ψ(s). σ rel =.7 ± ψ(s) A =.5 ±.6 α =.38 ±. = 3.3 ±. β =.89 ±. χ = 76.6 DoF = 75 ==> Prob = 43.3% Signal: di-gaussian with common mean Mean, N rel, σ and σ rel fixed by fit of full sample Candidates / 5. MeV/c X(387) 75 MeV/c < m ππ < 765 MeV/c Mass of J/ψππ in m(ππ) range (.75,.765) GeV/c 3 N X = 8 ± 3 m X = 387. ±. σ X = 5. ±. A = 5.53 ±.9 α =.48 ±.7 β = 5.3 ±.75 χ = 34.5 DoF = 35 ==> Prob = 49.8% J/ψππ Mass [GeV/c ] Signal: single Gaussian Mean and width fixed by fit of sample after m ππ > 5 MeV/c cut Background: A(x x ) α exp( βx) m ππ x fit parameters A, x, α, β A. Rakitin, MIT, Thesis Defense, June 7, 5 6

8 Dipion mass spectra ψ(s) X(387) 3 ψ(s) yield per MeV/c ππ Mass [GeV/c ] X(387) yield per MeV/c ππ Mass [GeV/c ] ψ(s) X(387) Sum of yields in each bin 53 ± ± 49 Yield from full-sample mass fit 53 ± 99 ± 54 A. Rakitin, MIT, Thesis Defense, June 7, 5 7

9 Detector corrections CDF detector does not find all X s need acceptance and efficiency corrections.. Generate MC matching data in p t, η and m ππ in fiducial region nature of X(387) = nature of ψ(s)? Cannot use p t (ψ(s)) for X Need p t (X) from data use S-wave m ππ parametrization for ψ(s) PRL 68, 8 (99) do not know exact m ππ spectrum for X(387) bootstrap ourselves by assuming S-wave for X(387) good approximation, no need to iterate further assign systematic uncertainty for it. Calculate ratio of m ππ spectra before and after detector 3. Use this ratio to correct data A. Rakitin, MIT, Thesis Defense, June 7, 5 8

10 Step : Generation of MC matching data Make sure MC p t and η match data by iterations: input flat p t -η distribution fiducial cuts: p t > 6 GeV/c, η <.6 events go through MC simulation of detector, reconstruction output p t -η distribution detector efficiency curve trigger and multiply input p t by ratio data/output corrected p t presume corrected η to be flat in fiducial region use corrected p t -η distribution as input for next MC iteration stop when iterations converge they converge after first one corrected p t = true p t A. Rakitin, MIT, Thesis Defense, June 7, 5 9

11 Getting p t for ψ(s) and X(387) from data Same slicing technique: Divide sample into p t slices Fit ψ(s) or X(387) mass in each slice Plot ψ(s) and X(387) yields Yield per GeV/c pt of Ψ(S) pt of X(387) versus p t same p t spectra for X(387) and ψ(s) within uncertainties. 3 pt, GeV/c If X(387) is a fragile molecule, one might not expect them to be Yield per GeV/c the same - 3 pt, GeV/c A. Rakitin, MIT, Thesis Defense, June 7, 5

12 Getting corrected p t of X(387) Upper left: X(387) p t from data pt spectrum for X(387), data Upper right: Detector efficiency curve (MC output from flat p t -η input) Efficiency curve for X(387), MC, S-wave m ππ Yield per GeV/c 5 Yield per GeV/c pt, GeV/c 3 pt, GeV/c True pt spectrum for X(387), S-wave m ππ 3 Yield per GeV/c Quadratic fit χ /ndf =.4/6, prob 96.7% =.5 3 pt, GeV/c p t a = -.48 ±.38 a = -. ±.7 True pt spectrum for X(387), S-wave m ππ Yield per GeV/c Quadratic fit χ /ndf =.4/6, prob 96.7% =.5 3 pt, GeV/c p t a = -.48 ±.38 a = -. ±.7 Lower plots: X(387) p t from data divided by eff. curve fit with exp(a + a p t + a p t ) a =.48 ±.38, a =. ±.7 A. Rakitin, MIT, Thesis Defense, June 7, 5

13 ψ(s) Data-MC match for p t X(387) pt of ψ(s), data-mc match Normalized yield per GeV/c Data, sliced Monte Carlo (S-wave) χ /N =.7/7 Prob =.4 % pt of X(387), data-mc match Normalized yield per GeV/c Data, sliced Monte Carlo (S-wave) χ /N =.7/5 Prob = 89. % 3 pt, GeV/c 3 pt, GeV/c A. Rakitin, MIT, Thesis Defense, June 7, 5

14 Step : Obtain detector corrections ψ(s) X(387) Number of entries per bin m ππ x for ψ(s), S-wave spectrum before detector ζ(m ππ ) -- m ππ spectrum after detector ζ(m ππ ) -- m ππ Ratio: before/after (scale on right-hand side) Fit with quadratic polynomial ξ(m ππ ) χ /N = 4.7/56 Prob = 9.5 % in each bin Ratio ζ/ζ Number of entries per bin m ππ for X(387), S-wave spectrum before detector ζ(m ππ ) -- m ππ spectrum after detector ζ(m ππ ) -- m ππ Ratio: before/after (scale on right-hand side) Fit with quadratic polynomial ξ(m ππ ) χ /N = 7./9 Prob = 9.8 % in each bin Ratio ζ/ζ ππ Mass [GeV/c ] ππ Mass [GeV/c ] Relatively flat efficiency corrections for high m ππ (region of interest) Flatter for X(387) than for ψ(s) A. Rakitin, MIT, Thesis Defense, June 7, 5 3

15 Step 3: Apply corrections ψ(s) X(387) 3 ψ(s) yield per MeV/c No detector efficiency corrections ππ Mass [GeV/c ] X(387) yield per MeV/c No detector efficiency corrections ππ Mass [GeV/c ] ψ(s) yield per MeV/c After detector efficiency corrections ππ Mass [GeV/c ] X(387) yield per MeV/c After detector efficiency corrections ππ Mass [GeV/c ] No visible shape difference detector efficiency corrections are almost negligible A. Rakitin, MIT, Thesis Defense, June 7, 5 4

16 Data-MC match for m ππ spectrum for ψ(s) Compare S-wave m ππ parametrization for ψ(s) Monte Carlo to corrected data see reason- Ψ(S) yield per MeV/c Data after eff. corr. MC χ /N = 43.3/7 Prob =.4 % able match Normalized ππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 5

17 Systematics For i-th m ππ slice Ni corr Systematics on yields N raw : signal shape description background shape description = N raw i ξ i Systematics on detector efficiency corrections ξ : m ππ spectrum parametrization (unknown true shape for X(387)) p t spectrum parametrization (large errors on p t spectrum from data) A. Rakitin, MIT, Thesis Defense, June 7, 5 6

18 Systematics on yields change signal or background description compare nominal and changed yields for each m ππ slice plot yield differences versus m ππ see if there is a trend if no apparent trend: calculate mean ν, RMS θ and sample variance σ ν = systematics cannot be determined better than ν ± σ ν θ N A. Rakitin, MIT, Thesis Defense, June 7, 5 7

19 Systematics on yields Example: count # of entries in peak plot N counted N fitted ignore first four slices with no ψ(s) yield systematics smaller than. ±.7 use.7 cand. as upper limit ψ(s) yield difference Yield diff due to signal shape change (count minus nominal fit) 6 mean ν =., rms θ = 3., sample variance σ ν = ππ Mass [GeV/c ] Another example: shift N rel by ± σ uniform.7% relative change in yield no change in shape discard it Fractional ψ(s) yield difference Yield difference due to ψ(s) rel.norm shift ππ Mass [GeV/c ] total ψ(s) yield syst. =.7 similarly obtained bkg. syst cand. same thing for X(387) total X(387) yield systematics is 8.4 cand. systematic uncertainty is small A. Rakitin, MIT, Thesis Defense, June 7, 5 8

20 High m ππ masses special treatment 3.69 Normally fix ψ(s) mass & width, but could let them float Both quite flat, except for last few slices: smearing at m ππ kinematic limit peak is close to background turn-on Let ψ(s) mass and width float for last two slices ψ(s) mass, GeV/c ππ Mass [GeV/c ] Similar problems for X(387): use different combinations of fixed/floating mass and width Let X(387) width float for last three slices difficult for fit to determine turn-on constrain from lower m ππ slices ψ(s) narrow width, GeV/c ππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 9

21 Special systematics for high m ππ masses Due to special treatment, use special syst. variations, in addition to regular ones: turn-on parameter x shift by ± σ fit range change by ± 5 MeV/c fix ψ(s) mass, and ψ(s) and X(387) width let X(387) mass float asymmetric Gaussian to fit the very last point for ψ(s) Compare yield variations with respect to nominal yields derive systematics: N last X = 8 ± 3(stat.) +5 6(syst.) N last X = 35 ± 5(stat.) +3 (syst.) N last X = ± 9(stat.) +8 (syst.) N last ψ(s) N last ψ(s) = 9 ± 43(stat.)+ (syst.) = 99 ± 6(stat.)+3 (syst.) A. Rakitin, MIT, Thesis Defense, June 7, 5

22 Example syst. on nd to last X(387) slice Candidates / 5. MeV/c Mass of J/ψππ in m(ππ) range (.765,.77) GeV/c N X = 35 ± 5 m X = 387. ±. σ X = 5. ±.7 A =.88 ±. α =.5 ±. β = 6.68 ±.53 *(x - 3.7) = ±. χ = 37.7 DoF = 35 8 Prob = 35.4% 6 4 Nominal fit: N X = 35 ± 5 Candidates / 5. MeV/c Candidates / 5. MeV/c Mass of J/ψππ in m(ππ) range (.765,.77) GeV/c J/ψππ Mass [GeV/c ] N X = 38 ± 5 m X = 387. ±. σ X = 5.6 ±. A =.79 ±. α =.4 ±. β = 5.8 ±.5 χ = 36.8 DoF = 36 ==> Prob = 44.% Mass of J/ψππ in m(ππ) range (.765,.77) GeV/c J/ψππ Mass [GeV/c ] N X = 4 ± m X = 387. ±. σ X = 3. ± 4.6 A =.84 ±. α =.38 ±.8 β = 4.76 ±.86 χ = 44.6 DoF = 45 ==> Prob = 49.4% X(387) width shifted by +σ: N X = 38 ± 5 (largest yield increase) Fit range +5 MeV/c : N X = 4 ± (largest yield decrease) J/ψππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5

23 Systematics For i-th m ππ slice N corr i Systematics on yields N raw : signal shape description background shape description = N raw i ξ i Systematics on detector efficiency corrections ξ : m ππ spectrum parametrization (unknown true shape for X(387)) p t spectrum parametrization (large errors on p t spectrum from data) A. Rakitin, MIT, Thesis Defense, June 7, 5

24 Systematics from m ππ shape for X(387) Big change of nominal (S-wave) m ππ spectrum: phase-space (Same for ψ(s)) m ππ for X(387), S-wave m ππ for X(387), Phase-Space 8 ζ(m ππ ) -- m ππ spectrum before detector ζ(m ππ ) -- m ππ spectrum after detector 35 4 ζ(m ππ ) -- m ππ spectrum before detector ζ(m ππ ) -- m ππ spectrum after detector 3 Number of entries per bin Ratio: before/after (scale on right-hand side) Fit with quadratic polynomial ξ(m ππ ) χ /N = 7./9 Prob = 9.8 % in each bin Ratio ζ/ζ Number of entries per bin Ratio: before/after (scale on right-hand side) Fit with quadratic polynomial ξ(m ππ ) χ /N = 8.3/9 Prob = 73. % 5 5 Ratio ζ/ζ in each bin ππ Mass [GeV/c ] ππ Mass [GeV/c ] Nominal (S-wave) det. eff. corr. curve Phase-space det. eff. corr. curve A. Rakitin, MIT, Thesis Defense, June 7, 5 3

25 Systematics from m ππ shape for X(387) Curve comparison Ratio γ PS (m ππ ) = phase space S wave. Inverse detector efficiency Correction curves: X(387) - S-wave, ξ(m ππ ) PS X(387) - phase-space, ξ (m ππ ) (m ππ )/ξ(m ππ ) for X(387) PS Inv. eff. corr. ratio ξ (m ππ - m π )/m max Efficiency corrections not very sensitive to m ππ shape ππ Mass, GeV/c We will include ratio γ PS (m ππ ) into theoretical fit to see general effect on m ππ shape (described later) A. Rakitin, MIT, Thesis Defense, June 7, 5 4

26 Systematics from p t shape for X(387) parametrize p t shape as exp(a + a p t + a p t ) shift a up and down by one sigma generate new MC with shifted a get shifted efficiency correction curves, divide them by nominal one (m ππ )/ξ(m ππ ) for X(387) ±σ Inv. eff. corr. ratio ξ pt "+ std. dev." nominal pt pt "- std. dev." nominal pt ππ Mass [GeV/c ] include ratio function γ ±σ (m ππ ) into theoretical fit to see general effect on m ππ shape same thing for ψ(s) A. Rakitin, MIT, Thesis Defense, June 7, 5 5

27 Naïve and simple Include detector eff. corr. into χ N i ± σ(n i ) raw yield in i-th point χ naïve = N i ξ i T i σ(n i )ξ i ξ i nominal detector efficiency correction function (integrated over i-th bin) T i theoretical function (integrated over i-th bin) Include m ππ and p t systematics (i.e. γ PS i and γ ±σ i ratio functions) into χ with floating coefficients a and b: χ = N i ξ i σ(n i )ξ i + a(γ PS i ) + a(γ PS i ) + b(γ ±σ i ) T i + b(γ ±σ i ) + a + b a = nominal (S-wave) m ππ parametrization ξ(m ππ ) a = changed (phase-space) m ππ parametrization ξ PS (m ππ ) b similar for p t shape Last two terms: a and b are expected to have central value of and standard deviation of A. Rakitin, MIT, Thesis Defense, June 7, 5 6

28 Theory models for ψ(s) + prior expt. data ψ(s) is well studied both theoretically and experimentally: Lots of theoretical models for m ππ spectrum shape - use them to fit data Large BES data sample (3k ψ(s)) available - compare with our fits Model Yan, [PRD 65 (98)] Voloshin-Zakharov [PRL45, 688 (98)] Novikov-Shifman [Z.Phys.C8, 43 (98)] Brown-Cahn [PRL35, (975)] Short description Multipole Expansion of QCD Lagrangian: for 3 S charmonium state for 3 S state with higher-order corection Chiral limit m π = plus phen. term λm π Elaborate VZ model Neglect chiral symmetry breaking, no strong angular correlations A. Rakitin, MIT, Thesis Defense, June 7, 5 7

29 ψ(s) yield per MeV/c Theoretical fits for ψ(s) CDF II Preliminary, 36 pb Ψ(S) J/ψπ + π S Multipole Expansion, higher-order corr (prob = 6.9%) PRD, 65 (98) 3 Multipole Expansion, no higher-order corr S (prob = 6.%) PRD, 65 (98) Voloshin - Zakharov (prob = 3.4%) PRL 45, 688 (98) Novikov - Shifman (prob =.3%) Z.Phys.C8, 43 (98) Brown - Cahn PRL 35, (975) ππ Mass [GeV/c ] first four models describe the data well Brown Cahn model does not work so well, because it neglects term correspponding to angular correlations between pions BES data [PRD6, 3 ()]: π + π - Mass (GeV/c ) A. Rakitin, MIT, Thesis Defense, June 7, 5 8

30 Each model has a fit parameter: Fit results for ψ(s) Model CDF fit Result from BES Diff. Yan B/A =.34 ±. B/A =.336 ±.9 ±.9.σ 3 S -state with χ /NDF = 37/6 χ /NDF = 6/45 higher-order corr. CL = 6.9% CL = 6.4% Yan B/A =.45 ±. B/A =.5 ±.4 ±.8.7σ 3 S -state without χ /NDF = 38/6 χ /NDF = 84/45 higher-order corr. CL = 6.% CL =.% Voloshin-Zakharov λ = 4.34 ±.5 λ = 4.35 ±.6 ±.7.4σ χ /NDF = 4/6 χ /NDF = 69/45 CL = 3.4% CL =.% Novikov-Shifman κ =.89 ±.7 κ =.86 ±.3 ±.6.3σ χ /NDF = 35/6 χ /NDF = 55/45 CL =.3% CL = 4.6% Brown-Cahn χ /NDF = 6/7 CDF consistent with BES within.7σ for all fits A. Rakitin, MIT, Thesis Defense, June 7, 5 9

31 Which models to use for X(387)? Consider J PC of dipion system in X(387) J/ψ π + π decay. For pions S = for dipion P = C = ( ) L = ( ) I. Two states possible: ++ dipion: isospin I = good for charmonium assignment charmonium: Yan model for 3 S, P and 3 D J decaying into 3 S π + π (multipole expansion) dipion: isospin I = isospin breaking if charmonium Note: virtual coupling to D D may bypass isospin conservation decay must proceed via J/ψρ use Breit-Wigner modified by 3-body J/ψ π + π phase space, Γ (m ππ M ρ ) +Γ /4 (Phase Space) A. Rakitin, MIT, Thesis Defense, June 7, 5 3

32 Theoretical fits for X(387) X(387) yield per MeV/c CDF II Preliminary, 36 pb X(387) J/ψπ + π - J/ψ ρ: prob = 36.% J/ψ ππ Phase-Space Multipole Expansions for cc: 3 S : prob = 7.7% x 5 P 3 D J ππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 3

33 Charmonium options for X(387) ++ dipion: Multipole Expansion predictions for 3 S, P, 3 D,,3 (Yan): compatible with 3 S, but no viable 3 S available incompatible with P or 3 D,,3 dipion: J/ψρ model: Breit-Wigner PS compatible with J/ψ ρ Three candidates can be excluded: candidate 3 P and 3 P : X(387) was not seen in γγ fusion 3 S : too heavy, must be close to 3 3 S = ψ(44) Two viable charmonium candidates remain: D and 3 P both decay into J/ψ π + π with isospin violation Compan s+ Dipion J PC J PC Known in decay tible into with J/ψ π + π data? S + η c (S) 3 S J/ψ ++ P + h c (P) ++ 3 P ++ χ c (P) 3 P ++ χ c (P) 3 P ++ χ c (P) D + Yes 3 D ψ(377) ++ 3 D ++ No 3 D 3 ++ No S + η c (S) 3 S ψ(s) ++ P + ++ No 3 P ++ Yes 3 P ++ Yes 3 P ++ Yes 3 S + Yes 3 3 S ψ(44) ++ A. Rakitin, MIT, Thesis Defense, June 7, 5 3

34 Exotic options for X(387) Most popular non-charmonium option for X(387) is a D -D molecule. Example: Swanson model [PLB588, 89 (4)] mixture of D -D, J/ψ ω, J/ψ ρ, D + -D For different dipion J PC : ++ dipion no predictions for m ππ spectrum shape dipion decay proceeds via J/ψ ρ compatible with data P(ϕ α ) (%) 8 6 D D * 4 D + D -* ωj/ψ ρj/ψ E B (MeV) Relative contribution of each component versus binding energy A. Rakitin, MIT, Thesis Defense, June 7, 5 33

35 C-parity of X(387) Whatever X(387) is dipion implies C-positive X(387): Compatible with CDF data Supported by recent Belle s observations of X(387) J/ψ ω and X(387) J/ψ γ Events/bin M(γJ/ψ) (MeV) A. Rakitin, MIT, Thesis Defense, June 7, 5 34

36 Conclusion: measured dipion mass spectrum in X(387) J/ψ π + π decay good agreement for m ππ spectrum shape for ψ(s) with large data sample from BES m ππ spectrum shape for X(387): compatible with C-negative 3 S -state (no viable 3 S -state available) compatible with C-positive J/ψρ hypothesis positive C-parity consistent with Belle s observations of X(387) J/ψ ω and X(387) J/ψ γ X(387) nature from m ππ spectrum shape: charmonium: D or 3 P, with isospin violating decay to J/ψ π + π could be exotics, such as D -D molecule exotic interpretation: new chapter in heavy flavor spectroscopy? A. Rakitin, MIT, Thesis Defense, June 7, 5 35

37 Backup A. Rakitin, MIT, Thesis Defense, June 7, 5 36

38 CDF II Preliminary, 36 pb 5 ± (stat.) Ψ(S) 35 - J/ψππ: p t > 6 GeV/c, η <.6 Candidates / 5 MeV/c M(ππ) > 5 MeV/c ± 3 (stat.) X(387) M(ππ) < 5 MeV/c J/ψππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 37

39 Getting corrected p t of ψ(s) Upper left: ψ(s) p t from data pt spectrum for ψ(s), data Upper right: Detector efficiency curve (MC output from flat p t -η input) Efficiency curve for ψ(s), MC, S-wave m ππ Yield per GeV/c Yield per GeV/c pt, GeV/c 3 pt, GeV/c True pt spectrum for ψ(s), S-wave m ππ Yield per GeV/c Quadratic fit χ /ndf = 7./8, prob 5.5% p t =.3 a = ±.6 a =.9 ±. True pt spectrum for ψ(s), S-wave m ππ Yield per GeV/c Quadratic fit χ /ndf = 7./8, prob 5.5% p t =.3 a = ±.6 a =.9 ± pt, GeV/c -6 3 pt, GeV/c Lower plots: X(387) p t from data divided by eff. curve Parametrized with e a +a p t +a p t a =.489 ±.8, a =.9 ±. A. Rakitin, MIT, Thesis Defense, June 7, 5 38

40 ψ(s) mass fit with different bkg. model Mass of J/ψππ in m(ππ) range (.5,.53) GeV/c Number of σ Candidates per.5 MeV/c J/ψππ Mass [GeV/c ] Residual plot of the fit above N = 88 ± 4 N rel =.5 ±. ψ(s) m = ±. ψ(s) σ ψ(s) =.7 ± χ. σ rel = 3.3 ±. = 55.6 DoF = 58 Prob = 56.6% J/ψππ Mass [GeV/c ] Pull distribution of the plot above 8 6 m =. ± σ =.97 ± (N hist - N fit )/σ fit 5 MeV/c < m ππ < 53 MeV/c Diff. bkg: polynomial instead of A(x x ) α exp( βx) High-side bkg defines shape N ψ(s) fit prob Nominal fit 835 ± % Diff. bkg fit: 88 ± % A. Rakitin, MIT, Thesis Defense, June 7, 5 39

41 ψ(s) mass fit with different bkg. model ψ(s) yield difference ψ(s) yield difference Yield diff due to background shape change 6 mean ν = -.498, rms θ = 9.555, sample variance σ ν = ππ Mass [GeV/c ] Yield diff due to skipping first few points 5 Full circles - start fit at higher mass =.45 ν = -.58, θ = 6.78, σ ν Open circles - start fit at lower mass =.39 ν =.643, θ = 7.93, σ ν ππ Mass [GeV/c ] Use polynomial bkg. instead of A(x x ) α exp( βx) Plot N diff.bkg. N normal Can t claim syst. smaller.498 ±.85 use. cand. as systematics Another bkg variation: add/skip a few points near background turn-on use.4 cand. as systematics Use.4 as ψ(s) bkg syst Use 3.6 as total ψ(s) yield systematics A. Rakitin, MIT, Thesis Defense, June 7, 5 4

42 X(387) mass fit with different signal model X(387) yield difference Fractional X(387) yield difference Yield diff due to signal shape change (count minus nominal fit) mean ν = -.7, rms θ = 5.496, sample variance σ ν = 4.9 Yield difference due to X(387) mass shift Full circles - shift by std. dev. up, ππ Mass [GeV/c ] ν = -.5, θ =.33, σ ν =. Open circles - shift by std. dev. down, ν =., θ =.3, σ ν = ππ Mass [GeV/c ] First five slices have no X(387) yield ignore them (smaller points) Count # of entries in peak Plot N counted N fitted No apparent systematic trend Can t claim syst. smaller -.7 ± 4.9 Use 4.9 cand. as systematics Shift X(387) mass by ± σ.5% relative change in yield Discard it Fractional X(387) yield difference Yield difference due to X(387) width shift Full circles - shift by std. dev. up, =. ν =.5, θ =.3, σ ν Open circles - shift by std. dev. down, ν = -.7, θ =.36, σ ν = ππ Mass [GeV/c ] Shift X(387) width by ± σ 7.% relative change in yield Discard it Use 4.9 as X(387) signal syst A. Rakitin, MIT, Thesis Defense, June 7, 5 4

43 X(387) mass fit with different bkg. model X(387) yield difference X(387) yield difference Yield diff due to background shape change = mean ν = 3.74, rms θ = 8.6, sample variance σ ν Yield diff due to skipping first few points ππ Mass [GeV/c ] Full circles - start fit at higher mass = 4.99 ν = -4.57, θ = 8.398, σ ν Open circles - start fit at lower mass = 6.34 ν = , θ =.67, σ ν ππ Mass [GeV/c ] Use polynomial bkg. instead of A(x x ) α exp( βx) Plot N diff.bkg. N normal Can t claim syst. smaller 3.74 ± cand. as systematics Add/skip a few points near turn-on 6.3 cand. as systematics Use 6.8 as X(387) bkg syst Use 8.4 as total X(387) systematics A. Rakitin, MIT, Thesis Defense, June 7, 5 4

44 Systematics from m ππ shape for ψ(s) Estimate this uncertainty by comparing S-wave to phase-space Number of entries per bin m ππ x for ψ(s), S-wave ζ(m ππ ) -- m ππ spectrum before detector ζ(m ππ ) -- m ππ spectrum after detector Ratio: before/after (scale on right-hand side) Fit with quadratic polynomial ξ(m ππ ) χ /N = 4.7/56 Prob = 9.5 % Ratio ζ/ζ in each bin Number of entries per bin m ππ for ψ(s), Phase-Space ζ(m ππ ) -- m ππ spectrum before detector ζ(m ππ ) -- m ππ spectrum after detector Ratio: before/after (scale on right-hand side) Fit with quadratic polynomial ξ(m ππ ) χ /N = 56.6/56 Prob = 45.8 % Ratio ζ/ζ in each bin ππ Mass [GeV/c ] ππ Mass [GeV/c ] Nominal (S-wave) det. eff. corr. curve Phase-space det. eff. corr. curve A. Rakitin, MIT, Thesis Defense, June 7, 5 43

45 Systematics from m ππ shape for ψ(s) Curve comparison Curve ratio: phase-space/s-wave. Inverse efficiency Correction curves: ψ(s) - S-wave, ξ(m ππ ) (PS) ψ(s) - phase-space, ξ (m ππ ) (m ππ )/ξ(m ππ ) for ψ(s) PS Inv. eff. corr. ratio ξ Half max-min dist. =.47% (m ππ - m π )/m max Efficiency corrections not very sensitive to m ππ shape ππ Mass, GeV/c We will include ratio function into theoretical fit to see general effect on m ππ shape A. Rakitin, MIT, Thesis Defense, June 7, 5 44

46 Syst. from p t shape for ψ(s) input for MC pt spectrum for ψ(s), data Efficiency curve for ψ(s), MC, S-wave m ππ Yield per GeV/c Yield per GeV/c pt, GeV/c 3 pt, GeV/c True pt spectrum for ψ(s), S-wave m ππ Yield per GeV/c Quadratic fit χ /ndf = 7./8, prob 5.5% p t =.3 a = ±.6 a =.9 ±. Shift by std. dev. up: a = Shift by std. dev. down: a = True pt spectrum for ψ(s), S-wave m ππ Yield per GeV/c Quadratic fit χ /ndf = 7./8, prob 5.5% p t =.3 a = ±.6 a =.9 ±. Shift by std. dev. up: a = Shift by std. dev. down: a = pt, GeV/c -6 3 pt, GeV/c A. Rakitin, MIT, Thesis Defense, June 7, 5 45

47 Syst. from p t shape for X input for MC pt spectrum for X(387), data 5 Efficiency curve for X(387), MC, S-wave m ππ 9 8 Yield per GeV/c 5 Yield per GeV/c pt, GeV/c 3 pt, GeV/c True pt spectrum for X(387), S-wave m ππ 3 Yield per GeV/c Quadratic fit χ /ndf =.4/6, prob 96.6% p t =.5 a = -.47 ±.38 a = -. ±.7 Shift by std. dev. up: a = Shift by std. dev. down: a = pt, GeV/c True pt spectrum for X(387), S-wave m ππ Yield per GeV/c Quadratic fit χ /ndf =.4/6, prob 96.6% p t =.5 a = -.47 ±.38 a = -. ±.7 Shift by std. dev. up: a = Shift by std. dev. down: a = pt, GeV/c A. Rakitin, MIT, Thesis Defense, June 7, 5 46

48 Systematics from p t shape for ψ(s) (m ππ )/ξ(m ππ ) for ψ(s) ±σ ξ pt "+ std. dev." nominal pt Half max-min dist. =.5% pt "- std. dev." nominal pt Half max-min dist. =.4% Inv. eff. corr. ratio ππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 47

49 ψ(s) yield per MeV/c CDF II Preliminary, 36 pb Ψ(S) J/ψπ + π S Multipole Expansion PRD, 65 (98) Prob = 6.9% ππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 48

50 ψ(s) yield per MeV/c CDF II Preliminary, 36 pb Ψ(S) J/ψπ + π S Multipole Expansion PRD, 65 (98) Prob = 6.9% Brown - Cahn PRL 35, (975) χ /ndf = 6/ ππ Mass [GeV/c ] A. Rakitin, MIT, Thesis Defense, June 7, 5 49

51 ! #" $ % & ' ( ) * & +, - ). / ( * / * : 9 <; A BC D E GF H IJ GF K K K L M B NO D K B K I PRQST VU W X XY Z[ ]Y \ `_^ a b c de > e gf L M B NO D K B K H h<i QS jk lnm oqp T VU W rs Y `Y\ ]Y _^ _ a 5 Nut L M B NO D B K H PRQST VU W X XY Z[ ]Y \ `_^ a v Bw x x 9 y ; z { = 8 L M B NO D K B K H! } v Bw ~ L M B NO D K B K H 8 #" ; : b c > ƒ A. Rakitin, MIT, Thesis Defense, June 7, 5 5

52 Systematics on third to last X(387) slice Nominal fit N X = 8 ± 3 Projected turn-on N X = 97 ± 8 X(387) width σ N X = 66 ± 9 Mass of J/ψππ in m(ππ) range (.75,.765) GeV/c 3 Candidates / 5. MeV/c N 5 X = 8 ± 3 m X = 387. ±. σ X = 5. ±. A = 5.53 ±.9 α =.48 ±.7 β = 5.3 ±.75 *(x - 3.7) = 5.85 ±.64 χ = 34.5 DoF = 35 Prob = 49.8% 5 5 Mass of J/ψππ in m(ππ) range (.75,.765) GeV/c 3 Candidates / 5. MeV/c N 5 X = 97 ± 8 m X = 387. ±. σ X = 5. ±. A = 5.7 ±.6 α =.56 ±.5 β = 6.3 ±.67 *(x - 3.7) = ±. χ = 36.3 DoF = 36 Prob = 46.4% 5 5 Mass of J/ψππ in m(ππ) range (.75,.765) GeV/c 3 Candidates / 5. MeV/c N 5 X = 66 ± 9 m X = 387. ±. σ X = 4.4 ±. A = 5.49 ±. α =.46 ±.8 β = 5. ±.94 χ = 34.5 DoF = 35 Prob = 49.9% J/ψππ Mass [GeV/c ] J/ψππ Mass [GeV/c ] J/ψππ Mass [GeV/c ] Residual plot of the fit above 5 Number of σ J/ψππ Mass [GeV/c ] Pull distribution of the plot above 4 m =. ±.43 σ =.9 ± Residual plot of the fit above 5 Number of σ J/ψππ Mass [GeV/c ] Pull distribution of the plot above m =.3 ±.48 σ =.94 ± Residual plot of the fit above 5 Number of σ J/ψππ Mass [GeV/c ] Pull distribution of the plot above m = -.3 ±.45 σ =.9 ± (N hist - N fit )/σ fit (N hist - N fit )/σ fit (N hist - N fit )/σ fit A. Rakitin, MIT, Thesis Defense, June 7, 5 5

53 Systematics on last X(387) slice Nominal fit N X = 8 ± X(387) width +σ N X = 8 ± Turn-on σ N X = 8 ± Mass of J/ψππ in m(ππ) range (.77,.775) GeV/c Candidates / 5. MeV/c N X = ± 9 m X = 387. ±. σ X = 3. ±.3 A =.69 ±.6 α =.4 ±.9 β = 3. ±.9 *(x - 3.7) = ±. χ = 35.6 DoF = 35 8 Prob = 45.% 6 4 Mass of J/ψππ in m(ππ) range (.77,.775) GeV/c Candidates / 5. MeV/c N X = 8 ± m X = ±. σ X = 3. ±.9 A =.69 ±.6 α =.7 ±.9 β = 3.44 ±.9 χ = 34. DoF = 34 8 Prob = 47.4% 6 4 Mass of J/ψππ in m(ππ) range (.77,.775) GeV/c Candidates / 5. MeV/c N X = 8 ± m X = 387. ±. σ X = 3. ±. A =.7 ±.7 α =.3 ±. β = 3.73 ±.34 *(x - 3.7) = ±. χ = 4. DoF = 35 8 Prob = 8.9% J/ψππ Mass [GeV/c ] J/ψππ Mass [GeV/c ] J/ψππ Mass [GeV/c ] Residual plot of the fit above 5 Number of σ J/ψππ Mass [GeV/c ] Pull distribution of the plot above m =.3 ±.5 σ =.95 ± Residual plot of the fit above 5 Number of σ J/ψππ Mass [GeV/c ] Pull distribution of the plot above 4 m = -. ±.43 σ =.9 ± Residual plot of the fit above 5 Number of σ J/ψππ Mass [GeV/c ] Pull distribution of the plot above m = -.38 ±.5 σ =.95 ± (N hist - N fit )/σ fit (N hist - N fit )/σ fit (N hist - N fit )/σ fit A. Rakitin, MIT, Thesis Defense, June 7, 5 5

54 ψ (S) γ η c (S) η c (S) hadrons hadrons hadrons hadrons radiative hadrons hadrons χ c (P) χ c (P) J/ψ (S) = J PC χ c (P) π γ γ γ γ γ γ γ γ h c (P) ππ η,π hadrons D D D D + S = L = S S Mass, MeV/c ψ (44) D D 3 3 D 3 3 D 3 P P P P X(387) ψ(377) ψ(46) χ (P) *!!!!!!!!!!!! " " " " " " # # # # # # # # # # # # # # # # # # $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ D D ~3S X cand X cand X cand X cand A. Rakitin, MIT, Thesis Defense, June 7, 5 53