Pinning down the J PC values of the X(3872)

Transcription

1 Pinning down the J PC values of the X(3872) K. Miyabayashi for S.K. Choi & S.L. Olsen Feb, 2005 Belle Analysis & Software Meeting

2 J PC possibilities for J violates parity (η c ) (χ c0 ) (ψ(3s)) (χ c1 ) (h c ) (ψ 2 ) (η c2 ) (χ c2 )

3 P-viol n & DD-allowed J PC sunlikely (reduce type size of these entries by x1/2) 0 -- violates parity 0 -+ (η c ) 0 ++ (χ c0 ) (ψ(3s)) (χ c1 ) (h c ) 2 -- (ψ 2 ) 2 -+ (η c2 ) 2 ++ (χ c2 ) 2 +-

4 Use e7 e37 data (include B K S π + π J/ψ) Signal Sidebands (47 ev) (114/10 = 11.4 ev)

5 Follow advice from Sherlock Holmes: Eliminate all other factors, & the one that remains must be the truth.* *The sign of four

6 Areas of investigation Angular correlations Search for radiative decays Fits to the M(ππ) distribution

7 Angular Correlations

8 Strategy: for each J PC, find a distrib 0 if we see any events there, we can rule it out example1 -- : sin 2 θ Kµ ψ is 1 -- Use ψ to check accept. θ Κµ K ψ : χ 2 /dof = 8.9/9 mpute angles in J/ψ restframe D.V. Bugg hep-ph/ v2

9 cosθ Kl for X(3872) events fit with sin 2 θ Kl + bkgd χ 2 /dof = 60.3/9 see 8 evts/bin expect 2~3evts/bin X(3872) is not 1 --! background scaled from sidebands

10 1 +- and 2 -- use J/ψ helicity angle θ J/ψ X K For the ψ π + π J/ψ, this should be ~flat θ J/ψ J/ψ cosθ J/ψ

11 1 +- and : sin 2 θ J/ψ χ 2 /dof=36/ : sin 2 θ J/ψ cos 2 θ J/ψ χ 2 /dof=27/9 cosθ J/ψ cosθ J/ψ can rule out 1 +- (Cl=10-4 %) 2 -- is unlikely (CL=0.16%)

12 0 -+ Rosner (PRD ) 0 -+ : sin 2 θ sin 2 ψ χ 2 /dof=31/9 θ cosθ ψ χ 2 /dof=61/9 safe to rule out 0 -+ cosψ

13 0 ++ θ lπ Rosner (PRD ) again In the limit where X(3872), ππ, & J/ψ rest frames coincide: dγ/dcosθ lπ sin 2 θ lπ χ 2 /dof = 59/9 rule out 0 ++ cosθ lπ

14 1 ++ : sin 2 θ l sin 2 χ Rosner (PRD ) 1 ++ compute angles in X(3872) restframe χ 2 /dof = 10.4/9 θ l χ K cosθ l χ 2 /dof = 8.1/ looks okay! cosχ

15 1 ++ again compute χ in ππ rest frame χ 2 /dof = 8.9/9 compute θ in J/ψ rest frame χ 2 /dof = 8.9/9 cosχ cosθ l

16 Reduce type size for J PC values that fail angle tests 0 -- violates parity 0 -+ (η c ) 0 ++ (χ c0 ) (ψ(3s)) (χ c1 ) 1 +- (h c ) 2 -- (ψ 2 ) 2 -+ (η c2 ) 2 ++ (χ c2 ) 2 +-

17 Observation of X(3872) γ J/ψ

18 Select B K J/ψ γ (include both K± & K s ) Tight J/ψ cuts K ± id>0.5 / Belle-standard good Ks E γ >40 MeV π 0 veto (χ 2 >4.0) K* veto (M(Kγ)>1.0 GeV) R 2 <0.4; cosθ B < 0.8 M bc 5.28 < GeV (2σ) E <0.034 GeV (2σ) E7 E37

19 M(γ J/ψ) B Kχ c1 ; χ c1 γ J/ψ X signal Region ±32 MeV X(3872)? M(γJ/ψ)

20 Expand χ c1 region Fit to determine σ M(γJ/ψ) =10.7 MeV M(γJ/ψ) m χc1 < 25 MeV (± 2.4σ) Use these fits to get means & sigmas for M bc and E N ev (χ c1 ) = 653 ± 26

21 M(γ J/ψ) in X(3872) region ±32 MeV ±32 MeV ±32 MeV Use this fit to get Efact for ARGUS sideband X(3872) No signif. peaking bkgnd scaled fit: 1.0 ± 2.1 evts N ev (X 3872 ) = 13.4 ± 4.4 Signif = 2lnL(1.0) -2lnL(13.4) = 5.1 σ

22 Br(X γ J/ψ) determination Br(X γ J/ψ) Br(X π + π J/ψ) = N ev (X γ J/ψ) N ev (χ c1 γ J/ψ) N ev (X π + π J/ψ) N ev (ψ π + π J/ψ) data: 0.30 ± 0.11 Br(B Kχ c1 )Br(χ c1 γ J/ψ) Br(B Kψ ) Br(ψ π + π J/ψ) ε(χ c1 γ J/ψ) ε(ψ γ J/ψ) ε(ψ π + π J/ψ) ε(x π + π J/ψ) from PDG 1.02 ± 0.22 ~1.02± 0.10 = 0.30 ± 0.11 ± 0.06 (Previous 90% CL upper limit was <0.4)

23 Evidence for C=+1 is becoming overwhelming B γ J/ψ only allowed for C=+1 same for B ω J/ψ (reported earlier) M(ππ) for X π + π J/ψ looks like a ρ X ππj/ψ (ππ-j/ψ in an S-wave) χ 2 /dof=63/39 X ρj/ψ (ρ-j/ψ in an S-wave) χ 2 /dof=35/39

24 C = -1 is ruled out reduce typesize of C=-1 entries 0 -- violates parity 0 -+ (η c ) 0 ++ (χ c0 ) (ψ(3s)) (χ c1 ) 1 +- (h c ) 2 -- (ψ 2 ) 2 -+ (η c2 ) 2 ++ (χ c2 ) 2 +-

25 Remaining states 1 ++ ρ & J/ψ in an S-wave 2 -+ a P-wave

26 Fits to the M(ππ) Distribution ρ q* X J/ψ q* X ρj/ψ in P-wave has a q* 3 centrifugal barrier

27 M(ππ) can distinguish ρ-j/ψ S- & P-waves S-wave: χ 2 /dof = 35/39 (CL= 67%) P-wave: χ 2 /dof = 80/39 (CL=0.014%) q* roll-off Shape of M(ππ) distribution near the kinematic limit favors S-wave q* 3 roll-off

28 ρ-j/ψ in a P-wave is unlikely reduce type-size of all J -+ entries 0 -- violates parity 0 -+ (η c ) 0 ++ (χ c0 ) (ψ(3s)) (χ c1 ) 1 +- (h c ) 2 -- (ψ 2 ) 2 -+ (η c2 ) 2 ++ (χ c2 ) 2 +-

29 The one which remains: 1 ++ (passes all the tests) χ 2 /dof = 10.4/9 χ 2 /dof = 35/39 cosθ l χ 2 /dof = 8.1/9 cosχ M(π + π ) & consistent with observations of: X γ J/ψ X ω J/ψ

30 Could the X(3872) be the χ c1? Mass is way off: 3872 vs MeV Br(X γ J/ψ) = 0.3 is much too small theory range Rough expectation for pure charmonium: Barnes, Godfrey hep-ph/ Γ(2 3 P 1 γ J/ψ) ~ 11 kev Γ(2 3 P 1 ππj/ψ) ~ Γ(ψ π ο J/ψ) ~ 0 (0.3 kev) ~30 isospin violating we measure 0.3; two orders-of-magnitude smaller; χ c1 component of the X(3872) must be small

31 Summary We learn a lot from angular distribs with ~50 evts Rule out 0 -+, 0 ++, 1 -- and 1 +- ; 2 is unlikely (CL~0.16%) B γj/ψ (plus ω J/ψ & M(ππ)) rules out all C=-1 M(ππ) favors S-wave ρ-j/ψ (P-wave CL=0.014%) Rules out 2 -+, 1 -+ & 0 -+ Only 1 ++ passes all tests angular distributions & M(ππ) fitted well χ c1 assignment unlikely (Br(γJ/ψ) is too small) DD* molecule models favor 1 ++ Tornqvist hep-ph/ Swanson PLB588, 189(2004)

32 plan Generate MC for each J PC compare MC distributions with data Search for X γψ (theory for χ c1 : ~ 6x γj/ψ ) PRD on X(3872) properties? angular studies other decay modes X γj/ψ include e39 data? X DD, DD*??, separate paper? X 3π J/ψ include e39 data? M(ππ) fits

33 Back-up slides

34 Q: why not do 2-d fits for angular distributions? A: We are not measuring parameters, we doing hypothesis testing, & so, we need a binned χ 2. With < 50 events, 2-dim binning with reasonable bin sizes will have 1event/bin.

35 Q: Is the M(γJ/ψ) look-back plot consistent with a 10.5 evt X γj/ψ signal? A: YES 13.4 evt Signal (yield fixed at value from M bc - E fit; σ scaled from χ c1 γj/ψ peak)