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

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

2. JPC possibilities for J ≤ 2

3. P-viol’n & DD-allowed JPCs unlikely(reduce type size of these entries by x1/2)

4. Use e7 – e37 data(include BKS p+p-J/y) Signal (47 ev) Sidebands (114/10 = 11.4 ev)

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

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

7. Angular Correlations

8. Strategy: for each JPC, find a distrib 0if we see any events there, we can rule it out y’is 1-- example1--: sin2qKm Use y’ to check accept. y’: c2/dof = 8.9/9 qKm K compute angles in J/y restframe D.V. Bugg hep-ph/0410168v2

9. |cosqKl| for X(3872) events c2/dof = 60.3/9 fit with sin2qKl + bkgd see 8 evts/bin expect 2~3evts/bin background scaled from sidebands X(3872) is not 1-- !

10. 1+- and 2-- use J/y helicity angle qJ/y For the y’p+p-J/y, this should be ~flat K X qJ/y J/y |cosqJ/y|

11. 1+- and 2-- 2--: sin2qJ/y cos2qJ/y 1+-: sin2qJ/y c2/dof=36/9 c2/dof=27/9 |cosqJ/y| |cosqJ/y| can rule out 1+- (Cl=10 -4%) 2-- is unlikely (CL=0.16%)

12. 0-+Rosner(PRD 70 094023) 0-+ : sin2q sin2y c2/dof=31/9 q |cosq| c2/dof=61/9 y safe to rule out 0-+ |cosy|

13. 0 ++Rosner(PRD 70 094023) again In the limit where X(3872), pp, & J/y rest frames coincide: dG/dcosqlp sin2qlp qlp c2/dof = 59/9 rule out 0++ |cosqlp|

14. compute angles in X(3872) restframe 1++ 1++: sin2ql sin2c Rosner (PRD 70 094023) c2/dof = 10.4/9 ql K |cosql| c c2/dof = 8.1/9 1++ looks okay! |cosc|

15. 1++ again compute c in pp rest frame compute q in J/y rest frame c2/dof = 8.9/9 c2/dof = 8.9/9 |cosc| |cosql|

16. Reduce type size for JPC values that fail angle tests

17. Observation of X(3872)g J/y

18. Select BK J/yg(include both K± & Ks) • Tight J/y cuts • K± id>0.5 / Belle-standard “good Ks” • Eg>40 MeV • p0 veto (c2>4.0) • K* veto (M(Kg)>1.0 GeV) • R2<0.4; |cosqB| < 0.8 • |Mbc – 5.28|<0.0055 GeV (2s) • |DE|<0.034 GeV (2s) • E7  E37

19. M(g J/y) BKcc1; cc1g J/y X signal Region ±32 MeV X(3872)? M(gJ/y)

20. Expand cc1 region Fit to determine sM(gJ/y) =10.7 MeV |M(gJ/y) – mcc1| < 25 MeV (± 2.4s) Use these fits to get means & sigmas for Mbc and DE Nev(cc1) = 653 ± 26

21. M(g J/y) in X(3872) region ±32 MeV ±32 MeV ±32 MeV Use this fit to get Efact for ARGUS sideband X(3872) Nev(X3872) = 13.4 ± 4.4 No signif. peaking bkgnd scaled fit: 1.0 ± 2.1 evts Signif =  2lnL(1.0) -2lnL(13.4) = 5.1 s

22. Br(Xg J/y) determination Br(Xg J/y) Br(Xp+p-J/y) = Nev(Xg J/y) Nev(cc1g J/y) Nev(Xp+p-J/y) Nev(y’ p+p-J/y) e(cc1g J/y) e(y’g J/y) e(y’ p+p-J/y) e(Xp+p-J/y) Br(BKcc1)Br(cc1g J/y) Br(BKy’) Br(y’p+p-J/y)   from PDG 1.02 ± 0.22 data: 0.30 ± 0.11 ~1.02± 0.10 = 0.30 ± 0.11 ± 0.06 (Previous 90% CL upper limit was <0.4)

23. Evidence for C=+1is becoming overwhelming • Bg J/y only allowed for C=+1 • same for B”w”J/y (reported earlier) • M(pp) for Xp+p-J/y looks like a r XppJ/y (pp-J/y in an S-wave) c2/dof=63/39 XrJ/y (r-J/y in an S-wave) c2/dof=35/39

24. C = -1 is ruled outreduce typesize of C=-1 entries

25. Remaining states • 1++r & J/y in an S-wave • 2-+ “ “ a P-wave

26. Fits to the M(pp)Distribution J/y XrJ/y in P-wave has a q*3 centrifugal barrier q* X r q*

27. M(pp) can distinguish r-J/y S- & P-waves P-wave: c2/dof = 80/39 S-wave: c2/dof = 35/39 (CL=0.014%) (CL= 67%) q* roll-off q*3 roll-off Shape of M(pp) distribution near the kinematic limit favors S-wave

28. r-J/y in a P-wave is unlikelyreduce type-size of all J-+ entries

29. “The one which remains:” 1++ (passes all the tests) c2/dof = 10.4/9 c2/dof = 35/39 |cosql| M(p+p-) c2/dof = 8.1/9 • & consistent with • observations of: • X g J/y • X”w” J/y |cosc|

30. Could the X(3872) be the cc1’ ? • Mass is way off: 3872 vs 3929  3990 MeV • Br(Xg J/y) = 0.3 is much too small theory range Rough expectation for pure charmonium: Barnes, Godfrey hep-ph/0311162 G(23P1 g J/y) ~ 11 keV G(23P1 ppJ/y) ~ G(y’ po J/y) ~ 0 (0.3 keV) ~30 isospin violating we measure 0.3; two orders-of-magnitude smaller; cc1’ 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gJ/y (plus “w”J/y & M(pp)) rules out all C=-1 • M(pp) favors S-wave r-J/y (P-wave CL=0.014%) • Rules out 2-+, 1-+ & 0-+ • Only 1++ passes all tests • angular distributions & M(pp) fitted well • cc1’ assignment unlikely (Br(gJ/y) is too small) • DD* molecule models favor 1++ • Tornqvist hep-ph/0308277 • Swanson PLB588, 189(2004)

32. plan • Generate MC for each JPC • compare MC distributions with data • Search for Xgy’ (theory for cc1’: ~ 6x gJ/y ) • PRD on X(3872) properties? • angular studies • other decay modes • XgJ/y  include e39 data? • XDD, DD* ?? , separate paper? • X3p J/y  include e39 data? • M(pp) 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 c2. With < 50 events, 2-dim binning with reasonable bin sizes will have ≤1event/bin.

35. Q: Is the M(gJ/y) look-back plot consistent with a 10.5 evt XgJ/y signal? A: YES 13.4 evt Signal (yield fixed at value from Mbc-DE fit; s scaled from cc1gJ/y peak)