Determination of the J PC of the X(3872) (Reviews of BN800) S.L. Olsen & S.K. Choi Apr, 2005 Belle General Meeting

J PC possibilities for J ≤ exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2- -(2)2- -(2) (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

P-viol’n & DD -allowed J PC s unlikely (reduce type size of these entries by x1/2) exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) Not 2  prod 0 +- exotic DD allowed DD allowed (  (3S)) Not ee   X 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2- -(2)2- -(2) (  c2 ) 2 ++ DD allowed  c2 ’ ) Not 2  prod 2 +- exotic DD allowed

Use e7 – e37 data (include B  K S     J/  ) Signal (47 ev) Sidebands (114/10 = 11.4 ev)

BF determination Br(B  KX(3872)) x Br(X   J/  ) = (1.31 ± 0.24(stat) ± 0.13(syst))x10 -5

Areas of investigation Search for radiative decay Angular correlations Fits to the M(pp) distribution

Observation of X(3872)   J/ 

Select B  K J/   (include both K ± & K s ) Tight J/  cuts K ± id>0.5 / Belle-standard “good Ks” E  >40 MeV  0 veto (  2 >4.0) K* veto (M(K  )>1.0 GeV) R 2 <0.4; |cos  B | < 0.8 |M bc – 5.28|< GeV (2  ) |  E|<0.034 GeV (2  ) E7  E37

M(  J/  ) X signal Region ± 32 MeV M(  J/  ) B  K  c1 ;  c1   J/  X(3872)?

N ev (  c1 ) = 653 ± 26 |M(  J/  ) – m  c1 | < 25 MeV ( ± 2.4  ) Expand  c1 region Fit to determine  M(  J/  ) =10.7 MeV Use these fits to get means & sigmas for M bc and  E

M bc &  E for 64 MeV-wide M(  J/  ) bins N ev (X 3872 ) = 13.4 ±  Background 2.6±0.6

M(  J/  ) look-back plot consistent with a 10.5 evt X   J/  signal (yield fixed at value from M bc -  E fit;  scaled from  c1   J/  peak) 13.4 evt Signal

Product BF determination Br(B  KX(3872)) x Br(X   J/  ) N ev (X   J/  ) N BB Br(J/   l +l- )  ( X   J/  ) = = (1.8 ± 0. 6(stat) ± 0.1(syst)) x 10 -6

C = -1 is ruled out reduce typesize of C=-1 entries exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) (  2 ) (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

Angular Correlations

Strategy: for each J PC, find a distrib  0 if we see any events there, we can rule it out  example 1 -- : sin 2  K  K compute angles in J/  restframe D.V. Bugg hep-ph/ v2

 ’  2 /dof = 16.3/9  ’ is 1 --  2 /dof = 60.3/9 for X(3872) events |cos  Kl |

1 +- and 2 -- use J/  helicity angle  J/  K X J/   J/  |cos  J/  | For the  ’      J/ , this should be ~flat

1 +- : sin 2  J/  2 -- : sin 2  J/  cos 2  J/  |cos  J/  |  2 /dof =31.6 /9  2 /dof =19.5 /9 can rule out is unlikely

0 -+ Rosner (PRD ) 0 -+ : sin 2  sin 2  safe to rule out 0 -+    2 /dof=17.7/9 |cos  | |cos  |  2 /dof=34.2/9

0 ++ Rosner (PRD ) again ll In the limit where X(3872), , & J/  rest frames coincide: d  /dcos  l   sin 2  l  |cos  l  | rule out 0 ++  2 /dof = 41.0/9  2 /dof = 30.1/9

1 ++ ll  1 ++ : sin 2  l sin 2  K Rosner (PRD )

 2 /dof = 5.0/9  2 /dof = 13.5/9  2 /dof = 11.4/9  2 /dof = 10.0/9 compute  in X and J  rest frame compute  in J  and  rest frame |cos  ||cos  l | 1 ++ looks okay!

Reduce type size for J PC values that fail angle tests exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) (  2 ) (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

Remaining states 1 ++  & J/  in an S-wave 2 -+ “ “ a P-wave

Fits to the M(  ) Distribution X   J/  in P-wave has a q* 3 centrifugal barrier X J/   q*

M(  )- dependence of the detection efficiency

M(  ) can distinguish  -J/  S- & P-waves S-wave:  2 / dof = 43.1/39 P-wave:  2 / dof = 71.0/39 q* roll-off q* 3 roll-off (CL=0.01%) (CL= 28%) Shape of M(  ) distribution near the kinematic limit favors S-wave

 -J/  in an S-wave:  2 /dof = 43.1/39  -J/  in an D-wave:  2 /dof = 73.1/39

 -J/  in a P-wave is unlikely reduce type-size of all J -+ entries exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) (  2 ) (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

“The one which remains:” 1 ++ passes all the tests & consistent with observations of: X   J/  X  ”  ” J/ 

Could the X(3872) be the  c1 ’ ?  (2 3 P 1   J/  ) ~ 11 keV  (2 3 P 1   J/  ) ~  (  ’    J/  ) ~ 0 (0.3 keV) ~30 isospin violating Barnes, Godfrey hep-ph/ Rough expectation for pure charmonium: we measure 0.3; two orders-of-magnitude smaller;   c1 ’ component of the X(3872) must be small Mass is way off: 3872 vs 3929  3990 MeV Br(X   J/  ) = 0.3 is much too small theory range

Summary B   J/  (plus “  ”J/  M(  )) rules out all C=-1 M(  ) favors S-wave  -J/  (P-wave CL=0.014%) –Rules out 2 -+, 1 -+ & 0 -+ Only 1 ++ passes all tests –angular distributions & M(  ) fitted well –  c1 ’ assignment unlikely (Br(  J/  ) is too small) –DD* molecule models favor 1 ++ Tornqvist hep-ph/ Swanson PLB588, 189(2004)