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Determination of the JPC of the X(3872)
(Reviews of BN800)
S.L. Olsen & S.K. Choi
Apr, 2005 Belle General Meeting
JPC possibilities for J ≤ 2
0 - -
exotic
violates parity
0-+
(c”)
0++
DD allowed
(c0’)
0+-
exotic
DD allowed
1- -
DD allowed
((3S))
1-+
exotic
DD allowed
1++
(c1’)
1+-
(hc’)
2- -
(2)
2- +
(c2)
2++
DD allowed
c2’)
2+-
exotic
DD allowed
P-viol’n & DD-allowed JPCs unlikely(reduce type size of these entries by x1/2)
0 - -
exotic
violates parity
0-+
(c”)
0++
DD allowed
(c0’)Not 2 prod
0+-
exotic
DD allowed
1- -
DD allowed
((3S))
Not ee X
1-+
exotic
DD allowed
1++
(c1’)
1+-
(hc’)
2- -
(2)
2- +
(c2)
2++
DD allowed
c2’)Not 2 prod
2+-
exotic
DD allowed
Areas of investigation
• Search for radiative decay
• Angular correlations • Fits to the M(pp) distribution
Select BK J/ (include both K± & Ks)
• 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)• R2<0.4; |cosB| < 0.8• |Mbc – 5.28|<0.0055 GeV (2)• |E|<0.034 GeV (2)• E7 E37
Nev(c1) = 653 ± 26
|M(J/) – mc1| < 25 MeV (± 2.4)
Expand c1 regionFit to determine
M(J/) =10.7 MeV
Use these fits to getmeans & sigmas
for Mbc and E
M(J/) look-back plot consistent with a 10.5 evt XJ/ signal
(yield fixed at value from Mbc-E fit;
scaled from c1J/ peak)
13.4 evtSignal
Product BF determination
Br(BKX(3872)) x Br(XJ/)
Nev(XJ/)NBB Br(J/l +l-) (XJ/)
=
= (1.8 ± 0. 6(stat) ± 0.1(syst)) x 10-6
C = -1 is ruled outreduce typesize of C=-1 entries
0 - -
exotic
violates parity
0-+
(c”)
0++
DD allowed
(c0’)
0+-
exotic
DD allowed
1- -
DD allowed
((3S))
1-+
exotic
DD allowed
1++
(c1’)
1+-
(hc’)
2- -
(2)2-
+
(c2)
2++
DD allowed
c2’)
2+-
exotic
DD allowed
Strategy: for each JPC, find a distrib 0if we see any events there, we can rule it
out
example1--: sin2K
K
compute angles inJ/ restframe
D.V. Bugg hep-ph/0410168v2
1+-: sin2J/
2--: sin2J/ cos2J/
|cosJ/|
2/dof =31.6 /9
2/dof =19.5 /9
can rule out 1+-
2-- is unlikely
0-+ Rosner (PRD 70 094023)
0-+ : sin2 sin2
safe to rule out 0-+
2/dof=17.7/9
|cos|
|cos|
2/dof=34.2/9
0 ++
Rosner (PRD 70 094023) again
l
In the limit whereX(3872), , & J/rest frames coincide:d/dcosl sin2l
|cosl|rule out 0++
2/dof = 41.0/9
2/dof = 30.1/9
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 Jand rest frame
|cos||cosl| 1++ looks okay!
Reduce type size for JPC values that fail angle tests
0 - -
exotic
violates parity
0-+
(c”)
0++
DD allowed
(c0’)
0+-
exotic
DD allowed
1- -
DD allowed
((3S))
1-+
exotic
DD allowed
1++
(c1’)
1+-
(hc’)
2- -
(2)
2- +
(c2)
2++
DD allowed
c2’)
2+-
exotic
DD allowed
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 nearthe kinematic limit favors S-wave
-J/ in a P-wave is unlikelyreduce type-size of all J-+ entries
0 - -
exotic
violates parity
0-+
(c”)
0++
DD allowed
(c0’)
0+-
exotic
DD allowed
1- -
DD allowed
((3S))
1-+
exotic
DD allowed1++
(c1’)
1+-
(hc’)
2- -
(2)
2- +
(c2)
2++
DD allowed
c2’)
2+-
exotic
DD allowed
Could the X(3872) be the c1’ ?
(23P1 J/) ~ 11 keV
(23P1 J/) ~ (’ J/) ~ 0 (0.3 keV)~30
isospin violating
Barnes, Godfrey hep-ph/0311162Rough expectation forpure 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• BJ/ (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/0308277• Swanson PLB588, 189(2004)