Pinning down the JPC values of the X(3872)
K. Miyabayashifor
S.K. Choi & S.L. Olsen
Feb, 2005 Belle Analysis & Software 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’)
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
Use e7 – e37 data(include BKS J/)
Signal(47 ev)Sidebands
(114/10 = 11.4 ev)
Follow advice from Sherlock Holmes:
Eliminate all other
factors, & the one that
remains must be the
truth.**The sign of four
Areas of investigation
• Angular correlations
• Search for radiative decays
• Fits to the M() distribution
Angular Correlations
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
’2/dof = 8.9/9
Use ’ to check accept.’ is 1--
|cosKl| for X(3872) events
X(3872) is not 1-- !
expect 2~3evts/bin
backgroundscaled fromsidebands
fit withsin2Kl + bkgd
2/dof = 60.3/9 see 8 evts/bin
1+- and 2--
use J/ helicity angle J/
KX
J/
J/
|cosJ/|
For the ’J/,this should be ~flat
1+- and 2--
can rule out 1+- (Cl=10 -4%) 2-- is unlikely (CL=0.16%)
|cosJ/|
1+-: sin2J/2--: sin2J/ cos2J/
2/dof=36/9 2/dof=27/9
|cosJ/|
0-+ Rosner (PRD 70 094023)
0-+ : sin2 sin2
safe to rule out 0-+
2/dof=31/9
|cos|
|cos|
2/dof=61/9
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 = 59/9
1++
l
1++: sin2l sin2
K
1++ looks okay!
compute angles inX(3872) restframe
|cosl|
2/dof = 10.4/9
|cos|
2/dof = 8.1/9
Rosner (PRD 70 094023)
1++ againcompute in rest frame
compute in J rest frame
2/dof = 8.9/92/dof = 8.9/9
|cosl||cos|
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
Observation of X(3872) J/
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
M( J/)
X signalRegion
±32 MeV
M(J/)
BKc1; c1J/
X(3872)?
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/) in X(3872) region
No signif. peaking bkgndscaled fit: 1.0 ± 2.1 evts Signif = 2lnL(1.0) -2lnL(13.4) = 5.1
±32 MeV±32 MeV ±32 MeV
Use this fit to get Efact for ARGUS
sideband
Nev(X3872) = 13.4 ± 4.4
X(3872)
Br(XJ/) determination
Br(XJ/)Br(XJ/) =
Nev(XJ/)Nev(c1J/)
Nev(XJ/)Nev(’ J/)
Br(BKc1)Br(c1J/)
Br(BK’) Br(’J/)
(c1J/)(’J/)
(’ J/)(XJ/)
data:0.30 ± 0.11
from PDG1.02 ± 0.22 ~1.02± 0.10
= 0.30 ± 0.11 ± 0.06
(Previous 90% CL upper limit was <0.4)
Evidence for C=+1is becoming
overwhelming• B J/ only allowed for C=+1• same for B””J/ (reported
earlier)• M() for XJ/ looks like a
XJ/(-J/ in an
S-wave)2/dof=35/39
XJ/(-J/ in an
S-wave)2/dof=63/39
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
Remaining states
•1++ & J/ in an S-wave •2-+ “ “ a P-wave
Fits to the M()
DistributionXJ/ in P-wave has aq*3 centrifugal barrierX
J/
q*
q*
M() can distinguish -J/ S- & P-waves
S-wave: 2/dof = 35/39 P-wave: 2/dof = 80/39
q*roll-off
q*3
roll-off
(CL=0.014%)(CL= 67%)
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
“The one which remains:” 1++
(passes all the tests)
|cosl|
2/dof = 10.4/9
|cos|
2/dof = 8.1/9M()
2/dof = 35/39
& consistent withobservations of:
•X J/ •X”” J/
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• We learn a lot from angular distribs with ~50
evts– Rule out 0 -+, 0++ , 1 -- and 1+-; 2– is unlikely
(CL~0.16%)
• 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)
plan
• Generate MC for each JPC
– compare MC distributions with data
• Search for X’ (theory for c1’: ~ 6x J/)
• PRD on X(3872) properties?– angular studies– other decay modes
• X J/include e39 data?• XDD, DD* ?? , separate paper?• X3 J/ include e39 data?
– M() fits
Back-up slides
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 2.
With < 50 events, 2-dim binning with reasonable bin sizes will have ≤1event/bin.
Q: Is the M(J/) look-back plot consistent with a 10.5 evt XJ/
signal?
A: YES
(yield fixed at value from Mbc-E fit;
scaled from c1J/ peak)
13.4 evtSignal