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