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

Use e7 – e37 data(include BKS J/)

Signal(47 ev)Sidebands

(114/10 = 11.4 ev)

BF determination

Br(BKX(3872)) x Br(XJ/)

= (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 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

Mbc & E for 64 MeV-wide M(J/) bins

Nev(X3872) = 13.4 ± 4.4 5.7

Background 2.6±0.6

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

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 = 16.3/9

’ is 1--

2/dof = 60.3/9 for X(3872) events

|cosKl|

1+- and 2--

use J/ helicity angle J/

KX

J/

J/

|cosJ/|

For the ’J/,this should be ~flat

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

1++

l

1++: sin2l sin2

K

Rosner (PRD 70 094023)

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

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()- 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 nearthe 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 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

& 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• 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)