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Study of dynamics of ππ transitions among ϒ(3S), ϒ(2S) and ϒ(1S)

in CLEO

Tomasz Skwarnicki Syracuse University

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 2

µ−

µ+

γ γ

γ

γ

e−

e+

π− π+

π+π− l+l−

π0π0 l+l−

Detector and events ϒ’→ππϒ, ϒ→ l+l−

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 3

Dalitz variables • Three body decay: ϒ’→ϒππ. If no coupling of ππ system to

ϒ’s polarizations then only 2 degrees of freedom.

22

22

q

r

M

M ππ

πϒ

=

=

2 2 2 2 (2 ) (1 )

2 2 2

3 (2 ) (1

2

2 2

)

2 2 2

2

3

2 2

4 ( , , )

( , , ) 2 2

os

2

c X S S

S S

M M m

m M M

a b c a b c ab

q r

q q

q

bc ca

π

π

θ ϒ ϒ

ϒ ϒ

+ + − − =

− Λ

Λ = + + − − −

X

• Use q2, cosθX

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 4

Matrix element • Heavy (bb) and light (ππ) degrees of freedom should approximately

factorize • Furthermore, since pions emitted in these transitions are soft, general

structure of the matrix element can be constrained from chiral symmetry (PCAC) [Brown,Cahn PRL, 35, 1 (75)] in non-relativistic limit:

[ ]22 1 2 1 2 2 1

1 2 1 2

2 2 1 2

( )( 2 ) ( ) ( )( ) ( )( )

, Polarization vectors of parent and daughter states , Four-vectors of pions, , their energies in parent rest fra

A B C

me

( )

M q m E E q q q q

q q E E

q q q M

πε ε ε ε ε ε ε ε

ε ε

′ ′ ′ ′= ⋅ − + ⋅ + ⋅ ⋅ + ⋅ ⋅

′ − ϒ − − ϒ

= + ≡ 2ππ

• Form factors A,B,C expected to be approximately constant (and real in the strict chiral limit)

[ ]1 2 1 2 2 1( )( ) ( )( Lo

)

rentz invari

, Fou

ant

r-vectors of parent

f

and da

orm:

ughter

E E P q P q P q P q

P P

′ ′⋅ ⋅ + ⋅ ⋅

′ − ϒ

∼ 1 22q q⋅

No cosθX dependence! Depends on both q2 and cosθX

Couples pions to ϒ’s polarizations

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 5

Initial Theory

• In Multipole Expansion model, the 3rd term involves magnetic interactions (spin flip) and can be neglected compared to the leading E1*E1 transition [Yan PR,D22,1652 (80)].

C 0≈ • In QCD-motivated calculation of soft-pion piece in E1*E1 transition,

expect S-wave to dominate in the non-relativistic limit producing M(ππ) distribution similar to the one due to the 1st term [Voloshin,Zakharov,PRL,45,688(80); Novikov, Shifman, ZP,C8,43(81)]

A B?

• Observation of ϒ(2S)→ϒ(1S)ππ with the same M(ππ) distribution was a great success of this theoretical framework and reinforced A-dominance dogma

• Consistent with the phenomenological observation by Brown&Cahn, that M(ππ) in ψ(2S)→J/ψ(1S)ππ was well reproduced by assuming B=C=0

[ ]22 1 2 1 2 2 1A B C( )( 2 ) ( ) ( )( ) ( )( )M q m E E q q q qπε ε ε ε ε ε ε ε′ ′ ′ ′= ⋅ − + ⋅ + ⋅ ⋅ + ⋅ ⋅

Mππ (GeV)

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 6

• A large body of theoretical work trying to explain the origin of this anomaly:

• Observation of double- peak structure of M(ππ) was proclaimed anomalous

– Large final state interactions [Belanger,DeGrand,Moxhay,PR,D39,257(89);Chakravarty,Kim,Ko,PR,D50,389(94)]

– σ-meson in ππ system [Komada,Ishida,Ishida,PL,B508,31(01);PL,B518,47(01);Uehara Prog.Theor.Phys.109,265(03)]

– Exotic ϒπ resonance [Voloshin,JTEP Lett.,37,69(83);Belanger et al ,PR,D39,257(89); Anisovich,Bugg,Sarantsev,Zhou,PR,D51,4619(95); Guo,Shen,Chiang,Ping,NP,A761,269(05).]

– Ad hoc constant term in amplitude [Moxhay,PR,D39,3497(89)] – Coupled channel effects [Lipkin,Thuan,PL,B206,349(88);Zhou,Kuang,PR,D44,756(91)] – 33S1-n3D1 mixing [Chakravarty,Kim,Ko,PR,D48,1212(93)]

– Relativistic corrections [Voloshin,PR,D74,054022(06)]

• Observed distributions of M(ππ) in ϒ(4S)→ϒ(1S)ππ and ϒ(4S)→ϒ(2S)ππ add to the interest (see the next talk!)

ϒ(3S)→ϒ(1S)ππ Anomaly

CLEO-III preliminary

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 7

This analysis • Much larger statistics for ϒ(3S)→ϒ(1S)ππ,

ϒ(3S)→ϒ(2S)ππ than previously available. – 1.14 fb-1 at ϒ(3S): 5M ϒ(3S) with CLEO-III detector

• Analyze also ϒ(2S)→ϒ(1S)ππ present in the same ϒ(3S) data sample (produced via ϒ(3S)→ϒ(2S)X, X=ππ or γγ): – 0.5M ϒ(2S)

• Perform 2D fit of A,B (and C) to [q2, cosθX] instead of 1D analysis of mππ – Assume A,B (and C) constant, but allow them to be

complex

• Better experimental insight into decay structure of ππ transitions!

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 8

Signal selection

ϒ(3S)→ϒ(1S)ππ

• Backgrounds are small

ϒ(3S)→ϒ(2S)ππ ϒ(3S) → X ϒ(2S), ϒ(2S)→ϒ(1S)ππ

ππ l+l− ϒ(1S) ϒ(1S)

With loose preselection

With final cuts

3113 events 1019

events 62 events

715 events

452 events

392 events

Recoil mass against ππ:

Di-lepton Mass:

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 9

co sθ

x

Expected “Dalitz” Plot Distributions

A2(q2-2mπ2)2 2AB(q2-2mπ2)E1E2 B 2E12E22

Matrix Elements Squared

Mππ2

Efficiency

Mππ2 co

sθ x

co sθ

x

(MC)

Efficiency taken into account in the fit, including MC statistical errors.

cosθ x Mππ

2

π+π− π0π0

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 10

π+π− data

µ+µ−

e+e−

ϒ(3S)→ϒ(1S)ππ ϒ(2S)→ϒ(1S)ππ ϒ(3S)→ϒ(2S)ππ

cosθX vs. Mππ

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 11

π0π0 data ϒ(3S)→ϒ(1S)ππ ϒ(2S)→ϒ(1S)ππ ϒ(3S)→ϒ(2S)ππ

µ+µ−

e+e−

cosθX vs. Mππ

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 12

Results for ϒ(3S)→ϒ(1S)ππ with C = 0

+1.19 ± 0.05-2.52 ± 0.03l+l−ππ

+1.31 ± 0.16 +1.07 ± 0.15

+1.16 ± 0.06 +1.18 ± 0.08

-2.43 ± 0.09µ+µ−π0π0 -2.52 ± 0.09e+e−π0π0

-2.51 ± 0.04µ+µ−π+π− -2.53 ± 0.05e+e−π+π−

Good checks of systematic effects

based on isospin symmetry and lepton universality.

Pions Lep’s Re(B/A) Im(B/A) In

di vi

du al

fi ts

C o

m b

f it

Statistical errors only

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 13

π0

π0π0

π0 π0

π0

π± π ±

π±

π± π±

π±

Projections: fit vs data (C = 0)

cosθx

Mππ

ϒ(3S)→ϒ(1S)ππ ϒ(2S)→ϒ(1S)ππ ϒ(3S)→ϒ(2S)ππ

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 14

Allowing C term in the fit to ϒ(3S)→ϒ(1S)ππ

• |C/A| « |B/A| as theoretically expected • Given statistical and systematic errors there is no evidence

that C-term (spin flip) is needed: |C/A| = 0.45±0.18±0.36 (

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 15

Results

• Assume no spin-flip transitions ( C=0 )

---0.4±1.10.0±1.1-0.39±0.33 ϒ(3S)→ϒ(2S)ππ

180±9o0.75±0.150.00±0.11-0.75±0.15 ϒ(2S)→ϒ(1S)ππ

155±2o2.79±0.051.19±0.07-2.52±0.04 ϒ(3S)→ϒ(1S)ππ

Arg(B/A)|B/A|Im(B/A)Re(B/A)

• Allowing C-term

2.89±0.250.45±0.40 ϒ(3S)→ϒ(1S)ππ

|B/A||C/A|

Preliminary!

Errors include systematic uncertainty

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 16

S,D-wave decomposition • We can extract a fraction of S- and D-wave components

implied by our fits: 2 2

2 2 2 00 20

A B

A B

( ) ( ,cos )

( ) ( ) ( ) (cos )B A B X

A B B X

M f q f q

S q S q Y D q Y

θ

θ

= +

= + +

S-wave D-wave

These functions are known analytically

With A,B fit to ϒ(3S)→ϒ(1S)ππ data (no errors shown)

• D-wave contribution is small, as expected

F ra

ct io

n of

am

pl itu

de s

qu ar

ed

A m

pl itu

de

Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 17

Conclusions • Di