Syracuse University · 2006. 11. 21. · Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwar...

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

in CLEO

Tomasz SkwarnickiSyracuse 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 eventsϒ’→ππϒ, ϒ→ l+l−


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

Mππ

πϒ

=

=

2 2 2 2(2 ) (1 )

22 2

3 (2 ) (1

2

22

)

2 2 2

2

3

2 2

4( , , )

( , , ) 2 2

os

2

c XS S

S S

M M m

mM M

a b c a b c ab

q r

qq

q

bc ca

π

π

θ ϒ ϒ

ϒ ϒ

+ + − −=

−Λ

Λ = + + − − −

X

• Use q2, cosθX


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 chiralsymmetry (PCAC) [Brown,Cahn PRL, 35, 1 (75)] in non-relativistic limit:

[ ]221 2 1 2 2 1

1 2 1 2

2 21 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


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

[ ]221 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)


• 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


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!


Signal selection

ϒ(3S)→ϒ(1S)ππ

• Backgrounds are small

ϒ(3S)→ϒ(2S)ππϒ(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

715events

452 events

392 events

Recoil mass against ππ:

Di-leptonMass:


cosθ

x

Expected “Dalitz” Plot Distributions

A2(q2-2mπ2)2 2AB(q2-2mπ

2)E1E2 B 2E12E2

2

Matrix Elements Squared

Mππ2

Efficiency

Mππ2

cosθ

x

cosθ

x

(MC)

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

cosθx Mππ

2

π+π− π0π0


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


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

µ+µ−

e+e−

cosθX vs. Mππ


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

divi

dual

fits

Co

mb

fit

Statistical errors only


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


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 (<1.1 90% CL).

statistics

bkg syst

neutrals syst charged

syst

overall syst

|B/A

|

|C/A|

}C=0 result


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


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

implied by our fits:2 2

2 2 200 20

A B

A B

( ) ( ,cos )

( ) ( ) ( ) (cos )BA 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)ππdata (no errors shown)

• D-wave contribution is small, as expected

Fra

ctio

n of

am

plitu

de s

quar

ed

Am

plitu

de


Conclusions• Di-pion transitions among ϒ(3S), ϒ(2S) and ϒ(1S)

are well described by a matrix element constrained by Chiral Symmetry for soft pionsystem, with form-factor parameters being complex and constant across the Dalitz plot.

• No evidence for significant coupling to heavy quark spins, as expected ( |C/A|=0.45±0.40 ).

• The ϒ(3S)→ϒ(1S)ππ anomaly explained by a large 2nd

term in the chiral matrix element (|B/A|=2.8±0.1) with a non-trivial phase ( arg(B/A)= 155±2o ).

• This term is smaller, but still significant in ϒ(2S)→ϒ(1S)ππ( |B/A|=0.75±0.12, arg(B/A)= 180±9o ).

Syracuse University · 2006. 11. 21. · Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwar...

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