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−
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
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
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 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
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 0ť 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)
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)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:
Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 9
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
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 dataϒ(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
divi
dual
fits
Co
mb
fit
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 (<1.1 90% CL).
statistics
bkg syst
neutrals syst charged
syst
overall syst
|B/A
|
|C/A|
}C=0 result
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 2 200 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
Upsilon dipion transition in CLEO DPF'06 Honolulu T. Skwarnicki 17
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 ).