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Transcript of Syracuse · PDF file 2006. 11. 21. · Upsilon dipion transition in CLEO DPF'06...

  • 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