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The hemisphere problem revisited

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					Measurement of Collins Asymmetries
    in e+e- Annihilation at Belle

           Workshop on Exclusive Reactions at
                                 <a href="talks/
                  High Momentum Transfer
                                 Sandorfi.pdf">


                 May 24th , Thomas Jefferson Laboratory

D. Gabbert       Illinois and RBRC
M. G.Perdekamp   Illinois and RBRC
K. Hasuko        RIKEN and RBRC
S. Lange         Frankfurt
M. Leitgab       Illinois
D. Mertens       Illinois
A. Ogawa         BNL and RBRC
R. Seidl         Illinois and RBRC
V. Siegle        RBRC

                  for the Belle Collaboration
               ----------- Outline ------------


    o Motivation
           Collins FF for global QCD analysis of single
           transverse asymmetries in pp and SIDIS


    o Collins Asymmetries from e+e-
           LEP first work on Delphi data in the 90s:
               Efremov, Smirnova, Tkatchev and
               Bonivento, Matteuzzi, Kotzinian
           Experimental technique
           Results




May 24th              Measurement of Collins Asymmetries at Belle   2
            Motivation Transversity Quark Distributions
            from Collins- and Interference-Fragmentation
   New HERMES results for Collins Asymmetries
   M. Diefenthaler, DIS 2007, Munich
                                                        Collins- and IFF- asymmetries
                                                        in SIDIS and pp are of the form
                                                         ~ Transversity (x) x CFF(z)

                                                         ~ Transversity (x) x IFF(z)

                                                        Collins- and IFF- asymmetries
                                                        in e+e- are of the form

                                                           ~ CFF(z1) x CFF(z2)

                                                           ~ IFF(z1) x IFF(z2)

                                                            global QCD analysis

May 24th                     Measurement of Collins Asymmetries at Belle          3
               Global Analysis:                                           RBRC Transversity Workshop 2000


                       Extract Transversity Distributions
SIDIS ⇒                        Factorization               e + e - ⇒ Collins x Collins
   transversity × Collins           +
                               Universality ?!                       Interference FF
   transversity × IFF
   HERMES, COMPASS,
                                                                      x Interference FF
   JLAB, EIC                                               Belle

                                                         RHIC / GSI
                                                         pp      ⇒
                    Transversity
                                                              A N for inclusive hadrons, Jets
                    Tensor Charge
      Theory




                                                              A T in Jets : transversity × Collins
                                                                           transversity × IFF
                                                         GSI
                                                              A TT Drell Yan :
   Lattice QCD: Tensor Charge
                                                                           transversity × transversity

   May 24th                 Measurement of Collins Asymmetries at Belle                     4
           First QCD Analysis                         Anselmino, Boglione, D’Alesio,
                                                      Kotzinian, Murgia, Prokudin, Turk
             of SIDIS + e+e- !                        Phys. Rev. D75:05032,2007




                                                            Fit includes:
                                                                HERMES SIDIS
                                                            + COMPASS SIDIS
                                                            + Belle e+e-

                                                                transversity dist.
                                                                + Collins FF




May 24th          Measurement of Collins Asymmetries at Belle                   5
Measurement of Collins Asymmetries
  In e+e- at KEK B with the Belle
         Phys.Rev.Lett.96:232002,2006
        and update at Spin 2006 in Kyoto
              Collins Effect in Quark Fragmentation
                                                               J.C. Collins, Nucl. Phys. B396, 161(1993)




              v
              sq                        v
                                     h, p h             φ
                        v                              v
                                                       ph ⊥
                q       k
r
k              : quark momentum                                   Collins Effect:
v                                                                 Fragmentation of a
sq             : quark spin
v                                                                 transversely polarized
ph             : hadron momentum                                  quark q into spin-less
v
ph ⊥           : transverse hadron momentum                       hadron h carries an
z h = Eh Eq                                                       azimuthal dependence:
                                                                           (           )
                                                                         v v        v
                                                                       ∝ k × ph ⊥ ⋅ sq
    = 2 Eh    s : relative hadron momentum
                                                                       ∝ sin φ

May 24th                Measurement of Collins Asymmetries at Belle                        7
           General Form of Fragmentation Functions



           Number density for finding
           hadron h from a transversely
           polarized quark, q:


           Dq ↑ ( z , ph ⊥ ) = D1q ,h ( z ) + H1⊥ q ,h ( z , ph ⊥
              h       v                                       2
                                                                    )
                                                                      ( kˆ × p )⋅ sv
                                                                             v
                                                                             h⊥    q

                                                                          zM h
                            unpolarized FF         Collins FF




May 24th                   Measurement of Collins Asymmetries at Belle                 8
                    Collins FF in e+e- : Need
                Correlation between Hemispheres !

           o Quark spin direction unknown: measurement of
             Collins function in one hemisphere is not possible
             sin φ modulation will average out.

           o Correlation between two hemispheres with
             sin φi Collins single spin asymmetries results in
             cos(φ1+φ2) modulation of the observed di-hadron
             yield.


               Measurement of azimuthal correlations for pion pairs
               around the jet axis in two-jet events!

May 24th                Measurement of Collins Asymmetries at Belle   9
                       Event Structure at Belle
                                 e+e- CMS frame:                2Eh
                                                             z=     ,          s = 10.52 GeV
Near-side Hemisphere:                                             s
  hi , i=1,Nn with zi                              e-
                                            Θ                                 <Nh+,-> = 6.4




                         e+
                                                                  Jet axis: Thrust
Spin averaged cross section:                            Far-side:
dσ (e + e − → h1h2 X ) 3α 2                             hj , j=1,Nf with zj
                      = 2 A( y )∑ ea D1 (z1 )D1 (z2 )
                                     2

     dΩdz1dz2          Q        a ,a



           1           ( cm ) 1
A( y ) = ⎛ − y + y 2 ⎞ = (1 + cos 2 Θ)
         ⎜           ⎟
         ⎝2          ⎠        4

May 24th                     Measurement of Collins Asymmetries at Belle               10
                                 Collins Fragmentation:
                       Angles and Cross Section cos(φ1+φ2) Method
                                                e+e- CMS frame:
 ϕ2−π                                      e-      Observables: N12(φ1+φ2), A12(z1,z2)
                                  Θ
r                                                                                                       ϕ1
Ph 2                                                                r
                                                                    Ph1
                                                                                      ϕ2
                                                                             ϕ1

                 e+
   2-hadron inclusive transverse momentum dependent cross section:
       dσ (e + e − → h1h 2 X )
                               = L B(y )cos (ϕ1 + ϕ 2 )H1 [1] (z1 )H1 [1] (z 2 )
                                                        ⊥           ⊥

         dΩdz1dz 2d qT2



                                                                               Net anti-alignment of
                          cm   1
       B(y ) = y(1 − y ) =       sin 2 Θ                                       transverse quark spins
                               4

       May 24th                         Measurement of Collins Asymmetries at Belle                11
                            Collins Fragmentation:
                   Angles and Cross Section cos(2φ0) Method
Observables: N0(φ0), A12(z1,z2)                  e+e- CMS frame:

          r              Θ
                               e-                                        •Independent of thrust-axis
          Ph 2
                                    A0    r                              •Convolution integral I
                                          Ph1                            over transverse momenta
                                                                         involved
                                                        ϕ0               [Boer,Jakob,Mulders:
                                                                         NPB504(1997)345]
                   e+
   2-hadron inclusive transverse momentum dependent cross section:
      dσ (e + e − → h1h 2 X )
                                                   (⎡
                                                                           )
                                                      ˆ ⋅ kT h ⋅ pT − kT ⋅ pT H1 H1 ⎤
                                                                               ⊥ ⊥
                              = L B(y )cos (2ϕ 0 )I ⎢ 2h   ˆ
        dΩdz1dz 2d 2qT                              ⎣                         M1M 2 ⎥
                                                                                    ⎦

                                                                     Net anti-alignment of
                         1
                        cm
      B(y ) = y(1 − y ) = sin 2 Θ                                    transverse quark spins
                         4

    May 24th                    Measurement of Collins Asymmetries at Belle                12
             Hadronic Events observed with Belle
                1.5 x 109 hadronic events in analysis




                                           v
                                          ∑ ˆ
                                           pi ⋅ n
           On resonance: 547fb-1 ,i =√s=10.52 GeV (published)
           ~1             thrust =
                                     particles
                                             v       ~ 0.5
           Off resonance: 29fb -1 , √s=10.58 GeV (preliminary)
                                      ∑ pi i

May 24th               Measurement of Collins Asymmetries at Belle   13
                   Gluon Emission



               dN           ⎡ qT 2
                                                                        ⎤
                         ∝ ∑⎢ 2      sin θ cos(2φ0 ) D1 ( z1 )D1 ( z 2 )⎥
                                        2

           dΩdz1dz 2 dqT    ⎣ Q + QT
                                   2
                                                                        ⎦




                         e-         QT
                                               e+
                                                               Frame:
                                                               v      v
                 z2                                 z1         p1 = − p2




May 24th                  Measurement of Collins Asymmetries at Belle       14
             Examples of Fits to Azimuthal Asymmetries




            N(φ)/N0




                                      2φ0                              (φ1+φ2)



D1 : spin averaged fragmentation function,
H1: Collins fragmentation function


 May 24th                Measurement of Collins Asymmetries at Belle        15
            Method to eliminate gluon contributions:
           Double ratios for unlike- and like sign pions
 Double ratio method:




                           ⎡   e 2 ( H Fav ⋅ H + H Unf ⋅ H ) ⎤
                sin (θ ) ⎢ ∑q
                                              Fav          Unf
                    2
           F~                                                  ⎥ cos(φ )
              1 + cos (θ ) ⎢ ∑ e 2 ( D Fav ⋅ D + DUnf ⋅ D ) ⎥
                     2                        Fav         Unf         0

                           ⎣ q                                 ⎦

                                         A0(z1,z2)
May 24th                Measurement of Collins Asymmetries at Belle        16
                                Two Double Ratios
Double ratios unlike/like-sign not very sensitive in separating favored and
disfavored Collins functions     look at unlike-sign/charge-sum
•   Unlike-sign pion pairs (U):
          (favored x favored + unfavored x unfavored)
•   Like-sign pion pairs (L):
          (favored x unfavored + unfavored x favored)
•    π±π0 pairs                                            UL
          (favored + unfavored) x (favored + unfavored)
•   A. Efremov et al. ([hep-ph/0603054]): charged ππ pairs are similar
    (and easier to handle) (C):
          (favored + unfavored) x (favored + unfavored)
                                                                               UC

    Observables:
                    A12(UL), A12(UC)                 published and input to
                    A0(UL) , A0(UC)                  fit by Anselmino et al.

    May 24th             Measurement of Collins Asymmetries at Belle           17
                      Final Charm Corrected Results for
                   e+ e- π π X (29fb-1, off-resonance Data)
                                                                        Phys.Rev.Lett.96:232002,2006

•   Significant non-zero
    asymmetries
•   Rising behavior vs. z
•   UL/C asymmetries about 40-
    50% of UL/L asymmetries
•   First direct measurements of
    the Collins function
•   UL/L data published


A0(UL/L)       (3.06 ± 0.57 ± 0.55)%
A12(UL/L)      (4.26 ± 0.68 ± 0.68)%
A0(UL/C)       (1.27 ± 0.49 ± 0.35)%
A12(UL/C)      (1.75 ± 0.59 ± 0.41)%


    May 24th              Measurement of Collins Asymmetries at Belle                   18
                   Preliminary Charm Corrected Results for
                    e+ e- π π X (547 fb-1 ,on-resonance)
•   Significance largely                                                 Preliminary
    increased
•   Behavior unchanged
•   Reduced systematics
•   Precise measurements of the
    Collins function




Integrated results:
A0(UL/L)      (2.67 ± 0.10 ± 0.26)%
A12(UL/L)     (3.55 ± 0.08 ± 0.15)%
A0(UL/C)        (1.11 ± 0.11 ± 0.22)%
A12(UL/C)       (1.46 ± 0.09 ± 0.13)%

     May 24th              Measurement of Collins Asymmetries at Belle       19
                             Summary and Outlook

               Summary:                                           Outlook:
•   Observation of large azimuthal             •   Future spin dependent FFs:
    asymmetries in light quark frag-                     update Collins FF
    mentation. Updated statistics:                       measure pT dependence
                                                         interference fragmentation
      ∫Ldt = 29 fb-1   547 fb-1
                                                         Collins FF for VMs
•   Double ratios reliably cancel                        Lambdas
    contributions from detector
    acceptance and gluon radiation.            •   Precision measurement of spin
                                                   averaged fragmentation func-
    important input for the                        tions as input to RHIC program
    transverse spin physics                        with inclusive hadrons and future
    programs at RHIC, HERMES,                      precision measurements in
    COMPASS and JLab                               SIDIS.



    May 24th              Measurement of Collins Asymmetries at Belle        20
Input also for precision
                Belle Impact on the Knowledge of FFs
measurements of quark
helicity distributions in
    Compilation of at
SIDIS, in particulardata              Belle: Charged h+/-, pions, kaons, protons
    available for electron-
a possible futurethe char-
    ged hadron collider.
polarized protonFF                   FF                                   h+,-
                                                         Belle MC
                                                                          pions
FF                                                                        kaons
                                                                          protons




                                             <1% of data sample
                                               work in progress
                                                                       precision
                                                                       at high z!


                      Eh                                                     Eh
                   z=                                                     z=
                      s /2                                                   s /2
     May 24th            Measurement of Collins Asymmetries at Belle          21
           What is Known Experimentally ?


                                            Hirai, Kumano,
                                            Nagai, Sudo
                                            hep-ph/0612009
                                            (including errors!)
                                                            Earlier work:
                                                            Kretzer
                                                            Binnewies, Potter, Albino
                                                            Kniehl, Kramer, Potter
                                                            Albino, Kniehl, Kramer




May 24th      Measurement of Collins Asymmetries at Belle                   22
                Motivation I ∆G from QCD Analysis of ALL
                for inclusive hadrons: π0,+,-, η, K+,-
PHENIX π0 cross section a |η|<0.35
                                                          Idea: QCD analysis of
 Phys.Rev.Lett.91:241803,2003                             LEP and Belle data will
                                                          fix uncertainty in know-
                                                          ledge of FFs (gluon FF,
                                                          flavor separation)




                                     Deviation connected to uncertainties
                                     in FFs   gluon FF!

   May 24th                  Measurement of Collins Asymmetries at Belle             23
             Why is the Collins Fragmentation
                   Function Interesting?
    o Very basic QCD process: Fundamental test
      case for any approach to solve QCD at soft scales.
    o Tests of universality and factorization between
      e+e-, DIS and p-p collisions
    o Symmetry properties
    o Evolution is fundamental QCD prediction
    o Connection between microscopic and
      macroscopic observables:

             Probe/analyzer for transverse quark spin
             critical input for transverse proton spin program
             at DESY, CERN, JLab and RHIC
May 24th          Measurement of Collins Asymmetries at Belle   24
May 24th   Measurement of Collins Asymmetries at Belle   25
                    KEKB: L>1.6 x 1034cm-2s-1 !!
                                                           1.5 x 109 hadronic events in analysis

•   KEKB                                           •Average Trigger rates:
     – Asymmetric collider                             Υ(4S) BB            11.5Hz
     – 8GeV e- + 3.5GeV e+                             q⎯q                 28 Hz
     – √s = 10.58GeV (Υ(4S))                           μμ + ττ             16 Hz
       e+e- Υ(4S) Β⎯Β                                    Bhabha                    4.4 Hz
     – Off-resonance: 10.52 GeV                          2γ                       35 Hz
       e+e- q⎯q (u,d,s,c)
     – Integrated Luminosity: > 600 fb-1
         > 60fb-1 => off-resonance



        KEKB                Belle detector




    May 24th                  Measurement of Collins Asymmetries at Belle               26
                        Good tracking and particle identification!

May 24th   Measurement of Collins Asymmetries at Belle      27
                 Belle is Well Suited for FF Measurements:


•   Good detector performance (acceptance, momentum resolution,
    pid)
•   Jet production from light quarks                                                  25




                                                              σ(e+e- → hadrons)(nb)
       off-resonance (60 MeV below resonance)
         (~10% of all data)
                                                                                      20




•   Intermediate Energy                                                               15



       Sufficiently high scale (Q2 ~ 110 GeV2)
          - can apply pQCD                                                            10




       Not too high energy (Q2 << MZ2)
          -avoids complication from Z interference
                                                                                      5




•    Sensitivity = A2sqrt(N) ~ x 25 (100) compared to LEP ϒ(2S) ϒ(3S)
                                                       ϒ(1S)                    ϒ(4S)
                                                                                      0
                                                                                      9.44 9.46   10.00 10.02   10.34   10.37   10.54    10.58   10.62


        ABelle / ALEP ~ x 2 (A scales as ln Q2)        e+e- Center-of-Mass Energy (GeV)

        ∫LBelle dt / ∫LLEP dt ~ x 46 (600)

     Total number of hadronic events ~ 1.5 x 109


    May 24th               Measurement of Collins Asymmetries at Belle                                                                  28
                      Applied Cuts, Binning
•   Originally off_resonance               •    Hemisphere cut
    data, now also                              (Ph 2 ⋅ n ) n ⋅ (Ph1 ⋅ n ) n < 0
                                                        ˆ ˆ            ˆ ˆ
    on_resonance data (29.1                •    QT < 3.5 GeV
    547 fb-1)
                                           •    Pion PID selection
•    Track selection:
     – pT > 0.1GeV
     – vertex cut:
        dr<2cm, |dz|<4cm                  z2
                                          1.0
•   Acceptance cut
     – -0.6 < cosθi < 0.9                              3         6         8         9


•   Event selection:                      0.7


     – Ntrack ≥ 3
                                                       2         5         7         8
                                          0.5
     – Thrust > 0.8                                    1         4         5         6

     – Z1, Z2>0.2                         0.3
                                                       0         1         2         3
                                          0.2

                                                 0.2       0.3       0.5       0.7       1.0   z1


    May 24th           Measurement of Collins Asymmetries at Belle                             29
                                  Experimental Issues

•   Cos2φ moments have two contributions:
     – Collins            Can be isolated either by subtraction or double ratio method
     – Radiative effects  Cancels exactly in subtraction method, and in LO of double
                                 ratios
•   Beam Polarization
    zero?                        cos(2φ) asymmetries for jets or γγ
•   False asymmetries
    from weak decays              Study effect in τ decays, constrain through D tagging
•   False asymmetries
    from misidentified
    hemispheres                   QT or polar angle cut
•   False asymmetries
    from acceptance              Cancels in double ratios, can be estimated in charge ratios,
                                  fiducial cuts
•   Decaying particles           lower z cut




    May 24th                 Measurement of Collins Asymmetries at Belle                  30
                Why is it Possible to Include Data on Resonance?
                           Different Thrust Distributions
                                                                                           25




                                                                   σ(e+e- → hadrons)(nb)
                                                                                           20


 e+ e-     qq̅, q∈uds
                                                                                           15




                                                                                           10




                         e+e- cc̅                                                          5




                                                                                                ϒ(1S)        ϒ(2S)     ϒ(3S)                 ϒ(4S)
  B+ B−                                                                                    0
                                                                                           9.44 9.46   10.00 10.02   10.34   10.37   10.54    10.58   10.62

                                                                                                e+e- Center-of-Mass                  Energy (GeV)
 B0 B0
                                              • small B contribution (<1%) in high thrust sample
                                              •>75% of X-section continuum under
                                                Υ (4S) resonance
                                              •29 fb-1    547 fb-1
              ∑ p ⋅ˆn    i
                                              •many systematic errors reduce with more
     thrust =    i                             statistics
               ∑p    i
                             i                • Charm-tagged Data sample also increases


May 24th                         Measurement of Collins Asymmetries at Belle                                                                 31
                     Collins Asymmetries I:
                       4x4 z1, z2 binning
   A0 (cos(2φ0)) moments                         A12 (cos(φ1 + φ2)) moments


                  PRELIMINAR                                      PRELIMINAR
                  Y                                               Y




             •   547 fb-1 charm corrected data sample,
             •   UL and UC double ratios
May 24th            Measurement of Collins Asymmetries at Belle         32
                    Collins Asymmetries II:
                sin2 θ/(1+cos2 θ) Binning (UL)

                                                  •   Nonzero quark
                 PRELIMINARY                          polarization ~ sin2 θ
                                                  •   Unpolarized de-
                                                      nominator ~ 1+cos2 θ
                                                  •   Clear linear behavior
                                                      seen when using either
                                                      thrustz or 2nd hadron as
      thrustz                                         polar angle
      θ2                                          •   Better agreement for
                                                      thrust axis (~approximate
                                                      quark axis)
                                                  •   UC plots similar




May 24th         Measurement of Collins Asymmetries at Belle          33
                          Collins Asymmetries III:
                              QT Binning (UL)

                     PRELIMINARY                       •   Reduced asymmetries in
                                                           low thrust sample
                                                       •   At low thrust significant
                                                           B contribution
                                                           (for t<0.8 ~20 % B
                                                            for t>0.8 < 1 % B)
                                                       •   A12 thrust axis
                                                           dependent
                                                       •   High QT (>3.5 GeV)
                                                           asymmetries from beam
                                                           related BG
                                                       •   UC plots similar

   Thrust>0.8
   Thrust<0.8 (not corrected for heavy
   quark contributions)
May 24th             Measurement of Collins Asymmetries at Belle           34
                Improved Systematic Errors (UC)
•   Tau contributions
•   PID systematics∗                                       A0 (cos(2φ0)) moments
•   MC double ratios
•   Charged ratios (π+π+ /π−π− )
•   Higher order terms
•   Double ratio-subtraction method

                                                           A12 (cos(φ1 + φ2)) moments
Reweighting asymmetries:
  underestimation of cos(φ1+φ2)
asymmetries rescaled by 1.21
Correlation studies:
  statistical errrors rescaled by 1.02 (UL)
and 0.55 (UC)
Beam polarization studies
  consistent with zero

    May 24th                Measurement of Collins Asymmetries at Belle         35
                 Collins Asymmetry                            Collins FF

 QCD analysis:
           (I) Efremov, Goeke, Schweitzer (Phys.Rev.D73:094025,2006):
               consistency between Belle, HERMES and COMPASS
               asymmetries.

           (II) Anselmino, Boglione, D’Alesio, Kotzinian, Murgia,
                Prokudin and Tuerk (hep-ph/0701006 ) extract transversity
                distributions and the Collins FF (see tomorrow).

           (III) UIUC fit to Belle data (work in progress):




May 24th              Measurement of Collins Asymmetries at Belle      36
            Spin Averaged FF + Collins Asymmetry

Kretzer FFs (also KKP)




Experimental double ratio:




 May 24th            Measurement of Collins Asymmetries at Belle   37
           Fits of the Belle Collins
                      Asymmetries A0 with∫Ldt = 29 fb-1




May 24th           Measurement of Collins Asymmetries at Belle   38
           Fits of the Belle Collins
                      Asymmetries A12 with∫Ldt = 29 fb-1




May 24th           Measurement of Collins Asymmetries at Belle   39
                      Results for the Collins FF

           A0                                                         A12

            H fav                                                  H fav
            D fav                                                  D fav


H  fav                                        H fav
D fav                                         D fav
                    H dis                                                   H dis
                    D dis                                                   D dis
            H fav
            D fav




                                   0<z<1
May 24th             Measurement of Collins Asymmetries at Belle                    40

				
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