114-Jun-07

The present and (near) future of The present and (near) future of DiDihadron hadron FFragmentation ragmentation FFunctionsunctions

((DiFFDiFF))

Marco Radici Pavia

Transverse momentum, spin, and position distributions of partonsin hadrons

ECT* (Trento), 11-15 June 2007

In collaboration with: A. Bacchetta (DESY) F. A. Ceccopieri (Univ. Parma)

214-Jun-07

Outline

- History: why DiFFDiFF ?

314-Jun-07

A

ah1

h2 h1 h2

a b

O(s0) A B

O(s) A A+B

de Florian & Vanni, P.L. B578 (04) 139

Konishi, Ukawa, VenezianoP.L. B78 (78) 243

B

Ak

l

i

rT

1/rT collinear singularities cancelled by D(i h1h2)

DiFFDiFF evolution equationstime-like analogue of Fracture Functions in SIDIS

Trentadue & Veneziano,P.L. B323 (94) 201

B A

Need DiFFDiFF in e+e- h1h2 X

b

B

see also de Majumder & Wang, P.R. D70 (04) 014007; D72 (05) 034007

414-Jun-07

Exp. info mostly on nontrivial spectrum in pair invariant mass Mh

ep ! e’ (+-) X √s=7.5 GeV PYTHIA output at HERMES kin.Q2 >1 GeV2 W2 >4 GeV2 no elastic and diffractive events

Mh(GeV)

e+e- +- √s=91.2 GeV z>0.1Abreu et al. (DELPHI), P.L. B298 (93) 236background subtracted

pp +- X √s=200 GeVAdams et al. (STAR), P.R.L. 92 (04) 092301

514-Jun-07

Ph

Subleading-twistBacchetta & Radici, P.R. D69 (04) 074026

Bianconi et al., P.R. D62 (00) 034008

Leading-twist analysis: full dependence of DiFFDiFF

+

T

Ph=P1+P2

R=(P1-P2)/2

Radici et al., P.R. D65 (02) 074031Bacchetta & RadiciP.R. D74 (06) 114007

\newcommand{\open}{< \kern -0.3 em \scriptscriptstyle{)}}

614-Jun-07

Outline

- History: why DiFFDiFF ?

- SIDIS: extract transversity with leading twist SSA via DiFF DiFF (HERMES, COMPASS)

714-Jun-07

SIDIS e p" ! e’ (h1h2) X

RT

partial wave (LM)

1 2LM

scattering plane

814-Jun-07

Partial wave expansion

c.m. frame

|()L=0ih()L=1|naïve T-odd from interference

SSA

Bacchetta & Radici, P.R. D67 (03) 094002

Collins et al., N.P. B420 (94) 565

914-Jun-07

Outline

- History: why DiFFDiFF ?

- SIDIS: extract transversity with leading twist SSA via DiFF DiFF (HERMES, COMPASS)

- e+e- : determine unknown DiFFDiFF (BELLE)

1014-Jun-07

DiFFDiFF from e+e- ! (+ -)jet 1 (+ -)jet 2 X

[ (Ph,R) (Ph,k) ]= R - l

Boer, Jakob, Radici, P.R. D67 (03) 094003

Leading-twist d very complicated; take

1114-Jun-07

“Artru-Collins” azimuthal asymmetry

same as in SIDIS

Artru & Collins, Z.P. C69 (96) 277

Boer, Jakob, Radici, P.R. D67 (03) 094003

1214-Jun-07

Outline

- History: why DiFFDiFF ?

- SIDIS: extract transversity with leading twist SSA via DiFF DiFF (HERMES, COMPASS)

- e+e- : determine unknown DiFFDiFF (BELLE)

1314-Jun-07

Jaffe, Jin, Tang, P.R.L. 80 (98) 1166

History of SSA: sign change at Mh=m?

• no calculation of qI (z) → SSA f(0,1) “figure of merit”• s-p interference from - elastic scattering phase shifts only; sign change from Re[]

Radici, Jakob, Bianconi, P.R. D65 (02) 074031

interference ~ Im[s p*]spectator model includingfull (z,Mh

2~m2) dependence

uncertainty band from •different fp / fs strength ratio• PDF input for h1(x)

Let’s apply Trento conventions

p s

Bacchetta et al., P.R. D70 (04) 117504

1414-Jun-07

(following Trento conventions)

( Hermes analysis: no dcos Van der Nat Transversity 2005 (Como – Italy) hep-ex/0512019

SSA : history of conventions

Bacchetta and Radici, P.R. D67 (03) 094002

(before Trento conventions) Radici, Jakob, Bianconi P.R. D65 (02) 074031

1514-Jun-07

ep" ! e’ (+-) X

PYTHIA output on HERMESkinematics:0.1<y<0.85 Q2 > 1 GeV2

0.023<x<0.4 W2>4 GeV2

excludes elastic and single/double diffractive events → semi-inclusive DIS

2. q → X2 → +- X2 (14.81%)

3. q → X3 → +- X3 (0.31%)

4. q → X’4 → +- (0 X’4) (8.65%)

5. q → η X’5 → π+π- (X X5) (2.05%)6. q → K0 X6 → π+π- X6 (3.41%)

1. All – (2+..+6) = background (70.77%)

395 114 events

239 043 events

1 888 065 events

Total2 667 889

(π+π-) pairs

Mh

History of SSA continues: upgrading the spectator model

1614-Jun-07

The spectator model :

2. q → ρ X2 → π+π- X2

3. q → ω X3 → π+π- X3

4. q → ω X’4 → π+π- (π0 X’4)

X1 = X2 = X3 = X4 = X p-wave channel = coherent sum |2.+3.+4.|

Warning: ω → [(π π)L=1 π]J=1

1. background ≡ q → π+π- X1 no resonance → real s-wave channel

max number of (π+π-) pairs in s-p interference ~ Im [ p-wave channel ]

s-wave

p-wave

parameters

X4

Bacchetta and Radici, P.R. D74 (06) 114007

narrow-width approx. M3~m (m–m – Mh)

1714-Jun-07

Fit PYTHIA distributions in z and Mh fix parameters

Mh

z

2.+3.+4. p-wave1. background s-waveTotalTotal + 5.+6.

PYTHIA: statistical error 1% no - interference at Mh~0.652 / dof ~ 20but model stat. error also 1% (~1/√#bin)

1814-Jun-07

6.6% scale uncertainty

z xMh

Model parameters fixed prediction of SSA @

Bacchetta and Radici, P.R. D74 (06) 114007

1914-Jun-07

u

d

from GRV98-LO @ Q2 = 2.5 GeV2

x

Strat KorSoffer et al., Korotkov et al., P.R. D65 (02) 114024 E.P.J. C18 (01) 639

Schw WakSchweitzer et al. WakamatsuP.R. D64 (01) 034013 P.L. B509 (01) 59

Theoretical uncertainty on SSA mostly from transversity input

Mh

2014-Jun-07

Flavor symmetry of model DiFFDiFF

2114-Jun-07

Strat Soffer et al., P.R. D65 (02) 114024

Wak WakamatsuP.L. B509 (01) 59

ω → (π+π-) π0

ρ → π+π-

bins 0.15 0.15 0.22 1.23

Future improvements upon the spectator model

data

model prediction

“bin” the model and fit the exp. data

Mh

3 beyond narrow-width approx. cure dip at Mh ~ 0.65 GeV

2214-Jun-07

Q2>1 GeV2 s=604 GeV2

Martin – SPIN Praha 2006hep-ex/0702002

0.004<x<0.4

isospin symmetry in d={p,n}

Prediction of SSA @ : deuteron target

0.03<x<0.4

Mh

Mh

but no Trento conventions!

x z

Mh

2314-Jun-07

0.1<y<0.9 Q2>1 GeV2 s=301 GeV2

Mh

…..

Mh

0.004<x<0.4

0.03<x<0.4

Prediction of SSA @ : proton target

2414-Jun-07

Outline

- History: why DiFFDiFF ?

- SIDIS: extract transversity with leading twist SSA via DiFF DiFF (HERMES, COMPASS)

- e+e- : determine unknown DiFFDiFF (BELLE)evolution

2514-Jun-07

h1 h2 de Florian & Vanni, P.L. B578 (04) 139

B

A

k

l

i

rT

DiFFDiFF D(z1,z2,Q2) evolution equations

which evolution equations for extended DiFF (extDiFF)extended DiFF (extDiFF) D(z1,z2,Mh

2,Q2)?

B A

1. recover DiFFDiFF evolution with Jet Calculus technique2. deduce extDiFFextDiFF evolution “ “ “ “ “ LL

2614-Jun-07

single-hadron fragmentation in Jet Calculus

LL branching strong ordering i j+kqj

2, qk2 << qi

2 <<1

no interf.

ladder diagram

Eij time-like perturbative parton

fragmentation function

h

calculable unknown

Konishi, Ukawa, VenezianoN.P. B157 (79) 45

i ji j i j

i

Q2 Q0

2

j

Eij

[at LL, resums all collinear sn logn(Q2/Q0

2) ]

scale

Eij

2714-Jun-07

Eia1,a2

hardprocess

2-h fragmentation in Jet Calculus

A :h1

h2

h1

h2

i j

+ B :

multi-ladder diagram

Eij Eb1

a1

Eb2a2

Q2 S2 Q0

2

Eij

2814-Jun-07

introducing the scale RT Mh h1

h2

rT

h1

h2

RT

fixing RT2 scale kj

2 S2 no longer arbitrary

B: RT

A:i j

scale kj2 arbitrary set to Q0

2

1. take Q02 RT

2 < Q2

u

1-u

2. take RT2 Q0

2

Q2 S2 Q0

2

2914-Jun-07

RT2 breaks degeneracy of terms A-B homogeneous evolution

conjecture: at LL, factorization with same kernel as 1h-fragmentation

Ceccopieri, Radici, Bacchetta, P.L. B650 (07) 81

evolution equations for extDiFFextDiFF

same for polarized extDiFFpolarized extDiFFwith Pij

3014-Jun-07

effect of evolution on extDiFFextDiFF

2. partial-wave expansion “commutes” with evolution

i jh1

h2

1. evolution affects “perturbative sector” z, but not the “soft”

3114-Jun-07

effect of evolution on extDiFFextDiFF

Q02 = 2.5 GeV2 HERMES

Q2 = 100 GeV2 BELLE

D1ss+pp

z

D1ss+pp

Mh

PRELIMINARY !

3214-Jun-07

Outline

- History: why DiFFDiFF ?

- SIDIS: extract transversity with leading twist SSA via DiFF DiFF (HERMES, COMPASS)

- e+e- : determine unknown DiFFDiFF (BELLE)evolution

- pp collision: determine all the unknowns with two measurements self extraction of transversity

3314-Jun-07

A + B(" ) ! (C1C2)C + X

ab(" ) ! c(" ) d

pa = xa PA

pb = xb PB

pc = PC / zc

PC=PC1+PC2 k jet axis PCT=0 but

PC¢PA / PC? large PC? hard scaleanalysis at leading twist o(1/|PC?|)

N.B. Sb around PB defined as SB

Sc around PC defined as RC

Sc = Sb

3414-Jun-07

A B(" ) ! (C1 C2)C X Bacchetta, Radici, P.R. D90 (04) 094032

3514-Jun-07

A B ! (C1 C2)C (D1 D2)D X

self-consistent extraction of

Bacchetta, Radici, P.R. D90 (04) 094032