the present and (near) future of di hadron f ragmentation f unctions ( diff )
DESCRIPTION
The present and (near) future of Di hadron F ragmentation F unctions ( DiFF ). Transverse momentum, spin, and position distributions of partons in hadrons. ECT* (Trento), 11-15 June 2007. Marco Radici. Pavia. In collaboration with: A. Bacchetta (DESY) - PowerPoint PPT PresentationTRANSCRIPT
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
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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