1

Transversity and Transversity and inclusive 2-pion inclusive 2-pion

productionproduction

Marco Radici Pavia

TJNAF, 18-20 May 2005

In collaboration with: A. Bacchetta (Univ. Regensburg)

2

how to extract transversity (at leading twist) ?

double polarized DY (Ralston-Soper ’79) : p" p" ! l+ l- X

no inclusive DIS !

initial state ! polarized Drell-Yan

chiral-odd partner in

final state ! semi-inclusive (SIR)

only transversity involved, no other unknowns, but

ATT small (NLO) by Soffer inequality (Martin, Schaefer, Stratmann, Vogelsang ’98

Barone, Calarco, Drago, ‘97)

presumably h1 for antiquarks in p is small ! use antiprotons: HESR@GSI doable with s=200 GeV2 (A. Bianconi and M.R., P.R. D71 (2005) 074014

and hep-ph/0504261 )

MonteCarlo simulation

3

production : e p" ! " X , p p" ! " X (E704,RHIC)

which mechanism ?!

? polarization of quark ! intuitively search for ? polarized final hadrons

Double Spin Asymmetry (DSA)

HESR@GSI can help in selecting models

SIR

{pq, q, kq} not all collinear

transfer q" to orbital motion of h ! Collins effect

asymmetry insin / k £ Ph ¢ ST

chiral-odd Collins function H1? :

extract it at e+e- facilities (Belle@RHIC)

4

Technical slide ! SIDIS : e p" ! e’ h X

Collins effect

leading twist:

S 0,

convolution

keep d enoughdifferential

(C = h+ S) to break the convolution […]

Single Spin Asymmetry needs

(Boer & Mulders ’98)

5

Superposition of effects : take reaction

observe ? momenta

in final state

explain SSA data with Collins effect

in initial state Sivers effect

third possibility :

in initial state Boer ‘99

generalized factorization schemeproof for Drell-Yan and low-pT SIDIS (Ji, Ma, Yuan, P.L. B597 (’04) 299 )universality still under debate ; evolution ?

search for effects ! SSA , but surviving sdkT

6

Collins effect

2 hadron semi-inclusive processe p" ! e’ (1 2) X p p" ! (12) X ..

! asymmetry in the azimuthal orientation of pair plane with respect to some reference plane survives sdkT

suggested for the first time by Collins, Heppelmann & Ladinski, 1994 but no twist analysis nor quantitative calculations (see also Ji 1994) then Jaffe, Jin, Tang 1998 ! suggestion of SSA from interference of () partial wavesand Bianconi, Boffi, Jakob, M.R., 2000 ! complete twist-2 analysis and first model calculation

7

Interference Fragmentation Functions for q ! (h1,h2) X with unpolarized h1,h2

hadronic tensor

Ph=P1+P2

R=(P1-P2)/2

functions of ( z, =z1/z1+z

2 , Mh

2, kT2, kT¢RT ) ! ( z, , Mh

2 )

( twist-2 Bianconi, Boffi, Jakob, M.R., 2000 ; twist-3 Bacchetta, M.R., 2004)

8

RT

e p" ! e’ (h1h2) X

leading-twist dleading-twist d

- no specific weight for

- easier factorization proof ; universality

- no admixture with other effects

unknown but …

most general !

- RT soft scale: evolution ? (e+e-, pp)

(L,M)

9

or extracted self consistently also from p-p collisions (Bacchetta, M.R. 2004 )

p p" ! () X

p p ! ()C ()D X

contains also

same as for gluons

available for spin ½ hadronotherwise chiral-odd g for spin ¸ 1

? from e+e- ! ()jet 1 ()jet 2 X (Artru, Collins ‘96; Boer, Jakob, M.R. ‘03)(e+e-)

(back)

10

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

leading twist

(Boer, Jakob, Radici, ’03)

“Artru-Collins” azimuthal asymmetry

same as in SIDIS

(back)

11

(Jaffe, Jin, Tang, ’98)

X |,Xih,X| ~ |()L=0ih()L=1| + |()L=1ih()L=0|

FSI from interference of () @ L=0 and () @ L=1

fragmentation in helicity basis collinear ep" ! e’ (+-) X

not general (z,Mh2) dependence !

IFF(z, (cos),Mh2) = n IFFn (z,Mh

2) Pn (cos)

2h c.m. frame

|RT| = |R|(M1,M2,Mh) sin

= a(M1,M2,Mh) + b(M1,M2,Mh) cos

12

n … Pn (cos)

(A. Bacchetta and M.R., 2003)

s-p interference

(Jaffe) (models)

(new model)

(AUT results)

13

ep" ! e’ (+-) X at leading twist

(Jaffe, Jin, Tang, 1998)

• no calculation of qI (z)• , stable particles• interference from - phase shifts only

(Radici, Jakob, Bianconi, 2002)

uncertainty band from:• different fp / fs strength ratio• f1(x), h1(x) from spectator model• f1(x), h1(x)=g1(x) from GRV98 & GRSV96

• f1(x), h1(x) = (f1+g1)/2 from “ “

spectator model

spectator model

Trento conventions ! reverse sign!

14

New model calculation (A. Bacchetta and M.R., in preparation)

spectator model in :

off-shell spectator :

p wave: incoherent sum of

resonant 0 ! +-

and

s d0 [ ! + - 0 ]

partial-wave analysis

s wave: incoherent sum of direct production

and K0S ! +-(sdcos d)

PRELIMIN

ARY

HERMES guess on

[M(+-)] corrected for acceptance

15

Breit-Wigner m, , m, mK0 , K0 from PDG

form factor

fit parameters

+ h.c.

+ same for K0

S

16

spectator model ! flavor symmetry

´

17

fit [GeV]

PRELIMIN

ARY

(def. of AUT)

removes all elastic, single and double diffractive events! only semi-inclusive

18

PRELIMINARY

f1, h1 from spectator model

f1, h1=g1 from GRV98 & GRSV96

19

Conclusions

• interpretation of upcoming HERMES 2 semi-inclusive data in terms of collinear fragmentation via IFF seems reasonable and feasible; work in progress…

• extraction of transversity via IFF more convenient with respect to Collins effect

• HESR@GSI will probably offer anther tool: collinear fully polarized Drell-Yan with antiprotons

Transverse spin physics without transverse momentais a real option

Transverse spin physics without transverse momentais a real option