physics workshopThe second

Frascati, 18-19 March 2004

How to do quark spin How to do quark spin without spinwithout spin

Marco Radici

Pavia

Why spin physics with unpolarized (anti)proton beams ?

⇒ spin structure of hadrons is far more rich than predictions of QCD in chiral symmetric phase, based on quark helicities

( unexplained Single Spin Asymmetries (SSA) of 10 ÷ 50 %like p p→ Λ↑⇓ X or p p↑ → π X ⇒ N (transverse) spin

structure not understood )

⇒ relation between ⊥ polarization and orbital angular motion of quarksimportance of pT distribution of quarks

intrinsic nonperturbative origin, not generated perturbatively by DGLAP equations

it is possible because of “T-odd” distribution / fragmentation functionsresidual interactions (“FSI”) inside hadrons / jets

SSA = 0 for pp↑ → π X for years because of T reversal !

study spin structure using unpolarized hadrons

We need transverse spin distribution (transversity) :

it completes the parton structure of N at leading twist

DDistribution FFunction in quark-N helicity basis (Jaffe)

struct. functionanalogue in Parton Model

F1 g1 ?

suppressed in inclusive DIS ⇐ helicity flip

for years h1 considered an higher-order effect !

Properties of transversity (report Barone, Drago & Ratcliffe ’02)

• helicity = chirality at leading twist ⇒ helicity flip ⇔ chiral-odd

|⊥ / T〉~ |+〉 ± |-〉 dσ⊥ – dσT ∝ 〈+|…|-〉+ 〈-|…|+〉dσ⊥ / T ∝ 〈⊥ / T| … |⊥ / T〉

chiral-odd nature is a quantum mechanical effect related to soft physics and (maybe) to dynamical breaking of chiral symmetry

• h1(x,Q2) = g1(x,Q2) in nonrelativistic theory because [boost , rotation] = 0

difference ⇒ info on relativistic dynamics of quarks in hadrons

• no δg ⇒ no mixing with gluons in evolution contrary to helicity g1

⇒ non-singlet evolution of δq = h1

cont’ed• axial charge (1st moment of g1) does not depend on scale Q2

• tensor charge (1st moment of h1) hasanomalous dimension γ ≠ 0

better place to test evolution

• tensor charge is C-odd ⇒ does not couple to quark-antiquark, gluons,singlet DF ⇒ more valence quark-like content of h1 ? Place to test CQM ?

• inequalities: |h1(x)| ≤ f1(x) (positivity) ; |2h1(x)| ≤ f1(x) + g1(x) (Soffer)

• from lattice: Σf h1f = 0.562 ± 0.088 (Aoki et al.) but QCDSF : g1 ∼ h1

(Schierholz et al.)• several (model) calculations

How to extract transversity ?

search for chiral-odd partner of h1 constraint: leading twist process

initial state polarized Drell-Yan (DY) :

final state

DIS :

semi-inclusive

annihilation :

semi-inclusive process ⊥ polarization of quark intuitively search for ⊥ polarized final hadrons

e p↑ → e’ Λ⇓ Xsemi-inclusive Λ production : p p↑ → Λ⇓ X

E704RHIC

Double Spin Asymmetry (DSA)

depolarization (spin transfer coefficient)

ASSIA can help in selectingmodels: DeGrand & Miettinen ’81

Andersson et al. ’79Dharmaratna & Goldstein ’90Anselmino et al. ’91....which mechanism ?!

in seminclusive DIS {pq, qγ, kq} not all collinear

⇒ transfer q↑ not to h↑ final hadron (DSADSA), but to orbital motion of h⇒ SSA SSA with intrinsic Ph⊥ dependence not integrated ⇒ Collins effect

asymmetry insin φ ∝ k × Ph ·ST

chiral-odd Collins function H1⊥ (z, kT) :

experimental evidence in several exps: SMC, E704, TJNAF (Hall B), HERMES → next talk

semi-classical picture : ⊥ polarized fragmenting quark ⇒ orbital angular momentum in string breaking and

creation of qq pair⇒ left / right asymmetry of produced hadron

(Artru , hep-ph/9310323)

Technical slide ! DIS : ep↑ → e’hX

Collins effect

leading twist:

φS ≠ 0,π

keep dσ enoughdifferential

convolution

(φC = φh+φS) does not break the convolution F […] (need model pT / kT dep.)

need (Boer & Mulders ’98)

SSA SSA

(for pp↑ → πX SSA ∼ f1 h1 H1⊥ (1) )

Problems• need to store Ph⊥ bin by bin

• beyond tree level, because of Ph⊥ dep., soft gluon contributions do notcancel → resum them in Sudakov form factors, that largely dilute the SSA for |Ph⊥ | � Q2 (Boer ’02) seen at small (unfavoured) SSA at HERMES ?

• evolution of h1 and H1⊥ (gluonic poles)? No factorization theorem yet

→ affect evolution of SSA (Boer, Mulders, Pijlman ’03)

H1⊥ from e+e- → π+π- X

seen at DELPHI ; possibly at BELLEbut • again Sudakov suppression beyond tree level

• asymmetric background from hard gluon radiation and weak decays

Collins function H1⊥ in ep↑ → e’h X or in pp↑ → h X

but Collins effect <s⊥ ·k × Ph> = <sin φC> =0 if no “FSI” h-X

T-reversal does not put constraints on H1⊥

H1⊥ is the prototype of IInterference FFragmentation FFunctions (IFF)

⇒ model H1⊥ requires modelling FSI of h inside jet

(Bacchetta et al. ’01 & ‘02)

|i >, |f > initial, final states of the system with quantum # i,f ; Tif trans. matrix

naive T-reversal transformation : T-i-fT-reversal → |Tif |2 = |T-f-i |2

no FSI ⇒ |i> ↔ |f > ; A = 0 T-reversal = naive T-reversal

A = |Tif |2 - |T-i-f |2

FSI ⇒ |i> ≠ |f > ; T-reversal OK

but A ≠ 0 ∝ ℑm [ Born × rescatt.* ]

naïve T-odd ≡ T-odd (but no violation of fundamental laws of nature!)

DIS ep↑ → e’h X ; cross section at leading twist contains also

Sivers effect → SSA seen (but small) at HERMES

Sivers function is chiral-even but T-odd ! possible interpretation of SSA ∼ f1 f1T

⊥ D1 in pp↑ → π X as Initial State Interaction (“ISI”) (Anselmino et al. ’03 ; Collins ’02)

(see also Brodsky et al. ‘02Qiu & Sterman “gluonic pole”Efremov & Teryaev ….)

GPD picture : ⊥ polarized proton⇒ quark u(d) shifted down(up) ⇒ orbital angular momentum

described with GPD E → κp⇒ left / right asymmetry(Burkardt , hep-ph/0209117)

Break for a summary : take reaction

explain asymmetry in data withobserve ⊥ momenta

Collins effectin final state

Sivers effectin initial state

third possibility :

Boer ‘99in initial state

h1 for antiquarks is presumably small → use antiprotons!

H1⊥ , f1T

⊥ T-odd, not forbidden. Why ? Technical reason

hadronic bilocal matrix element → distribution function

but color-gauge invariant definition requires

“tower” operatordominant p+

“FSI” quark-hadron ⇒ T-odd(Pijlman, Boer, Mulders ’03)

light-cone gauge

N.B.

DIS ep↑ → e’h X

3 sources of SSA ; if φS = 0 → disentangle Collins from Sivers ?moreover breaking of collinear factorization → Sudakov dilution of SSA

⇒ SSASSA with two unpolarized hadrons inside the same jet

asymmetry in sin φ ∝ P1×P2 ·ST = Ph × R ·ST

Ph = P1+P2R = P1 – P2

(Collins et al. ’94thenJaffe, Jin, Tang ’98systematic analysisBianconi, Boffi, Jakoband M.R. ’00)

→ collinear factorization → no dilution of SSA→ Sivers effect “washed away”still a SSA survives in φ ≡ φR

bilocal hadronic matrix element → leading-twist projections → IFF

functions of z, ξ=P1-/P

h-, kT

2, RT2,

kT ·RT

e p↑ → e’ (h1 h2) X

(M.R., Jakob, Bianconi, ’02)

chiral-odd and T-oddagain, no FSI → 〈sin φR 〉= 0 → SSA = 0

Example: ep↑ → e’(ππ) X “FSI” from interference L=0 ↔ L=1 (≡ ρ) channelsL=1 ↔ L=1 channels

analysis extended to twist 3 (Bacchetta and M.R. ’04) (Bacchetta and M.R. ’03)

at TJNAF

πN data at t =2mπ2 → σπN = (50÷ 70) MeV →

but lattice calculations ⇒ σπN ∼ (20 – 50) MeV !

0

20

40

60

80

100

0 2 4 6 8 10 12

no factorization proof available yet, but check universality of IFF at twist 2

from e+e- → (π π)jet 1 (π π)jet 2 X (Artru & Collins ’96)

• collinear factorization → no Sudakov suppression• possibility at BELLE ; no asymmetric background from hard g expected

(Boer, Jakob, M.R., ’03)azimuthal asymmetry at leading twist

same as in SIDIS

Another azimuthal asymmetry with longitudinally polarized fragmenting quark

with

dσ ∝ { … F [ g1 G1⊥ ] … }

AG ∼ G1⊥ G1

⊥

jet handedness correlation

pQCD → C<0data → C>0 ! ≷ 0

deviation from data related to CP-violating effects of QCD vacuum?

(Efremov & Kharzeev, ’96)

search for transversity in double polarized DY : p↑p↑ → l+l - X(historically the 1st: Ralston & Soper ’79)

Collins-Soper frame: qT(γ*) in (xz) plane

ATT small (NLO) by Soffer inequality (Martin, Schaefer, Stratmann, Vogelsang ‘99)

presumably h1 for antiquarks in p is small → use antiprotons!

single polarized DY : pp↑ → l+l - X (Boer ’99)

SSA to test Siversfunction from SSA to test

transversity againstbut need h1

⊥ from or

unpolarized DY :

NA10 results for πA → µ+µ- X parametrized as

Leading twist 2 units of Lz → cos 2φ

pQCD → λ ∼ 1 ; µ ∼ ν ∼ 0higher twistsfactorization breaking do not work!

(q-Dq model: Boer, Brodsky, Hwang ’03)

2(1-x1) A(x2,pT)

A(x2,pT)

2x1 A(x2,pT)

480.000 events

Bianconi (for the ASSIA coll.)

Bianconi (for the ASSIA coll

Advertising….

Fragmentation functions Database (Jakob,Radici)

http://www.pv.infn.it/~radici/FFdatabase

(linked from CTEQ and Durham web pages)

topical workshop:

Transversity: new develompments in nucleon spin structure

ECT*, Trento (Italy), June 14-18 2004

E. De SanctisW.D. NowakM.R.G. Van der Steenhoven (chair)