how to do quark spin without spin
TRANSCRIPT
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 !
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)
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)