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Strangeness and Spin in Fundamental Physics
Mauro Anselmino: The transverse spin structure of the nucleon Delia Hasch: The transverse spin structure of the nucleon – exp.Elliot Leader: The longitudinal spin structure of the nucleonWerner Vogelsang: QCD spin physics in hadronic interactionsNaohito Saito: Spin Physics at RHIC - experiment Raimondo Bertini: Spin physics with strangeness
Spin lectures
Spin seminars Robert Jaffe: Gluon spin basics
Harut Avakian: Spin Physics at JLabMariaelena Boglione: The first way to transversity
Varenna, June 19-29, 2007
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–
Parton transverse motion, spin-k┴
correlation, orbiting? )()()( xqxqxqT
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frame c.m. * sin p)Φ(ΦPA SπTT PpS
Transverse single spin asymmetries in SIDIS, experimentally observed (D. Hasch)
z
y
xΦSΦπ
X
p
S
PT
in collinear configurations there cannot be (at LO) any PT
Xhp *
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Mauro Anselmino: The transverse spin structure of the nucleon - II
About partonic intrinsic motion and SSA
Estimate of transverse motion of quarks
TMDs: spin-intrinsic motion correlations in distribution and fragmentation functions
Sivers and Collins functions; SSA in SIDIS
Coupling Collins function and Transversity
What do we learn from Sivers functions?
The full structure of TMDs in SIDIS
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p p
Q2 = M2
qT
qL
l+
l–*
Plenty of theoretical and experimental evidence for transverse motion of partons within nucleons and
of hadrons within fragmentation jets
GeV/c 0.2 fm 1 pxuncertainty principle
gluon radiation
±1
± ±k┴
Partonic intrinsic motion
qT distribution of lepton
pairs in D-Y processes
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Hadron distribution in jets in e+e– processes
pT distribution
of hadrons in SIDIShXp *
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Parton Model with intrinsic motion
Assume: struck parton carries 4-momentum k
k
P
k’
02 k
) ,0 ,0 ,( 00 PPP
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);,();,(ˆd);,(d 222 QzDQyQxf hq
lqlq
q qlhXlp
pkk
factorization holds at large Q2, and
QCDT kP Ji, Ma, Yuan
zqP
PPz h
h
pkP zT
observables at
:
Q
kO
SIDIS in parton model with intrinsic k┴
xxB
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Elementary Mandelstam variables:
The on shell condition for the final quark
implies
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cos1
21)(ˆ 2 y
Q
ksxkls
cos
1
21)1( )(ˆ 2
yQ
kysxklu
22)(ˆ Qllt
neglecting terms one has
hB zzxx
cos1)2(4)1(1ˆˆˆ 2
2
422 yy
Q
ky
y
Qusd lqlq
“Cahn effect”
hh
lhXlp
ΦBAΦ
cosd
d
pkP zT
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assuming:
one finds:
with
clear dependence on (assumed to be constant)and
Find best values by fitting data on Φh and PT dependences
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EMC data, µp and µd, E between 100 and 280 GeV
M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin, C. Türk
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Large PT data explained by
NLO QCD corrections
EMC data
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How does intrinsic motion help with SSA?One can introduce spin-k┴ correlation in the Parton Distribution Functions (PDFs) and in the parton Fragmentation Functions (FFs)
X
pS
k
Only possible (scalar) correlation is
)( kpS
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)ˆˆ( ),(),(
)ˆˆ( ),(2
1),(),(
1/
//,/
kpS
kpSkS
kxfM
kkxf
kxfkxfxf
qTpq
pq
Npqpq
TMDs: Sivers function
Boer-Mulders function
)ˆˆ( ),(2
1),(
2
1
)ˆˆ( ),(2
1),(
2
1),(
1/
///,
kps
kpsks
pq
qpq
Npqpq
kxhM
kkxf
kxfkxfxfq
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)ˆˆ( ),(
),(
)ˆˆ( ),(2
1 ),(),(
1/
//,/
pps
ppsps
qqq
hqh
qqqh
Nqhqh
pzHMz
ppzD
pzDpzDzDq
Collins function
)ˆˆ( ),(
),(2
1
)ˆˆ( ),(2
1 ),(
2
1),(
1/
///,
ppS
ppSpS
Tqh
Nqhq
pzDMz
ppzD
pzDpzDzD
Polarizing fragmentation function
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Sivers effect in SIDIS
)ˆˆ( ),(2
1),(),(
/// ,
kpSk kxfkxfxfpq
Npqpq
),(),(ˆ),(,/
,
pkk zDydxfd hqq pq
),(),(ˆd)ˆˆ(),(/
pkkpS zDykxf
ddhqq pq
N
)sin( S
qTpq
N fM
kf
1/
2
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q
hq
lqlq
pqSh
Shhq
lqlq
Spq
N
q Sh
Sh
ShShΦΦUT
pzDdQ
dkxfddΦdΦ
ΦΦpzDdQ
dΦkxfddΦdΦ
dddΦdΦ
ΦΦdddΦdΦA Sh
),(ˆ
),(
)sin( ),(ˆ
)sin( ),(
][
)sin(] [ 2
2/2
2/
2
)sin(
k
k
)ˆˆ( ),(2
1
),(),(
/
//
kpS
k
kxf
kxfxf
pq
N
pqpq
kPp zT
qTpq
N fM
kf
1/
2
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Brodsky, Hwang, Schmidt model for Sivers function
X
p
S
)sin( ST TPPpS
+ –
q q
diquark
diquark
needs k┴ dependent quark distribution in p↑: Sivers function
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M.A., M. Boglione, U.D’Alesio, A.Kotzinian, F. Murgia, A Prokudin
Fit of HERMES data on)sin( S
UTA
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Deuteron target hd
hupd
N
pu
NUT DDffA Sh
4 //
)sin(
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First p┴ moments of extracted Sivers
functions, compared with models
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
data from HERMES and COMPASS
),( 4
/
2
)1(1
)1(
kxfm
kkd
ff
pq
N
p
qTq
N
hep-ph/0511017
?11d
Tu
T ff
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The first and 1/2-transverse moments of the Sivers quark distribution functions, defined in Eqs. (3, 9), as extracted in Refs. [20, 21, 23]. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The curves indicate the 1-σ regions
of the various parameterizations.
),( )( 12)2/1(
1
kxf
M
kdxf q
Tq
T k
M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan
),( 2
12
22)1(
1
kxf
M
kdf q
Tq
T k
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Spin effect comes from fragmentation of a transversely polarized quark
)ˆˆ( ),(2
1
),(),(
/
//
pps
p
qqqhN
qhqh
pz
pzDzD
initial q spin is transfered to final q', which
fragments
)sin()ˆˆ( '' Shqq pps
q
q’
Collins effect in SIDIS
)ˆˆ( ),(),( //
ppsp qqqh
N
qh
N pzzD
x
y
CΦ
SΦ hΦ
qs
qs
ll
TP
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][
)sin( ]d[d 2)sin(
dddΦdΦ
ΦΦdΦdΦA
Sh
ShShΦΦUT
Sh
),( ),(ˆ
)sin(),(ˆ
),(
//22
/212
)sin(
q pqpq
lqlq
Sh
q Shqh
Nlqlq
qSh
ΦΦUT
pzDkxfdQ
dddΦdΦ
ΦΦzDdQ
dkxhddΦdΦ
A Sh
k
pk
lqlqlqlq ddd ˆˆˆ
),(),(ˆd),(/1
pk zDykxhdd
qh
N
q q
Collins effect in SIDIS couples to transversity, seminar of E. Boglione for combined
extraction
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fit to HERMES data on)sin( Sh
UTA
W. Vogelsang and F. Yuan
Soffer-saturated h1 ||2 1 qqh
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A. V. Efremov, K. Goeke and P. Schweitzer(h1 from quark-soliton model)
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COMPASS measured Collins and Sivers asymmetries for positive (●) and negative (○) hadrons
dhuhpd
N
pu
NUT DDffA Sh
////
)sin( 4
small values due to
deuteron target:
cancellation between u and d contributions
dh
N
uh
NduUT DDhhA Sh
//11)sin( 4
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S
kp̂
k
number density of partons with longitudinal
momentum fraction x and transverse momentum k┴, inside a proton with spin S
0),( ,/2 a pa xfddx kkk S
M. Burkardt, PR D69, 091501 (2004)
What do we learn from the Sivers distribution?
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),(ˆ 2
ˆ cosˆ sin
)ˆˆ( ),(ˆ2
1),(ˆ
/
2
//2
kxfkdkdx
kxfkxfddx
pa
NSS
pa
Npa
a
ji
kpSkkk
Total amount of intrinsic momentum carried by partons of flavour a
for a proton moving along the +z-axis and polarization vector
jiS ˆ sinˆ cos SS
S
ak
)sin()ˆˆ( SkpS
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GeV/c ˆ cosˆ sin 13.0
GeV/c ˆ cosˆ sin 14.003.002.0
0.050.06-
jik
jik
SSd
SSu
uk
dk? 0
du kk
Sivers functions extracted from AN data in Xpp give also opposite results,
with
036.0 032.0 du kk
Numerical estimates from SIDIS dataU. D’Alesio
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Sivers function and proton anomalous magnetic momentM. Burkardt, S. Brodsky, Z. Lu, I. Schmidt
Both the Sivers function and the proton anomalous magnetic moment are related to correlations of proton wave functions with opposite helicities
? ),( 1
0 /
2qpq
N Ckxfddx k
in qualitative agreement with large z data:
d
uΦΦ
UT
ΦΦ
UT
S
S
A
A
) sin(
) sin(
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APA,
aka,
The leading-twist correlator, with intrinsic k┴, contains several other functions .....
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8 leading-twist spin-k┴ dependent distribution functions
Courtesy of Aram Kotzinian
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Polarized SIDIS cross section, up to subleading order in 1/Q
Kotzinian, NP B441 (1995) 234
Mulders and Tangermann, NP B461 (1996) 197
Boer and Mulders, PR D57 (1998) 5780
Bacchetta et al., PL B595 (2004) 309
Bacchetta et al., JHEP 0702 (2007) 093
SIDISLAND