Post on 31-Dec-2015
description
The Role of Semi Inclusive DIS Data
in Determining Polarized PDFs
E. Leader (London), A. Sidorov (Dubna), D. Stamenov (Sofia)
Saclay, Paris, 17 September 2010
OUTLINE
A combined NLO QCD analysis of inclusive and semi inclusive DIS world data is presented
Summary
The recent COMPASS data on A1p and A1dπ(+/-), A1d
K(+/-) are included
Impact of SIDIS on polarized PDFs and higher twist
A quark flavor decomposition of the polarized sea
The higher twist corrections (HT) to g1 are accounted for (in contrast to the other analyses)
The main goal to answer the question how the helicity of the nucleon is divided up among its constituents:
Sz = 1/2 = 1/2 (Q2) + G (Q2) + Lz (Q2)
= ssdduu
the parton polarizations q and G are the first moments
12 2
0Δq(Q ) ( , )dx q x Q
1
0
22 ),()ΔG(Q QxGdx
of the helicity densities: ),( ,),(),,( 222 QxGQxuQxu
To determine the shape of the polarized parton densities
one of the best tools to study
the structure of nucleon
Inclusive DIS
Q2 = -q2 = 4EE`sin2 l`
l k`
k
N
x = Q2/(2M)
P
q = E – E`
Fi(x, Q2) gi(x, Q2)
unpolarized SF polarized SF
DIS regime ==> Q2 >> M2, >> M
2222 10 4 , 41 GeVWGeVQ
preasymptotic region
Inclusive DIS Cross Section Asymmetries
Measured quantities ,||
dd
ddA
dd
ddA |
)()()(2121 | ||
, , , ggAAAA where A1, A2 are the virtual photon-nucleon asymmetries
If A|| and are measured 11 /Fg
If only A|| is measured
| | 2 1
1
(1 )A g
D F
2 2 2 24 /M x Q - kinematic factor
NB. cannot be neglected in the JLab, SLAC and HERMES kinematic regions
A the best quantity to test QCD and to determine PDFs
Theory In QCD 2 2 21 1 , 1g ( , ) g ( , ) g ( , )LT TMC HTx Q x Q x Q
)4
4
(Q
ΛO2221 /),(h),(g QQxQx HT
2 22 2
1
1 ( ) ( )( , ) [( ) (1 ) ]
2 2 2
fN
s s GLT q q
q f
Q Q Cg x Q e q q C G
N
functionst coefficien , WilsonCC Gq
In NLO pQCD
dynamical HT power corrections (=3,4)=> non-perturbative effects (model dependent)
polarized PD evolve in Q2
according to NLO DGLAP eqs.
2 42 2 2
1 , 1 2 4g ( , ) g ( , ) ( , ) ( )TMC
LT TMC LT
M Mx Q x Q h x Q O
Q Q
Nf (=3) - the number of flavors
target mass corrections which are calculable in QCDA. Piccione, G. Ridolfi
logarithmic in Q2
2 22 2
1
1 ( ) ( )( , ) [( ) (1 ) ]
2 2 2
fN
s s GLT q q
q f
Q Q Cg x Q e q q C G
N
can be determined from polarized inclusive DIS data !
IMPORTANT
Due to the lack of the charged current neutrino data only
the sums
2222 10 4 , 41 GeVWGeVQ
The HT corrections to g1 are NOT negligible in the preasymptotic region and have to be accounted for
An important difference between the kinematic regions of the unpolarized and polarized data sets
)/( 22 QO
preasymptotic region
A half of the present inclusive data are at moderate Q2 and W2:
LSS, Phys. Rev. D75 (2007) 074027
f
f
h
hh
F
gQzxA
~),,(
1
121
ef2 qf(x,Q2) Df
h (z,Q2)
ef2 qf(x,Q2) Df
h (z,Q2)
Semi-inclusive processes
Fragmentation functions
In LO QCD
In NLO QCD the Wilson coefficients have to be included
qallow to separate and q
z)(x,ijΔC
22 1 2
11
( , , )h h
hh
g gA x z Q
F
NLO1
NLO1
1
11
),(
),(
),(
),(),(
2
2
2
22
expexp
QxF
Qxg
QxF
QxgQxA h
h
h
hh
Fit to the data
Inclusive DIS
Semi-inclusive DIS
expexp )(
)()(
1
11
1
1 HTTMCNLO
F
gg
F
g
N.B. It is NOT known at present how to account for the HT and TMC corrections in SIDIS processes. Fortunately, they should be less important due to the kinematic region of the present SIDIS data.
2χ
2χ
0.0031.269 ))(Δ(Δ)Δ(Δ 223 DFQdd)(Quuga
A
0.0250.585=3))((2 ))(())(( 2228 DFQssQddQuua
Sum
Rules
Input parton densities at Q20 = 1 GeV2
(more general expressions than those in our previous analyses)
)1()1(),(
)1()1(),( )(
)1(),(
)1()1(),(
)1()1(),)((
)1()1(),)((
20
20
20
20
20
5.020
xxxAQxG
xxxAQxsss
xxAQxd
xxxAQxu
xxxAQxdd
xxxxAQxuu
GGG
G
sss
s
ddd
uuu
u
ddd
d
uuuu
u
, ; ( 02)quu u s Gdd d
MRST
16 free parameters
For the fragmentation functions Dqh(z, Q2) the DSS
(de Florian, Sassot, Stratmann) ones have been used
The inverse Mellin transformation method has been used to calculate g1N(x, Q2), g1N
h (x, z, Q2) and F1Nh (x, z, Q2) from
their moments.
DATA
Inclusive DIS – 841 experimental points
Semi inclusive DIS – 202 experimental points
Total – 1043 exp points
Nr of the free parameters – 26 (16 for PDFs and 10 for HT)
The systematic errors are added quadratically to the statistical ones
The positivity constraints on polarized PDFs are imposed
Unpolarized NLO MRST’02 PDFs have been used to calculate F1Nh
LSS’10 PDFs – this fit, LSS’06 – a fit to DIS data alone (PR D75, 2007)
A flavor decomposition of the polarized sea due to SIDIS data
are determined without additional assumptions
and Δ Δu( ) d( )x x
Changing in sign very unexpected
( )s x
Changing in sign ΔG(x) - such a solution has been already found from inclusive DIS data N.B. In the QCD analyses of inclusive DIS data:
sea sea 2 Δu Δu Δd Δd (Δs+Δs) /Flavor symmetric sea :convention
Error bands Δχ2 = 1
∆s(x)
Our s(x) differs from that one obtained by DSSV (less negative at x<0.03 and less positive for large x). Note that DSSV have used the assumption for s(x)
ds In contrast to a changing in sign s(x) coming from SIDIS, in all the QCD analyses of inclusive DIS data a negative [s(x)+ s(x)]/2 for any x in the measured region is obtained
The determination of s(x) from SIDIS strongly depends on FFs (COMPASS – PL B680 (2009) 217) and the new FFs (de Florian, Sassot, Stratmann) are crucially responsible for the unexpected behavior of s(x)Obtaining a final and unequivocal result for s(x) remains a challenge for further research on the internal spin structure of the nucleon
¯
¯¯
May be the assumption ∆s(x)=∆s(x) in SIDIS is not correct ?
∆s(x) is controversial !
ΔG(x, Q2)
The present polarized DIS and SIDIS data cannot rule out the solution with a positive gluon polarization
2 20 0.888 0.883( ) ( )DF DFG node Gx x
The sea quark densities obtained in the fits with positive and node xΔG are almost identical.
SIDIS data do NOT help to constrain better the gluonpolarization.
1. Via Open Charm production (q=c) c D0 K-p+ and D*+D0p+
COMPASS: ΔG/G = -0.08 +/- 0.21 +/- 0.11 at <xg>=0.11 and <µ2> = 13 GeV2
LO treatment. All deuteron data included (C. Franco, DIS 2010, Florence)
2. Via High-pt hadron pairs (q=u,d,s) - Detect 2 hadrons (mostly pions) COMPASS, HERMES - 2 determinations:
• Q2 > 1 GeV2
• Q2 < 1 GeV2
g qq
Photon- Gluon Fusion
Determination of ∆G from direct measurements
∆G/G – two methods, three measurements
Unfortunately, the direct measurements give us information on G in narrow range of x
Comparison with directly measured G/G
ΔG/G from high pt hadron pairsµ2 = 3 GeV2
ΔG/G from open charm production
The most precise values of G/G, the COMPASS ones, are consistent with both of the polarized gluon densities determined in our combined QCD analysis
Both of our solutions for ΔG/G are also in agreement with the COMPASS experimental value, especially the changing in sign xΔG.
The direct measurements of ΔG/G at COMPASS cannot distinguish between the positive and node xΔG(x) obtained from our QCD analysis
As expected the SIDIS data do not influence essentially the sums
already well determined from the inclusive DIS data.
Our densities are well consistent with those obtained by DSSV.
( ) and ( ) u u d d
Higher twist effects
g1N = (g1
N )LT,TMC + hN(x)/Q2
Compared to HT(LSS’06): The values of HT(p) are practically not changed while the new values of HT(n) are smaller and almost compatible with zero within the errors for x > 0.1 . We consider this change of HT(n) as a result of the new behavior of Δs(x), positive for x > 0.03. In addition, the new A1
p COMPASS data impact on the smallest x point of HT(p,n).
The first moments of higher twist
Thanks to the very precise inclusive DIS CLAS data the first moments of HT corrections are also well determined.
np,N ,)( 75.0
0045.0
xhdxh NN
In agreement with the instanton model predictions and the values obtained from the analyses of the first moment of g1
(p-n) (Deur et al., PR D78, 032001, 2008. ; R. Pasechnik et al. PR D78, 071902, 2008)
2 )005.0028.0( GeVhp
2 (0.018 0.008) n
h GeV
2 ( 0.046 0.009) p n
h h GeV 2 ( 0.011 0.009) p n
h h GeV
In agreement with 1/NC expansion in
QCD (Balla et al., NP B510, 327, 1998)|| ||
npnphhhh
0 np
hh
Impact of the future DIS CLAS12 data on PDFs uncertainties
Using the 11 GeV highly polarized electron beam of the energy-upgraded CEBAF at JLab very accurate data in 0.075 ≤ x ≤ 0.775, 1.01 ≤ Q2 ≤ 12.05
A significant improvement of the data accuracy do NOT impact on Δs errors?!
Impact of the future SIDIS CLAS12 data on PDFs uncertainties
Kinematic region: 0.04 ≤ x ≤ 0.76, 1.01 ≤ Q2 ≤ 10.16 GeV2
s G a0 = MS
LSS’06 (node xG) -0.058 ± 0.006 0.034 ± 0.490 0.235 ± 0.045
LSS’10 (node xG) -0.055 ± 0.006 -0.396 ± 0.431 0.254 ± 0.042
LSS’10 (xG pos) -0.063 ± 0.004 0.255 ± 0.187 0.207 ± 0.034
Sz = ½ = ½ (Q2) + G (Q2) + Lq (Q2) + Lg(Q2)
= - 0.27 (0.36) +/- 0.43 (0.19) + Lq (Q2) + Lg(Q2)
To be determined from forward
extrapolations of generalized PDFs
Q2 = 4 GeV2
Due to the ambiguity of the gluon polarization the quark-gluon spin contribution to the total spin of the nucleon is still not well determined.
First moments of Δs(x), ΔG(x) and ΔΣ(x) at
SUMMARY
The SIDIS data, as well the direct measurements of ΔG/G, cannot help to distinguish between the positive and changing in sign solutions for ΔG(x) – the ambiguity of the form of ΔG(x) remains still large.
A combined NLO QCD analysis of inclusive and semi inclusive world DIS data is presented
In contrast to the other analyses the target mass and higher twist corrections to the spin structure function g1 are taken into account
Due to SIDIS data
Changing in sign Δs(x), but different from the DSSV one - less negative at x < 0.03 and less positive for x > 0.03
Δs(x)SIDIS differs essentially from a negative Δs(x)DIS obtained from all the QCD analyses of inclusive DIS data. This behavior strongly depends on the kaon FFs used. A model independent extraction of kaon FFs would help to solve this inconsistency.
The sea quark densities Δu and Δd are determined¯ ¯
¯
¯ ¯
0.21-0.1
1
17
g 1.32 0
f0. 5
KTeV experiment Fermilab: PRL 87 (2001) 13201
e 0
-decay
SU(3)f prediction for the form factor ratio g1/f1
Experimental result
1A
1
g g 1.269 .003
f
A good agreement with the exact SU(3)f symmetry !
From exp. uncertainties SU(3) breaking is at most of order 20%
NA48 experiment at CERN g1/f1 = 1.20 +/- 0.05 (PLB 645 (2007) 36)
Kinematatic factor 2 = 4M2x2/Q2 cannot be neglected for most of the data sets (JLab, SLAC, HERMES)
The approximation A1th
≈ (g1/F1)th used by some of the
groups in the preasymptotic region is not reasonable !
Which inclusive data to chose for QCD fits – A1 or g1/F1 ?
A1= g1/F1 - 2 g2/F1
The QCD treatment of g2 is not well known
The best manner to determine the polarized PDFs is to perform QCD fits to the data on g1/F1
N.B.
(g1)QCD = (g1)LT + (g1)HT+TMC (F1)QCD = (F1)LT + (F1)HT+TMC
LT(LO, NLO) 1/ln(Q22 2/Q2, TMC M2/Q2
There are essentially two methods to fit the data (accounting or not accounting for the HT corrections to g1)
2 21 1
2 21 1exp
g (x,Q ) g (x,Q )
F (x,Q ) F (x,Q )
LT
LT
OK in pure DIS region where HT can be ignored
11 1
1 1 expexp
( ) ( )
( )
g g g
F F
LT HT+TMC
The two methods are equivalent in the pre-asymptotic region only if the (HT+TMC) terms cancel in the ratio g1/F1
PDFsGRSV, DSSV, LSS
LSS 2x(F1)exp = (F2)exp(1 + γ2)/(1+ Rexp)
21 1 1 1
21 1 1 1exp
( , ) ( ) ( ) ( )1
( , ) ( ) ( ) ( )
g x Q g g F
F x Q F g F
LT HT+TMC HT+TMC
LT LT LT
1 1
1 1
( ) ( )( ) ( )
g Fg FHT+TMC HT+TMC
LT LT is fulfilled
Fits to g1/F1 data using for the ratio
1 1 1
1 1 exp
( ) ( ) ( ) or
( ) ( )LT LT HT TMC
LT
g g g
F F
will lead to the same results if the condition
If not (which is the case), the ignored HT terms in g1 and F1, according to the Ist method, will be absorbed into the extracted PDFs
Pre-asymptotic region
LSS’06 vs DSSV
11 1
1 1 expexp
( ) ( )
( )
g g
F
g
F
LT/N HT+TMCLOLSS
21
21
2 21 1exp
gg (x, (xQ )
F (x,Q ) F (x
,Q )
,Q )
L
LT
T/NLO
/NLO
DSSV
In the DSSV analysis the TM and HT corrections are not taken into account for both g1 and F1 structure functions
F1(x, Q2)LT/NLO was calculated using the NLO MRST’02 PDFs
DSSV: A first NLO global analysis of DIS, SIDIS and RHIC polarized pp scattering data
The difference between F1(exp) and F1(MRST)LT is a measure of the size of
TMC and HT corrections which cannot be ignored in the pre-asymptotic region
As expected, the curves corresponding to g1tot(LSS)/F1(exp) and
g1LT(DSSV)/F1
LT (MRST) practically coincide (an exception for x > 0.2 !)
although different expressions for g1 and F1 were used in the fit
proton
Surprisingly g1LT(LSS) and
g1LT(DSSV) coincide for x > 0.1
although the HT+TMC, taken into account in LSS and ignored in the DSSV analysis, do NOT cancel in the ratio g1/F1 in the
pre-asymptotic region
PUZZLE ???
2 21 1
2 21 1exp
g (x,Q ) g (x,Q )
(1+F (x,Q ) F ( )) x,Q
LT/NLO2
LT/NLO
1 1
1 1
( ) ( )1 )
( ) ( )
g F
g F 2HT+TMC HT+TMC
LT LT
γ
In the DSSV fit, a factor is introduced for the data in the pre-asymptotic region (CLAS, JLab/Hall A and SLAC/E143). There is NO rational explanation for a such correction !! Except for the fact that it is impossible to achieve a good description of these data, especially for the CLAS one, without this correction.
???
It turns out that accidentally more or less (4-18%) accounts for the TM and HT corrections to g1 and F1
in the ratio g1/F1 ONLY for x > 0.1
2(1 γ )
2 2 2 2γ 4 /NM x Q2(1 γ )