Update of comparison of QCD fits
29/01/2008
Joël Feltesse
1
Outlook
• Double minimum with H1 param
• Double (triple) minimum with ZEUS-Jet
and Inbetween parametrisations
• Last comparisons between results of JF
(H1fitter) and ACS programmes.
Joël Feltesse
2
H1-ZEUS data set. Gluon at Q2 = 4 GeV2 for various input param.
Ref
Inbetween
H1-Par.
data set
H1-Z
With error
band
Zeus-S
Zeus-J
Large
difference
with H1-par.
Gluon!!
20/11/2007
Joël Feltesse
3
Reminder
• JF :Two types of solutions pending on the
parameteristion:
– Humpy gluon with H1param and Inbetween
– Straight gluon at low x with ZEUS-J and
ZEUS-S
• Mandy : one only type of solution for all 4
parameterisations:
– Straight(smooth) gluon at low x
Joël Feltesse
4
New test
• Use H1 parametrisation but giving as input to Minuit the
initial values of the parameter of a straight gluon.
• Surprising results
– Initial straight gluon gives after minimisation a straight gluon :
Chi2 = 446 [fit_2]
– Initial humpy gluon gives after mininisation a humpy gluon : Chi2
= 456 [[fit_1]
– No way (so far) to jump by minimisation from the humpy gluon to
to the other !!
– Double minimum also observed with QCDFIT (Li) and with ZEUS
package (Mandy)
Joël Feltesse
5
Joël Feltesse
6
Joël Feltesse
7
Joël Feltesse
8
Comparison of output values of parameters
at Q02 = 4 GeV2
JF output, H1 Param. H1PDF2k init. values
Fit_1, chi2 = 456.4
NO. NAME
VALUE
ERROR
1 Bg
-0.93489
0.38909E-01
2 Cg
9.2298
0.73734
3 Dg
11398.
8871.4
4 BU
-0.21035
0.79069E-02
5 CU
4.8602
0.17934
6 FU
274.36
52.835
7 AD
0.15956
0.88072E-02
8 CD
4.0076
0.33801
9 CUbar
6.2007
0.63037
10 CDbar
5.8054
1.3173
JF output, H1-Param with mandy init.values
Fit_2, chi2 = 446.0
NAME
VALUE
ERROR
1 Bg
-0.85283E-01 0.35957E-01
2 Cg
0.13562E+02 0.12354E+01
3 Dg
0.16840E+02 0.65782E+01
4 BU
-0.20143E+00 0.40238E-02
5 CU
0.48627E+01 0.19240E+00
6 FU
0.26490E+03 0.54386E+02
7 AD
0.17032E+00 0.53413E-02
8 CD
0.40289E+01 0.32759E+00
9 CUbar
0.72805E+01 0.50364E+00
10 CDbar
0.47830E+01 0.11619E+01
Where PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )
Joël Feltesse
9
Obvious questions
• Is the double minimum feature unique to H1
parameterisation ?
• Is the double minimum unique to H1/ZEUS
combined data set ?
• Is the chi2 difference always in favor of a straight
gluon ?
Joël Feltesse
10
Double minimum with ZEUS-Jet
parameterisation (and ZEUS HQ treatment) ?
– Initial straight gluon gives after minimisation a
straight gluon : Chi2 = 443.9
– Initial humpy gluon gives after minimisation a humpy
gluon : Chi2 = 456.3
→ Results similar to H1 parametrisation
Joël Feltesse
11
Joël Feltesse
12
Double minimum with Inbetween
parameterisation (and H1 HQ treatment) ?
– Initial straight gluon gives after minimisation a straight gluon :
Chi2 = 442.3
– Initial humpy gluon gives after mininisation a humpy gluon : Chi2
= 433.8 ! the smallest Chi2 so far
BUT
→
– Dvalence negative at large x is an unphysical solution (Mandy).
It even gives a negative CC x-sec at large x !
– Initial humpy gluon and dvalence density forced to be positive
gives after minimisation a new minimum with a humpy gluon :
Chi2 = 450.1 !
Joël Feltesse
13
Joël Feltesse
14
Joël Feltesse
15
Double minimum with only H1 data (from
H1PDF2k) and H1 parameterisation ?
– Initial straight gluon gives after minimisation a
straight gluon : Chi2 = 547.3
– Initial humpy gluon gives after mininisation a humpy
gluon : Chi2 = 536.8. Smaller than the straight gluon
minimum (relief).
– Remark : as for the publication the fit has been
performed with full correlation taken into account.
Joël Feltesse
16
In short
When fitting H1Z combined data sets Minuit minimisation finds two
minimum independently of the parameterisation (H1-param., Inbetween,
ZEUS-Jet).
Each time, the straight gluon minimum is slightly favored (Chi2 smaller
by 6 to 13 units) provided unphysical solutions are removed.
Is the double minimum a problem ?
Is there a third minimum ?
I feel uneasy than Minuit is not capable to jump alone from a minimum to
a better one.
The double minimum is also observed when using H1 published data
sets but then favoring the humpy solution.
→ Better find a way to get one only robust minimum (Li’s talk)
Joël Feltesse
17
Considering only the straight gluon
solutions. How different are the 3 fits ?
Reminder. All fits with : Q2min = 3.5 GeV2,
573 data points and all errors uncorrelated.
H1 param (10 parameters), chi2 = 446.1
Inbetween (12 parameters), chi2 = 442.3
ZEUS-JET (11 parameters), chi2 = 443.9
Chi2 are very close, but PDFs are not so close →
Joël Feltesse
18
Joël Feltesse
19
Joël Feltesse
20
Joël Feltesse
21
Staight Gluon. Technical comparison
between JF and Mandy
ZEUS J Parameterisation
Chi2_J = 443.9 Chi2_M = 440.8
Val_J Err_J Val_M Err_M Dif/Err
Gluon Bg
-0.092
Gluon Cg
12.934
Gluon Dg
15.036
u valence Buv 0.590
u valence Cuv 3.817
u valence Duv 2.450
d valence Cdv 4.866
d valence Ddv 2.597
Sea Asea
0.567
Sea Bsea
-0.210
Sea Csea
3.662
0.028 -0.104
0.844 13.323
4.350 17.633
0.037 0.616
0.121 3.825
0.755 2.103
0.726 4.803
2.030 2.089
0.019 0.582
0.004 -0.206
0.541 3.743
Joël Feltesse
0.034
0.925
5.879
0.039
0.138
0.744
0.910
2.362
0.022
0.004
0.655
0.396
-0.440
-0.508
-0.693
-0.067
0.463
0.077
0.677
-0.735
-0.712
-0.135
22
Staight Gluon. Technical comparison
between JF and Mandy
H1 Parameterisation
Chi2_J = 446.
Val_J
Gluon Bg
Gluon Cg
Gluon Dg
B_U
C_U
F_U
A_D
C_D
C_Ubar
C_Dbar
Err_J
-0.085
0.036
13.562 1.235
16.840 6.578
-0.201 0.004
4.863
0.192
264.900 54.386
0.170
0.005
4.029
0.328
7.280
0.504
4.783
1.162
Joël Feltesse
Chi2_M = 439.3
Val_M
Err_M
Dif/Err
-0.090
13.372
16.648
-0.201
4.882
268.61
0.172
4.016
7.724
4.584
0.035
0.290
0.425
0.004
0.096
6.951
0.005
0.323
0.520
0.157
0.139
0.154
0.029
-0.218
-0.098
-0.068
-0.271
0.038
-0.881
0.172
23
Staight Gluon. Technical comparison
between JF and Mandy
Inbetween Parameterisation
Chi2_J = 442.3.
Chi2_M = 437.9
Val_J Err_J Val_M Err_M Dif/Err
Gluon Bg
-0.091
Gluon Cg
11.433
Gluon Dg
11.341
u valence Buv 0.545
u valence Cuv 3.831
u valence Duv 3.496
d valence Cdv 5.042
d valence Ddv 6.006
Sea BDbar
-0.210
Sea CDbar
4.958
Sea CDbar
3.895
0.028
1.026
3.970
0.047
0.107
1.028
0.605
3.279
0.004
1.722
0.851
Joël Feltesse
-0.098
11.406
11.952
0.556
3.853
3.501
5.054
6.559
-0.209
4.615
4.615
0.034
1.310
5.463
0.058
0.112
1.230
0.713
4.585
0.005
0.869
0.869
0.242
0.023
-0.129
-0.211
-0.206
-0.004
-0.019
-0.490
-0.368
0.264
-0.837
24
Conclusion
• The largest difference between JF and Mandy on fit
results has been understood.
• Technical comparison between JF and Mandy :
agreement at the ~ 0.3 sigma level on parameter values
for all choices of parameterisation, although Chi2 of
Mandy are always a bit smaller.
• At present, should concentrate on understanding
(improving) the remaining differences between
parameterisations and move to more elaborate fits, for
example on HQ treatment and with treatment of
correlations between errors.
Joël Feltesse
25
APPENDIX
Joël Feltesse
26
PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )
ZEUS-JET parametrisation (11 parameters)
A
From Sum
Rule
From Sum
Rule
gluon
uv
B
C
D
F
0.
0.
Ubar
U
From Sum
Rule
dv
= Buv
0.
Dbar
D
ubar - dbar
Sea
from
from
from
0.
Z_S_11 fit Z_S_11 fit Z_S_11 fit
0.
0.
0.
Quite simple but questionable assumption on ubar -dbar
Joël Feltesse
Where U = u +c and D = d+ 27
s+b
PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )
H1 parametrisation (10 parameters)
A
From Sum
Rule
gluon
B
C
D
F
0.
uv
A(Ubar ) = = B (U)
A(U)
ubar/dbar→1
as x → 0.
Ubar
U
0.
0.
From Sum
Rule
0.
dv
A(Dbar ) =
A(D)
Dbar
D
= B(U)
0.
0.
= B(U)
From Sum
Rule
0.
ubar - dbar
Sea
Very strong assumptions on B’s,
questionable assumption
on ubar/dbar as x → 0.
Joël Feltesse
28
PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )
In between (EP) 12 parameters
A
B
From Sum
Rule
From Sum
Rule
ubar/dbar→1 = B (Dbar)
as x → 0.
gluon
uv
Ubar
C
D
F
0.
0.
0.
0.
U
From Sum
Rule
dv
= B (uv)
0.
0.
Dbar
0.
D
ubar - dbar
Sea
Weaker assumptions on B’s. Less model dependence
Joël Feltesse
questionable assumption
on ubar/dbar as x → 0.
29
EXTRAS
Joël Feltesse
30
Joël Feltesse
31
Joël Feltesse
32
Joël Feltesse
33
Joël Feltesse
34