Joël Feltesse 1

Update of comparison of QCD fits

29/01/2008

Joël Feltesse 2

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 3

Ref

Zeus-S

Inbetween

Zeus-J

With errorband

Gluon!!

Large differencewith H1-par.

H1-ZEUS data set. Gluon at Q2 = 4 GeV2 for various input param.

H1-Par.data setH1-Z

20/11/2007

Joël Feltesse 4

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 5

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 6

Joël Feltesse 7

Joël Feltesse 8

Joël Feltesse 9

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 10

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 11

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 12

Joël Feltesse 13

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 14

Joël Feltesse 15

Joël Feltesse 16

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 17

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 18

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 19

Joël Feltesse 20

Joël Feltesse 21

Joël Feltesse 22

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 0.028 -0.104 0.034 0.396 Gluon Cg 12.934 0.844 13.323 0.925 -0.440 Gluon Dg 15.036 4.350 17.633 5.879 -0.508 u valence Buv 0.590 0.037 0.616 0.039 -0.693 u valence Cuv 3.817 0.121 3.825 0.138 -0.067 u valence Duv 2.450 0.755 2.103 0.744 0.463 d valence Cdv 4.866 0.726 4.803 0.910 0.077 d valence Ddv 2.597 2.030 2.089 2.362 0.677 Sea Asea 0.567 0.019 0.582 0.022 -0.735 Sea Bsea -0.210 0.004 -0.206 0.004 -0.712 Sea Csea 3.662 0.541 3.743 0.655 -0.135

Joël Feltesse 23

Staight Gluon. Technical comparison between JF and Mandy

H1 Parameterisation Chi2_J = 446. Chi2_M = 439.3

Val_J Err_J Val_M Err_M Dif/Err

Gluon Bg -0.085 0.036 -0.090 0.035 0.139 Gluon Cg 13.562 1.235 13.372 0.290 0.154 Gluon Dg 16.840 6.578 16.648 0.425 0.029 B_U -0.201 0.004 -0.201 0.004 -0.218 C_U 4.863 0.192 4.882 0.096 -0.098 F_U 264.900 54.386 268.61 6.951 -0.068 A_D 0.170 0.005 0.172 0.005 -0.271 C_D 4.029 0.328 4.016 0.323 0.038 C_Ubar 7.280 0.504 7.724 0.520 -0.881 C_Dbar 4.783 1.162 4.584 0.157 0.172

Joël Feltesse 24

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 0.028 -0.098 0.034 0.242 Gluon Cg 11.433 1.026 11.406 1.310 0.023 Gluon Dg 11.341 3.970 11.952 5.463 -0.129 u valence Buv 0.545 0.047 0.556 0.058 -0.211 u valence Cuv 3.831 0.107 3.853 0.112 -0.206 u valence Duv 3.496 1.028 3.501 1.230 -0.004 d valence Cdv 5.042 0.605 5.054 0.713 -0.019 d valence Ddv 6.006 3.279 6.559 4.585 -0.490 Sea BDbar -0.210 0.004 -0.209 0.005 -0.368 Sea CDbar 4.958 1.722 4.615 0.869 0.264 Sea CDbar 3.895 0.851 4.615 0.869 -0.837

Joël Feltesse 25

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 26

APPENDIX

Joël Feltesse 27

PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )

ZEUS-JET parametrisation (11 parameters) A B C D F

gluon From Sum Rule

0.

uv From Sum Rule

0.

Ubar

U

dv From Sum Rule

= Buv 0.

Dbar

D

ubar - dbar from Z_S_11 fit

from Z_S_11 fit

from Z_S_11 fit

0. 0.

Sea

0. 0.

Quite simple but questionable assumption on ubar -dbar

Where U = u +c and D = d+ s + b

Joël Feltesse 28

PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )

H1 parametrisation (10 parameters) A B C D F

gluon From Sum Rule

0.

uv

Ubar A(Ubar ) = A(U)

= B (U) 0. 0.

U ubar/dbar→1 as x → 0.

From Sum Rule

dv

0.

Dbar A(Dbar ) = A(D)

= B(U) 0. 0.

D

= 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 29

PDF parametrisation : x f(x) = A xB (1 - x)C (1 + D x + F x3 )

In between (EP) 12 parameters A B C D F

gluon From Sum Rule

0.

uv From Sum Rule

0.

Ubar ubar/dbar→1 as x → 0.

= B (Dbar) 0. 0.

U

dv From Sum Rule

= B (uv) 0.

Dbar

0. 0.

D

ubar - dbar

Sea

Weaker assumptions on B’s. Less model dependencequestionable assumption on ubar/dbar as x → 0.

Joël Feltesse 30

EXTRAS

Joël Feltesse 31

Joël Feltesse 32

Joël Feltesse 33

Joël Feltesse 34