update of comparison of qcd fits

Joël Feltesse 1

Update of comparison of QCD fits

29/01/2008

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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.

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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

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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

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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)

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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 )

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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 ?

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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

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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 !

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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.

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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)

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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 →

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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

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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

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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

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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.

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APPENDIX

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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

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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.

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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.

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EXTRAS

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