Addendum to: Predictions for Higgs production at the Tevatron and the associated uncertainties
aa r X i v : . [ h e p - ph ] S e p Addendum to: Predictions for Higgs production at the Tevatronand the associated uncertainties
Julien Baglio and Abdelhak Djouadi , Laboratoire de Physique Th´eorique, Universit´e Paris-Sud XI et CNRS, F-91405 Orsay, France. Theory Unit, CERN, 1211 Gen`eve 23, Switzerland.
Abstract
In a recent paper, we updated the theoretical predictions for the production crosssections of the Standard Model Higgs boson at the Tevatron and estimated the variousuncertainties affecting these predictions. We found that there is a large theoreticaluncertainty, of order 40%, on the cross section for the main production channel, gluon-gluon fusion into a Higgs boson. Since then, a note from the Higgs working groups ofthe CDF and D0 collaborations criticizing our modeling of the gg → H cross sectionhas appeared. In this addendum, we answer to this criticism point by point and, inparticular, perform an analysis of σ ( gg → H ) for a central value of the renormalizationand factorization scales µ = M H for which higher order corrections beyond next-to-next-to-leading order (that we discarded in our previous analysis) are implicitlyincluded. Our results show that the new Tevatron exclusion bound on the Higgs bosonmass, M H = 158–175 GeV at the 95% confidence level, is still largely debatable. Introduction
In an earlier paper [1], we updated the theoretical predictions for the production cross sec-tions of the Standard Model Higgs boson at the Tevatron collider, focusing on the two mainsearch channels, the gluon–gluon fusion mechanism gg → H and the Higgs–strahlung pro-cesses q ¯ q → V H with V = W/Z , including all relevant higher order perturbative QCD [2]and electroweak corrections [3, 4]. We then estimated the various theoretical uncertaintiesaffecting these predictions: the scale uncertainties which are viewed as a measure of the un-known higher order effects, the uncertainties from the parton distribution functions (PDFs)and the related errors on the strong coupling constant α s , as well as the uncertainties dueto the use of an effective field theory (EFT) approach in the determination of the radiativecorrections in the gg → H process at next-to-next-to-leading order (NNLO). We found thatwhile the cross sections are well under control in the Higgs–strahlung processes, the uncer-tainty being less that ≈ ≈ ≈
10% errorassumed by the CDF and D0 experiments in their earlier analysis that has excluded theHiggs mass range M H = 162–166 GeV at the 95% confidence level (CL) [5]. As gg → H is byfar the dominant production channel in this mass range, we concluded that these exclusionlimits should be reconsidered in the light of these large theoretical uncertainties.1fter our paper appeared on the archives, some criticisms have been made by the mem-bers of the Tevatron New Physics and Higgs working group (TevNPHWG) of the CDF andD0 collaborations [6] concerning the theoretical modeling of the gg → H production crosssection that we proposed. This criticism appeared on the web in May 2010, but we got awareof it only during ICHEP, i.e. end of July 2010, where, incidentally, the new combined analy-sis of CDF and D0 for the Higgs search at the Tevatron was released [7]. In this addendum,we respond to this criticism point by point and, in particular, perform a new analysis of the gg → H cross section at NNLO for a central value of the renormalization and factorizationscales µ = M H , for which higher order corrections beyond NNLO (that we discarded withsome justification in our previous analysis) are implicitly included. We take the opportunityto also comment on the new CDF/D0 results with which the excluded Higgs mass range wasextended to M H =158–175 GeV at the 95% CL .
1. The normalization of the gg → H cross section
One of the points put forward in our paper is to suggest to consider the gg → H produc-tion cross section up to NNLO [2–4], σ NNLOgg → H , and not to include the soft–gluon resumationcontributions [9]. The main reason is that, ultimately, the observable that is experimentallyused is the cross section σ cutsgg → H in which selection cuts have been applied and the theoreticalprediction for σ cutsgg → H is available only to NNLO [10]. This argument has been criticized bythe TevNPHWG for the reason that we are potentially missing some important higher ordercontributions to the cross section. It turns out, however, that our point is strengthened inthe light of the new CDF/D0 combined analysis [7]. Indeed, in this analysis, the gg → H cross section has been broken into the three pieces which yield different final state signaltopologies for the main decay H → W W ( ∗ → ℓℓνν , namely ℓℓνν +0 jet, ℓℓνν +1 jet and ℓℓνν +2 jets or more: σ NNLOgg → H = σ → H + σ → H + σ ≥ → H (1)These channels have been analyzed separately and these individual components, with σ → H evaluated at NNLO, σ → H evaluated at NLO and σ ≥ → H evaluated at LO, represent respec-tively ≈ ≈
30% and ≈
10% of the total gg → H cross section at NNLO. Since thesethree pieces add up to σ NNLOgg → H , we do not find appropriate to have a different normalizationfor the jet cross sections and for the total sum and, thus, to include soft–gluon resumationin the latter while it is not taken into account in the former.Nevertheless, we are ready to admit that we may have underestimated the total produc-tion cross section, as with the central value of the renormalization and factorization scales µ R = µ F = µ = M H that we have adopted for evaluating σ NNLOgg → H , we are missing the > ∼
10% increase of the cross section due to higher order contributions and, in particular,to soft–gluon resumation. As most criticism on our paper focused on this particular issue(overlooking many other important points that we put forward), we present here an analysisof the cross section in which these higher order effects are implicitly taken into account. Some of the points that we discuss here have also been presented by one of us (JB) in the Higgs Huntingworkshop in Orsay which followed ICHEP [8].
2s pointed out by Anastasiou and collaborators some time ago, see e.g. Refs. [4, 11] (andalso Ref. [12]), the effects of soft–gluon resumation at NNLL [9] can be accounted for in σ NNLOgg → H by lowering the central value of the renormalization and factorization scales from µ = M H to µ = M H . If the scale value µ = M H is chosen, the central value of σ NNLOgg → H increases by more than 10% and there is almost no difference between σ NNLOgg → H ( µ = M H )and σ NNLLgg → H ( µ = M H ) as calculated for instance by de Florian and Grazzini [13].This is explicitly shown in Fig. 1 where σ NNLOgg → H with central scales µ = M H and µ = M H (that we calculate following the same lines as the ones discussed in section 2 of our paper)are compared to σ NNLLgg → H with µ = M H (for which the numbers are given in Ref. [13]). Forinstance, for M H ≈
160 GeV, while there is a ≃
14% difference between σ NNLOgg → H ( µ = M H )and σ NNLLgg → H ( µ = M H ), there is almost no difference between the later and σ NNLOgg → H ( µ = M H ) σ ( gg → H ) [fb] µ = M H )NNLLNNLO (cid:0) µ = M H (cid:1) σ ( gg → H ) [fb] M H [ GeV ] 20019018017016015014013012016001000600300200100
Figure 1: The gg → H cross section at the Tevatron as a function of M H : at NNLO forcentral scales at µ = M H and µ = M H and at NNLL for a scale µ = M H . In the insert,shown are the deviations when one normalizes to σ NNLOgg → H ( µ = M H ).As a result of this choice, our normalization for the inclusive gg → H cross section is nowthe same as the ones of Refs. [4, 13] which were adopted in the combined CDF/D0 analyses.
2. The scale uncertainty
The next important issue is the range of variation that one should adopt for the renormaliza-tion and factorization scales, a variation which leads to an uncertainty band that is supposedto be a measure of the unknown (not yet calculated) higher order contributions to the crosssection. In our paper, we have advocated the fact that since the NLO and NNLO QCDcorrections in the gg → H process were so large, it is wiser to extend the range of scalevariation from what is usually assumed. From the requirement that the scale variation ofthe LO or NLO cross sections around the central scale µ catch the central value of σ NNLOgg → H ,we arrived at the minimal choice, µ ≤ µ R , µ F ≤ µ for µ = M H . Note that the scale choice µ = M H in gg → H does not only mimic the inclusion of the effect of soft–gluon resumation, but it also improves the convergence of the perturbative series and is more appropriateto describe the kinematics of the process [11].
3n addition, we proposed that the scales µ R and µ F are varied independently and withno restriction such as ≤ µ R /µ F ≤ σ NNLOgg → H due to scale variation were obtained for equal µ R and µ F values: for a centralscale µ = M H , one had σ NNLOmin for µ R = µ F = 3 µ and σ NNLOmax for µ R = µ F = µ .Adopting the central scale choice µ = M H , for the scale variation of the leading–order gg → H cross section to catch the central value of σ NNLOgg → H ( µ ), as shown in the left-hand sideof Fig. 2, we again need to consider the domain13 µ ≤ µ R = µ F ≤ µ , µ = 12 M H (2)for the scale variation. Notice that now, we choose for simplicity to equate µ R and µ F so thatthere is no more discussion about the possibility of generating artificially large logarithms ifwe take two widely different µ R /µ F scales.Adopting this domain for µ F = µ R , we obtain the result shown in the right–hand sideof Fig. 2 for the scale variation of the NNLO cross section around the central scale µ = M H . Averaged over the entire Higgs mass range, the final scale uncertainty is about ≃ +15% , −
20% which, compared with our previous result for the scale variation of σ NNLOgg → H with µ = M H is the same for the minimal value but smaller for the maximal value. Notethat if we had chosen the usual domain µ ≤ µ R = µ F ≤ µ , the scale variation wouldhave been of about ≈ +10% , −
12% for M H ≈
160 GeV. κ = κ = κ = µ R = µ F = m H LO at µ R = µ F = m H σ ( gg → H ) [fb] M H [ GeV ] 20019018017016015014013012014001000600300200100
NNLO at µ R = µ F = m H σ ( gg → H ) [fb] κ = µ R = µ F = m H σ ( gg → H ) [fb] M H [ GeV ] 20019018017016015014013012014001000600300200100
Figure 2: Left: the scale variation of σ LO gg → H as a function of M H in the domain µ /κ ≤ µ R = µ F ≤ κµ for µ = M H with κ = 2 , σ NNLO gg → H ( µ R = µ F = M H ).Right: the uncertainty band of σ NNLO gg → H as a function of M H for a scale variation µ /κ ≤ µ R = µ F ≤ κµ with µ = M H and κ = 3. In the inserts shown are the relative deviations.It is important to notice that if the NNLO gg → H cross section, evaluated at µ = M H ,is broken into the three pieces with 0,1 and 2 jets, and one applies a scale variation for theindividual pieces in the range µ ≤ µ R , µ F ≤ µ , one obtains with selection cuts similarto those adopted by the CDF/D0 collaborations [14]:∆ σ/σ | scale = 60% · (cid:0) +5% − (cid:1) + 29% · (cid:0) +24% − (cid:1) + 11% · (cid:0) +91% − (cid:1) = (cid:0) +20 . − . (cid:1) (3)4veraged over the various final states with their corresponding weights, an error on the“inclusive” cross section which is about +20% , −
17% is derived . This is very close to theresult obtained in the CDF/D0 analysis [7] which quotes a scale uncertainty of ≈ ± . µ ≤ µ R = µ F ≤ µ for the scalevariation of the total inclusive cross section σ NNLOgg → H , leads to a scale uncertainty that is veryclose to that obtained when one adds the scale uncertainties of the various jet cross sectionsfor a variation around the more “consensual” range µ ≤ µ R , µ F ≤ µ .We also note that when breaking σ NNLOgg → H into jet cross sections, an additional error dueto the acceptance of jets is introduced; the CDF and D0 collaborations, after weighting,have estimated it to be ± .
3. PDF and α s uncertainties Another issue is the uncertainties due to the parameterization of the PDFs and the corre-sponding ones from the value of the strong coupling constant α s . In their updated analysis [7],the CDF and D0 collaborations are now including the uncertainties generated by the exper-imental error in the value of α s and considering the PDF+∆ exp α s uncertainty, but there isstill a little way to go as the problem of the theoretical error on α s is still pending.For the new analysis that we present here for σ NNLOgg → H with a central scale µ = M H ,we have only slightly changed our previous recipe for calculating the errors due to PDFsand α s : we still use the grids provided by the MSTW collaboration [15] for PDF+∆ exp α s ,take the 90%CL result and add in quadrature the impact of the theoretical error ∆ th α s using again the sets provided by the MSTW collaboration. However, contrary to the case µ = M H where the value ∆ th α s = 0 .
003 at NLO (∆ th α s = 0 .
002 at NNLO) as suggested byMSTW [15] was sufficient to achieve a partial overlap of the MSTW and ABKM predictions(which, together with the CTEQ prediction, are given in the left–hand side of Fig. 3) whenincluding their respective error bands, we need in the case µ = M H an uncertainty of∆ th α s = 0 . α s theoretical uncertainty, which is approximately the differ-ence between the MSTW and ABKM central α s values, the results for σ NNLO gg → H using onlythe MSTW parametrisation are displayed in the right–hand side of Fig. 3. Shown arethe 90% confidence level PDF, PDF+∆ exp α s and PDF+∆ exp+th α s uncertainties, with thePDF+∆ exp α s and PDF+∆ th α s combined in quadrature. We thus obtain a PDF+∆ exp+th α s total uncertainty of ±
15% to 20% on the central cross section depending on the M H value.This is larger than the 12.5% error which has been assumed in the most recent CDF/D0 com-bined analysis [7] (and even larger than the ≈ ±
8% assumed in the earlier analysis [5]). We The error might be reduced when including higher–order corrections in the 1 jet and 2 jet cross sections. = M H / σ ( gg → H ) [fb] ABKM 09CTEQ 2008MSTW 2008 µ = M H / σ ( gg → H ) [fb] M H [ GeV ] 2001901801701601501401301201101002000180016001400120010008006004002000
MSTW σ ( gg → H ) [ fb ] PDFPDF + ∆ exp α s PDF + ∆ exp+th α s MSTW σ ( gg → H ) [ fb ] M H [ GeV ] Figure 3: Left: the gg → H cross section at NNLO for µ = M H as a function of M H when the MSTW, CTEQ and ABKM parameterizations are used. Left: the 90%CL PDF,PDF+∆ exp α s and PDF+∆ exp+th α s uncertainties on σ NNLO gg → H in the MSTW parametrisation.In the inserts, shown in % are the deviations with respect to the central MSTW value.believe that if the effect of the theoretical error on α s is taken into account in the Tevatronanalysis of σ ( gg → H ), we will arrive at a much closer agreement.We would like to insist on the fact that this recipe is only one particular way, and byno means the only one, of parameterizing the PDF uncertainty. A possibly more adequateprocedure to evaluate this theoretical uncertainty would be to consider the difference be-tween the central values given by various PDF sets. In the present gg → H case, while theMSTW and CTEQ parameterizations give approximately the same result as shown previ-ously, ABKM gives a central NNLO cross section that is ≈
25% smaller than that obtainedusing the MSTW set . The PDF uncertainty, in this case, would be thus ≈ − , +0%.We also note that there is another recipe that has been suggested by the PDF@LHCworking group for evaluating PDF uncertainties for NNLO cross sections (besides takingthe envelope of the predicted values obtained using several PDF sets) [16]: take the MSTWPDF+∆ exp α s error and multiply it by a factor of two. In our case, this would lead to anuncertainty of ≈ ±
25% which, for the minimal value, is close to the recipe discussed justabove, and is larger than what we obtain when considering the PDF+∆ exp+th α s uncertaintygiven by MSTW. We thus believe that our estimate of the PDF+ α s uncertainty that wequote here is far from being exaggeratedly conservative.
4. Combination of the various uncertainties
The last issue that remains to be discussed and which, to our opinion is the main one, is theway of combining the various sources of theoretical errors. Let us first reiterate an importantcomment: the uncertainties associated to the PDF parameterisations are theoretical errors The gg → H cross section is even smaller if one uses the new NNLO central PDF sets recently releasedby the HERAPDF collaboration [17] rather than the ABKM PDF set. .As a result, the scale and PDF uncertainties, cannot be combined in quadrature asdone, for instance, by the CDF and D0 collaborations. This is especially true as in the gg → H process, a strong correlation between the renormalization and factorization scalesthat are involved (and that we have equated here for simplicity, µ R = µ F ), the value of α s and the gg densities is present. For instance, decreasing (increasing) the scales will increase(decrease) the gg → H cross section not only because of the lower (higher) α s ( µ R ) value thatis obtained and which decreases (increases) the magnitude of the matrix element squared(that is proportional to α s at leading order and the cross section is minimal/maximal for thehighest/lowest µ R = µ F values), but also because at the same time, the gg densities becomesmaller (larger) for higher (smaller) µ F = p Q values. See Ref. [16] for details.Thus, not only the scale and PDF uncertainties cannot be added in quadrature, they alsocannot be added linearly because of the aforementioned correlation. We therefore stronglybelieve that the best and safest procedure to combine the scale and PDF+ α s uncertaintiesis the one proposed in our paper, that is, to estimate directly the PDF+ α s uncertainties onthe maximum and minimum cross sections with respect to the scale variation, σ ± ∆ σ + µ .In addition, there is a last theoretical error which should be included, related to the useof the EFT approach for the b–quark loop at NNLO QCD (together with the parametricand scheme uncertainty on the b –quark mass) and for the electroweak radiative corrections,which amount to a few %. These uncertainties, discussed in detail in section 3.2 of our paper,are also purely theoretical uncertainties and should be added linearly to the combined scaleand PDF+ α s uncertainty (as there is no apparent correlation between them).Doing so for the gg → H NNLO cross section with a central scale µ = M H , we obtainthe total error shown in Fig. 4, that we compare to the ≈ ±
22% error assumed in the CDF/D0analysis. For M H = 160 GeV for instance, we obtain ∆ σ/σ ≈ +41% , − µ = M H which amounted to ∆ σ/σ ≃ +48% , − M H = 160 GeV, a total uncertainty of ∆ σ/σ ≈ − −
37% withour procedure. On the other hand, one has an error of ≈ − In statistical language, both the scale and PDF uncertainties have a flat prior. A more elaborateddiscussion on this issue will appear in a separate publication [18]. α s uncertainties were added in quadrature andthe EFT approach error linearly (the latter being ignored by the CDF/D0 collaborations). σ ( gg → H ) [fb] ∆ total (CDF/D0) ∆ total (NNLO+EW) σ ( gg → H ) [fb] M H [ GeV ] 20019018017016015014013012016001000600300200100
Figure 4: The production cross section σ ( gg → H ) at NNLO for the QCD and NLO forthe electroweak corrections at the Tevatron at a central scale µ F = µ R = M H with theuncertainty band when all theoretical uncertainties are added using our procedure. It iscompared to σ ( gg → H ) at NNLL [13] with the errors quoted by the CDF/D0 collaboration[7]. In the insert, the relative deviations compared to the central value are shown. Summary
We have updated our analysis on the theoretical predictions for the Higgs production crosssection in the gg → H process at the Tevatron, by assuming a central scale µ R = µ F = µ = M H which seems more appropriate to describe the process and implicitly accountsfor the bulk of the higher order contributions beyond NNLO. We have then estimated thetheoretical uncertainties associated to the prediction: the scale uncertainty, the uncertaintiesfrom the PDF parametrisation and the associated error on α s , as well as uncertainties dueto the use of the EFT approach for the mixed QCD-electroweak radiative corrections andthe b -quark loop contribution. In Table 1, we summarise the results that we have obtained:the first column shows the central cross section obtained at NNLO with µ = M H and theother columns the individual uncertainties and the total absolute and relative uncertaintieswhen the latter are combined using our procedure.While our central value agrees now with the ones given in Refs. [4,13] and adopted by theCDF/D0 collaborations, the overall theoretical uncertainty that we obtain is approximatelytwice the error assumed in the latest Tevatron analysis to obtain the exclusion band 158GeV ≤ M H ≤
175 GeV on the Higgs mass [7]. This is a mere consequence of the differentways to combine the individual scale and PDF+ α s uncertainties and, to a lesser extent, theimpact on the theoretical uncertainty on α s and the EFT uncertainties which have not beenconsidered by the CDF/D0 collaborations. We have provided arguments in favor of ourprocedure to combine the scale and PDF uncertainties and we therefore still believe that theCDF/D0 exclusion limit on the Higgs mass should be reconsidered.8 eferences [1] J. Baglio and A. Djouadi, arXiv:1003.4266 [hep-ph].[2] H. Georgi, S.L. Glashow, M. Machacek and D.V. Nanopoulos, Phys. Rev. Lett. 40(1978) 692; A. Djouadi, M. Spira and P. Zerwas, Phys. Lett. B264 (1991) 440; S.Dawson, Nucl. Phys. B359 (1991) 283; D. Graudenz, M. Spira and P.M. Zerwas, Phys.Rev. Lett. 70 (1993) 1372; M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Nucl.Phys. B453 (1995) 17; R.V. Harlander and W. Kilgore, Phys. Rev. Lett. 88 (2002)201801; C. Anastasiou and K. Melnikov, Nucl. Phys. B646 (2002) 220; V. Ravindran,J. Smith and W.L. Van Neerven, Nucl. Phys. B665 (2003) 325.[3] S. Actis, G. Passarino, C. Sturm and S. Uccirati, Nucl. Phys. B811 (2009) 182.[4] C. Anastasiou, R. Boughezal and F. Pietriello, JHEP 0904 (2009) 003.[5] The CDF and D0 collaborations, “Combination of Tevatron searches for the StandardModel Higgs boson in the W + W − decay mode”, Phys. Rev. Lett. 104 (2010) 061802.[6] See the web site: http://tevnphwg.fnal.gov/results/SMHPubWinter2010/gghtheoryreplies may2010.html .[7] The CDF and D0 collaborations, “Combined CDF and D0 Upper Limits on StandardModel Higgs-Boson Production with up to 6.7 fb − of Data”, arXiv:1007.4587 [hep-ex].B. Kiminster on the behalf of CDF and D0 collaborations, “Higgs boson searches atthe Tevatron”, talk given at ICHEP 2010, July 26th 2010.[8] Higgs Hunting, Workshop held in Orsay–France, 29–31 July 2010, http://indico.lal.in2p3.fr/conferenceDisplay.py?confid=1109 .[9] S. Catani, D. de Florian, M. Grazzini and P. Nason, JHEP 0307 (2003) 028.[10] C. Anastasiou, K. Melnikov and F. Petriello, Nucl. Phys. B 724, 197 (2005)[arXiv:hep-ph/0501130]; M. Grazzini, JHEP 0802, 043 (2008) [arXiv:0801.3232 [hep-ph]].[11] C. Anastasiou, “Higgs production via gluon fusion”, talk given at Higgs Hunting [8].[12] For a review, see: A. Djouadi, Phys. Rept. 457 (2008) 1.[13] D. de Florian and M. Grazzini, Phys. Lett. B674 (2009) 291.[14] C. Anastasiou et al., JHEP 0908 (2009) 099.[15] A. Martin, W. Strirling, R. Thorne and G. Watt, Eur. Phys. J. C63 (2009) 189; ibid EPJC64 (2009) 653. See also the web site: hhtp://projects.hepforge.org/mstwpdf/ [16] R. Thorne, “PDFs, constraints and searches at LHC”, talk given at Higgs Hunting [8].[17] The NNLO PDF sets can be found at: .918] J. Baglio et al., in preparation. 10 H σ NNLOgg → H [fb] scale PDF PDF+ α exp s α th s EW b–loop total % total100 1849 +318 −
371 +102 −
109 +210 −
201 +219 −
199 +45 −
45 +42 −
42 +817 −
648 +44 . − .
105 1603 +262 −
320 +91 −
98 +184 −
176 +192 −
174 +41 −
41 +39 −
39 +700 −
565 +43 . − .
110 1397 +219 −
277 +83 −
89 +163 −
156 +170 −
152 +37 −
37 +35 −
35 +602 −
496 +43 . − .
115 1222 +183 −
242 +75 −
81 +144 −
138 +151 −
134 +33 −
33 +32 −
32 +521 −
437 +42 . − .
120 1074 +156 −
211 +69 −
73 +129 −
123 +135 −
119 +30 −
30 +29 −
29 +454 −
386 +42 . − .
125 948 +134 −
186 +63 −
67 +115 −
110 +121 −
106 +28 −
28 +24 −
24 +397 −
342 +41 . − .
130 839 +115 −
164 +57 −
61 +104 −
99 +108 −
94 +25 −
25 +21 −
21 +349 −
304 +41 . − .
135 746 +100 −
145 +53 −
56 +94 −
89 +98 −
84 +23 −
23 +18 −
18 +309 −
272 +41 . − .
140 665 +88 −
129 +48 −
51 +85 −
80 +88 −
76 +21 −
21 +16 −
16 +275 −
243 +41 . − .
145 594 +78 −
115 +45 −
47 +77 −
73 +80 −
68 +19 −
19 +14 −
14 +246 −
218 +41 . − .
150 532 +69 −
103 +41 −
44 +70 −
66 +73 −
61 +17 −
17 +13 −
13 +221 −
197 +41 . − .
155 477 +61 −
92 +38 −
40 +64 −
60 +67 −
55 +15 −
15 +10 −
10 +198 −
176 +41 . − .
160 425 +54 −
82 +35 −
37 +58 −
54 +60 −
50 +11 −
11 +9 − −
155 +41 . − .
162 405 +51 −
78 +33 −
35 +56 −
52 +58 −
48 +9 − − −
146 +40 . − .
164 386 +48 −
75 +32 −
34 +53 −
50 +55 −
45 +8 − − −
139 +40 . − .
165 377 +47 −
73 +31 −
33 +52 −
48 +54 −
44 +7 − − −
135 +40 . − .
166 368 +46 −
71 +31 −
33 +51 −
47 +53 −
44 +6 − − −
132 +40 . − .
168 352 +44 −
68 +30 −
31 +49 −
46 +51 −
42 +5 − − −
126 +40 . − .
170 337 +42 −
65 +29 −
30 +47 −
44 +49 −
40 +4 − − −
119 +40 . − .
175 303 +37 −
59 +26 −
28 +43 −
40 +45 −
36 +2 − − −
106 +40 . − .
180 273 +33 −
53 +24 −
26 +39 −
36 +41 −
33 +1 − − −
95 +40 . − .
185 245 +30 −
47 +22 −
24 +36 −
33 +38 −
30 +1 − − −
87 +41 . − .
190 222 +27 −
43 +21 −
22 +33 −
30 +35 −
27 +2 − − −
79 +41 . − .
195 201 +24 −
39 +19 −
20 +31 −
28 +32 −
25 +2 − − −
72 +41 . − .
200 183 +22 −
35 +18 −
19 +28 −
26 +30 −
23 +2 − − −