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QCD Uncertainties

Search for the Truth Quark at Fermilab involves analysis of SEMILEPTONIC events using theoretical QCD calculations that may not be accurate at some relevant energies.  Fermilab's semileptonic value of the Truth quark mass is around 180 GeV.  CDF at Fermilab, in hep-ex/9601008, has studied 19.5 pb^(-1) of data and concluded that "The cross section for jets with ET greater than 200 GeV is significantly higher than current predictions based on third-order alpha_s perturbative QCD calculations." Their Figure 1 shows that the percent difference between data and NLO QCD prediction using MRSD0' Parton Distribution Functions get up to 50 percent at about 360 GeV, which would be the energy level of a Truth Quark-Antiquark pair for the Fermilab semileptonic value of about 180 GeV for the Truth Quark mass.  I think that this is a good example of the type of uncertainty that has led some people at Fermilab to an incorrect interpretion of data as evidence for a semileptonic Truth Quark mass of 180 GeV.  It seems to me to be natural to expect that as you go to higher energies, third-order perturbative QCD may become inaccurate, and you may need to go to higher-order perturbative QCD, at least to fourth-order, to get agreement with experiment.  It also seems to me that the 200-400 GeV energy range at which discrepancies (with respect to third-order QCD) begin to appear and to grow large (50 percent at 360 GeV) may be a likely range for such higher-order perturbative QCD effects to begin to appear and to grow large, thus explaining the data.  Thanks to Kristi Bridges-Jentoft-Nilsen at Georgia Tech for helpful discussions on these points.  The New York Times coverage of the results of the CDF paper hep-ex/9601008 is an interesting example of science journalism.Leader and Stamenov have proposed that such things as composite quarks are not necessary to explain the excess of jets at high ET,  because the excess can be explained by a QCD fixed point such as proposed by Patrascioiu and Seiler who contend that PQCD and asymptotic freedom are NOT true properties of physical QCD. If so, the renormalization group equation I used to calculate ALPHA_s is not valid, so that ALPHA_s = 0.106 is not the true value for 91 GeV under the D4-D5-E6 model.  The true 91 GeV value for the D4-D5-E6 model ALPHA_s should be higher, closer to the high-energy experimental ALPHA_s = 0.123. 


Alexei Morozov and Antti J. Niemi, in theirpaper, Can Renormalization Group Flow End in a Big Mess?,hep-th/0304178, say: "... The field theoretical renormalizationgroup equations have many common features with the equations ofdynamical systems. In particular, the manner how Callan-Symanzikequation ensures the independence of a theory from its subtractionpoint is reminiscent of self-similarity in autonomous flows towardsattractors. Motivated by such analogies we propose that besidesisolated fixed points, the couplings in a renormalizable field theorymay also flow towards more general, even fractal attractors. Thiscould lead to Big Mess scenarios in applications tomultiphase systems, from spin-glasses and neural networks tofundamental ... theory. We argue that ... such chaotic flows ... poseno obvious contradictions with the known properties of effectiveactions, the existence of dissipative Lyapunov functions, and eventhe strong version of the c-theorem. We also explain the difficultiesencountered when constructing effective actions with chaoticrenormalization group flows and observe that they have many commonvirtues with realistic field theory effective actions. We concludethat if chaotic renormalization group flows are to be excluded,conceptually novel no-go theorems must be developed. ... in theclassical Yang-Mills theory chaotic behaviour has already been wellestablished ... Consequently such chaotic behaviour will not beconsidered here. Obviously, a chaotic RG flow also necessitates theconsideration of field (string) theories with at least threecouplings. In the present article we shall be interested in thepossibility of chaotic RG flows in the IR limits of quantum field andstring theories. ... we consider limit cycles from the point of viewof RG flows, and inspect vorticity as a RG scheme independent toolfor describing multicoupling flows. ... we explain how to constructmodel effective actions from the beta-function flows. In particular,we explain how the construction fails in case of chaotic flows andsuggests this parallels the problems encountered in constructingactual field theory effective actions. This also explains why it isvery hard to construct actual field theory models with chaotic RGflow. ...".


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