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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, 
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 their paper, Can Renormalization Group Flow End in a Big Mess?, hep-th/0304178, say: "... The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental ... theory. We argue that ... such chaotic flows ... pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed. ... in the classical Yang-Mills theory chaotic behaviour has already been well established ... Consequently such chaotic behaviour will not be considered here. Obviously, a chaotic RG flow also necessitates the consideration of field (string) theories with at least three couplings. In the present article we shall be interested in the possibility of chaotic RG flows in the IR limits of quantum field and string theories. ... we consider limit cycles from the point of view of RG flows, and inspect vorticity as a RG scheme independent tool for describing multicoupling flows. ... we explain how to construct model effective actions from the beta-function flows. In particular, we explain how the construction fails in case of chaotic flows and suggests this parallels the problems encountered in constructing actual field theory effective actions. This also explains why it is very hard to construct actual field theory models with chaotic RG flow. ...".


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