%From: "R. Sekhar Chivukula" %Date: Wed, 28 Jun 95 13:43:36 -0400 %Date (revised): Wed, 28 Jun 95 13:54:49 -0400 %Date (revised): Wed, 20 Sep 95 11:16:10 -0400 %LATEX VERSION %PROCEEEDINGS/REVIEW VOLUMES --- TRIM SIZE OF 8+" X 6" FOR 20% REDUCTION %LAST UPDATE --- 6/6/95 %------------------------------------------------------------------------ \documentstyle[12pt,epsf]{article} %PROCEEEDINGS/REVIEW VOLUMES --- TRIM SIZE OF 8+" X 6" FOR 20% REDUCTION %LAST UPDATE --- 6/6/95 %------------------NEW ADDITIONS TO EXISTING ARTICLE.STY------------------ \catcode`\@=11 \long\def\@makefntext#1{ \protect\noindent \hbox to 3.2pt {\hskip-.9pt $^{{\ninerm\@thefnmark}}$\hfil}#1\hfill} \def\thefootnote{\fnsymbol{footnote}} \def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}} \def\ps@myheadings{\let\@mkboth\@gobbletwo \def\@oddhead{\hbox{} \rightmark\hfil\ninerm\thepage} \def\@oddfoot{}\def\@evenhead{\ninerm\thepage\hfil \leftmark\hbox{}}\def\@evenfoot{} \def\sectionmark##1{}\def\subsectionmark##1{}} 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\newcommand{\eeq}{\end{equation}} \newcommand{\beqa}{\begin{eqnarray}} \newcommand{\eeqa}{\end{eqnarray}} \newcommand{\infinity}{\infty} %\renewcommand{\theequation}{\thesection.\arabic{equation}} \newcounter{ehsctr} \newcommand{\NPB}[1]{{\it Nucl. Phys.}\ {\bf B{#1}}} \newcommand{\PLB}[1]{{\it Phys. Lett.}\ {\bf B{#1}}} \newcommand{\PRD}[1]{{\it Phys. Rev.}\ {\bf D{#1}}} \newcommand{\PRL}[1]{{\it Phys. Rev. Lett.}\ {\bf #1}} \newcommand{\NCA}[1]{{\it Nuovo Cim.}\ {\bf {#1}A}} \newcommand{\hc}{ {\rm h.c.} } \newcommand{\ME}{ M_{ETC} } \newcommand{\gE}{ g_{ETC} } \newcommand{\TC}{technicolor} \newcommand{\ETC}{extended technicolor} \newcommand{\lae}{\begin{array}{c}\,\sim\vspace{-21pt}\\< \end{array}} \newcommand{\gae}{\begin{array}{c}\,\sim\vspace{-21pt}\\> \end{array}} \hyphenation{sub-sti-tut-ing quad-rat-ic fer-mions hy-per-charge in-ter-ac-tions } \textwidth 6.0in \textheight 8.6in \pagestyle{empty} \topmargin -0.25truein \oddsidemargin 0.30truein \evensidemargin 0.30truein %\flushbottom \parindent=1.5pc \baselineskip=15pt \begin{document} \setcounter{footnote}{0} \renewcommand{\thefootnote}{\fnsymbol{footnote}} \centerline{\normalsize\bf ISOSPIN BREAKING AND THE TOP-QUARK MASS IN} \baselineskip=22pt \centerline{\normalsize\bf MODELS OF DYNAMICAL ELECTROWEAK SYMMETRY BREAKING\footnote{Talk presented by R.~S.~Chivukula at the {\it Workshop on Top Quark Physics}, Iowa State University, Ames, IA, May 25-26, 1995 and the {\it Yukawa International Seminar `95}, Yukawa Institute, Kyoto, Aug. 21-25, 1995}} \baselineskip=16pt \centerline{\footnotesize R.S. Chivukula, B.A. Dobrescu, and J. Terning} \baselineskip=13pt \centerline{\footnotesize\it Physics Department, Boston University} \baselineskip=12pt \centerline{\footnotesize\it 590 Commonwealth Ave.} \centerline{\footnotesize\it Boston, MA 02215 USA} \centerline{\footnotesize E-mail: sekhar@bu.edu, dobrescu@budoe.bu.edu, terning@calvin.bu.edu} \baselineskip=16pt \centerline{\footnotesize\sf BUHEP-95-22 \& hep-ph/9506450} \vspace*{0.9cm} \abstracts{ In this talk we review the physics of top-quark mass generation in models of dynamical electroweak symmetry breaking and the constraints on this physics arising from limits on the deviation of the weak interaction $\rho$-parameter from one. We then discuss top-color assisted technicolor in this context. } \normalsize\baselineskip=15pt \setcounter{footnote}{0} \renewcommand{\thefootnote}{\alph{footnote}} \section{$m_t$ in Models of Dynamical Electroweak Symmetry Breaking} \label{sec:mt} In technicolor models, the masses of the ordinary fermions are due to their coupling, through additional, broken, extended-technicolor (ETC) gauge-interactions\cite{ETC}, to the technifermions: \beq \epsfxsize 4cm \centerline{\epsffile{tETC.eps}} \eeq \noindent which leads to a mass for the top-quark \beq m_t \approx {g^2 \over M^2_{ETC}} \langle\bar{U} U \rangle_{M_{ETC}}\ , \eeq \noindent where we have been careful to note that it is the value of the technifermion condensate renormalized at the scale $M_{ETC}$ which is relevant. For a QCD-like technicolor, where there is no substantial difference between $\langle\bar{U} U \rangle_{M_{ETC}}$ and $\langle\bar{U} U \rangle_{\Lambda_{TC}}$, we can use naive dimensional analysis\cite{dimanal} to estimate the technifermion condensate, arriving at a top-quark mass \beq m_t \approx {g^2 \over M^2_{ETC}} 4 \pi F^3\ , \eeq \noindent where $F$ is the analog of the pion decay-constant (93 MeV, in my normalization) in QCD. We can invert this relation to find the characteristic mass-scale of top-quark mass-generation \beq {M_{ETC} \over g} \approx 1\ {\rm TeV} \left({F \over 246\ {\rm GeV}}\right)^{3\over 2} \left({175\ {\rm GeV} \over m_t}\right)^{1\over 2}. \label{blitz} \eeq We immediately see that the scale of top-quark mass generation is likely to be {\it quite} low, unless the value of the technifermion condensate ($\langle\bar{U} U \rangle_{M_{ETC}}$) can be raised significantly above the value predicted by naive dimensional analysis. The prospect of such a low ETC-scale is both tantalizing and problematic. As we will see in the next section, constraints from the deviation of the weak interaction $\rho$ parameter from one suggest that the scale may have to be larger than one TeV. The most promising approach\cite{strongETC} to enhance the technifermion condensate and accommodate the top-quark mass is ``strong-ETC''. As the size of the ETC-coupling approaches the critical value for chiral symmetry breaking, it is possible to enhance the running technifermion self-energy $\Sigma(k)$ at large momenta (see Figure \ref{figone}). \begin{figure}[htb] \vspace{0.25cm} \epsfxsize 8cm \centerline{\epsffile{evans_fig1.eps}} \caption{Plot\protect\cite{evans} of technifermion self energy $\Sigma(k)$ vs. momentum (both in TeV), as predicted by the gap-equation in the rainbow approximation, for various strengths of the ETC coupling relative to their critical value $g_C$.} \label{figone} \vspace{0.25cm} \end{figure} \noindent Since the technifermion condensate is related to the trace of the fermion propagator. \beq \langle\bar{U} U \rangle_{M_{ETC}} \propto \int^{M^2_{ETC}} dk^2 \Sigma(k)\ , \eeq \noindent a slowly-falling running-mass translates to an enhanced condensate\footnote{More physically, in terms of the relevant low-energy theory, it can be shown that the enhancement of the top-quark mass is due to the dynamical generation of a light scalar state\cite{Comp}}. \begin{figure}[htb] \vspace{0.25cm} \epsfxsize 8cm \centerline{\epsffile{evans_fig3.eps}} \caption{Plot\protect\cite{evans} of top mass (in GeV) vs. ETC coupling ($g/g_c$ in \%), as predicted by gap-equation in the rainbow approximation, for ETC scales of 10 and 100 TeV.} \label{figtwo} \vspace{0.25cm} \end{figure} Unfortunately, there is no such thing as a free lunch. As we see from Fig. \ref{figtwo}, the enhancement of the technifermion self-energy in strong-ETC theories comes at the cost of a ``fine-tuning" of the strength of the ETC coupling relative to the critical value where the ETC interactions would, in and of themselves, generate chiral symmetry breaking. In the context of the NJL approximation\cite{NJL}, we find that enhancement of the top quark mass is directly related to the severity of this adjustment, \beq {\langle\bar{U} U \rangle_{\Lambda_{TC}}\over \langle\bar{U} U \rangle_{M_{ETC}}} \approx {\Delta g^2 \over g^2_c}~, \label{price} \eeq \noindent where $\Delta g^2 \equiv g^2 - g^2_C$. \section{$\Delta\rho_*$} \label{sec:deltarho} The physics which is responsible for top-quark mass generation must violate custodial $SU(2)$ since, after all, this physics must give rise to the disparate top- and bottom-quark masses. \subsection{Direct Contributions} ETC operators which violate custodial isospin by two units ($\Delta I = 2$) are particularly dangerous\cite{isospin2}. Denoting the right-handed technifermion doublet by $\psi_R$, consider the operator \beq {g^2 \over M^2} \left(\bar{\Psi}_R \gamma_\mu \sigma_3 \Psi_R\right)^2~~, \label{cohler} \eeq \noindent which can be interpreted as the (mass-)mixing of the $Z$ with an isosinglet ETC gauge-boson \beq \epsfxsize 5cm \centerline{\epsffile{fig1a_hacked.ps}} \eeq \noindent and give rise to a contribution to $\Delta\rho_*$\footnote{ Contributions of this sort occur naturally in ETC-models which give rise to the top-quark mass\protect\cite{wu}.}. If there are $N_D$ doublets of the technifermions and they give rise to a contribution to $M^2_W$ proportional to $N_D F^2$, the contribution of the operator in eqn. (\ref{cohler}) to the $\rho$ parameter can be calculated to be \beqa \Delta\rho_* & \approx & {2 g^2 \over M^2} {N^2_D F^4 \over v^2} \\ & \approx & 12\%\ g^2 \left({N_D F^2 \over (246 \ {\rm GeV})^2}\right)^2 \left({1 \ {\rm TeV} \over M}\right)^2 ~. \label{important} \eeqa \noindent Current limits\cite{tc2isospin} on the parameter $T$ ($\Delta \rho_* = \alpha T$) imply that $\Delta\rho_* \lae 0.4\% $. There are two ways in which one may try to satisfy this constraint. The equation above implies \beq {M\over g} \gae 5.5\ {\rm TeV} \left( {N_D F^2 \over (246\ {\rm GeV})^2}\right)\ . \eeq \noindent If $N_D F^2 \approx (246\ {\rm GeV})^2$, that is if the sector giving rise to the top-quark mass is responsible for the bulk of EWSB, then the scale $M$ must be much larger than the naive 1 TeV expectation in QCD-like technicolor. Comparing this with eqns. (\ref{blitz}) and (\ref{price}) above, we see that the enhancement of the condensate needed requires a fine-tuning of order 3\% ($\approx (1/5.5)^2$) in order to produce a top-quark mass of order 175 GeV. Alternatively, we may re-write the bound as \beq F \lae {105\ {\rm GeV} \over \sqrt{N_D}} \left( {M/g \over 1\ {\rm TeV}}\right)^{1\over 2} \eeq \noindent If $M/g$ is of order 1 TeV, it is necessary that the sector responsible for top quark mass generation {\em not} give rise to the bulk of EWSB. This is essentially what happens in multiscale models \cite{multi,chiraltc} and in top-color assisted technicolor \cite{top-color}. \subsection{Indirect Contributions} A second class of potentially dangerous contributions come from isospin violation in the technifermion mass spectrum. In a manner analogous to the contribution\cite{Drho} of the $t-b$ mass splitting to $\Delta \rho$, any difference in the dynamical masses of two technifermions in the {\em same} doublet will give rise to deviations in the $\rho$ parameter from one. The size of this effect can be estimated \`a la Pagels-Stokar\cite{pagels}, \beq \Delta \rho_* \propto {N_D\, d \over 16 \pi^2} \left({\Sigma_U(0) - \Sigma_D(0)}\over v\right)^2~~, \eeq \noindent where $N_D$ and $d$ are the the number of doublets and dimension of the technicolor representation respectively. Since we require $\Delta \rho_* \lae 0.4$\%, the equation above implies \beq N_D\, d \left({\Delta\Sigma(0)\over m_t}\right)^2 \lae 1.3 \, \, . \label{ilimit} \eeq \noindent {}From this we see that, $\Delta \Sigma(0)$ must be less than of order $m_t$ \footnote{Perhaps, given the crude approximations involved, one may be able to live with $d=2$ in the fundamental of and $SU(2)$ technicolor group with one doublet.}. However, if the $t$ and $b$ get their mass from the same technidoublet, then at the ETC-scale we expect that there is no difference between the $t$, $b$ and the corresponding technifermions\cite{strongETC} \beqa \Delta\Sigma(M_{ETC})& \equiv & \Sigma_U(M_{ETC}) - \Sigma_D(M_{ETC}) \approx \nonumber \\ \Delta m(M_{ETC}) & \equiv & m_t(M_{ETC}) - m_b(M_{ETC})~. \label{problem} \eeqa \noindent Furthermore, if QCD is the only interaction which contributes to the scaling of the $t$ and $b$ masses, we expect $\Delta m(M_{ETC}) \approx m^{pole}_t$, and from scaling properties of the technifermion self-energies, we expect $\Delta\Sigma(0) \gae \Delta \Sigma(M_{ETC})$. There are two ways to avoid these constraints. One is that perhaps there are {\it additional} interactions which contribute to the scaling of the top- and bottom-masses below the ETC scale, and hence that $\Delta m(M_{ETC}) \ll m_t^{pole}$. This would be the case if the $t$ and/or $b$ get only a {\em portion} of their mass from the technicolor interactions, and would imply that the third generation must have (strong) interactions different from the technifermions (and possibly from the first and second generations). Another possibility is that the $t$ and $b$ get mass from {\em different} technidoublets, each of which have isospin-symmetric masses. The first alternative is the solution chosen in top-color assisted technicolor models (see below), while the latter has only recently begun to be explored\cite{isosymmetric}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Case Study: Top-Color Assisted Technicolor} \label{sec:tcii} Recently\cite{top-color}, Hill has introduced a model in which a top-condensate is driven by the combination of a strong, but spontaneously broken and non-confining, isospin-symmetric top-color interaction and an additional (either weak or strong) isospin-breaking $U(1)$ interaction which couple only to the third generation quarks. At low-energies, the top-color and hypercharge interactions of the third generation quarks may be approximated by four-fermion operators \beq {\cal L}_{4f} = -{{4\pi \kappa_{tc}}\over{M^2}}\left[\overline{\psi}\gamma_\mu {{\lambda^a}\over{2}} \psi \right]^2 -{{4\pi \kappa_1}\over{M^2}}\left[{1\over3}\overline{\psi_L}\gamma_\mu \psi_L +{4\over3}\overline{t_R}\gamma_\mu t_R -{2\over3}\overline{b_R}\gamma_\mu b_R \right]^2~, \label{L4t} \eeq \noindent where $\psi$ represents the top-bottom doublet, $\kappa_{tc}$ and $\kappa_1$ are related respectively to the top-color and $U(1)$ gauge-couplings squared, and where (for convenience) we have assumed that the top-color and $U(1)$ gauge-boson masses are comparable and of order $M$. In order to produce a large top quark mass without giving rise to a correspondingly large bottom quark mass, the combination of the top-color and extra hypercharge interactions are assumed to be critical in the case of the top quark but not the bottom quark: \beq \kappa^t_{eff} = \kappa_{tc} +{1\over3}\kappa_1 > \kappa_c = {{3\pi}\over{8}} > \kappa^b_{eff}=\kappa_{tc} -{1\over 6}\kappa_1~. \label{kc} \eeq The contribution of the top-color sector to electroweak symmetry breaking can be quantified by the $F$-constant of this sector. In the NJL approximation\cite{NJL}, for $M$ of order 1 TeV, and $m_t \approx 175$ GeV, we find \beq f_t^2 \equiv {{N_c }\over{8\pi^2}}\, m_t^2 \log\left({{M^2}\over{m_t^2}}\right) \approx (64\ {\rm GeV})^2~. \label{ft} \eeq \subsection{Direct Isospin Violation} As $f_t$ is small compared to 246 GeV, technicolor is necessary to produce the bulk of EWSB and to give mass to the light fermions. However, the heavy and light fermions must mix --- hence, we would naturally expect that at least some of the {\it technifermions} carry the extra $U(1)$ interaction. If the additional $U(1)$ interactions violate custodial symmetry\footnote{It has been noted\cite{isosymmetric} that if the top- and bottom-quarks receive their masses from {\em different} technidoublets, it is possible to assign the extra $U(1)$ quantum numbers in a custodially invariant fashion.}, the $U(1)$ coupling will have to be quite small to keep this contribution to $\Delta \rho_*$ small\cite{tc2isospin}. We will illustrate this in the one-family technicolor\cite{onefam} model, assuming that techniquarks and technileptons carry $U(1)$-charges proportional to the hypercharge of the corresponding ordinary fermion\footnote{Note that this choice is anomaly-free.}. We can rewrite the effective $U(1)$ interaction of the technifermions as \beq {\cal L}_{4T1} =-{{4\pi \kappa_1}\over{M^2}}\left[{1\over3}\overline{\Psi}\gamma_\mu \Psi +\overline{\Psi}_R\gamma_\mu \sigma^3 \Psi_R -\overline{L} \gamma_\mu L + \overline{L}_R \gamma_\mu\sigma^3 L_R \right]^2~, \label{L4T} \eeq \noindent where $\Psi$ and $L$ are the techniquark and technilepton doublets respectively. {}From the analysis given above (eqn. (\ref{important})), we see that the contribution to $\Delta \rho_*$ is\cite{tc2isospin}: \beq \Delta \rho_{*}^{\rm T} \approx 152\% \ \kappa_1 \left({{1\ {\rm TeV}}\over{M}}\right)^2~. \label{rhoT} \eeq \noindent Therefore if $M$ is of order 1 TeV, and the extra $U(1)$ has isospin-violating couplings to technifermions, $\kappa_1$ must be extremely small. \subsection{Indirect Isospin Violation} In principle, since the isospin-splitting of the top and bottom are driven by the combination of top-color and the extra $U(1)$, the technifermions can be degenerate. In this case, the only indirect contribution to the $\rho$ parameter at one-loop is the usual contribution coming from loops of top- and bottom-quarks\cite{Drho}. However, since there are additional interactions felt by the third-generation of quarks, there are ``two-loop'' contributions of the form \beq \epsfxsize 5cm \centerline{\epsffile{fig1b_hacked.ps}} \label{twoloop} \eeq This contribution yields\cite{tc2isospin} \beq \Delta \rho_{*}^{\rm tc} \approx 0.53\% \left({\kappa_{tc}\over \kappa_c}\right) \left(1\ {\rm TeV}\over M\right)^2 \left(f_t \over 64\ {\rm GeV}\right)^4 {}~. \label{rhot} \eeq \noindent Combining this with eqn. (\ref{ft}), we find that \beq M \gae 1.4\ {\rm TeV} \eeq \noindent for $\kappa_{tc} \approx \kappa_c$. This immediately puts a constraint on the mass of the top-color gluon which is comparable to the direct limits currently obtained by CDF\cite{cdftwojet}. \subsection{Fine-Tuning} Finally, we must require that the sum of the effects of eqns. (\ref{rhoT}) and (\ref{rhot}) do not give rise to an experimentally disallowed contribution to the $\rho$ parameter. Equation (\ref{rhoT}) implies that $\kappa_1$ must either be very small, or $M$ very large. However, we must also simultaneously satisfy the constraint of eqn. (\ref{kc}), which implies that \beq {\Delta\kappa_{tc}\over\kappa_c} = \left|{{\kappa_{tc}-\kappa_c} \over \kappa_c}\right| \le {1 \over 3} {\kappa_1\over \kappa_c}~, \label{dktc} \eeq \noindent Therefore, if $M$ is low and $\kappa_1$ is small, the top-color coupling must be tuned close to the critical value for chiral symmetry breaking. On the other hand, if $\kappa_1$ is not small and $M$ is relatively large the {\em total} coupling of the top-quark must be tuned close to the critical NJL value\cite{NJL} for chiral symmetry breaking in order to keep the top-quark mass low, \beq {\Delta\kappa_{eff}\over\kappa_c} = {{\kappa^t_{eff}-\kappa_c}\over \kappa_c} = {{{m^2_t\over M^2}\log{M^2\over m^2_t}} \over {1-{{m^2_t\over M^2}\log{M^2\over m^2_t}}}}~. \label{dkefft} \eeq These two constraints are shown in Fig. \ref{figfour}. For $M>$ 1.4 TeV, we find that either $\Delta\kappa_{tc}/ \kappa_c$ or $\Delta\kappa_{eff}/\kappa_c$ must be tuned to less than 1\%. This trade-off in fine tunings is displayed in figure 4. For the ``best" case where both tunings are of order 1\%, $M=4.5$ TeV. \begin{figure}[htb] \vspace{0.25cm} \epsfxsize 8cm \centerline{\epsffile{fig3_hacked.ps}} \caption{The amount of fine-tuning required\protect\cite{tc2isospin} in the ${\rm TC}^2$ model. The dashed line is the amount of fine-tuning in $\Delta\kappa_{eff}$ required to keep $m_t$ much lighter than $M$, see equation (\ref{dkefft}). The solid curve shows the amount of fine-tuning (see equation (\ref{dktc})) in $\Delta\kappa_{tc}$ required to satisfy the bound $\Delta \rho_* < 0.4$\%. The region excluded by the experimental constraint on $\Delta \rho_*$ is above the solid curve.} \label{figfour} \vspace{0.25cm} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusions} \label{sec:concl} We have seen that a large top quark mass has a number of important implications for dynamical electroweak symmetry breaking: \begin{itemize} \item[$\bullet$] A large top-quark mass naturally implies, in models of dynamical electroweak symmetry breaking, the possibility of a correspondingly low scale for the scale of top flavor-physics. \item[$\bullet$] The physics responsible for the large isospin breaking in the $t-b$ mass splitting can lead to potentially dangerous ``direct" and ``indirect" effects in the $W$ and $Z$ masses. \item[$\bullet$] The direct and indirect effects can be mitigated if the sector which is responsible for the top- and bottom-masses does {\em not} provide the bulk of electroweak symmetry breaking and, conversely, if the sector responsible for the $W$ and $Z$ masses gives rise to only a {\em small portion} of the top- and bottom-masses. This can happen only if the top and bottom feel {\em strong} interactions which are not shared by the technifermions and, possibly, the first two generations. \item[$\bullet$] In top-color assisted technicolor, the extra top-color interactions give rise to additional indirect contributions to $\Delta \rho$, and we must require that $M_{g} \gae 1.4\ {\rm TeV}$. Furthermore, If the extra $U(1)$ has isospin-violating couplings to technifermions, we require fine-tuning of order 1\%. \end{itemize} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \centerline{\bf Acknowledgments} We thank Tom Appelquist, Nick Evans, and Ken Lane for helpful conversations, and Mike Dugan for help in preparing the manuscript. R.S.C. acknowledges the support of an NSF Presidential Young Investigator Award, and a DOE Outstanding Junior Investigator Award. {\em This work was supported in part by the National Science Foundation under grant PHY-9057173, and by the Department of Energy under grant DE-FG02-91ER40676.} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{99} \frenchspacing \bibitem{ETC} S. Dimopoulos and L. Susskind, \NPB{155} (1979) 237; E. Eichten and K. Lane, \PLB{90} (1980) 125. \bibitem{dimanal}A. Manohar and H. Georgi, \NPB{234} (1984) 189. \bibitem{strongETC} T. Appelquist, M. Einhorn, T. Takeuchi, and L.C.R. Wijewardhana, {\em Phys. Lett.} {\bf 220B}, 223 (1989); V.A. Miransky and K. Yamawaki, {\em Mod. Phys. Lett.} {\bf A4}, 129 (1989); K. Matumoto {\em Prog. Theor. Phys. Lett.} {\bf 81}, 277 (1989) . \bibitem{evans} N. Evans, \PLB{331} (1994) 378. \bibitem{Comp}R.S.~Chivukula, K.~Lane, and A.G.~Cohen, {\em Nucl. Phys.} {\bf B 343}, 554 (1990); T. Appelquist, J. Terning, and L. Wijewardhana, {\em Phys. Rev.} {\bf 44}, 871 (1991). \bibitem{NJL} Y. Nambu and G. Jona-Lasinio, {\em Phys. Rev.} {\bf 122} (1961) 345. \bibitem{isospin2}T. Appelquist et al., {\em Phys. Rev.} {\bf D31} (1985) 1676. \bibitem{wu} See, for example, G.-H. Wu, these proceedings and hep-ph/9412206. \bibitem{top-color}C.T. Hill, these proceedings and \PLB{345} (1995) 483. \bibitem{onefam}E. Farhi and L. Susskind, {\em Phys. Rev.} {\bf D20} (1979) 3404. \bibitem{tc2isospin}R.S. Chivukula, B.A. Dobrescu, and J. Terning, hep-ph/9503203. \bibitem{multi}K. Lane and E. Eichten, {\em Phys. Lett.} {\bf B222} (1989) 274. \bibitem{chiraltc}J. Terning, hep-ph/9410233, {\em Phys. Lett.} {\bf B344} (1995) 279. \bibitem{Drho}M. Einhorn, D. Jones, and M. Veltman, {\em Nucl. Phys.} {\bf B191} (1981) 146. \bibitem{pagels} H. Pagels and S. Stokar, {\em Phys. Rev.} {\bf D20} (1979) 2947; B. Holdom, \PLB{226} (1989) 137. \bibitem{isosymmetric}K. Lane and E. Eichten, hep-ph/9503433. \bibitem{cdftwojet} A. Beretvas, these proceedings, and F. Abe {\it et. al.}, CDF collaboration, FERMILAB-PUB-94/405-E. \end{thebibliography} \end{document} tc}J. Terning, hep-ph/9410233, {\em Phys. Lett.} {\bf B344} (1995) 279. \bibitem{Drho}M. Einhorn, D. Jones, and M. Veltman, {\em Nucl. 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np 1578 980 a 1580 980 li st 3 w np 1580 980 a 1583 980 li st 2 w np 1583 980 a 1585 980 li st 3 w np 1585 980 a 1588 980 li st 1590 981 a np 1588 980 a 1590 981 li st 2 w np 1590 981 a 1592 981 li st 3 w np 1592 981 a 1595 981 li st 2 w np 1595 981 a 1597 981 li st 3 w np 1597 981 a 1600 981 li st 2 w np 1600 981 a 1602 981 li st 3 w np 1602 981 a 1605 981 li st 2 w np 1605 981 a 1607 981 li st 2 w np 1607 981 a 1609 981 li st 3 w np 1609 981 a 1612 981 li st 2 w np 1612 981 a 1614 981 li st 1617 982 a np 1614 981 a 1617 982 li st 2 w np 1617 982 a 1619 982 li st 3 w np 1619 982 a 1622 982 li st 2 w np 1622 982 a 1624 982 li st 188 1117 a 5.0 setlinewidth 410 606 a 3 w np 410 606 a 413 606 li st 415 607 a np 413 606 a 415 607 li st 418 608 a np 415 607 a 418 608 li st 420 610 a np 418 608 a 420 610 li st 423 612 a np 420 610 a 423 612 li st 425 614 a np 423 612 a 425 614 li st 427 616 a np 425 614 a 427 616 li st 430 618 a np 427 616 a 430 618 li st 432 621 a np 430 618 a 432 621 li st 435 623 a np 432 621 a 435 623 li st 437 625 a np 435 623 a 437 625 li st 440 627 a np 437 625 a 440 627 li st 442 630 a np 440 627 a 442 630 li st 444 632 a np 442 630 a 444 632 li st 447 634 a np 444 632 a 447 634 li st 449 636 a np 447 634 a 449 636 li st 452 638 a np 449 636 a 452 638 li st 454 641 a np 452 638 a 454 641 li st 457 643 a np 454 641 a 457 643 li st 459 645 a np 457 643 a 459 645 li st 462 647 a np 459 645 a 462 647 li st 464 649 a np 462 647 a 464 649 li st 466 651 a np 464 649 a 466 651 li st 469 653 a np 466 651 a 469 653 li st 471 655 a np 469 653 a 471 655 li st 474 657 a np 471 655 a 474 657 li st 476 659 a np 474 657 a 476 659 li st 479 660 a np 476 659 a 479 660 li st 481 662 a np 479 660 a 481 662 li st 483 664 a np 481 662 a 483 664 li st 486 666 a np 483 664 a 486 666 li st 488 667 a np 486 666 a 488 667 li st 491 669 a np 488 667 a 491 669 li st 493 671 a np 491 669 a 493 671 li st 496 672 a np 493 671 a 496 672 li st 498 674 a np 496 672 a 498 674 li st 500 675 a np 498 674 a 500 675 li st 503 677 a np 500 675 a 503 677 li st 505 678 a np 503 677 a 505 678 li st 508 680 a np 505 678 a 508 680 li st 510 681 a np 508 680 a 510 681 li st 513 683 a np 510 681 a 513 683 li st 515 684 a np 513 683 a 515 684 li st 517 685 a np 515 684 a 517 685 li st 520 686 a np 517 685 a 520 686 li st 522 688 a np 520 686 a 522 688 li st 525 689 a np 522 688 a 525 689 li st 527 690 a np 525 689 a 527 690 li st 530 691 a np 527 690 a 530 691 li st 532 693 a np 530 691 a 532 693 li st 534 694 a np 532 693 a 534 694 li st 537 695 a np 534 694 a 537 695 li st 539 696 a np 537 695 a 539 696 li st 542 697 a np 539 696 a 542 697 li st 544 698 a np 542 697 a 544 698 li st 547 699 a np 544 698 a 547 699 li st 549 700 a np 547 699 a 549 700 li st 551 701 a np 549 700 a 551 701 li st 554 702 a np 551 701 a 554 702 li st 556 703 a np 554 702 a 556 703 li st 559 704 a np 556 703 a 559 704 li st 561 705 a np 559 704 a 561 705 li st 564 706 a np 561 705 a 564 706 li st 566 707 a np 564 706 a 566 707 li st 569 708 a np 566 707 a 569 708 li st 571 709 a np 569 708 a 571 709 li st 2 w np 571 709 a 573 709 li st 576 710 a np 573 709 a 576 710 li st 578 711 a np 576 710 a 578 711 li st 581 712 a np 578 711 a 581 712 li st 583 713 a np 581 712 a 583 713 li st 586 714 a np 583 713 a 586 714 li st 2 w np 586 714 a 588 714 li st 590 715 a np 588 714 a 590 715 li st 593 716 a np 590 715 a 593 716 li st 595 717 a np 593 716 a 595 717 li st 3 w np 595 717 a 598 717 li st 600 718 a np 598 717 a 600 718 li st 603 719 a np 600 718 a 603 719 li st 2 w np 603 719 a 605 719 li st 607 720 a np 605 719 a 607 720 li st 610 721 a np 607 720 a 610 721 li st 2 w np 610 721 a 612 721 li st 615 722 a np 612 721 a 615 722 li st 617 723 a np 615 722 a 617 723 li st 3 w np 617 723 a 620 723 li st 622 724 a np 620 723 a 622 724 li st 624 725 a np 622 724 a 624 725 li st 3 w np 624 725 a 627 725 li st 629 726 a np 627 725 a 629 726 li st 632 727 a np 629 726 a 632 727 li st 2 w 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741 li st 707 742 a np 705 741 a 707 742 li st 3 w np 707 742 a 710 742 li st 712 743 a np 710 742 a 712 743 li st 2 w np 712 743 a 714 743 li st 3 w np 714 743 a 717 743 li st 719 744 a np 717 743 a 719 744 li st 3 w np 719 744 a 722 744 li st 2 w np 722 744 a 724 744 li st 727 745 a np 724 744 a 727 745 li st 2 w np 727 745 a 729 745 li st 731 746 a np 729 745 a 731 746 li st 3 w np 731 746 a 734 746 li st 2 w np 734 746 a 736 746 li st 739 747 a np 736 746 a 739 747 li st 2 w np 739 747 a 741 747 li st 3 w np 741 747 a 744 747 li st 746 748 a np 744 747 a 746 748 li st 2 w np 746 748 a 748 748 li st 3 w np 748 748 a 751 748 li st 753 749 a np 751 748 a 753 749 li st 3 w np 753 749 a 756 749 li st 2 w np 756 749 a 758 749 li st 761 750 a np 758 749 a 761 750 li st 2 w np 761 750 a 763 750 li st 3 w np 763 750 a 766 750 li st 768 751 a np 766 750 a 768 751 li st 2 w np 768 751 a 770 751 li st 3 w np 770 751 a 773 751 li st 775 752 a np 773 751 a 775 752 li st 3 w np 775 752 a 778 752 li st 2 w np 778 752 a 780 752 li st 783 753 a np 780 752 a 783 753 li st 2 w np 783 753 a 785 753 li st 2 w np 785 753 a 787 753 li st 790 754 a np 787 753 a 790 754 li st 2 w np 790 754 a 792 754 li st 3 w np 792 754 a 795 754 li st 2 w np 795 754 a 797 754 li st 800 755 a np 797 754 a 800 755 li st 2 w np 800 755 a 802 755 li st 2 w np 802 755 a 804 755 li st 807 756 a np 804 755 a 807 756 li st 2 w np 807 756 a 809 756 li st 3 w np 809 756 a 812 756 li st 2 w np 812 756 a 814 756 li st 817 757 a np 814 756 a 817 757 li st 2 w np 817 757 a 819 757 li st 2 w np 819 757 a 821 757 li st 3 w np 821 757 a 824 757 li st 826 758 a np 824 757 a 826 758 li st 3 w np 826 758 a 829 758 li st 2 w np 829 758 a 831 758 li st 3 w np 831 758 a 834 758 li st 836 759 a np 834 758 a 836 759 li st 2 w np 836 759 a 838 759 li st 3 w np 838 759 a 841 759 li st 2 w np 841 759 a 843 759 li st 846 760 a np 843 759 a 846 760 li st 2 w np 846 760 a 848 760 li st 3 w np 848 760 a 851 760 li st 2 w np 851 760 a 853 760 li st 855 761 a np 853 760 a 855 761 li st 3 w np 855 761 a 858 761 li st 2 w np 858 761 a 860 761 li st 3 w np 860 761 a 863 761 li st 865 762 a np 863 761 a 865 762 li st 3 w np 865 762 a 868 762 li st 2 w np 868 762 a 870 762 li st 3 w np 870 762 a 873 762 li st 2 w np 873 762 a 875 762 li st 877 763 a np 875 762 a 877 763 li st 3 w np 877 763 a 880 763 li st 2 w np 880 763 a 882 763 li st 3 w np 882 763 a 885 763 li st 887 764 a np 885 763 a 887 764 li st 3 w np 887 764 a 890 764 li st 2 w np 890 764 a 892 764 li st 2 w np 892 764 a 894 764 li st 3 w np 894 764 a 897 764 li st 899 765 a np 897 764 a 899 765 li st 3 w np 899 765 a 902 765 li st 2 w np 902 765 a 904 765 li st 3 w np 904 765 a 907 765 li st 2 w np 907 765 a 909 765 li st 911 766 a np 909 765 a 911 766 li st 3 w np 911 766 a 914 766 li st 2 w np 914 766 a 916 766 li st 3 w np 916 766 a 919 766 li st 2 w np 919 766 a 921 766 li st 924 767 a np 921 766 a 924 767 li st 2 w np 924 767 a 926 767 li st 2 w np 926 767 a 928 767 li st 3 w np 928 767 a 931 767 li st 2 w np 931 767 a 933 767 li st 936 768 a np 933 767 a 936 768 li st 2 w np 936 768 a 938 768 li st 3 w np 938 768 a 941 768 li st 2 w np 941 768 a 943 768 li st 2 w np 943 768 a 945 768 li st 948 769 a np 945 768 a 948 769 li st 2 w np 948 769 a 950 769 li st 3 w np 950 769 a 953 769 li st 2 w np 953 769 a 955 769 li st 3 w np 955 769 a 958 769 li st 2 w np 958 769 a 960 769 li st 962 770 a np 960 769 a 962 770 li st 3 w np 962 770 a 965 770 li st 2 w np 965 770 a 967 770 li st 3 w np 967 770 a 970 770 li st 2 w np 970 770 a 972 770 li st 975 771 a np 972 770 a 975 771 li st 2 w np 975 771 a 977 771 li st 3 w np 977 771 a 980 771 li st 2 w np 980 771 a 982 771 li st 2 w np 982 771 a 984 771 li st 3 w np 984 771 a 987 771 li st 989 772 a np 987 771 a 989 772 li st 3 w np 989 772 a 992 772 li st 2 w np 992 772 a 994 772 li st 3 w np 994 772 a 997 772 li st 2 w np 997 772 a 999 772 li st 2 w np 999 772 a 1001 772 li st 1004 773 a np 1001 772 a 1004 773 li st 2 w np 1004 773 a 1006 773 li st 3 w np 1006 773 a 1009 773 li st 2 w np 1009 773 a 1011 773 li st 3 w np 1011 773 a 1014 773 li st 2 w np 1014 773 a 1016 773 li st 2 w np 1016 773 a 1018 773 li st 1021 774 a np 1018 773 a 1021 774 li st 2 w np 1021 774 a 1023 774 li st 3 w np 1023 774 a 1026 774 li st 2 w np 1026 774 a 1028 774 li st 3 w np 1028 774 a 1031 774 li st 2 w np 1031 774 a 1033 774 li st 1035 775 a np 1033 774 a 1035 775 li st 3 w np 1035 775 a 1038 775 li st 2 w np 1038 775 a 1040 775 li st 3 w np 1040 775 a 1043 775 li st 2 w np 1043 775 a 1045 775 li st 3 w np 1045 775 a 1048 775 li st 2 w np 1048 775 a 1050 775 li st 1052 776 a np 1050 775 a 1052 776 li st 3 w np 1052 776 a 1055 776 li st 2 w np 1055 776 a 1057 776 li st 3 w np 1057 776 a 1060 776 li st 2 w np 1060 776 a 1062 776 li st 3 w np 1062 776 a 1065 776 li st 2 w np 1065 776 a 1067 776 li st 1070 777 a np 1067 776 a 1070 777 li st 2 w np 1070 777 a 1072 777 li st 2 w np 1072 777 a 1074 777 li st 3 w np 1074 777 a 1077 777 li st 2 w np 1077 777 a 1079 777 li st 3 w np 1079 777 a 1082 777 li st 2 w np 1082 777 a 1084 777 li st 1087 778 a np 1084 777 a 1087 778 li st 2 w np 1087 778 a 1089 778 li st 2 w np 1089 778 a 1091 778 li st 3 w np 1091 778 a 1094 778 li st 2 w np 1094 778 a 1096 778 li st 3 w np 1096 778 a 1099 778 li st 2 w np 1099 778 a 1101 778 li st 3 w np 1101 778 a 1104 778 li st 1106 779 a np 1104 778 a 1106 779 li st 2 w np 1106 779 a 1108 779 li st 3 w np 1108 779 a 1111 779 li st 2 w np 1111 779 a 1113 779 li st 3 w np 1113 779 a 1116 779 li st 2 w np 1116 779 a 1118 779 li st 3 w np 1118 779 a 1121 779 li st 2 w np 1121 779 a 1123 779 li st 1125 780 a np 1123 779 a 1125 780 li st 3 w np 1125 780 a 1128 780 li st 2 w np 1128 780 a 1130 780 li st 3 w np 1130 780 a 1133 780 li st 2 w np 1133 780 a 1135 780 li st 3 w np 1135 780 a 1138 780 li st 2 w np 1138 780 a 1140 780 li st 2 w np 1140 780 a 1142 780 li st 1145 781 a np 1142 780 a 1145 781 li st 2 w np 1145 781 a 1147 781 li st 3 w np 1147 781 a 1150 781 li st 2 w np 1150 781 a 1152 781 li st 3 w np 1152 781 a 1155 781 li st 2 w np 1155 781 a 1157 781 li st 2 w np 1157 781 a 1159 781 li st 3 w np 1159 781 a 1162 781 li st 1164 782 a np 1162 781 a 1164 782 li st 3 w np 1164 782 a 1167 782 li st 2 w np 1167 782 a 1169 782 li st 3 w np 1169 782 a 1172 782 li st 2 w np 1172 782 a 1174 782 li st 3 w np 1174 782 a 1177 782 li st 2 w np 1177 782 a 1179 782 li st 2 w np 1179 782 a 1181 782 li st 3 w np 1181 782 a 1184 782 li st 1186 783 a np 1184 782 a 1186 783 li st 3 w np 1186 783 a 1189 783 li st 2 w np 1189 783 a 1191 783 li st 3 w np 1191 783 a 1194 783 li st 2 w np 1194 783 a 1196 783 li st 2 w np 1196 783 a 1198 783 li st 3 w np 1198 783 a 1201 783 li st 2 w np 1201 783 a 1203 783 li st 3 w np 1203 783 a 1206 783 li st 1208 784 a np 1206 783 a 1208 784 li st 3 w np 1208 784 a 1211 784 li st 2 w np 1211 784 a 1213 784 li st 2 w np 1213 784 a 1215 784 li st 3 w np 1215 784 a 1218 784 li st 2 w np 1218 784 a 1220 784 li st 3 w np 1220 784 a 1223 784 li st 2 w np 1223 784 a 1225 784 li st 3 w np 1225 784 a 1228 784 li st 2 w np 1228 784 a 1230 784 li st 1232 785 a np 1230 784 a 1232 785 li st 3 w np 1232 785 a 1235 785 li st 2 w np 1235 785 a 1237 785 li st 3 w np 1237 785 a 1240 785 li st 2 w np 1240 785 a 1242 785 li st 3 w np 1242 785 a 1245 785 li st 2 w np 1245 785 a 1247 785 li st 2 w np 1247 785 a 1249 785 li st 3 w np 1249 785 a 1252 785 li st 2 w np 1252 785 a 1254 785 li st 1257 786 a np 1254 785 a 1257 786 li st 2 w np 1257 786 a 1259 786 li st 3 w np 1259 786 a 1262 786 li st 2 w np 1262 786 a 1264 786 li st 2 w np 1264 786 a 1266 786 li st 3 w np 1266 786 a 1269 786 li st 2 w np 1269 786 a 1271 786 li st 3 w np 1271 786 a 1274 786 li st 2 w np 1274 786 a 1276 786 li st 3 w np 1276 786 a 1279 786 li st 1281 787 a np 1279 786 a 1281 787 li st 3 w np 1281 787 a 1284 787 li st 2 w np 1284 787 a 1286 787 li st 2 w np 1286 787 a 1288 787 li st 3 w np 1288 787 a 1291 787 li st 2 w np 1291 787 a 1293 787 li st 3 w np 1293 787 a 1296 787 li st 2 w np 1296 787 a 1298 787 li st 3 w np 1298 787 a 1301 787 li st 2 w np 1301 787 a 1303 787 li st 2 w np 1303 787 a 1305 787 li st 1308 788 a np 1305 787 a 1308 788 li st 2 w np 1308 788 a 1310 788 li st 3 w np 1310 788 a 1313 788 li st 2 w np 1313 788 a 1315 788 li st 3 w np 1315 788 a 1318 788 li st 2 w np 1318 788 a 1320 788 li st 2 w np 1320 788 a 1322 788 li st 3 w np 1322 788 a 1325 788 li st 2 w np 1325 788 a 1327 788 li st 3 w np 1327 788 a 1330 788 li st 2 w np 1330 788 a 1332 788 li st 1335 789 a np 1332 788 a 1335 789 li st 2 w np 1335 789 a 1337 789 li st 2 w np 1337 789 a 1339 789 li st 3 w np 1339 789 a 1342 789 li st 2 w np 1342 789 a 1344 789 li st 3 w np 1344 789 a 1347 789 li st 2 w np 1347 789 a 1349 789 li st 3 w np 1349 789 a 1352 789 li st 2 w np 1352 789 a 1354 789 li st 2 w np 1354 789 a 1356 789 li st 3 w np 1356 789 a 1359 789 li st 1361 790 a np 1359 789 a 1361 790 li st 3 w np 1361 790 a 1364 790 li st 2 w np 1364 790 a 1366 790 li st 3 w np 1366 790 a 1369 790 li st 2 w np 1369 790 a 1371 790 li st 3 w np 1371 790 a 1374 790 li st 2 w np 1374 790 a 1376 790 li st 2 w np 1376 790 a 1378 790 li st 3 w np 1378 790 a 1381 790 li st 2 w np 1381 790 a 1383 790 li st 3 w np 1383 790 a 1386 790 li st 2 w np 1386 790 a 1388 790 li st 1391 791 a np 1388 790 a 1391 791 li st 2 w np 1391 791 a 1393 791 li st 2 w np 1393 791 a 1395 791 li st 3 w np 1395 791 a 1398 791 li st 2 w np 1398 791 a 1400 791 li st 3 w np 1400 791 a 1403 791 li st 2 w np 1403 791 a 1405 791 li st 3 w np 1405 791 a 1408 791 li st 2 w np 1408 791 a 1410 791 li st 2 w np 1410 791 a 1412 791 li st 3 w np 1412 791 a 1415 791 li st 2 w np 1415 791 a 1417 791 li st 3 w np 1417 791 a 1420 791 li st 1422 792 a np 1420 791 a 1422 792 li st 3 w np 1422 792 a 1425 792 li st 2 w np 1425 792 a 1427 792 li st 2 w np 1427 792 a 1429 792 li st 3 w np 1429 792 a 1432 792 li st 2 w np 1432 792 a 1434 792 li st 3 w np 1434 792 a 1437 792 li st 2 w np 1437 792 a 1439 792 li st 3 w np 1439 792 a 1442 792 li st 2 w np 1442 792 a 1444 792 li st 2 w np 1444 792 a 1446 792 li st 3 w np 1446 792 a 1449 792 li st 2 w np 1449 792 a 1451 792 li st 1454 793 a np 1451 792 a 1454 793 li st 2 w np 1454 793 a 1456 793 li st 3 w np 1456 793 a 1459 793 li st 2 w np 1459 793 a 1461 793 li st 2 w np 1461 793 a 1463 793 li st 3 w np 1463 793 a 1466 793 li st 2 w np 1466 793 a 1468 793 li st 3 w np 1468 793 a 1471 793 li st 2 w np 1471 793 a 1473 793 li st 3 w np 1473 793 a 1476 793 li st 2 w np 1476 793 a 1478 793 li st 3 w np 1478 793 a 1481 793 li st 2 w np 1481 793 a 1483 793 li st 2 w np 1483 793 a 1485 793 li st 1488 794 a np 1485 793 a 1488 794 li st 2 w np 1488 794 a 1490 794 li st 3 w np 1490 794 a 1493 794 li st 2 w np 1493 794 a 1495 794 li st 3 w np 1495 794 a 1498 794 li st 2 w np 1498 794 a 1500 794 li st 2 w np 1500 794 a 1502 794 li st 3 w np 1502 794 a 1505 794 li st 2 w np 1505 794 a 1507 794 li st 3 w np 1507 794 a 1510 794 li st 2 w np 1510 794 a 1512 794 li st 3 w np 1512 794 a 1515 794 li st 2 w np 1515 794 a 1517 794 li st 2 w np 1517 794 a 1519 794 li st 1522 795 a np 1519 794 a 1522 795 li st 2 w np 1522 795 a 1524 795 li st 3 w np 1524 795 a 1527 795 li st 2 w np 1527 795 a 1529 795 li st 3 w np 1529 795 a 1532 795 li st 2 w np 1532 795 a 1534 795 li st 2 w np 1534 795 a 1536 795 li st 3 w np 1536 795 a 1539 795 li st 2 w np 1539 795 a 1541 795 li st 3 w np 1541 795 a 1544 795 li st 2 w np 1544 795 a 1546 795 li st 3 w np 1546 795 a 1549 795 li st 2 w np 1549 795 a 1551 795 li st 2 w np 1551 795 a 1553 795 li st 3 w np 1553 795 a 1556 795 li st 1558 796 a np 1556 795 a 1558 796 li st 3 w np 1558 796 a 1561 796 li st 2 w np 1561 796 a 1563 796 li st 3 w np 1563 796 a 1566 796 li st 2 w np 1566 796 a 1568 796 li st 2 w np 1568 796 a 1570 796 li st 3 w np 1570 796 a 1573 796 li st 2 w np 1573 796 a 1575 796 li st 3 w np 1575 796 a 1578 796 li st 2 w np 1578 796 a 1580 796 li st 3 w np 1580 796 a 1583 796 li st 2 w np 1583 796 a 1585 796 li st 3 w np 1585 796 a 1588 796 li st 2 w np 1588 796 a 1590 796 li st 2 w np 1590 796 a 1592 796 li st 3 w np 1592 796 a 1595 796 li st 1597 797 a np 1595 796 a 1597 797 li st 3 w np 1597 797 a 1600 797 li st 2 w np 1600 797 a 1602 797 li st 3 w np 1602 797 a 1605 797 li st 2 w np 1605 797 a 1607 797 li st 2 w np 1607 797 a 1609 797 li st 3 w np 1609 797 a 1612 797 li st 2 w np 1612 797 a 1614 797 li st 3 w np 1614 797 a 1617 797 li st 2 w np 1617 797 a 1619 797 li st 3 w np 1619 797 a 1622 797 li st 2 w np 1622 797 a 1624 797 li st 188 1117 a 3.3 setlinewidth 410 358 a 3 w np 410 358 a 413 358 li st 2 w np 413 358 a 415 358 li st 418 359 a np 415 358 a 418 359 li st 420 360 a np 418 359 a 420 360 li st 423 362 a np 420 360 a 423 362 li st 425 363 a np 423 362 a 425 363 li st 427 365 a np 425 363 a 427 365 li st 430 367 a np 427 365 a 430 367 li st 432 369 a np 430 367 a 432 369 li st 435 372 a np 432 369 a 435 372 li st 437 374 a np 435 372 a 437 374 li st 440 377 a np 437 374 a 440 377 li st 442 381 a np 440 377 a 442 381 li st 444 384 a np 442 381 a 444 384 li st 447 388 a np 444 384 a 447 388 li st 449 391 a np 447 388 a 449 391 li st 452 395 a np 449 391 a 452 395 li st 454 399 a np 452 395 a 454 399 li st 457 404 a np 454 399 a 457 404 li st 459 408 a np 457 404 a 459 408 li st 462 413 a np 459 408 a 462 413 li st 464 417 a np 462 413 a 464 417 li st 466 422 a np 464 417 a 466 422 li st 469 427 a np 466 422 a 469 427 li st 471 432 a np 469 427 a 471 432 li st 474 437 a np 471 432 a 474 437 li st 476 443 a np 474 437 a 476 443 li st 479 448 a np 476 443 a 479 448 li st 481 453 a np 479 448 a 481 453 li st 483 459 a np 481 453 a 483 459 li st 486 464 a np 483 459 a 486 464 li st 488 470 a np 486 464 a 488 470 li st 491 475 a np 488 470 a 491 475 li st 493 481 a np 491 475 a 493 481 li st 496 486 a np 493 481 a 496 486 li st 498 492 a np 496 486 a 498 492 li st 500 498 a np 498 492 a 500 498 li st 503 503 a np 500 498 a 503 503 li st 505 509 a np 503 503 a 505 509 li st 508 515 a np 505 509 a 508 515 li st 510 520 a np 508 515 a 510 520 li st 513 526 a np 510 520 a 513 526 li st 515 531 a np 513 526 a 515 531 li st 517 537 a np 515 531 a 517 537 li st 520 542 a np 517 537 a 520 542 li st 522 548 a np 520 542 a 522 548 li st 525 553 a np 522 548 a 525 553 li st 527 558 a np 525 553 a 527 558 li st 530 564 a np 527 558 a 530 564 li st 532 569 a np 530 564 a 532 569 li st 534 574 a np 532 569 a 534 574 li st 537 580 a np 534 574 a 537 580 li st 539 585 a np 537 580 a 539 585 li st 542 590 a np 539 585 a 542 590 li st 544 595 a np 542 590 a 544 595 li st 547 600 a np 544 595 a 547 600 li st 549 605 a np 547 600 a 549 605 li st 551 610 a np 549 605 a 551 610 li st 554 614 a np 551 610 a 554 614 li st 556 619 a np 554 614 a 556 619 li st 559 624 a np 556 619 a 559 624 li st 561 629 a np 559 624 a 561 629 li st 564 633 a np 561 629 a 564 633 li st 566 638 a np 564 633 a 566 638 li st 569 642 a np 566 638 a 569 642 li st 571 647 a np 569 642 a 571 647 li st 573 651 a np 571 647 a 573 651 li st 576 655 a np 573 651 a 576 655 li st 578 660 a np 576 655 a 578 660 li st 581 664 a np 578 660 a 581 664 li st 583 668 a np 581 664 a 583 668 li st 586 672 a np 583 668 a 586 672 li st 588 676 a np 586 672 a 588 676 li st 590 680 a np 588 676 a 590 680 li st 593 684 a np 590 680 a 593 684 li st 595 687 a np 593 684 a 595 687 li st 598 691 a np 595 687 a 598 691 li st 600 695 a np 598 691 a 600 695 li st 603 698 a np 600 695 a 603 698 li st 605 702 a np 603 698 a 605 702 li st 607 705 a np 605 702 a 607 705 li st 610 708 a np 607 705 a 610 708 li st 612 712 a np 610 708 a 612 712 li st 615 715 a np 612 712 a 615 715 li st 617 718 a np 615 715 a 617 718 li st 620 721 a np 617 718 a 620 721 li st 622 724 a np 620 721 a 622 724 li st 624 727 a np 622 724 a 624 727 li st 627 730 a np 624 727 a 627 730 li st 629 733 a np 627 730 a 629 733 li st 632 736 a np 629 733 a 632 736 li st 634 739 a np 632 736 a 634 739 li st 637 741 a np 634 739 a 637 741 li st 639 744 a np 637 741 a 639 744 li st 641 747 a np 639 744 a 641 747 li st 644 749 a np 641 747 a 644 749 li st 646 752 a np 644 749 a 646 752 li st 649 754 a np 646 752 a 649 754 li st 651 757 a np 649 754 a 651 757 li st 654 759 a np 651 757 a 654 759 li st 656 762 a np 654 759 a 656 762 li st 658 764 a np 656 762 a 658 764 li st 661 766 a np 658 764 a 661 766 li st 663 768 a np 661 766 a 663 768 li st 666 771 a np 663 768 a 666 771 li st 668 773 a np 666 771 a 668 773 li st 671 775 a np 668 773 a 671 775 li st 673 777 a np 671 775 a 673 777 li st 676 779 a np 673 777 a 676 779 li st 678 781 a np 676 779 a 678 781 li st 680 783 a np 678 781 a 680 783 li st 683 785 a np 680 783 a 683 785 li st 685 787 a np 683 785 a 685 787 li st 688 789 a np 685 787 a 688 789 li st 690 790 a np 688 789 a 690 790 li st 693 792 a np 690 790 a 693 792 li st 695 794 a np 693 792 a 695 794 li st 697 796 a np 695 794 a 697 796 li st 700 797 a np 697 796 a 700 797 li st 702 799 a np 700 797 a 702 799 li st 705 801 a np 702 799 a 705 801 li st 707 802 a np 705 801 a 707 802 li st 710 804 a np 707 802 a 710 804 li st 712 806 a np 710 804 a 712 806 li st 714 807 a np 712 806 a 714 807 li st 717 809 a np 714 807 a 717 809 li st 719 810 a np 717 809 a 719 810 li st 722 812 a np 719 810 a 722 812 li st 724 813 a np 722 812 a 724 813 li st 727 815 a np 724 813 a 727 815 li st 729 816 a np 727 815 a 729 816 li st 731 817 a np 729 816 a 731 817 li st 734 819 a np 731 817 a 734 819 li st 736 820 a np 734 819 a 736 820 li st 739 821 a np 736 820 a 739 821 li st 741 823 a np 739 821 a 741 823 li st 744 824 a np 741 823 a 744 824 li st 746 825 a np 744 824 a 746 825 li st 748 827 a np 746 825 a 748 827 li st 751 828 a np 748 827 a 751 828 li st 753 829 a np 751 828 a 753 829 li st 756 830 a np 753 829 a 756 830 li st 758 831 a np 756 830 a 758 831 li st 761 833 a np 758 831 a 761 833 li st 763 834 a np 761 833 a 763 834 li st 766 835 a np 763 834 a 766 835 li st 768 836 a np 766 835 a 768 836 li st 770 837 a np 768 836 a 770 837 li st 773 838 a np 770 837 a 773 838 li st 775 839 a np 773 838 a 775 839 li st 778 840 a np 775 839 a 778 840 li st 780 841 a np 778 840 a 780 841 li st 783 842 a np 780 841 a 783 842 li st 785 843 a np 783 842 a 785 843 li st 787 844 a np 785 843 a 787 844 li st 790 845 a np 787 844 a 790 845 li st 792 846 a np 790 845 a 792 846 li st 795 847 a np 792 846 a 795 847 li st 797 848 a np 795 847 a 797 848 li st 800 849 a np 797 848 a 800 849 li st 802 850 a np 800 849 a 802 850 li st 804 851 a np 802 850 a 804 851 li st 807 852 a np 804 851 a 807 852 li st 809 853 a np 807 852 a 809 853 li st 3 w np 809 853 a 812 853 li st 814 854 a np 812 853 a 814 854 li st 817 855 a np 814 854 a 817 855 li st 819 856 a np 817 855 a 819 856 li st 821 857 a np 819 856 a 821 857 li st 824 858 a np 821 857 a 824 858 li st 2 w np 824 858 a 826 858 li st 829 859 a np 826 858 a 829 859 li st 831 860 a np 829 859 a 831 860 li st 834 861 a np 831 860 a 834 861 li st 836 862 a np 834 861 a 836 862 li st 2 w np 836 862 a 838 862 li st 841 863 a np 838 862 a 841 863 li st 843 864 a np 841 863 a 843 864 li st 3 w np 843 864 a 846 864 li st 848 865 a np 846 864 a 848 865 li st 851 866 a np 848 865 a 851 866 li st 853 867 a np 851 866 a 853 867 li st 2 w np 853 867 a 855 867 li st 858 868 a np 855 867 a 858 868 li st 860 869 a np 858 868 a 860 869 li st 3 w np 860 869 a 863 869 li st 865 870 a np 863 869 a 865 870 li st 868 871 a np 865 870 a 868 871 li st 2 w np 868 871 a 870 871 li st 873 872 a np 870 871 a 873 872 li st 875 873 a np 873 872 a 875 873 li st 2 w np 875 873 a 877 873 li st 880 874 a np 877 873 a 880 874 li st 2 w np 880 874 a 882 874 li st 885 875 a np 882 874 a 885 875 li st 887 876 a np 885 875 a 887 876 li st 3 w np 887 876 a 890 876 li st 892 877 a np 890 876 a 892 877 li st 2 w np 892 877 a 894 877 li st 897 878 a np 894 877 a 897 878 li st 2 w np 897 878 a 899 878 li st 902 879 a np 899 878 a 902 879 li st 904 880 a np 902 879 a 904 880 li st 3 w np 904 880 a 907 880 li st 909 881 a np 907 880 a 909 881 li st 2 w np 909 881 a 911 881 li st 914 882 a np 911 881 a 914 882 li st 2 w np 914 882 a 916 882 li st 919 883 a np 916 882 a 919 883 li st 2 w np 919 883 a 921 883 li st 924 884 a np 921 883 a 924 884 li st 2 w np 924 884 a 926 884 li st 928 885 a np 926 884 a 928 885 li st 3 w np 928 885 a 931 885 li st 933 886 a np 931 885 a 933 886 li st 3 w np 933 886 a 936 886 li st 938 887 a np 936 886 a 938 887 li st 3 w np 938 887 a 941 887 li st 943 888 a np 941 887 a 943 888 li st 2 w np 943 888 a 945 888 li st 948 889 a np 945 888 a 948 889 li st 2 w np 948 889 a 950 889 li st 3 w np 950 889 a 953 889 li st 955 890 a np 953 889 a 955 890 li st 3 w np 955 890 a 958 890 li st 960 891 a np 958 890 a 960 891 li st 2 w np 960 891 a 962 891 li st 965 892 a np 962 891 a 965 892 li st 2 w np 965 892 a 967 892 li st 3 w np 967 892 a 970 892 li st 972 893 a np 970 892 a 972 893 li st 3 w np 972 893 a 975 893 li st 977 894 a np 975 893 a 977 894 li st 3 w np 977 894 a 980 894 li st 2 w np 980 894 a 982 894 li st 984 895 a np 982 894 a 984 895 li st 3 w np 984 895 a 987 895 li st 989 896 a np 987 895 a 989 896 li st 3 w np 989 896 a 992 896 li st 2 w np 992 896 a 994 896 li st 997 897 a np 994 896 a 997 897 li st 2 w np 997 897 a 999 897 li st 1001 898 a np 999 897 a 1001 898 li st 3 w np 1001 898 a 1004 898 li st 2 w np 1004 898 a 1006 898 li st 1009 899 a np 1006 898 a 1009 899 li st 2 w np 1009 899 a 1011 899 li st 3 w np 1011 899 a 1014 899 li st 1016 900 a np 1014 899 a 1016 900 li st 2 w np 1016 900 a 1018 900 li st 3 w np 1018 900 a 1021 900 li st 1023 901 a np 1021 900 a 1023 901 li st 3 w np 1023 901 a 1026 901 li st 2 w np 1026 901 a 1028 901 li st 1031 902 a np 1028 901 a 1031 902 li st 2 w np 1031 902 a 1033 902 li st 2 w np 1033 902 a 1035 902 li st 1038 903 a np 1035 902 a 1038 903 li st 2 w np 1038 903 a 1040 903 li st 3 w np 1040 903 a 1043 903 li st 1045 904 a np 1043 903 a 1045 904 li st 3 w np 1045 904 a 1048 904 li st 2 w np 1048 904 a 1050 904 li st 1052 905 a np 1050 904 a 1052 905 li st 3 w np 1052 905 a 1055 905 li st 2 w np 1055 905 a 1057 905 li st 3 w np 1057 905 a 1060 905 li st 1062 906 a np 1060 905 a 1062 906 li st 3 w np 1062 906 a 1065 906 li st 2 w np 1065 906 a 1067 906 li st 1070 907 a np 1067 906 a 1070 907 li st 2 w np 1070 907 a 1072 907 li st 2 w np 1072 907 a 1074 907 li st 3 w np 1074 907 a 1077 907 li st 1079 908 a np 1077 907 a 1079 908 li st 3 w np 1079 908 a 1082 908 li st 2 w np 1082 908 a 1084 908 li st 1087 909 a np 1084 908 a 1087 909 li st 2 w np 1087 909 a 1089 909 li st 2 w np 1089 909 a 1091 909 li st 3 w np 1091 909 a 1094 909 li st 1096 910 a np 1094 909 a 1096 910 li st 3 w np 1096 910 a 1099 910 li st 2 w np 1099 910 a 1101 910 li st 3 w np 1101 910 a 1104 910 li st 1106 911 a np 1104 910 a 1106 911 li st 2 w np 1106 911 a 1108 911 li st 3 w np 1108 911 a 1111 911 li st 2 w np 1111 911 a 1113 911 li st 1116 912 a np 1113 911 a 1116 912 li st 2 w np 1116 912 a 1118 912 li st 3 w np 1118 912 a 1121 912 li st 2 w np 1121 912 a 1123 912 li st 1125 913 a np 1123 912 a 1125 913 li st 3 w np 1125 913 a 1128 913 li st 2 w np 1128 913 a 1130 913 li st 3 w np 1130 913 a 1133 913 li st 1135 914 a np 1133 913 a 1135 914 li st 3 w np 1135 914 a 1138 914 li st 2 w np 1138 914 a 1140 914 li st 2 w np 1140 914 a 1142 914 li st 1145 915 a np 1142 914 a 1145 915 li st 2 w np 1145 915 a 1147 915 li st 3 w np 1147 915 a 1150 915 li st 2 w np 1150 915 a 1152 915 li st 3 w np 1152 915 a 1155 915 li st 1157 916 a np 1155 915 a 1157 916 li st 2 w np 1157 916 a 1159 916 li st 3 w np 1159 916 a 1162 916 li st 2 w np 1162 916 a 1164 916 li st 1167 917 a np 1164 916 a 1167 917 li st 2 w np 1167 917 a 1169 917 li st 3 w np 1169 917 a 1172 917 li st 2 w np 1172 917 a 1174 917 li st 3 w np 1174 917 a 1177 917 li st 1179 918 a np 1177 917 a 1179 918 li st 2 w np 1179 918 a 1181 918 li st 3 w np 1181 918 a 1184 918 li st 2 w np 1184 918 a 1186 918 li st 3 w np 1186 918 a 1189 918 li st 1191 919 a np 1189 918 a 1191 919 li st 3 w np 1191 919 a 1194 919 li st 2 w np 1194 919 a 1196 919 li st 2 w np 1196 919 a 1198 919 li st 3 w np 1198 919 a 1201 919 li st 1203 920 a np 1201 919 a 1203 920 li st 3 w np 1203 920 a 1206 920 li st 2 w np 1206 920 a 1208 920 li st 3 w np 1208 920 a 1211 920 li st 2 w np 1211 920 a 1213 920 li st 2 w np 1213 920 a 1215 920 li st 1218 921 a np 1215 920 a 1218 921 li st 2 w np 1218 921 a 1220 921 li st 3 w np 1220 921 a 1223 921 li st 2 w np 1223 921 a 1225 921 li st 3 w np 1225 921 a 1228 921 li st 1230 922 a np 1228 921 a 1230 922 li st 2 w np 1230 922 a 1232 922 li st 3 w np 1232 922 a 1235 922 li st 2 w np 1235 922 a 1237 922 li st 3 w np 1237 922 a 1240 922 li st 2 w np 1240 922 a 1242 922 li st 1245 923 a np 1242 922 a 1245 923 li st 2 w np 1245 923 a 1247 923 li st 2 w np 1247 923 a 1249 923 li st 3 w np 1249 923 a 1252 923 li st 2 w np 1252 923 a 1254 923 li st 3 w np 1254 923 a 1257 923 li st 1259 924 a np 1257 923 a 1259 924 li st 3 w np 1259 924 a 1262 924 li st 2 w np 1262 924 a 1264 924 li st 2 w np 1264 924 a 1266 924 li st 3 w np 1266 924 a 1269 924 li st 2 w np 1269 924 a 1271 924 li st 1274 925 a np 1271 924 a 1274 925 li st 2 w np 1274 925 a 1276 925 li st 3 w np 1276 925 a 1279 925 li st 2 w np 1279 925 a 1281 925 li st 3 w np 1281 925 a 1284 925 li st 2 w np 1284 925 a 1286 925 li st 2 w np 1286 925 a 1288 925 li st 1291 926 a np 1288 925 a 1291 926 li st 2 w np 1291 926 a 1293 926 li st 3 w np 1293 926 a 1296 926 li st 2 w np 1296 926 a 1298 926 li st 3 w np 1298 926 a 1301 926 li st 2 w np 1301 926 a 1303 926 li st 1305 927 a np 1303 926 a 1305 927 li st 3 w np 1305 927 a 1308 927 li st 2 w np 1308 927 a 1310 927 li st 3 w np 1310 927 a 1313 927 li st 2 w np 1313 927 a 1315 927 li st 3 w np 1315 927 a 1318 927 li st 2 w np 1318 927 a 1320 927 li st 1322 928 a np 1320 927 a 1322 928 li st 3 w np 1322 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1092 840 li st 1161 834 a np 1092 840 a 1161 834 li st 1229 826 a np 1161 834 a 1229 826 li st 1298 813 a np 1229 826 a 1298 813 li st 1366 792 a np 1298 813 a 1366 792 li st 1400 769 a np 1366 792 a 1400 769 li st 1411 762 a np 1400 769 a 1411 762 li st 1434 739 a np 1411 762 a 1434 739 li st 1448 712 a np 1434 739 a 1448 712 li st 1469 675 a np 1448 712 a 1469 675 li st 1503 511 a np 1469 675 a 1503 511 li st 1526 88 a np 1503 511 a 1526 88 li st -37 1148 a eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF t 1161 834 a np 1092 840 a 1161 834 li st 1229 826 a np 1161 834 a 1229 826 li st 1298 813 a np 1229 826 a 1298 813 li st 1366 792 a np 1298 813 a 1366 792 li st 1400 769 a np 1366 792 a 1400 769 li st 1411 762 a np 1400 769 a 1411 762 li st 1434 739 a np 1411 762 a 1434 739 li st 1448 712 a np 1434 739 a 1448 712 li st 1469 675 a np 1448 712 a 1469 675 li st fig1a_hacked.ps000064400000440000044000001056210577430523000152740ustar00e-printse-prints00000000000000%!PS-Adobe-2.0 %%Title: drho-2loop.feynman %%Creator: John Terning %%CreationDate: Thu Feb 23 14:35:32 1995 %%For: terning %%DocumentFonts: (atend) %%Pages: 0 0 %%BoundingBox: 44 504 495 603 %%NXNextStepVersion: 3.0 %%EndComments %%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0 %! % NeXT Printing Package % Version: 3.0 % Copyright: 1988, NeXT, Inc. /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /_NXfindfont /findfont load def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. So if currentshared is true, % we call the normal findfont and return that /currentshared where {pop currentshared} {false} ifelse {_NXfindfont} {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll getinterval cvn exch FontDirectory 2 index known {pop FontDirectory exch get} {_NXfindfont dup /Encoding get StandardEncoding eq { dup length dict exch {1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall dup /Encoding NextStepEncoding put definefont }{exch pop} ifelse }ifelse }ifelse }bind def }{pop}ifelse /_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string __NXdef}ifelse __NXImageString}__NXbdef /_NXDoImageOp{ 3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def chans 2 add 2 roll parr 0 chans getinterval astore pop 5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse 4 index mul /totbytes exch def pop exch pop gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore {0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end }__NXbdef /alphaimage{1 add _NXDoImageOp}def _NXLevel2{ /NXCalibratedRGBColorSpace where{pop}{ /NXCalibratedRGBColorSpace {mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped {cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin /MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def /WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse /nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef /nxsetgray{dup dup nxsetrgbcolor}__NXbdef /_NXCalibratedImage{exch{array astore dup length true}{false}ifelse 8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if 8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def} {2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef } { /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /colorimage{_NXDoImageOp}__NXbdef /nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef /setpattern{pop .5 setgray}__NXbdef /_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef } ifelse /_NXSetCMYKOrRGB where{pop}{ mark{systemdict /currentwindow get exec}stopped {{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark }ifelse %%EndProcSet gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore %%EndProlog %%BeginSetup /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc closepath } def /line { moveto rlineto stroke } def /setup { setlinewidth 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%8 execuserobject setfont %0 nxsetgray %254 455 moveto (Figure 1) show %grestore %grestore %0 0 1 setup %gsave %8 execuserobject setfont %0 nxsetgray %[1 0 0 -1 0 291] concat % 8 execuserobject setfont % 0 nxsetgray % 256 150 moveto (Figure 2) show % grestore % grestore % 0 0 1 setup % gsave % 8 execuserobject setfont % 0 nxsetgray % [1 0 0 -1 0 586] concat % 40 execuserobject setfont % 0 nxsetgray % 52 298 moveto (W, Z) show % grestore % grestore % 0 0 1 setup % gsave % 40 execuserobject setfont % 0 nxsetgray % [1 0 0 -1 0 576] concat % 40 execuserobject setfont % 0 nxsetgray % 455 293 moveto (W, Z) show % grestore grestore 0 0 1 setup gsave 40 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 1122] concat 40 execuserobject setfont 0 nxsetgray 73 566 moveto () show grestore grestore 0 0 1 setup gsave 40 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 1128] concat 40 execuserobject setfont 0 nxsetgray 463 569 moveto () show grestore grestore 0 setgray 0.333333 setgray gsave 0 0 540 720 rectclip [1 0 0 -1 0 720] concat grestore grestore showpage %%Trailer %%DocumentFonts: Helvetica-Oblique %%+ Helvetica %%EOFhow % grestore grestore 0 0 1 setup gsave 40 execuserobject setfont 0 nxsetgray [1 0 0 -1 0 1122] concat 40 exefig1b_hacked.ps000064400000440000044000001243370577430530400153040ustar00e-printse-prints00000000000000%!PS-Adobe-2.0 %%Title: drho-2loop.feynman %%Creator: John Terning %%CreationDate: Thu Feb 23 14:35:32 1995 %%For: terning %%DocumentFonts: (atend) %%Pages: 0 0 %%BoundingBox: 44 210 495 337 %%NXNextStepVersion: 3.0 %%EndComments %%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0 %! % NeXT Printing Package % Version: 3.0 % Copyright: 1988, NeXT, Inc. /__NXdef{1 index where{pop pop pop}{def}ifelse}bind def /__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def /UserObjects 10 array __NXdef /defineuserobject{ exch dup 1 add dup UserObjects length gt{ array dup 0 UserObjects putinterval /UserObjects exch def }{pop}ifelse UserObjects exch 3 -1 roll put }__NXbdef /undefineuserobject{UserObjects exch null put}__NXbdef /execuserobject{UserObjects exch get exec}__NXbdef /__NXRectPath{4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath}__NXbdef /__NXProcessRectArgs{ 1 index type /arraytype eq{ exch 0 4 2 index length 1 sub{ dup 3 add 1 exch{1 index exch get exch}for 5 1 roll 5 index exec }for pop pop }{exec}ifelse }__NXbdef /rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef /rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef /rectstroke{ gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{ {gsave __NXRectPath null concat stroke grestore} dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs }{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore }__NXbdef /_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef /xyshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index 2 mul 1 add get add exch 3 index 3 index 2 mul get add exch moveto pop }for pop pop }__NXbdef /xshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show exch 3 index 3 index get add exch moveto pop }for pop pop }__NXbdef /yshow{ 0 1 3 index length 1 sub{ currentpoint 4 index 3 index 1 getinterval show 3 index 3 index get add moveto pop }for pop pop }__NXbdef /arct{arcto pop pop pop pop}__NXbdef /setbbox{pop pop pop pop}__NXbdef /ucache{}__NXbdef /ucachestatus{mark 0 0 0 0 0}__NXbdef /setucacheparams{cleartomark}__NXbdef /uappend{systemdict begin cvx exec end}__NXbdef /ueofill{gsave newpath uappend eofill grestore}__NXbdef /ufill{gsave newpath uappend fill grestore}__NXbdef /ustroke{ gsave newpath dup length 6 eq {exch uappend concat}{uappend}ifelse stroke grestore }__NXbdef /__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse /ustrokepath{ newpath dup length 6 eq{ exch uappend __NXustrokepathMatrix currentmatrix exch concat strokepath setmatrix }{uappend strokepath}ifelse } __NXbdef /upath{ [exch {/ucache cvx}if pathbbox /setbbox cvx {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx } __NXbdef /setstrokeadjust{pop}__NXbdef /currentstrokeadjust{false}__NXbdef /selectfont{exch findfont exch dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef /_NXCombineArrays{ counttomark dup 2 add index dup length 3 -1 roll { 2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch }repeat pop pop pop }__NXbdef /flushgraphics{}def /setwindowtype{pop pop}def /currentwindowtype{pop 0}def /setalpha{pop}def /currentalpha{1.0}def /hidecursor{}def /obscurecursor{}def /revealcursor{}def /setcursor{4 {pop}repeat}bind def /showcursor{}def /NextStepEncoding where not{ /NextStepEncoding StandardEncoding 256 array copy def 0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave /Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute /Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright 176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior 204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave /aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute /ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth /ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute /ucircumflex 246/udieresis/yacute 252/thorn/ydieresis] {dup type /nametype eq {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse }forall pop /NextStepEncoding NextStepEncoding readonly def /_NXfstr 128 string dup 0 (_NX) putinterval def /_NXfindfont /findfont load def /findfont{ % Because we can never let NextStepEncoding get into % SharedFontDirectory, we cannot reencode a font to NextStepEncoding % if we are in shared mode. 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sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end }__NXbdef /alphaimage{1 add _NXDoImageOp}def _NXLevel2{ /NXCalibratedRGBColorSpace where{pop}{ /NXCalibratedRGBColorSpace {mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped {cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin /MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def /WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse /nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef /nxsetgray{dup dup nxsetrgbcolor}__NXbdef /_NXCalibratedImage{exch{array astore dup length true}{false}ifelse 8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if 8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def} {2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef } { /setcmykcolor{ 1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll 4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef /currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef /colorimage{_NXDoImageOp}__NXbdef /nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef /setpattern{pop .5 setgray}__NXbdef /_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef } ifelse /_NXSetCMYKOrRGB where{pop}{ mark{systemdict /currentwindow get exec}stopped {{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark }ifelse %%EndProcSet gsave -20 -28 translate /__NXbasematrix matrix currentmatrix def grestore %%EndProlog %%BeginSetup /oval { translate scale newpath 0.5 0.5 0.5 0 360 arc closepath } def /line { moveto rlineto stroke } def /setup { setlinewidth 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