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\centerline{\bf\Large $V$-$A$ theory: a view from the outside}
\begin{center}
Ashok Das\\
Department of Physics and Astronomy, 
University of Rochester,\\ 
Rochester, NY 14627, USA\\
and\\
Saha Institute of Nuclear Physics, 
1/AF Bidhannagar,\\ 
Calcutta 700064, INDIA
\end{center}
\bigskip

\centerline{\bf Abstract}

In this talk I will review the $V$-$A$ theory within the context of the prevalent experimental results at the time.
\bigskip

It is a great pleasure for me to be able to participate in this
celebration in honor of Professor George Sudarshan. Let me say
right away that unlike the other speakers in this session, I
haven't had the opportunity to collaborate with George yet. On the other hand, George is 
still young  and who knows!

Much of what is being discussed in this session happened many,
many years ago. I am, of course, not going to tell you how old I am. Let me
simply say that all of this happened long before my time, which is the reason for
the title of my talk. The only reason I agreed to speak in this
session is because George is a dear friend, a former student of
Rochester and I felt that I had access to all the resources of
Rochester. This was before I knew who else were going to be
speaking in this session and that the organizers had kindly
deprived me of part of my resources, thank you very much!

So, I had to work very hard, go back to the old papers and the
archives and reconstruct events. What I learnt is that the story
of $V$-$A$ theory is a fascinating one. You can even think of this as
one of the stories of  {\em Sheherazade} in the {\em Arabian
Nights}. As we all know these are very intricately woven stories
that naturally lead from one story  to the next. In fact, if  only 
{\em Sheherazade} were aware of the story of $V$-$A$, you can hear her starting the
story as, \lq\lq A long time ago, there was....". The difference
is that the ``long time" in this case can be quantified. You have
already heard that it all happened 50 years ago, but let me simply
say that ``it all happened that many years ago".

\begin{figure}[ht]
\begin{center}
\includegraphics[scale=1.2]{both}
\end{center}
\centerline{Once upon a time there was .....}
\end{figure}

The story of $V$-$A$ has two aspects to it. There is, of course, the
physics aspect that I will come to. But, more important is the
sociological aspect. Many younger people in the audience may not
know that the Rochester conference which started in Rochester in 1951 
was one of the first successful
international conferences in high energy physics in this country. Over the years, the
character of this conference has, of course, changed enormously. 
The first Rochester conference, for example, had only 50
participants and lasted for just one day.
\begin{center}
\includegraphics[scale=.8]{second}
\end{center}
\medskip

The discussions in these conferences were friendly but intense
and this was the venue for announcing new results. So, it was an
exciting place to be in. If you think arranging visas for foreign
visitors is difficult now, you should think again. Things were not
at all easy at that time.
\begin{center}
\includegraphics[scale=.75]{rochester}
\end{center}

The other sociological aspect is that it is around this time that
Bob Marshak started recruiting smart foreign graduate students
into the university. Even the university was not fully supportive,
but in his characteristic way, Marshak prevailed. It is in this
way that both George Sudarshan and Susumu Okubo  arrived into the
middle of all the exciting things that were happening in Rochester
around the Rochester conferences.
$$
\begin{array}{cc}
\includegraphics[scale=1]{ecgokubo1} &
\includegraphics[scale=1]{ecgokubo2}
\end{array}
$$
\centerline{Young graduate students in the middle of all the excitement.}
\medskip

The physics aspect can be summarized by saying that it was a very
exciting period, I guess because everything was so confusing. To
me the most impressive thing about the $V$-$A$ theory is that it was
formulated in the face of experimental results that did not
support its predictions. In physics  experiments are expected to
give guidance to theorists. Sometimes an experiment may itself be
wrong, but then it is the responsibility of other experiments to
``weed out" the wrong experiment. On the other hand, when repeated
experiments stand by a result, it is generally foolish to propose
a theory that contradicts the accepted experimental results.
However, this is exactly what  Sudarshan and Marshak did in
proposing the $V$-$A$ theory simply because they had a desire to have a universal
theory of weak interactions and the
predictions of their theory were subsequently vindicated by more careful
experiments. Basically, there was a combination of wrong
experiments that had completely dominated the physics scene before
the $V$-$A$ theory. Let me explain this in some detail.

The story of weak interactions started with the observations of
nuclear $\beta$ decays and the developments in the field can be
divided into two phases: a phase prior to the discovery of parity
violation and a phase after this discovery. In the earlier phase,
with more and more studies on nuclear decays, it was established
that there are three kinds of nuclear beta decays \cite{fermi,gamow}:
\begin{enumerate}
\item Fermi transitions: $\Delta J = 0,\quad 0\rightarrow 0.$\quad (${\rm
O}^{14}\rightarrow {\rm N}^{14} + e^{+} + \nu$) 
\item Gammow-Teller transitions: $\Delta J = 1$.\quad (${\rm
He}^{6}\rightarrow {\rm Li}^{6} + e + \bar{\nu}$) 
\item Mixed transitions: $\Delta J = 0,\quad 0\not\rightarrow 0$. \quad
($n\rightarrow p + e + \bar{\nu}$)
\end{enumerate}
In addition to the nuclear $\beta$ decays, it was also observed
(1948) that the {\em muon} decays through weak interactions as
$$
\mu^{-} \rightarrow e + \nu + \bar{\nu}.
$$
Tiomno and Wheeler \cite{tiomno} were the first to carry out a systematic
study of the strengths of all these decays which suggested a
universal nature of the weak force governing all of these decays
(Puppi's triangle):
\begin{center}
\includegraphics[scale=1]{puppi}
\end{center}

As a result, the Fermi theory of  $\beta$ decay \cite{fermi} involving a current-current 
interaction of vector currents (in analogy with QED)  
was generalized to an interaction of the form
$$
H_{\rm int} = \sum_{i} C_{i} J_{i}J^{i\, \dagger},\quad
J_{i} = J_{i}^{\rm hadron} + J_{i}^{\rm lepton},
$$
where the generalized ``current" had the generic form
$$
J_{i} = \bar{\psi}_{1}\Gamma_{i}\psi_{2}, \quad i= S,V,T,A,P.
$$
Namely, the generalized ``current" involved all the five bilinear
covariants of Dirac matrices. On the other hand, since the nucleons inside the
nucleus were nonrelativistic, one could immediately deduce:
\begin{enumerate}
\item Only $S, V$ terms contribute to Fermi transitions (since
they do not change spin). 
\item Only $T, A$ terms can contribute
to Gamow-Teller transitions (since these can change spin).
\end{enumerate}
The pseudoscalar term vanishes in the nonrelativistic limit and,
therefore, nothing could be deduced about this coupling. Furthermore, 
since Fermi and Gammow-Teller transitions were observed, it meant that 
one cannot have vanishing couplings for  both $S,V$ or both $T,A$ 
terms in the interaction.  The form of the interaction
Hamiltonian can, of course, be constrained further by experimental
studies.

However, before I describe the experimental results, let me point
out a theoretical result that will play a crucial role in the
later developments. It was already known from cosmic ray studies
that the {\em pion} decays through weak interactions through the channel
$$
\pi^{-} \rightarrow \mu^{-} + \bar{\nu}.
$$
However, the decay involving the electron
$$
\pi^{-} \rightarrow e^{-} + \bar{\nu},
$$
had never been seen. That was a bit puzzling at the time since
$e,\mu$ had similar properties except for their mass difference.
Based on the universal interaction hypothesis of Tiomno and
Wheeler, a theoretical calculation was carried out by Ruderman and
Finkelstein \cite{ruderman} for the ratio of the decay rates for the two
modes 
\begin{center}
\includegraphics[scale=1]{pidecay}
\end{center}
and their results are expressed in the table ($f$ denotes forbidden)
\begin{center}
\includegraphics[scale=1]{table1}
\end{center}
I have highlighted the relevant numbers for the appropriate
couplings. Since the only allowed channels through which the {\em pion}
can decay to electrons are the $P$ and the $A$ channels and since
this decay is so rare, theoretically, the $P$ ($P$-scalar) channel was ruled
out (This is the channel on which we had no information in the
nonrelativistic limit). Therefore, experimentally one had to look
at only the $S,V,T,A$ channels.

The way experiments looked for these terms in the decay
process is by looking at the end spectrum of the electron energy
in the decay or by looking at the angular correlation between the
electron and the neutrino which can be determined from the
recoil of the nucleus. For example, the angular correlation can be
parameterized as
$$
f(\theta) \sim 1 + \lambda\ \frac{v}{c} \cos\theta,
$$
where $v$ denotes the speed of the electron. (In writing this I
have neglected a term known as the {\em Fierz interference} term
which was not observed experimentally.) Theoretically, the
parameter $\lambda$ can be calculated for the different channels
and  takes the values
\begin{center}
\includegraphics[scale=1]{lambda}
\end{center}
So, for example in the decay of ${\rm He}^{6}$ (which is a
Gammow-Teller decay), $\lambda$ was determined to have the value $\lambda
= \frac{1}{3}$ so that one would conclude the coupling for Gamow-Teller transitions 
to be primarily of $T$ type \cite{ruby}.
\begin{center}
\includegraphics[scale=1]{ruby}
\end{center}
One can summarize the results of many of these experiments at the time as \cite{wu}
\begin{center}
\includegraphics[scale=1]{table2}
\end{center}
This suggested that the $\beta$ decays were governed by $S,T$
couplings. On top of that the leading search for the
$\pi\rightarrow e+\nu$ led to the result \cite{lokanathan}
$$
\frac{\Gamma(\pi\rightarrow e + \nu)}
{\Gamma(\pi\rightarrow \mu + \nu)} = (-3 \pm 9)
\times 10^{-5}.
$$
This further ruled against an interaction of $A$ type and
supported the $S,T$ couplings. Thus, the dominant sentiment in the
theoretical physics community at the time was that the generalized
Fermi theory with $S,T$ couplings was responsible for the weak
decays.

Then came the proposal by Lee and Yang \cite{lee} that parity is
violated in weak interactions which was soon \cite{wu1} established in
the Gamow-Teller decay of ${\rm Co}^{60}$ which also showed that
parity is violated maximally in these decays. Violation of parity
necessitated that  the interaction Hamiltonian should be further
generalized to
$$
H_{\rm int} =  \sum_{i} \bar{\psi}_{1}\Gamma_{i}
\psi_{2}\ \bar{\psi}_{3} \Gamma^{i}\left(C_{i} + C'_{i}
\gamma_{5}\right)\psi_{4} + {\rm hermitian\ conjugate},\quad i=S,V,T,A.
$$
As a result, experiments needed to be analyzed afresh.
Surprisingly, however, the large volume of experimental data in
$\beta$ decays were unaffected by violation of parity since they
involved measuring parity invariant quantities. However, there
were two new experiments that are worth talking about. First,
there was the experiment \cite{allen} which studied the transitions:
$$
{\rm Ar}^{35}\rightarrow {\rm Cl}^{35} + e^{+} + \nu, \quad {\rm
(Fermi)},\quad {\rm Ne}^{19} \rightarrow {\rm F}^{19} + e^{+} +
\nu\quad {\rm (Mixed)}.
$$
The angular correlation measurements in these decays gave a value
of $\lambda\approx 0.9$ supporting a strong $V$ coupling in the
interactions.
\begin{center}
\includegraphics[scale=1]{argon}
\end{center}
However, these results were in contradiction with most other
results including one of their own earlier experiments. (Let me
remark here  parenthetically that IUPAC changed the symbol
for Argon from ${\rm A}^{35}$ to ${\rm Ar}^{35}$ in 1957.) The second was
a better experiment \cite{lattes} designed to search for $\pi\rightarrow e +
\nu$ decays and it gave  even a lower limit on the ratio to
be
$$
\frac{\Gamma (\pi \rightarrow e + \nu)}{\Gamma (\pi
 \rightarrow \mu + \nu)} = (-0.4\pm 9)\times 10^{-6},
$$
and, therefore, in spite of the new component of parity violation
in the theory, the general sentiment continued to be that the interactions
were of $S,T$ type.

However, at this point, there was a new twist  from the
theoretical side. Observing that all the parity violating
experiments involved a neutrino, it was argued that it is the
neutrino that is responsible for the violation of parity and this
resurrected the two component theory of neutrinos. Salam \cite{salam} was the one
who introduced the concept of $\gamma_{5}$ invariance into the
neutrino equations. ``Chirality" or handedness crept into this
discussion through the works of Watanabe \cite{watanabe} and it was clear
that unlike other particles, neutrinos were either left-handed or
right-handed. Various $\beta$ asymmetry measurements showed that
if the neutrino was left-handed, the interaction will have a
$(V,A)$ form while if it was right-handed $(S,T)$ form would be
favored. (Handedness of neutrino will be measured only a year
later in a beautiful experiment by Goldhaber et al. \cite{goldhaber})  The {\em
muon} decay experiments, on the other hand, seemed to support a
$(V,A)$ form of the interactions. The idea of a universal Fermi
theory was, therefore, in jeopardy and the confusion that
prevailed is best summarized by the remarks of T. D. Lee in the
seventh Rochester conference (1957)

``$\cdots$ {\em We turn to the universal Fermi interaction, which
is an attempt to gain a more unified understanding of certain of
the weak interactions. We draw the famous triangle representing
the interactions of interest. Beta decay information tells us that
the interaction between $(p,n)$ and $(e,\nu)$ is scalar and
tensor, while the two component theory plus the law of
conservation of leptons implies that the coupling between
$(e,\nu)$ and $(\mu,\nu)$ is vector. This means that the universal
Fermi interaction cannot be realized in the way we have expressed
it} $\cdots$"

This basically summarizes the climate in which 
Sudarshan and Marshak proposed the universal $V$-$A$ theory \cite{sudarshan}. Their desire was to
have a universal Fermi theory and was not based primarily on symmetry
principles which came only after the fact. Let me try to
reconstruct here their reasoning for proposing such a structure
for the theory.  First, since neutrinos have a definite
handedness, they satisfy
$$
\left(1 \pm \gamma_{5}\right) \psi^{\rm (R,L)} = 0
= \bar{\psi}^{\ \rm (R,L)} \left(1\mp \gamma_{5}\right),
$$
depending on their handedness. Since the
longitudinal polarization of the electron in the ${\rm Co}^{60}$ decay
is negative (predominantly left-handed), this then determined that the current 
in the lepton
sector would involve $(S,T)$ couplings if the neutrino is right
handed and $(V,A)$ couplings if the neutrino is left handed. From
the $\beta$ decay experiments, therefore, it would correspond to choosing between
the ${\rm He}^{6}$ or the ${\rm Ar}^{35}$ results respectively. I want to emphasize here 
that the ${\rm He}^{6}$ results were the commonly accepted ones at the time and the 
${\rm Ar}^{35}$ results were not generally in favor.  The muon decay, on
the other hand, favored the $(V,A)$ coupling which can be seen in the following way. 
The current involving the neutrino and the antineutrino (with well defined handedness)
$$
\bar{\psi}_{\nu}\left(1\mp\gamma_{5}\right) \Gamma_{i} \left(1\pm \gamma_{5}\right)\psi_{\nu} = 0,\quad {\rm for}\ i=S,T,P,
$$
and is nontrivial only for $i=V,A$. Therefore,  if one wants a
universal theory for all the interactions, one must choose the results of the ${\rm
Ar}^{35}$ experiment over the commonly accepted ${\rm He}^{6}$
results. That is exactly what Sudarshan and Marshak did. Such a choice then leads to 
the universal $V$-$A$ theory of the form

\begin{eqnarray*}
\begin{array}{ll}
 H_{\rm int} = G
\bar{\psi}_{1}\gamma_{\mu}(1+\gamma_{5})\psi_{2}
 \bar{\psi}_{3}\gamma^{\mu}(1+\gamma_{5})\psi_{4} +
{\rm hermitian\ conjugate},& C_{i} = C'_{i},\  i =V,A;\ C_{V}=C_{A},\\
\noalign{\vskip 6pt}%
&C_{i} = C^{\prime}_{i} =0,\  i= S,T.
\end{array}
\end{eqnarray*}
On the other hand, such an interaction would predict the {\em
pion} to decay into an electron. Subsequently, several new
experiments measured the ratio for this decay leading to the value \cite{anderson}
$$
\frac{\Gamma (\pi \rightarrow e + \nu)}{\Gamma (\pi
\rightarrow \mu + \nu)} = \left(1.03\pm 0.20\right)\times
10^{-4},
$$
which vindicated the $V$-$A$ hypothesis. Many of the $\beta$ decay
experiments were soon redone and corrected for the errors in the
older results.

Once a $V$-$A$ structure for the interaction was proposed, its symmetry 
properties, which are important for later developments, followed. For example,
it was realized that the interaction Hamiltonian is invariant under a $\gamma_{5}$
transformation. It was also observed that the $V$-$A$ structure is invariant under
the {\em Fierz rearrangement}. In fact, the combination $S$-$T+P$ is also invariant,
but as I have tried to emphasize, the $P$ interactions do not enter the weak interaction
Hamiltonian. However, I do not have time to get into these. 

You can almost hear it now. At the conclusion of this triumphant
story, the curious emperor, {\em Sheheriyar},  asks {\em Sheherazade}, ``What
happened next?" Like a good story teller, politely and
respectfully, {\em Sheherazade} reminds the emperor that it is almost
dawn and that it may be better to rest a little and continue the
next day, to which the emperor agrees. After a sumptuous dinner the following evening, 
{\em Sheherazade}
meets the emperor  at the appointed hour and resumes her story.
``You see, your excellency, ....", she continues and as we have
learnt from Professor Weinberg's talk  this morning, the story of
$V$-$A$ leads naturally to the story of the Standard Model. The
story (of {\em Sheherazade} and of scientific discoveries), of course,
continues. However, unlike {\em Sheherazade}, I have only half an hour
and, therefore, let me thank  you all for your attention and stop here.
\bigskip


\noindent{\bf Acknowledgment:}

This work was
supported in part by US DOE Grant number DE-FG 02-91ER40685.



 
\begin{thebibliography}{10}

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\bibitem{gamow} G. Gamow and E. Teller, Phys. Rev. {\bf 49}, 895 (1936).

\bibitem{tiomno} J. Tiomno and J. A. Wheeler, Rev. Mod. Phys. {\bf 21}, 153 (1949). See also O. Klein, Nature {\bf 161}, 897 (1948); G. Puppi, Nuovo Cim. {\bf 5}, 587 (1948). 

\bibitem{ruderman} M. Ruderman and R. Finkelstein, Phys. Rev. {\bf 76}, 1458 (1949).  

\bibitem{ruby} B. M. Rustad and S. L. Ruby, Phys. Rev. {\bf 97}, 991 (1955).

\bibitem{wu} C. S. Wu in, {\em Theoretical Physics in the Twentieth Century}, ed. M. Fierz and V. F. Weisskopf (Interscience Publishers Inc, New York,1960).

\bibitem{lokanathan} S. Lokanathan and J. Steinberger, Suppl. Nuovo Cim. {\bf 1}, 151 (1955). 

\bibitem{lee} T. D. Lee and C. N. Yang, Phys. Rev. {\bf 104}, 254 (1956). 

\bibitem{wu1} C. S. Wu {\em et al}, Phys. Rev. {\bf 105}, 1413 (1957). 

\bibitem{allen} W. B. Herrmannsfeldt, D. R. Maxson, P. St\"{a}heln and J. S. Allen, Phys. Rev. {\bf 107}, 641 (1957). 

\bibitem{lattes} H. L. Anderson and C. M. G. Lattes, Nuovo Cim. {\bf 6}, 1356 (1957).

\bibitem{salam} A. Salam, Nuovo Cim. {\bf 5}, 229 (1957); L. Landau, Nucl. Phys. {\bf 3}, 127 (1957); T. D. Lee and C. N. Yang, Phys. Rev. {\bf 105}, 1671 (1957).

\bibitem{watanabe} S. Watanabe, Phys. Rev. {\bf 106}, 1306 (1957).
 
\bibitem{goldhaber} M. Goldhaber, L. Grodzins and A. W. Sunyar, Phys. Rev. {\bf 109}, 1015 (1958).  

\bibitem{sudarshan} E. C. G. Sudarshan and R. E. Marshak, {\em Proceedings of Padua-Venice Conference on Mesons and Newly Discovered Particles}, (1957); {\em ibid} Phys. Rev. {\bf 109}, 1860 (1958). 

\bibitem{anderson} H. L. Anderson, T. Fuji, R. H. Miller and L. Tau, Phys. Rev. {\bf 119} (1960). 




\end{thebibliography}

\end{document}
