Re: How real are the "Virtual" partticles?

From: Franz Heymann (notfranz.heymann_at_btopenworld.com)
Date: 03/09/05 

Date: Wed, 9 Mar 2005 08:03:30 +0000 (UTC)

"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in message
news:422AC49F.3030502@univie.ac.at...
> Franz Heymann wrote:
> > "Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in message
> > news:4225B962.6070905@univie.ac.at...
> >
> >>Franz Heymann wrote:
> >>
> >>>"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> wrote in message
> >>>news:421F2395.9070900@univie.ac.at...
> >>>
> >>>
> >>>>PD wrote:
> >>>>
> >>>>
> >>>>
> >>>>>If I see a peak in the invariant mass of a combination of two
> >
> > electrons
> >
> >>>>>seen in a detector, then I take it that I've seen evidence of a
> >>>>>particle decaying into those two electrons, especially if other
> >>>>>parameters of the final state points to a fixed set of quantum
> >
> > numbers
> >
> >>>>>(such as spin=0 or spin=1). If that peak has some width to it,
> >
> > that's
> >
> >>>>>evidence of the finite lifetime of the decaying particle, and
> >
> > indeed
> >
> >>>>>any decay that is "off-peak" in this invariant mass can be said
> >
> > to
> >
> >>>>>point to the decay of a virtual particle. Neutral pions,
J/psi's,
> >
> > Z
> >
> >>>>>bosons, all fit this description.
> >>>>>
> >>>>>This doesn't seem to me to be relegated to a "mathematical
> >
> > trick".
> >
> >>>>>Virtual particles are as "real" as real particles -- the
boundary
> >
> > is a
> >
> >>>>>soft, fuzzy one.
> >>>>
> >>>>You mix up unstable particles and virtual particles. These are
> >
> > distinct
> >
> >>>>concepts.
> >>>>
> >>>>What you see as a peak in a spectrum is a resonance, the
signature
> >
> > of an
> >
> >>>>unstable particle.
> >>>
> >>>And if you turn the Feynman diagram which describes the
production
> >
> > of
> >
> >>>this unstable particle through 90 deg, why does this real
particle
> >>>magically becomes a virtual particle
> >>
> >>It doesn't!
> >>
> >>Unstable particles are modelled exactly like stable particles,
> >>namely as external lines in a Feynman diagram.
> >>Virtual particles in Feynman diagrams are exactly those
> >>which are not given by external lines.
> >>
> >>Hence what is real and what is virtual is not affected by a
> >>diagram rotation - this only affects what is input oand what is
> >
> > output.
> >
> > I am not happy with that.
> > Let me illustrate my unhappiness with a specific example.
> > Take the resonant elastic scattering case:
> >
> > pi + p --> Z --> pi + p
> >
> > I hope we both agree that the Z is produced as a real but unstable
> > particle in the s-channel.
>
> No. Z is a virtual particle since it is an intermediate line.

You are doing nothing to alleviate my unhappiness.
If the Z were a virtual prticle, it would not be on its mass shell and
a mass measurement would not be possible by studying the reaction.

My undertanding is that the line corresponding to the Z is the
trajectory of a real Z travelling from its birth to its decay.
It just happens that its life time is exceedingly short.
My understanding is that the s-channel Feynman diagram which produces
the excited Z is simply a conflation of two separate Feynman diagrams,
one in which p+pi interact to produce the Z, followed by one in which
the Z decays.

(It occurs to me to warn readers that the Z of which we speak is not
the Z0 boson, but a nucleon excited state.)

> The line appears only in the standard perturbative formalism for the
> computation of the in/out cross section not involving Z, and would
not
> be there if that cross section was computed by another method.
> That's why it is virtual only.

But it is observed, and its (complex) mass is actually measured.

> One can also see it by computing
> the momentum balance and check that the momentum does not lie
> on the Z's (complex) mass shell, as would be needed for a real Z.

Oh? Sorry, but the Z is no less real than the pi0.
If the pi0 can decay into two photons, then it can also be created
bytwo photons.
Feel free , therefore to draw a Feynman diagram showing a pi0 produced
in the s-channel by an interaction of two photons, and decaying.

They both happen to have imaginary parts to their masses. 

-- 
Franz
"A first-rate laboratory is one in which mediocre scientists can
produce outstanding work"
P.M.S. Blackett

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