Date: Mon, 27 Mar 2000 12:11:20 -0800
From: Burton Richter <BRichter@SLAC.Stanford.EDU>
Subject: Neutrino Factory Report -- Draft One
In-reply-to: <200003241900.NAA19718@b0ig16.fnal.gov>
To: sgeer@b0ig16.fnal.gov, schellman@fnal.gov
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Subject:  Neutrino Factory Report -- Draft One


Dear Steve and Heidi:


The first draft of "Physics at a Neutrino Factory" is an impressive piece
of work, especially considering the short time in which all of this was
pulled together.  I appreciate having my name on the author list, but I
really didn't do any work and it doesn't belong there.  Below I make two
general comments and then a few specific ones which may be only nit
picking. 


One:

<paraindent><param>left</param>I think it would be useful to at least
have an appendix comparing the neutrino factory with what I will loosely
call Minos-II.  There is an intermediate step possible between the Minos
program and the program of a neutrino factory.  That step makes a 4 MW
proton source available for neutrino production (the present Fermilab
beam, if I have the numbers correct, gives about 400 kW), and creates a
new detector.  A neutrino factory may be an appropriate long-term goal,
but a considerable amount of R&D is needed to prove its feasibility (muon
cooling, for example) and it will be very expensive.  A step that could
be taken at Fermilab very much sooner would involve an upgrade of the
Fermilab machine, probably the creation of the narrow-band beam, and a
new detector.  If I look at Table 1 (Page 11 of the draft) and multiply
the Minos high-energy wide-band beam numbers by a factor of ten, I do
better than a muon ring of 20 GeV and I think the narrow-band beam would
make the comparison even more favorable.  A narrow-band beam should have
lower background than the wide-band horn-focused beam, possibly make
muon-neutrino oscillations to electron neutrinos as detectable as
oscillations to tau neutrinos are with the present Minos.  I think that
the rebuilds of the injector linac and the FNAL booster could be done for
no more than 5% to 10% of the cost of a neutrino factory.

</paraindent>

>> This is an important point. We have tried to add a bit more to
>> the end of section 3.2 to address this, although more needs to 
>> be done in the future ... and perhaps we will extend the study 
>> to address this point further. The Fermilab MI can take up to a factor 
>> of 4 more beam with suitable upgrades. With this and a factor
>> of a few bigger detector an order of magnitude statistics can 
>> be imagined. However precise measurements (sin^2 2theta_23
>> and delta m^2_32) are limited by systematics ... for example on 
>> the flux. In addition for the atmospheric dm^2 scale one 
>> wants to go much further away ... 7000 km for example. In the 
>> long run it appears that a neutrino factory is a winner even for 
>> the all nu_mu physics. In the short run, an upgraded proton source
>> built early on the path to a neutrino factory might well have
>> solid physics payoff.


Two:

<paraindent><param>left</param>I did not find the discussions of
backgrounds in the electron-neutrino physics program to be convincing.  I
see two problems here.  It is necessary to separate electron-neutrino
oscillations to muon neutrinos and tau neutrinos to get at the physics. 
Electron neutrinos that produce right-sign taus give rise to right-sign
electrons and muons at a rate of 17% each from the tau decay.  Only in
the case where the electron neutrino dominantly goes into either muon or
tau neutrino, is the separation relatively simple.  If they are
comparable, it is very messy and it will take a very special detector to
separate them out.

Muon-neutrino oscillations to tau neutrinos give rise to wrong-sign
leptons.  The muons are easily identified by a magnetic field while the
electrons are not except in a very special and very difficult to build
detector.  Since the number of taus coming from the muon neutrinos is
expected to be much larger than the number coming from electron neutrinos
on the basis of what we know now, this is a very serious problem.  The
only relatively clean way to separate the right-sign from the wrong-sign
taus that I can see is to use the one-prong hadronic decays and measure
the sign of the hadrons.  This is intermediate in difficulty between
measuring the electron sign (nearly impossible, and measuring the
muon-sign easy).   

>> For the popular 3-flavor mixing scenarios nu_e -> nu_tau is 
>> suppressed by a substantial factor compared with nu_e -> nu_mu 
>> (cos^2 2theta_23 c.f. sin^2 2theta_23). In addition, after 
>> paying for the muonic BR there is only at most a very small
>> contribution from nu_e -> nu_tau in the wrong sign muon samples
>> expected. This is included in some of the fits that have been
>> made to study the precision with which parameters can be measured.

>> There is certainly a challenge in measureing nu_e -> nu_tau, which
>> requires massive (few kt) detectors that can reconstruct taus 
>> (to dig them out from nu_e -> nu_mu) and measure their charge 
>> (to separate them from nu_mu -> nu_tau). The charge sign measurement
>> needs to be at the 2 - 3 sigma level to adequately fight the 
>> background. 

</paraindent>

Three A:

<paraindent><param>left</param>Equations 7) and 8) on Page 6 are correct
as written only for muon decays at zero degrees.  The problem lies in the
definition of x-max.  You have defined x as the fraction of the muon
energy, and, even for decay angles as small as that given in Table 2 on
Page 12, the maximum neutrino energy is significantly less than the muon
energy.  This may be nit picking.

>> Thankyou for pointing this out. We have modified the text. Note 
>> that none of the numbers quoted in tables or plots use this 
>> approximation.

</paraindent>

Three B:

<paraindent><param>left</param>There is, I think, a related problem with
Figure 1 on Page 7.  The text talks about decays at zero degrees and for
such decays there would be no electron anti-neutrinos for muon
polarization of minus one.  I think what must have happened here is that
people used in the assumed  angular divergence and that is what gives the
flux of electron anti-neutrinos in the figure.  The figure and the text
can easily be brought into agreement.

>> Essentially you are right. The non-zero nu_e flux for fully polarized 
>> muons in the figure arises because the flux is averaged over a 
>> finite angular region. We have added a sentence in the caption to
>> clarify this.


</paraindent>

Three C:

<paraindent><param>left</param>I am surprised at the relatively low ratio
of tau neutrino to muon-neutrino cross sections at high energy shown in
Figure 2 on Page 8.  Far above threshold, I would expect this ratio to be
nearer to one.  On Page 12 you refer to another calculation that gives
bigger tau yields.  I would think that is a more plausible calculation
and you should use it instead.

>> The calculation of Casper yields 20-30% higher tau rates. 
>> It probably should be used in the future.

</paraindent>

I look forward to seeing the final version.  Keep up the good work. 

>> Thankyou for your encouragement.

Burt