Re: mu+ Polarization Query

[Claude Petitjean <claude.petitjean@psi.ch>]

Dear all,

after consulting with a muSR guy who knows, the situation
conc. muon spins and decay-positron directions is as follows:

a) pi+ decay at rest (producing "surface mu+):
    This produces "foreward decay" mu+
    (i.e. the neutrino which is lefthanded goes backward)
    the mu+ is also 100% polarized with its spin looking
    backward (= upstream the beam line).

    The positrons go preferentially in the direction of the
    muon spin, i.e. upstream the beamline.

b) pi+ decay in flight (producing "cloud" mu+)

    b1) low momenta (typically < 30 MeV/c):
        This produces also "foreward decay" mu+,
        therefore same situation as a)

    b2) higher pi+ momenta with collection of the
        lower energy edge of the mu+ spectrum. This is
        how pion decay (or cloud) channels are
        usually operated.
        This produces mostly "backward decay" mu+,
        i.e. the neutrino goes foreward (downstream
        the beamline). the mu+ spin looks foreward
        and the e+ go also preferentially foreward,
        i.e. downstream the beamline.

c) negative pion, muon decays: everything is just
    opposite, of course.

Note: "foreward" and "backward" pion decays are with
       reference to the center of mass system, of course.

I hope, I did not cause too much confusion! I also
conclude that Toms description below is correct.

Regards, Claude



Tom Banks wrote:

>>In pi- decay, as anti-neutrinos are right handed, the mu- produced
>>must be right handed in the pi CMS, i.e. 100% polarized along
>>their momentum direction. If one tunes the channel momentum to
>>say 33 MeV/c, in the lab system we would collect 33 MeV/c muons from
>>
>>  - forward decay in the pion CMS from pions with very small momentum
>>    <5 MeV/c.
>>  - backward decay in the pion CMS from pions with 85 MeV/c.
>>
>>My understanding is that the backward decay muons dominate, giving
>>a mu- polarization opposite to the beam direction.
> 
> 
> 
> Dear Peter,
> 
> your explanation seems to be consistent with Bernhard's opinion that the
> mu+ are polarized in the direction of the beam momentum (i.e. pointed
> downstream).  His argument was predicated largely on the polarization
> flip
> which occurs around 30 MeV, as illustrated in Figure 7 of the PiE3
> document you referenced:
> 
>    http://aea.web.psi.ch/beam2lines/pie3.pdf
> 
> Bernhard says that you (Peter) and he observed this delicate spin flip
> in
> 2004 before Run8 production began.  When below the 30 MeV threshold, mu+
> are polarized opposite the beam momentum; above the 30 MeV threshold,
> mu+
> are polarized in the direction of the beam momentum.  Our operational
> momentum was safely above the ~30 MeV threshold, so the mu+ were pointed
> downstream.
> 
> So, the Run8 muon polarizations were:
> 
>    mu- : upstream   (-z-direction)
>    mu+ : downstream (+z-direction)
> 
> Since the "upper" (+y-direction) gondolas are the first to see a peak in
> the muSR precession, the mu+ must precess from
> 
>    +z  ->  +y  ->  -z  ->  -y
> 
> This means that our saddle-coil magnet's field lines pointed in the
> +x-direction.
> 
> Thanks for your input,
> Tom
> 
> 
>