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< \input{non_osci.tex}
< %%
< %%
---
> 
> \subsection{Non-oscillation physics at a Neutrino Factory}
> 
> The study of the utility of intense neutrino beams from a muon storage ring in
> determining the parameters governing non-oscillation physics was begun
> in 1997~\cite{rajageer}. More complete studies can be found in~\cite{INTRO:ref9} and recently a European group has brought out an
> extensive study on this topic~\cite{cern-nonosc}.
> 
> A Neutrino Factory can measure individual parton distributions within the
> proton for all light quarks and anti-quarks.
> It could improve valence distributions 
> by an order of magnitude in the kinematical range $x\gsim 0.1$ in the
> unpolarized case.
> The individual components of the sea ($\bar{u}$, $\bar{d}$, ${s}$ and
> $\bar{s}$), as well as the gluon, would be measured with relative
> accuracies in the range of 1--10\%, for $0.1\lsim x \lsim 0.6$. A
>  full exploitation of the Neutrino Factory
> potential for polarized measurements of the shapes of
> individual partonic densities requires an {\it a priori} knowledge of
> the polarized gluon density. 
> The forthcoming set of polarized deep inelastic scattering
> experiments at CERN, DESY and RHIC may provide 
> this information.
> 
> The situation is also very bright for measurements of $C$-even
> distributions. Here, the first moments of singlet, triplet and octet
> axial charges can be measured with
> accuracies that are up to one order of magnitude better than the
> current uncertainties. In particular, the improvement in the
> determination of the singlet axial charge would allow a definitive
> confirmation or refutation of the anomaly scenario compared to the
> `instanton' or `skyrmion' scenarios, at least if the theoretical
> uncertainty originating from the small-$x$ extrapolation can be kept under
> control. The measurement of the octet axial charge with a few percent
> uncertainty will allow a determination of the strange contribution to
> the proton spin better than 10\%, and allow stringent tests of models
> of $SU(3)$ violation when compared to the direct determination from
> hyperon decays.
> 
> A measurement of $\as(M_Z)$ and
> $\sin^2\theta_W$ will involve different systematics from current 
> measurements and will therefore provide an important consistency check of
> current data, although the
> accuracy of these values is not expected to be improved.
> The weak mixing angle can be measured in both the hadronic and leptonic
> modes with a precision of approximately
> $2\times 10^{-4}$, dominated by the statistics and the luminosity
> measurement.
> This determination would be
> sensitive to different classes of new-physics contributions.
> 
> Neutrino interactions are a very good source of clean, sign-tagged charm
> particles. A Neutrino Factory can measure charm production with raw event rates up to
> 100 million charm events per year with $\simeq$ 2 million double-tagged events.
> (Note that charm production becomes significant for storage ring energies
> above 20~GeV).
> Such large samples are suitable for precise extractions of branching ratios
> and decay constants, the study of spin-transfer
> phenomena, and the study of nuclear effects in deep inelastic scattering. 
> The ability to run with both hydrogen and
> heavier targets will provide rich data sets useful for
> quantitative studies of nuclear models.
> The study of $\Lambda$ polarization both in the target and in the
> fragmentation regions will help clarify the intriguing problem of
> spin transfer. 
> 
> 
> Although the neutrino beam energies are well below any reasonable threshold for new physics, the large statistics makes it possible to search for
> physics beyond the Standard Model. The high intensity neutrino beam allows
> a search for the production and decay of neutral heavy leptons 
> with mixing angle sensitivity two orders of magnitude better than present
> limits in the 30--80 MeV range.
> The exchange of new gauge bosons
> decoupled from the first generation of quarks and leptons can be seen
> via enhancements of the inclusive charm production rate, with a
> sensitivity well beyond the present limits. 
> A novel neutrino magnetic moment search  technique that uses oscillating
> magnetic fields at the neutrino beam source could discover large
> neutrino magnetic moments predicted by some theories. 
> Rare lepton-flavor-violating decays of muons in the ring could be tagged
> in the deep inelastic scattering final states
> through the detection of wrong-sign electrons and muons, or of prompt
> taus. 
> 
> \subsection{Physics that can be done with Intense Cold Muon Beams}
> 
> Experimental studies of muons at low and medium energies have had a
> long and distinguished history, starting with the first search for
> muon decay to electron plus gamma-ray~\cite{Hincks-Pontecorvo}, and
> including along the way the 1957 discovery of the nonconservation of
> parity, in which the $g$ value and magnetic moment of the muon were
> first measured~\cite{Garwinetal}.  The years since then have brought
> great progress: limits on the standard-model-forbidden decay $\mu\to
> e\gamma$ have dropped by nine orders of magnitude, and the muon
> anomalous magnetic moment $a_\mu=(g_\mu-2)/2$ has yielded one of the
> more precise tests ($\approx1$ ppm) of physical theory~\cite{BNLg-2}.
> 
> The front end of a Neutrino Factory has the potential to provide
> $\sim10^{21}$ muons per year, five orders of magnitude beyond the most
> intense beam currently available\footnote{The $\pi$E5 beam at PSI,
> Villigen, providing a maximum rate of $10^9$ muons/s~\cite{Edgecock}.}.
> Such a facility could enable precision measurements of the muon
> lifetime $\tau_\mu$ and Michel decay parameters as well as sensitive
> searches for lepton-flavor nonconservation (LFV), a possible ($P$- and
> $T$-violating) muon electric dipole moment (EDM)
> $d_\mu$~\cite{HIMUS99}, and $P$ and $T$ violation in muonic atoms. It
> could also lead to an improved direct limit on the mass of the muon
> neutrino~\cite{numass}. Of these possibilities,
> Marciano~\cite{Marciano97} has suggested that muon LFV (especially
> coherent muon-to-electron conversion in the field of a nucleus) is the
> ``best bet" for discovering signatures of new physics using low-energy
> muons; measurement of $d_\mu$ could prove equally exciting but is not
> yet as well developed, being only at the Letter of Intent stage at
> present~\cite{EDMLOI}\footnote{Experimentalists might argue that
> extending such measurements as $\tau_\mu$ and the Michel parameters is
> worthwhile whenever the state of the art allows substantial
> improvement. However, their comparison with theory is dominated by
> theoretical uncertainties. Thus, compared to Marciano's ``best bets,"
> they represent weaker arguments for building a new facility.}.
> 
> The search for $\mu\to e \gamma$ is also of great interest. The MEGA
> experiment recently set an upper limit $B(\mu^+\to
> e^+\gamma)<1.2\times10^{-11}$~\cite{MEGA}. Ways to extend sensitivity
> to the $10^{-14}$ level have been
> discussed~\cite{Cooper97}. Sensitivity greater than this may be
> possible but will be difficult since at high muon rate there will be
> background due to accidental coincidences; a possible way around this
> relies on the correlation between the electron direction and the
> polarization direction using a polarized muon beam. The
> $\mu$-to-$e$-conversion approach does not suffer from this drawback
> and has the additional virtue of sensitivity to possible new physics
> that does not couple to the photon.
> 
> In the case of precision measurements ($\tau_\mu$, $a_\mu$, etc.),
> new-physics effects can appear only as small corrections arising from
> the virtual exchange of new massive particles in loop diagrams. In
> contrast, LFV and EDMs are forbidden in the standard model, thus their
> observation at any level constitutes evidence for new physics. The
> current status and prospects for advances in these areas are
> summarized in Table~\ref{tab:LEmuons}. It is worth recalling that LFV
> as a manifestation of neutrino mixing is suppressed as $(\delta
> m^2)^2/m_W^4$ and is thus entirely negligible. However, a variety of
> new-physics scenarios predict observable effects.
> Table~\ref{tab:newmuphys} lists some examples of limits on new physics
> that would be implied by nonobservation of $\mu$-to-$e$ conversion
> ($\mu^-N\to e^-N$) at the $10^{-16}$ level~\cite{Marciano97}.
> 
> \begin{table}
> \caption[Current and future tests in low energy muons] {Some current
> and future tests for new physics with low-energy muons
> (from~\protect\cite{Marciano97}, \protect\cite{PDG}, and
> \protect\cite{Aoki01}). Note that the ``Current prospects" column
> refers to anticipated sensitivity of experiments currently approved or
> proposed; ``Future" gives estimated sensitivity with the Neutrino Factory
> front end. (The $d_\mu$ measurement is still at the Letter of Intent
> stage and the reach of experiments is not yet entirely
> clear.)\label{tab:LEmuons}}
> \begin{center}
> \begin{tabular}{|lccc|}
> \hline
> Test & Current bound & Current prospects & Future \\
> \hline
> $B(\mu^+\to e^+\gamma)$ & $<1.2\times10^{-11}$ &
> $\approx5\times10^{-12}$ & $\sim10^{-14}$\\ $B(\mu^-{\rm Ti}\to
> e^-{\rm Ti})$ & $<4.3\times10^{-12}$ & $\approx2\times10^{-14}$ &
> $<10^{-16}$\\ $B(\mu^-{\rm Pb}\to e^-{\rm Pb})$ & $<4.6\times10^{-11}$
> & & \\ $B(\mu^-{\rm Ti}\to e^+{\rm Ca})$ & $<1.7\times10^{-12}$ & & \\
> $B(\mu^+\to e^+e^-e^+)$ & $<1\times10^{-12}$ & & \\ $d_\mu$ &
> $(3.7\pm3.4)\times10^{-19}\,e\cdot$cm & $10^{-24}\,e\cdot$cm? & ? \\
> \hline
> \end{tabular}
> \end{center}
> \end{table}
> 
> \begin{table}
> \caption[New physics probed by $\mu\rightarrow e$ experiments]
> {Some examples of new physics probed by the nonobservation of 
> $\mu\rightarrow e$ conversion at the $10^{-16}$ level 
> (from~\protect\cite{Marciano97}).\label{tab:newmuphys}}
> \begin{center}
> \begin{tabular}{|lc|}
> \hline
> New Physics & Limit \\
> \hline
> Heavy neutrino mixing & $|V_{\mu N}^*V_{e N}|^2<10^{-12}$\\ Induced
> $Z\mu e$ coupling & $g_{Z_{\mu e}}<10^{-8}$\\ Induced $H\mu e$
> coupling & $g_{H_{\mu e}}<4\times10^{-8}$\\ Compositeness &
> $\Lambda_c>3,000\,$TeV\\
> \hline
> \end{tabular}
> \end{center}
> \end{table}
> 
> Precision studies of atomic electrons have provided notable tests of
> QED ({ e.g,}\ the Lamb shift in hydrogen) and could in principle be
> used to search for new physics were it not for nuclear corrections.
> Studies of muonium ($\mu^+e^-$) are free of such corrections since it
> is a purely leptonic system. Muonic atoms also can yield new
> information complementary to that obtained from electronic atoms. A
> number of possibilities have been enumerated by Kawall {\it et
> al.}~\cite{Kawall97} and Molzon~\cite{Molzon97}. As an example we
> consider the hyperfine splitting of the muonium ground state, which
> has been measured to 36 ppb~\cite{Mariam} and currently furnishes the
> most sensitive test of the relativistic two-body bound state in
> QED~\cite{Kawall97}. The precision could be further improved with
> increased statistics.  The theoretical error is 0.3 ppm but could be
> improved by higher-precision measurements in muonium and muon spin
> resonance, also areas in which the Neutrino Factory front end could
> contribute. Another interesting test is the search for
> muonium-antimuonium conversion, possible in new-physics models that
> allow violation of lepton family number by two units. The current
> limit is $R_g \equiv G_C / G_F< 0.0030$~\cite{PDG}, where $G_C$ is the
> new-physics coupling constant and $G_F$ is the Fermi coupling
> constant. This sets a lower limit of $\approx 1 \,$TeV$/c^2$ on the
> mass of a grand-unified dileptonic gauge boson and also constrains
> models with heavy leptons~\cite{Abela}.
> 
> 
> 
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