Received: from fsgi02.fnal.gov by b0ig16.fnal.gov via ESMTP (950413.SGI.8.6.12/940406.SGI) for id QAA29353; Tue, 28 Mar 2000 16:02:05 -0600 Received: from localhost (hawker@localhost) by fsgi02.fnal.gov (980427.SGI.8.8.8/970903.SGI.AUTOCF) via ESMTP id QAA10710; Tue, 28 Mar 2000 16:02:03 -0600 (CST) Date: Tue, 28 Mar 2000 16:02:03 -0600 From: Eric Hawker To: "Steve Geer, x2395" cc: Deborah Harris , Heidi Schellman , sgeer@fnal.gov, raja@fnal.gov, dharris@fnal.gov, rhbob@fnal.gov, spentz@fnal.gov, parke@fnal.gov Subject: My edits.... In-Reply-To: <200003271603.KAA25695@b0ig16.fnal.gov> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Hi all, Here is my list of edits, nit-picks, and suggestions so far.... Author list: add E.D. Zimmerman >> done p4. - rewrite 1st sentence of into. I suggest something like.... New accelerator technologies point to the possibility that in the near future an accelerator complex could be built to produce and store $10^{19-21} high energy muons per year. >> First sentence has been adjusted p13 2nd sentence typo - it should be \nu_{\mu} not \nu_mu >> done p17 1st sentence - bad hyphen in last word of sentence 7th sentence (I think) - "cant" either needs a ' or should be written as "can not". >> fixed I guess from Fritz's comments that I did not put the most recent version of his section into the non-oscillatio section....here is the most recent version that I have of what he has written....plus a few minor edits of my own of his section >> fixed Eric \section*{Anomolous Lepton Production} An experiment near the storage ring at a neutrino factory could be highly sensitive to exotic processes resulting in production of $e^-$, $\mu^+$, or $\tau$ of either charge. While such a search is interesting in its own right, it is also useful to rule out exotic contributions to long-baseline neutrino oscillation signals. The neutrino beam from a muon storage ring would consist of a virtually pure combination of $\bar{\nu}_e$ and $\nu_\mu$ (or charge-conjugate). Also, at the source of the neutrino beam, the $\bar{\nu}_e$ and $\nu_\mu$ will not have had time to oscillate into other flavors: For a 20 GeV muon storage ring with a 700 m straight section, and neutrino oscillations with $\Delta m^2 \ = \ 3.5 \times 10^{-3} \ \rm eV^2$, the oscillation probability is $\approx 5 \times 10^{-9}$. Furthermore, the neutrino flux is highest at the source. One could distinguish between exotic processes and the beginning of a neutrino oscillation by exploiting their differing dependence on energy and distance. Specifically, these exotic processes would probably have a flat or rising dependence on the neutrino energy $E_\nu$. In contrast, a neutrino oscillation would have a $1/E_\nu^2$ dependence. Also, if the distance $L$ of the experiment changes, the rate of exotic events would decrease with the flux as $1/L^2$. In contrast, the neutrino oscillation probability would increase as $L^2$ (for $L$ small compared to the oscillation period), and so the rate of oscillated events would be independent of $L$. Current understanding of muon interactions allows for exotic processes in two forms. Anomalous lepton production could occur if muons decay to neutrino flavors other than those in the usual decay $\mu \to e \bar{\nu}_e \nu_\mu$, and the anomalous neutrinos then interact in the target. Alternatively, they could be produced if a $\bar{\nu}_e$ or $\nu_\mu$ interacts with the target via an exotic process. The only direct experimental limit on exotic $\mu \to e \bar{\nu}_x \nu_y$ decays is $BR(\mu \to e \bar{\nu}_\mu \nu_e) < 1.3\%$\cite{PDG}. Indirect limits are also very weak. The contribution of non- $V-A$ interactions to the muon decay rate has been limited to 8\%\cite{PDG}. Also, the total muon decay rate is one of the main measurements used to constrain electroweak parameters\cite{PDG}. To first order, \begin{equation} \frac{1}{\tau_\mu} = \frac{G_F m_\mu^5}{192\pi^3} . \end{equation} Assuming the standard model, $G_F$ is determined to 1 part in $10^5$ from muon lifetime measurements. If there are exotic contributions to the muon lifetime, the measured value of $G_F$ would be shifted from the true value. Since \begin{equation} m_W \propto G_F^{-1/2} , \end{equation} the 0.1\% uncertainty on $m_W$ corresponds to a 0.4\% shift in the muon lifetime. Finally, the CKM matrix element $V_{ud}$ is determined from the rate of nuclear $\beta$-decays relative to the muon lifetime. The assumption of unitarity on the CKM matrix gives us the following constraint on the first row: \begin{equation} |V_{ud}|^2 + |V_{us}|^2 + |V_{ud}|^2 = 1 . \end{equation} The experimental determination is\cite{PDG}: \begin{equation} |V_{ud}|^2 + |V_{us}|^2 + |V_{ud}|^2 = 0.991 \pm 0.005 . \end{equation} The uncertainty on this constraint corresponds to a 0.5\% shift in the muon lifetime. Additional contributions to the muon decay rate would lead to a downward shift in the determined value of $|V_{ud}|^2$ from the true value. We conclude that exotic decay modes of the muon with branching ratios totaling 0.5\% are possible without contradicting current measurements or tests of the standard model. As a concrete example of such an exotic process we consider R-parity-violating supersymmetric models. These models lead to lepton-number-violating vertices with couplings $\lambda$, and muon decay processes such as $\mu \to e \bar{\nu_\tau} \nu_\tau$ as shown in Fig.~\ref{exotics:decay}. The matrix element for these decays turns out to have the same form as for the standard W-exchange. The current constraints on the couplings $\lambda$ are reviewed in Ref.~\cite{dreiner}. These constraints allow a branching ratio of 0.4\% for the process in Fig.~\ref{exotics:decay}. Similar processes are allowed for anomalous lepton production as shown for example also in Fig.~\ref{exotics:decay}. Estimates for allowed rates are in progress~\cite{quigg}. These diagrams involve the $\lambda '$ couplings. Currently, the best limit on one of these couplings, $\lambda'_{231}$, is from $\nu_\mu$ deep-inelastic scattering, so existing neutrino data is already providing constraints! The search for these types of effects at the muon storage ring could be input into a decision on whether to build a muon-proton collider where they could be studied in more detail. As a start on estimating the capabilities of an experiment at the neutrino source, we consider the detector concept illustrated in Fig.~\ref{exotics:detector}. This concept consists of a repeating sequence of 1.5 mm-thick Tungsten sheets with Silicon tracking, separated by 4 mm. Tungsten, being dense, provides a high target mass while being thin enough for a produced $\tau$ to have a high probability of hitting the Silicon. The impact parameter of the $\tau$ decay products is typically 90 microns with a broad distribution, so we would like a hit resolution of 5 microns or better. Although there is a lot of multiple scattering in the tungsten, the short extrapolation distance provides for a good impact parameter resolution on the $\tau$ decay products. This configuration has been optimized for a 50 GeV muon beam. For lower energy beams, the planes should be spaced more closely, and the Tungsten thickness perhaps reduced. Studies of detectors with passive target mass and tracking with emulsion sheets~\cite{emulsion} suggest that we can expect $\tau$ reconstruction efficiencies as high as 30\%. We would propose placing such a detector in a magnetic field, and measuring the momentum of muons and hadrons should be straightforward. However, each Tungsten sheet is 0.4 radiations lengths thick, and while we should obtain good energy resolution for electromagnetic showers, it will not be feasible to measure the charge of an electron before it showers. In summary, with a total mass of 6 tons of Tungsten, 200 $\rm m^2$ of Silicon tracking, and $5\times 10^{20}$ muon decays at 50 GeV, we expect a total of 35 billion neutrino interactions. Thus, there is much potential for detecting very rare exotic processes if we can adequately reduce backgrounds. Detailed simulations and studies of possible Silicon tracking technologies are needed to quantify this. \begin{figure}[h] \begin{center} \mbox{\epsfxsize=2.8in\epsffile{exotic_decay.eps}} \mbox{\epsfxsize=2.8in\epsffile{exotic_interaction.eps}} \end{center} \caption{Example of exotic muon decay in R-parity-violating SUSY (Left), and an example of an exotic neutrino interaction in R-parity-violating SUSY (Right).} \label{exotics:decay} \end{figure} \begin{figure} \epsfysize=1.5in \centerline{ \epsffile{exotic_detector.eps}} \caption{One plane of a detector for $\tau$ production.} \label{exotics:detector} \end{figure} \begin{thebibliography}{[9999]} \setlength{\baselineskip}{3.0ex} \bibitem{PDG} Review of Particle Properties, C.~Caso {\it et. al.}, Euro. Phys. J. {\bf C}3, 1 (1998). \bibitem{dreiner} H. Dreiner, hep-ph/9707435 \bibitem{quigg} Chris Quigg, private communication \bibitem{emulsion} K. Kodama {\it et. al.} (OPERA Collaboration), CERN/SPSC 98-25. \\ A. E. Asratyan {\it et. al.}, hep-ex/0002019 \end{thebibliography} \end{document}