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this paper gives an overview of the neutrino physics possibilities at a future muon storage ring , which can be either a muon collider ring or a ring dedicated to neutrino physics that uses muon collider technology to store large muon currents . it summarizes a previous more detailed description of these topics by this author  @xcite .    after a general characterization of the neutrino beam and its interactions , some crude quantitative estimates are given for the physics performance of a muon ring neutrino experiment ( murine ) consisting of a high rate , high performance neutrino detector at a 250 gev muon collider storage ring . neutrinos are emitted from the decay of muons in the collider ring : @xmath0    the thin pencil beams of neutrinos for experiments will be produced from long straight sections in either the collider ring or a ring dedicated to neutrino physics . from relativistic kinematics , the forward hemisphere in the muon rest frame will be boosted , in the lab frame , into a narrow cone with a characteristic opening half - angle , @xmath1 , given in obvious notation by @xmath2    the large muon currents and tight collimation of the neutrinos results in extremely intense beams  intense enough even to constitute a potential off - site radiation hazard  @xcite . for the example of 250 gev muons , the neutrino beam will have an opening half - angle of approximately 0.4 mrad . the final focus regions around collider experiments are important exceptions to equation  [ eq : thetanu ] since the muon beam itself will have an angular divergence in these regions that is large enough to significantly spread out the neutrino beam .    for tev - scale neutrinos , the neutrino cross - section is approximately proportional to the neutrino energy , @xmath3 . the charged current ( cc ) and neutral current ( nc ) interaction cross sections for neutrinos and antineutrinos have numerical values of  @xcite : @xmath4    these cross sections are easily converted into approximate experimental event rates for the example used in reference  @xcite of a 250 + 250 gev collider with a 200 meter straight section . for a general purpose detector subtending the boosted forward hemisphere of the neutrino beam : @xmath5 ,                                              \label{eq : genevents}\ ] ] where @xmath6 is the detector length . for a long baseline detector in the center of the neutrino beam : @xmath7}{(l[km])^2 } } ,                                              \label{eq : longevents}\ ] ] where @xmath8 is the detector mass and @xmath9 the distance from the neutrino source . these event rates are several orders of magnitude higher than in today s neutrino beams from accelerators . figure  [ detector_fig ] is an example of the sort of high rate general purpose neutrino detector that would be well matched to the intense neutrino beams . note the contrast with the kilotonne - scale calorimetric targets used in today s high rate neutrino experiments . the neutrino target is a 1 meter long stack of ccd tracking planes with a radius of 10 cm chosen to match the beam radius at approximately 200 meters from production for a 250 gev muon beam . it contains 750 planes of 300 micron thick silicon ccd s , corresponding to a mass per unit area of approximately 50 @xmath10 , about 2.5 radiation lengths and 0.5 interaction lengths . equation  [ eq : genevents ] predicts a very healthy @xmath11 cc interactions per year for this target .    besides providing the mass for neutrino interactions , the tracking target allows precise reconstruction of the event topologies from charged tracks , including event - by - event vertex tagging of those events containing charm or beauty hadrons or tau leptons . given the favorable vertexing geometry and the few - micron typical ccd hit resolutions , it is reasonable to expect almost 100 percent efficiency for b tagging , perhaps 70 to 90 percent efficiency for charm tagging and excellent discrimination between b and c decays .    the target in figure  [ detector_fig ] is surrounded by a time projection chamber ( tpc ) tracker in a vertical dipole magnetic field . the characteristic de / dx signatures from the tracks would identify each charged particle . further particle i d is provided by the cherenkov photons that are produced in the tpc gas then reflected by a spherical mirror at the downstream end of the tracker and focused onto a read - out plane at the upstream end of the target . the mirror is backed by electromagnetic and hadronic calorimeters and , lastly , by iron - core toroidal magnets for muon i d . the dominant interaction of tev - scale neutrinos is deep inelastic scattering ( dis ) off nucleons ( i.e. protons and neutrons ) . there are 2 types of dis : neutral current ( nc ) and charged current ( cc ) scattering . in neutral current ( nc ) scattering , the neutrino is deflected by a nucleon ( @xmath12 ) and loses energy with the production of several hadrons ( @xmath13 ) : @xmath14 this comprises about 25 percent of the total cross section and is interpreted as elastic scattering off one of the many quarks inside the nucleon through the exchange of a virtual neutral z boson : @xmath15    charged current ( cc ) scattering is similar to nc scattering except that the neutrino turns into its corresponding charged lepton : @xmath16 where @xmath6 is an electron / muon for electron / muon neutrinos . at the more fundamental quark level a charged w boson is exchanged with a quark ( @xmath17 ) , which is turned into another quark species ( @xmath18 ) whose charge differs by one unit . @xmath19    the relativistically invariant quantities that are routinely extracted in dis experiments are 1 ) feynman @xmath20 , the fraction of the nucleon momentum carried by the struck quark , 2 ) the inelasticity , @xmath21 , which is related to the scattering angle of the neutrino in the neutrino - quark com frame , and 3 ) the momentum - transfer - squared , @xmath22 . murine s will have the further capability of reconstructing the hadronic 4-vector , resulting in a much better characterization of each interaction . the final state quark always `` hadronizes '' at the nuclear distance scale , combining with quark - antiquark pairs to produce the several hadrons seen in the detector . final state c and b quarks can be identified by vertex tagging of the decaying charm or beauty hadrons that contain them , and some statistically based flavor tagging will also be available for u , d or s final state quarks , using so - called `` leading particle effect ''  @xcite . neutrino interactions are interesting both in their own right and as probes of the quark content of nucleons , so a murine has wide - ranging potential to make advances in many areas of elementary particle physics . this section gives an overview for measurements involving the ckm quark mixing matrix , nucleon structure and qcd , electroweak measurements , neutrino oscillations and , finally , studies of charmed hadrons . there is considerable theoretical interest in the mixture of final state quarks produced in cc interactions . the struck quark can be converted into any of the three final state quarks that differ by one unit of charge : a down ( d ) , strange ( s ) , or bottom(b ) quark can be converted into an up ( u ) , charmed ( c ) , or top ( t ) quark and vice versa . in practice , production of the heavy top quark is kinematically forbidden at these energies and the production of other quark flavors is influenced by their mass . beyond this , the standard model of elementary particle physics ( sm ) predicts the probability for the interaction to be proportional to the absolute square of the appropriate element in the so - called cabbibo - kobayashi - maskawa ( ckm ) quark mixing matrix , a unitary matrix with 4 free parameters whose values are not predicted by the sm . improved measurements involving the ckm matrix will test the sm hypothesis . it is of particular interest that one of the 4 parameters is a complex phase that is postulated as an explanation for cp violation  the intriguing experimental phenomenon that particles may have tiny deviations from the properties that mirror those of their antiparticles . the experimentally determined values for the 9 mixing probabilities are given in table  [ ckm_table ]  @xcite , along with their current percentage uncertainties and speculative projections  @xcite for how the uncertainties could be reduced by a murine . from the large improvements in 4 of the 9 uncertainties it is clear that a murine has potential for tremendous improvements in measuring the quark mixing matrix , and more detailed studies are clearly desirable .    . quark mixing probabilities . threshold suppression due to quark masses has been neglected . in practice , this will reduce the mixing probabilities to the heavier c and b quarks to below the values given in the table and will prevent any mixing to the top quark . the second row for each quark gives current percentage uncertainties in quark mixing probabilities and speculative projections of the uncertainties after analyses from a murine . the two uncertainties in brackets have not been measured directly from tree level processes . the uncertainties assume that no unitarity constraints have been used . [ cols="^ , < , < , < " , ]     another major motivation for murine s is the potential for greatly improved measurements of nucleon structure functions  the momentum distributions of quarks inside the nucleon . this provides  @xcite important tests of quantum chromodynamics ( qcd )  the theory of the strong interaction that is widely accepted for its elegance and simplicity but which has not been experimentally verified at the level of the electroweak theory . a murine might well be the best single experiment of any sort for the examination of perturbative qcd  @xcite . neutrino physics has also had an important historical role in measuring the electroweak mixing angle , which is simply related to the mass ratio of the w and z intermediate vector bosons : @xmath23 now that @xmath24 has been precisely measured at lep , measurements of @xmath25 in neutrino physics can be directly converted to predictions for the w mass . the comparison of this prediction with direct @xmath26 measurements in collider experiments constitutes a precise prediction of the sm and a sensitive test for exotic physics modifications to the sm  @xcite . reference  @xcite estimates that the predicted uncertainty in @xmath26 from a murine analysis might be of order 10 mev , which improves by more than an order of magnitude on today s neutrino experiments  @xcite and is comparable with the projected best direct measurements from future collider experiments . a neutrino property that is currently drawing much interest is the question of whether neutrinos have a non - zero mass . if they do then it is possible for the 3 neutrino flavors to mix , perhaps producing neutrino oscillations that can be observed using a neutrino beam . the probability for an oscillation between two of the flavors is given by@xcite :    @xmath27.l[km ] }                                              { e_\nu [ gev ] } \right ) ,                                          \label{eq : oscprob}\ ] ]    where the first term gives the mixing strength and the second term gives the distance dependence . reference  @xcite obtains the following order - of - magnitude mass limit for an assumed long - baseline detector with reasonable parameters and with full mixing : @xmath28 independent of the distance to the detector . similarly , a mixing probability sensitivity for @xmath29 events in a short - baseline detector is found to be as low as @xmath30 for the most favorable value of @xmath31 . both of these estimates apply generically to all 3 possible mixings between 2 flavors : @xmath32 , @xmath33 and @xmath34 . ( see also reference  @xcite for another discussion of neutrino oscillations at a murine . ) the @xmath31 estimate is more than an order of magnitude better than any proposed accelerator or reactor experiments for @xmath34 and @xmath33 , and is competitive with the best such proposed experiments for @xmath32 . the estimated value for @xmath35 is even more impressive orders of magnitude better than in any other current or proposed experiment for each of the three possible oscillation .    as an interesting final topic , murine s should be rather impressive factories for the study of charm  with a clean , well reconstructed sample of several times @xmath36 charmed hadrons produced in @xmath29 neutrino interactions . there are several interesting physics motivations for charm studies at a murine  @xcite . as an example , particle - antiparticle mixing has yet to be observed in the charm sector  @xcite , and it is quite plausible  @xcite that a murine would provide the first observation of @xmath37 mixing . the intense neutrino beams at muon collider complexes should usher in an exciting new era of neutrino physics experiments , with great advances expected in both traditional and new areas of neutrino physics . king , _ neutrino physics at a muon collider _ , proc . workshop on physics at the first muon collider and front end of a muon collider , fermilab , november 6 - 9 , 1997 . king , _ assessment of the prospects for muon colliders _ , paper submitted in partial fulfillment of requirements for ph.d . , columbia university , new york ( 1994 ) ; b.j . king , _ a characterization of the neutrino - induced radiation hazard at tev - scale muon colliders _ , bnl center for accelerator physics internal report 162-muon-97r , to be submitted for publication . see , for example , chris quigg , _ neutrino interaction cross sections _ , fermilab - conf-97/158-t . values extracted from andrzej j. buras , _ ckm matrix : present and future _ , tum - hep-299/97 . janet m. conrad , michael h. shaevitz and tim bolton , _ precision measurements with high energy neutrino beams _ , hep - ex/9707015 , submitted to rev . mod ( 1997 ) k.s . et al . _ ( ccfr / nutev collaboration ) _ a precision measurement of electroweak parameters in neutrino - nucleon scattering _ , fnal - pub-97/001-e . b.j . king , columbia university ph.d . thesis , 1994 ; nevis report : nevis-283 , cu-390 , nevis preprint r-1500 ( 1994 ) . barnett et al . , physical review d54 , 1 ( 1996 ) and 1997 off - year partial update for the 1998 edition available on the pdg www pages ( url : http://pdg.lbl.gov/ ) . s. geer , _ the physics potential of neutrino beams from muon storage rings _ , proc . workshop on physics at the first muon collider and front end of a muon collider , fermilab , november 6 - 9 , 1997 . i.i bigi , _ open questions in charm decays deserving an answer _ , cern - th.7370/94 , und - hep-94-big08 ( 1994 ) . i.i bigi , _ the expected , the promised and the conceivable - on cp violation in beauty and charm decays . _ , und - hep-94-big11 ( 1994 ) . tiehui ( ted ) liu , _ the d0-dobar mixing search  current status and future prospects _ , hutp-94/e021 ( 1994 ) . gustavo burdman , _ charm mixing and cp violation in the standard model _ , fermilab - conf-94/200 ( 1994 ) .
an overview is given of the neutrino physics potential of future muon storage rings that use muon collider technology to produce , accelerate and store large currents of muons .