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the search for supersymmetric particles is now an integral part of all current , as well as future , experimental programs at high - energy colliders . aside from many attractive features of supersymmetry ( susy ) @xcite , the driving force for these searches comes from the recognition that weak - scale susy , which is introduced to solve the gauge hierarchy problem , requires that the susy partners of the standard model ( sm ) particles must be accessible to experiments that probe the tev energy scale . if this is the case , a large number of gluinos and squarks will be produced at future hadron colliders such as the cern lhc ( operated at @xmath21 tev with luminosity @xmath22 @xmath23s@xmath24 ) and very large hadron collider ( vlhc ; operated at @xmath25200 tev with @xmath22@xmath26 @xmath23s@xmath24 ) . once produced , gluinos and squarks will subsequently decay to the lightest neutralino ( @xmath3 ) . this means that such hadron colliders will become the `` neutralino factory '' , which is capable of producing up to @xmath1 @xmath3 s per year . the @xmath3 is usually assumed to be the lightest supersymmetric particle ( lsp ) and thus stable if @xmath6-parity is conserved . it will then escape the detector , resulting in the famous missing energy signature for susy @xcite . however , the @xmath3 might not be altogether stable : if there exists another superparticle lighter than @xmath3 , such as the gravitino ( @xmath4 ) or axino ( @xmath5 ) , the @xmath3 will decay into , _ e.g. _ , @xmath27 @xcite or @xmath28 @xcite . such a light gravitino naturally exists in gauge - mediated susy breaking ( gmsb ) models [ 512 ] as well as in a class of no - scale supergravity ( sugra ) models @xcite . a light axino can also exist in sugra models with the peccei - quinn ( pq ) symmetry @xcite . as another possibility , the violation of @xmath6-parity leads to the unstable @xmath3 even if it is the lsp . the @xmath3 will then decay into such modes as @xmath29 , @xmath30 and @xmath31 @xcite . if the @xmath3 decay takes place inside the detector , the resultant event topology would be very different from that in case of the stable @xmath3 . the experimental signatures have recently been studied for the @xmath3 decay into @xmath27 [ 1625 ] and @xmath28 @xcite , motivated by the single @xmath32 event observed in the cdf experiment at the tevatron @xcite . for the cdf event interpreted as the signal of the @xmath3 decay , the inferred decay length @xmath7 is much below 1 m. however , subsequent reports on diphoton @xmath33 distribution observed in the cdf @xcite and d@xmath34 @xcite experiments , as well as the analysis of the lep data at @xmath35 gev @xcite , do not give any further evidence for the @xmath3 decay into photon(s ) with such short @xmath7 . therefore , the possibility is still open for the @xmath3 decay into @xmath27 or @xmath28 occurring mostly outside the detector . actually , such a slow decay of @xmath3 appears to be favored at least for relatively light @xmath3 : original gmsb models @xcite prefer relatively high susy breaking scale , @xmath36 gev @xcite , implying @xmath37 km for @xmath38 gev . in case of the @xmath18 decay , the allowed range of the pq symmetry breaking scale , @xmath1 gev@xmath39 gev @xcite , leads to @xmath40 km for @xmath38 gev . if the @xmath3 decay is slow and mostly occurs outside the detector , the signature observed in usual collider experiments will be indistinguishable from that of the stable @xmath3 . hence the signal of the @xmath3 decay would be missed entirely . even if a significant part of @xmath3 s produced at hadron colliders decay into photon(s ) inside the detector , it might be hard to detect the signature with usual detectors , because a huge number of particles produced will make it difficult to identify a single photon not coming from the interaction point . in addition , the detectors for the approved experiments at the lhc are not designed to measure the direction of each photon precisely . therefore , in order to search for a slow decay of @xmath3 , we propose a dedicated experiment with the interaction point surrounded by a thick shield , by which most of the collision products are dumped . the @xmath3 would go through the shield and decay in a long decay tunnel . the decay product of @xmath3 can then be detected by a detector located at the end of the tunnel . we show that the slow arrival time and the large off angle ( to the direction of the interaction point ) of the decay product will provide an unambiguous signal of slowly decaying @xmath3 s . we also show that , in case of the @xmath3 decay into a photon and a light invisible particle such as @xmath4 and @xmath5 , the mass of @xmath3 can be determined by using the correlation between the energy and the arrival time of the decay photon . furthermore , by reconstructing the decay kinematics with the estimated decay position , one can determine whether the final state is two - body or not . the remainder of this paper is organized as follows . we first show in section  [ sec : lhc ] how the lhc can be the neutralino factory . in section  [ sec : model ] , we briefly review the theoretical models of the @xmath3 decay into a gravitino or an axino . our strategy of the search for a slow decay of @xmath3 is then described in section  [ sec : scheme ] . in section  [ sec : mass ] , we illustrate the method of determining the mass of @xmath3 after the discovery of its decay . section  [ sec : vlhc ] is devoted to the discussion of the @xmath3 decay search at vlhc . we also discuss in section  [ sec : other ] other searches which are possible with our setup , _ i.e. _ , ( i )  other decay modes of @xmath3 , ( ii )  slow decays of any other longlived neutral or charged particles , and ( iii )  heavy stable charged particles . finally , we present our conclusions in section  [ sec : conc ] . a realistic design for the detector is investigated with monte carlo simulations in appendix  [ sec : dete ] . in appendix [ sec : munu ] , we estimate the rates of high - energy prompt neutrinos and muons , which can go through the iron shield and thus become the potential background . to simulate the @xmath3 production and decay at the lhc , we first generate various susy processes in @xmath41 collisions at @xmath21 tev using isajet 7.13 @xcite with the cteq2l parton distribution functions @xcite . in most cases , the dominant products are the gluino ( @xmath42 ) and squark ( @xmath43 ) , which will then decay into @xmath3 s through @xmath44 and @xmath45 if @xmath46 , and @xmath47 and @xmath48 if @xmath49 . if the gluino and squark are heavy ( @xmath50 tev ) , the production of gauginos ( charginos and neutralinos ) could become dominant . as an example , we take @xmath51 , @xmath52 and @xmath53 , and assume the gaugino mass unification , which is known to roughly hold not only in sugra models but also in most of gmsb models . figure  [ fig : cross ] shows the total cross sections for the production of gluinos , squarks and gauginos , as well as the anticipated numbers of events per 100 fb@xmath24 , at the lhc as a function of @xmath54 . we note that each susy event contains two @xmath3 s in the final state . also shown in this figure are the corresponding values of @xmath55 , which results from the gaugino mass unification . it is worth noting that the cross sections increase by a factor up to @xmath56 when the next - to - leading order qcd corrections are properly included @xcite . for the discussion below , we select three representative gluino and neutralino masses : @xmath57 gev and @xmath58 gev ( case  1 ) ; @xmath59 gev and @xmath60 gev ( case 2 ) ; and @xmath61 gev and @xmath62 gev ( case  3 ) .    figure  [ fig : angle ] shows the angular distributions of @xmath3 s produced at the lhc for ( a )  case  1 , ( b )  case  2 , and ( c )  case  3 . the integrated luminosity is taken to be 100 fb@xmath24 , which corresponds to the runtime of @xmath63 s with @xmath22 @xmath23s@xmath24 . the total numbers of produced @xmath3 s are @xmath64 , @xmath65 and @xmath66 for case  1 , 2 and 3 , respectively . it can be seen that most of @xmath3 s are produced in the forward direction . more events can thus be detected if one installs a detector at a smaller angle @xmath67 with respect to the colliding proton beam . we here choose @xmath68 ( or @xmath69 ) for the central axis of the detector by compromising the rate of the signal and that of the potential background ( high - energy prompt neutrinos and muons ) as discussed in appendix  [ sec : munu ] . figure  [ fig : eneut ] shows the energy spectra of produced @xmath3 s pointing to the detector which covers @xmath70 and an elevation angle of @xmath71 . we find that , in all three cases , the majority of @xmath3 s are produced with relatively low energies , _ i.e. _ , the energy spectra have a peak at @xmath72 to 2 . this means that most of the produced @xmath3 s are not extremely relativistic , having @xmath73 . this makes the time measurement of the decay products a powerful tool for the identification of slowly decaying @xmath3 s . supersymmetry ( susy ) is widely acknowledged to be the best motivated extension of the sm . this is not only because it provides a natural solution to the gauge hierarchy problem , but also there exist many pieces of indirect evidence , such as the correct prediction of @xmath74 , the convergence of the sm gauge couplings at very high energies , and the heaviness of the top quark as required by the radiative breaking of the electroweak gauge symmetry . moreover , susy can provide a plausible candidate for cosmological dark matter . these hints , as a whole , appear to constitute circumstantial evidence for susy . susy , however , must be broken because no susy partners of ordinary particles have been discovered . the breaking of susy is usually conceived to occur in a hidden sector at some very high energies , which will probably remain unaccessible to direct collider experiments at least in the near future . thus the investigation into the origin of the susy breaking is of great importance since it could be the unique window to look into the world of such high energies , perhaps up to the planck scale . two scenarios have been proposed on how the susy breaking is communicated from the hidden sector to the observable sector : in one scenario , as in supergravity ( sugra ) models @xcite , susy breaking is mediated by gravity . in this case , the susy breaking scale @xmath16 is necessarily of order @xmath75 gev to give the superparticle masses around the weak scale . the other is the gauge - mediated susy breaking ( gmsb ) scenario [ 512 ] , where susy is broken at a scale as low as @xmath76@xmath63 gev , and the gauge interactions act as the messengers of susy breaking . because of this relatively low value of @xmath16 , the mass degeneracy among squarks or sleptons , which results from the fact that gauge interactions are flavor blind , is hardly broken by the evolution to the weak scale , in contrast to sugra models . this ensures sufficient suppression of flavor changing neutral current ( fcnc ) processes . in addition , gmsb models may also provide a solution to the susy @xmath77 problem @xcite . these two scenarios also lead to distinctive consequences concerning cosmological dark matter . in sugra models , the lightest neutralino ( @xmath3 ) is usually the lsp , and can be the dominant component of dark matter . on the other hand , gmsb models naturally predict that the gravitino ( @xmath4 ) comes out to be the lsp . the gravitino with mass @xmath78 kev is claimed to be a good candidate for warm dark matter @xcite . we note that it is practically impossible to directly detect the gravitino dark matter in laboratories , in contrast to the neutralino dark matter , whose direct detection is being pursued in many experiments .    in this way , for finding the future direction of particle physics and cosmology , it is of crucial importance to determine which scenario is realized in nature . as will be shown later , our experiment to search for a slow decay of @xmath3 can probe a wide range of @xmath7 , which corresponds to @xmath16 of order @xmath76 to @xmath79 gev in case of the @xmath13 decay . this covers much of the @xmath16 range presently considered in gmsb models . the gravitino mass @xmath80 is related to @xmath16 ( on the condition of the vanishing cosmological constant ) by @xmath81 where @xmath82 gev is the reduced planck mass . this leads to @xmath83 and 24 kev for @xmath84 and @xmath63 gev , respectively . note that the gravitino heavier than @xmath2 kev overcloses the universe in the standard cosmology . such a heavy gravitino , however , is still allowed to be the dark matter if the reheating temperature after the inflation is low enough @xcite .    the longitudinal component of the gravitino , _ i.e. _ , the goldstino , couples to matter with weak ( not gravitational ) interaction strength proportional to @xmath85 . through this coupling , the @xmath3 will decay to a photon and a gravitino with a partial width of @xcite @xmath86 where @xmath87 is the square of the photino admixture of the @xmath3 . if the @xmath3 is a pure bino , @xmath88 . this partial width is most likely to be the dominant one if the @xmath3 is the next - to - lightest supersymmetric particle ( nlsp ) with not too small @xmath87 , resulting in the decay length @xmath89 for @xmath90 gev and @xmath91 gev , this decay length is much longer than a typical detector size , leading that most of the decays will occur outside the detector . it has recently been pointed out @xcite that such large @xmath16 ( @xmath92 gev ) is expected in original gmsb models @xcite . in addition , other gmsb models [ 911 ] tend to predict that susy breaking occurs at relatively high ( @xmath93 gev ) energies , although @xmath94@xmath0 gev can naturally fit in with a very recent model @xcite . equation  ( [ eq : ctau_g ] ) also indicates that the measurement of both @xmath14 and @xmath7 will give direct information on @xmath16 . the peccei - quinn ( pq ) symmetry was introduced to solve the strong @xmath77 problem @xcite . this symmetry should be explicitly broken , leading to a light pseudoscalar , the axion ( @xmath95 ) , whose mass is related to the pq symmetry breaking scale @xmath19 by @xmath96 where @xmath97 is the qcd anomaly factor of the pq symmetry . the axion is one of good candidates for dark matter owing to its feeble interaction with matter . the allowed range of @xmath19 is confined to @xmath1@xmath98 gev @xcite from laboratory experiments as well as from astrophysical and cosmological considerations . if both the pq symmetry and susy hold in nature , there should exist the fermionic superpartner of the axion , the axino ( @xmath5 ) . the axino can remain light even after the susy breaking in sugra models @xcite . in particular , the axino with mass @xmath99 kev could serve as warm dark matter @xcite as is the case for the gravitino . if such a light axino exists , the @xmath3 can decay into @xmath28 . in case of the @xmath3 being a pure bino , the decay width can be written as @xcite @xmath100 which corresponds to the decay length @xmath101 the lower limit on the pq symmetry breaking scale , @xmath102 gev , implies @xmath40 km for @xmath38 gev . we propose a completely new type of collider experiment , which is schematically shown in fig . [ fig : scheme ] . gluinos and squarks ( and possibly gauginos ) are produced in @xmath41 collisions at the interaction point and promptly decay into @xmath3 s . the @xmath3 s then enter the decay tunnel after going through the shield , by which most of the collision products are dumped . as a simple example , we here consider an iron shield of 10 m thickness , and take the tunnel length to be @xmath103 m , although a much longer tunnel is certainly possible . the acceptance of the tunnel is taken to be @xmath70 and an elevation angle of @xmath71 . we choose this angle @xmath67 by compromising the rate of the signal and that of the potential background ( see appendix  [ sec : munu ] ) . two layers of the anti - coincidence hodoscopes possibly with track detectors are installed just on the back end of the shield for the rejection of punchthrough muons . it can also be used for the trigger of heavy longlived charged particles . in addition , the scintillation counters and/or track detectors can be installed on the wall around the decay tunnel to reject potential background events produced by cosmic rays . if the @xmath3 decays to a photon and a light invisible particle in the tunnel , the decay photon will reach the end of the tunnel and enter a shower detector which has a spherical front face , and initiate the electromagnetic shower . the incident position , angle , and energy of the photon , as well as the arrival time relative to the rf clock of the accelerator , are measured by the detector .    instead of the bulk iron shield , we can use ( at extra costs ) an `` active '' @xmath104-shield , consisting of segmented calorimeters , magnetized iron plates and the muon trackers . this setup will enable us to measure the total ( and missing ) transverse energy of the event and to tag the existence of high - energy muons . the decay probability of @xmath3 within a distance of @xmath105 is given by @xmath106 where @xmath107 is the lorentz factor , and @xmath7 is the decay length . as a typical case , the probability that the @xmath3 with @xmath108 decays in the tunnel ( 10 m @xmath109 51.6 m ) is calculated to be 20% for @xmath110 m , and 2.4% for @xmath111 m.    in the following monte carlo simulations , we assume that the decay photon is emitted isotropically with energy equal to @xmath112 in the rest frame of the @xmath3 , as is the case for the @xmath13 decay with @xmath113 . the photon 4-momentum ( @xmath114 , @xmath115 ) in the laboratory frame is then calculated by the lorentz boost . we show in fig . [ fig : sample ] a typical generated event of the @xmath3 decay into a photon and a light invisible particle . figure  [ fig : neut ] shows the distributions of the lorentz factor @xmath116 for @xmath3 s entering the decay tunnel for case  1 , 2 and 3 in ( a ) , ( b ) and ( c ) , respectively . the numbers of @xmath3 s entering the tunnel are @xmath117 , @xmath118 and @xmath119 for case  1 , 2 and 3 , respectively , for total integrated luminosity of 100 fb@xmath24 , which we assume for all the simulation plots shown in this paper . the distributions of @xmath116 for @xmath3 s decaying in the tunnel are also shown in fig . [ fig : neut ] . we here take as an example the decay lengths calculated by eq . ( [ eq : ctau_g ] ) for @xmath120 gev , _ i.e. _ , @xmath121 km , 350 m , and 52 m for @xmath58 gev ( case  1 ) , 78 gev ( case  2 ) and 115 gev ( case  3 ) , respectively . the resultant numbers of @xmath3 s decaying in the tunnel are @xmath122 , @xmath123 and @xmath124 for case  1 , 2 and 3 , respectively . also shown in this figure by hatched histograms are the distributions for @xmath3 s whose decay photons enter the shower detector . the corresponding energy spectra of the decay photons are shown in fig . [ fig : gamma ] for ( a )  case  1 , ( b )  case  2 , and ( c )  case  3 . the spectra have a peak at @xmath125 and extend up to @xmath15 gev .    the clear separation of the @xmath3 decay signal from the potential background , _ i.e. _ , high - energy prompt neutrinos and muons as well as the cosmic - ray events , can be attained by measuring the arrival time and the off angle @xmath126 to the direction of the interaction point ( see fig . [ fig : scheme ] ) . figure  [ fig : psitof ] shows the scatter plots of @xmath126 vs.  the arrival time for ( a )  case  1 , ( b )  case  2 , ( c )  case  3 , and ( d )  background neutrinos and muons ( @xmath127 ) . the background @xmath127 events all have @xmath128 , and arrive in narrow bunch structure ( here we assume @xmath129 ns ) . on the other hand , most of the decay photons have large @xmath126 ( up to @xmath130 ) and arrive with significant delay ( typically 120 ns ) , because most of the produced @xmath3 s are not extremely relativistic . we show in fig . [ fig : tof ] the arrival time distributions . the evidence for a slow decay of the heavy parent particles is clear in the peak position , which is displaced by about 2 ns from the exact bunch position , as well as in the long tail after the peak . the decay length @xmath7 can in principle be estimated from the distribution of the events in the scatter plot of @xmath126 vs.  the arrival time . moreover , one could measure @xmath7 from the variation of the signal count rate correlated with the change of @xmath131 , which can be performed by moving the detector on rails . together with the measured value of @xmath14 ( see section  [ sec : mass ] ) , one can determine the strength of the interaction which governs the @xmath3 decay . in particular , if one interprets the observed events as the @xmath13 ( @xmath18 ) decay , the susy breaking scale @xmath16 ( the pq symmetry breaking scale @xmath19 ) can be determined . the large off angle @xmath126 and the slow arrival time are the generic features of slowly decaying heavy particles , and will thus always provide a clear signature of slowly decaying @xmath3 s . based on this prospect , we now estimate the explorable range of the decay length @xmath7 . figures  [ fig : psitof ] and [ fig : tof ] represent typical examples of the off angle @xmath126 and the arrival time distributions for @xmath7 much longer than ( cases  1 and 2 ) or comparable to ( case  3 ) the tunnel length . for longer @xmath7 , the characteristic shape of the distribution will not change , while the number of detected events will decrease in proportion to @xmath132 . in order to estimate the longest explorable decay length , we assume that 10 events with such a characteristic distribution are enough to discover the signal .    for @xmath7 much shorter than the tunnel length , most of the detected events will be due to the @xmath3 decaying immediately after going through the shield . such events will show the smaller off angle and shorter arrival time as compared to the cases shown in figs . [ fig : psitof ] and [ fig : tof ] . the off angle will nevertheless have finite non - zero values ( typically of 1 to @xmath133 ) , and the arrival time will definitely be deviated ( by 1 to 10 ns ) from that of background @xmath127 events , because the @xmath3 flies at least the shield thickness before decaying . in estimating the shortest explorable decay length , we assume 100 such events are enough to discover the signal . figure  [ fig : reach ] shows the resultant explorable range of @xmath7 for various @xmath14 at the lhc with 300 fb@xmath24 . it can be seen that the explorable range of @xmath7 is wide , _ i.e. _ , 0.2 m to @xmath8 km for @xmath9 gev , and 1 m to 2 km for @xmath10 gev . we also show in this figure the predicted curves of @xmath7 for the @xmath3 decay into @xmath27 and @xmath28 for typical values of @xmath16 and @xmath19 , respectively . we find that one can explore @xmath16 in a wide range of @xmath134 to @xmath12 gev through the @xmath13 decay . this range includes an interesting case of @xmath135 gev , where the gravitino has mass @xmath78 kev and can be the dominant component of dark matter in the standard cosmology . in case of the @xmath18 decay , @xmath19 can be explored up to @xmath136 gev for @xmath38 gev . after discovering the signal of the @xmath3 decay , one can determine the mass of @xmath3 by using the correlation between the energy and the arrival time of the decay photon , if enough number of decay events can be accumulated .    for this purpose , we first extract the approximate time - of - flight ( tof ) of @xmath3 , @xmath137 , from the time difference between the signal of the shower detector and the rf clock of the accelerator , as illustrated in fig . [ fig : time ] . in this process , we assume that each @xmath3 comes from the closest possible bunch of the proton beam on the condition of @xmath138 . the probability of attributing an event to a wrong starting bunch is small , _ i.e. _ , 2025% for the three cases described above . using the extracted value of @xmath137 , we define the parameter @xmath139 as @xmath140 where @xmath141 is the distance from the interaction point to the front face of the shower detector . the distributions of @xmath142 are shown in fig . [ fig : beta ] for ( a )  case  1 , ( b )  case  2 , ( c )  case  3 , and ( d )  background @xmath127 . there is an upper cutoff at @xmath143 , which results from the modulation of @xmath137 by the bunch spacing of 25 ns . the background @xmath127 events make a sharp peak at @xmath144 with no tail in contrast to the @xmath3 decay signal .    figure  [ fig : scan ] shows the scatter plots of @xmath114 vs.   @xmath145 for ( a )  case  1 , ( b )  case  2 , and ( c )  case  3 . the photon energy resolution is assumed to be @xmath146 . the lower cutoff of @xmath147 at @xmath56 corresponds to the above - mentioned cutoff of @xmath142 at @xmath148 . one can also find an edge with constant ratio of @xmath114 to @xmath147 . this edge is composed of the events in which the decay occurs near the front face of the shower detector with the decay photon emitted toward the flight direction of the @xmath3 . for such events , @xmath141 and @xmath137 are nearly the same as the actual flight length and tof of the @xmath3 , respectively , and the decay photon has the full energy of the @xmath3 , _ i.e. _ , @xmath149 , resulting in the edge corresponding with @xmath150 . from the position of this edge , the mass of @xmath3 can be determined with an accuracy of @xmath151% . for this purpose , the shower detector should be designed to measure the photon energy in a wide range of 10 to 1000 gev . figure  [ fig : mass ] shows the corresponding distributions of @xmath152 for cases  1 to 3 . an upper endpoint at @xmath150 can be seen in each case . we now try to determine the nature of the @xmath3 decay , _ i.e. _ , whether it is two - body or not . although the symmetric peak at @xmath153 in fig . [ fig : mass ] may be the first hint of the two - body decay , we can prove the two - body nature by directly reconstructing the decay kinematics . for this purpose , we first select events with @xmath154 based on the @xmath126 distribution shown in fig . [ fig : psi ] for ( a )  case  1 , ( b )  case  2 , ( c )  case  3 , and ( d )  background @xmath127 . after this @xmath126 cut , only events in which the @xmath3 decays relatively near the shower detector can survive . the efficiency of this cut is @xmath155 for each of the three cases . figure  [ fig : scanc ] shows the scatter plots of @xmath114 vs.  @xmath147 for cases  1 to 3 after the cut of @xmath154 . it can be seen that only photons with relatively low energies survive . thus the two methods of determining the @xmath3 mass , _ i.e. _ , the use of the edge in the scatter plot of @xmath114 vs.  @xmath147 , and the direct reconstruction of the decay kinematics , are complementary in that different events are mainly used in these two methods . we then simply assume that the decay position d is the middle point between c and e , both of which are defined in fig . [ fig : scheme ] . using this assumption , the velocity of the @xmath3 can be approximately expressed by @xmath156 where @xmath157 and @xmath158 represent the flight path of the @xmath3 and that of the photon , respectively . one can then calculate the reconstructed mass as @xmath159 where @xmath160 is the angle between the momentum of the @xmath3 and that of the photon ( see fig . [ fig : scheme ] ) . figure  [ fig : recon ] shows the distributions of @xmath161 for ( a )  case  1 , ( b )  case  2 , and ( c )  case  3 . it can be seen that the @xmath3 mass can be determined with an accuracy of @xmath162% for each case . if one finds a peak in the distribution of @xmath161 at the right position expected from the edge in the scatter plot of @xmath114 vs.  @xmath147 , one can conclude that the observed events are really the signature of the two - body decay of @xmath3 into a photon and an invisible particle . very large hadron collider ( vlhc ) @xcite has been discussed recently as a post - lhc machine , being operated at @xmath25200 tev with @xmath22@xmath26 @xmath23s@xmath24 . we stress here that the vlhc will become the neutralino factory much more powerful than the lhc . figure  [ fig : vcross ] shows the total cross sections for the production of gluinos , squarks and gauginos , as well as the anticipated numbers of events per 1000 fb@xmath24 , in @xmath41 collisions at @xmath25 tev as a function of @xmath54 . also shown in this figure are the corresponding values of @xmath55 . figure  [ fig : vreach ] shows the explorable range of @xmath7 for the @xmath3 decay at the vlhc with 3000 fb@xmath24 . as in fig . [ fig : reach ] , the upper end of the explorable region corresponds to the level of 10 decay events detected , and the lower one is derived from the condition that 100 decay events are detected . the explorable range of @xmath7 is found to be 0.1 m to @xmath163 km for @xmath9 gev , 0.2 m to @xmath164 km for @xmath10 gev , and 1 m to 1 km for @xmath165 gev . we also show in this figure the predicted curves of @xmath7 for the @xmath13 and @xmath18 decays for typical values of @xmath16 and @xmath19 , respectively . it is found that one can extend the reach for @xmath16 up to @xmath166 gev through the @xmath13 decay . in case of the @xmath18 decay , @xmath19 can be explored up to @xmath20 gev for relatively light @xmath3 . it is worth noting that our experiment is unique in that one can explore such a high value of @xmath19 in laboratories . in addition , our experiment can be performed under very high luminosity exceeding @xmath26 @xmath23s@xmath24 , in contrast to usual collider experiments . one can search for other modes of the @xmath3 decay by using the setup proposed in this paper . if the @xmath3 is sufficiently heavy , it can decay into @xmath167 or @xmath168 ( where @xmath169 is the higgs boson ) in the gravitino lsp scenario @xcite . in case the @xmath3 is higgsino - like , the @xmath168 decay can even be dominant . since the @xmath170 and @xmath169 bosons subsequently decay into @xmath171 or @xmath172 , the visible signature of these @xmath3 decays will be two hadron jets or two leptons without any signal in the anti - coincidence hodoscopes . with the help of track detectors at the end of the decay tunnel , the decay point can be exactly located , which makes the kinematical analysis of the decay and the mass determination much more streightforward than in case of the @xmath13 decay described in section  [ sec : mass ] . the @xmath3 can also decay into such modes as @xmath29 , @xmath30 and @xmath31 through weak violation of @xmath6-parity @xcite . furthermore , the decay of other longlived neutral particles , _ e.g. _  heavy neutrinos , can be detected with the same setup and method . our setup can also be used to search for slow decays of heavy longlived charged particles . although the existence of such particles would in principle be indicated in collider experiments by charged particle tracks with ionization larger than the minimum one , the signature of their decay will be missed if it occurs mostly outside the detector . on the other hand , with our setup , one can clearly detect the decay signal of such longlived particles as in case of the @xmath3 decay . the `` anti - coincidence '' hodoscopes can be used as the trigger counter . there are several candidates for longlived charged particles in susy models . for example , if the gravitino or axino is the lsp , a charged superparticle such as the slepton ( @xmath173 ) can be the nlsp , and may decay into @xmath174 with @xmath7 much longer than the detector size . the chargino ( @xmath175 ) can be another example of the longlived nlsp if the mass difference between the @xmath175 and the @xmath3 ( assumed to be the lsp ) is so small that it can decay only via @xmath176 @xcite . weak violation of @xmath6-parity would also allow the existence of longlived charged particles @xcite . in this case , the slepton can be the lsp , decaying slowly via , _ e.g. _ , @xmath177 . furthermore , heavy longlived charged particles could also exist in the susy breaking sector and messenger sectors of gmsb models @xcite . there are also many other speculations on heavy longlived charged particles [ 4649 ] . if the @xmath7 of heavy charged particles is extremely long , they will appear to be `` stable '' particles even in our experiment . one can search for such particles with our setup by precisely measuring their time - of - flight over 40 m distance between the `` anti - coincidence '' hodoscopes and the shower detector at the end of the tunnel . the @xmath178 distribution for heavy stable charged particles is expected to have a long tail following the peak at @xmath179 , in contrast to muons which make a sharp peak at @xmath180 . long flight path in our setup leads to excellent resolution of @xmath181 , which will provide a clear signal for the heavy stable charged particle . one could then determine its mass by measuring its momentum with magnetized iron and tracking chambers , which can be installed either in the active shield or at the very end of the shower detector . we have investigated the detection of a slow decay of the lightest neutralino ( or any other longlived particles ) at the cern lhc and at vlhc . after pointing out that such hadron colliders will become the `` neutralino factory '' producing @xmath0@xmath1 @xmath3s / yr if susy particles actually exist below @xmath2 tev , we have shown that a slow decay of @xmath3 can be detected in a dedicated experiment in which the collision products are dumped by a thick shield . the decay product of @xmath3 can then be detected by a detector located at the end of a long decay tunnel . the slow arrival time and the large off angle @xmath126 of the decay product will provide a clear signature of slowly decaying @xmath3 s . considering the @xmath3 decay into a photon and a light invisible particle such as the gravitino ( @xmath4 ) or axino ( @xmath5 ) , we find that one can explore the decay length ( @xmath7 ) of @xmath3 in a wide range , _ i.e. _ , 0.2 m to @xmath8 km for @xmath9 gev and 1 m to 2 km for @xmath10 gev for the case of the lhc . this corresponds to the range of the susy breaking scale @xmath11 to @xmath12 gev in case of the @xmath13 decay . at vlhc , one can extend the explorable range of @xmath14 up to @xmath15 gev , and that of @xmath16 up to @xmath17 gev . in case of the @xmath18 decay , one can explore the pq symmetry breaking scale @xmath19 up to @xmath20 gev . the mass of the decaying particle can be determined with an accuracy of @xmath151% using the correlation between the energy and the arrival time of the decay photon . with the setup we propose , one can also search for ( i )  other decay modes of @xmath3 such as @xmath6-parity violating one , ( ii )  the decay of any other longlived neutral or charged particles , and ( iii )  heavy stable charged particles . the experiment we proposed in this paper is a completely new type of collider experiment , which may turn out to be of crucial importance . the civil engineering of the intersection region at future hadron colliders has to be designed so that it can accommodate long decay tunnels for such experiments . all the calculations were performed on the rs/6000 workstations of the international center for elementary particle physics ( icepp ) , university of tokyo . k.m . acknowledges a fellowship from the japan society for the promotion of science . figure  [ fig : dete ] shows a schematical view of a realistic design for the shower detector which we have investigated . to separate electromagnetic showers initiated by photons from the background , we design the detector consisting of the preshower detector ( ps ) , two parts of the electromagnetic calorimeter ( em1 and em2 ) , three planes of plastic scintillators ( s1 , s2 and s3 ) , the lead absorber ( l1 ) , and the hadron calorimeter ( had ) . in addition , we can install the tracking chambers both in front of and behind the whole detector for the definite detection of high - energy muons ( and possibly heavy stable charged particles ) . the preshower detector ( ps ) comprises two planes of multiwire proportional chambers ( mwpcs ) with cathode pad readout , with 2@xmath182 and 1@xmath182 lead converter in front , respectively ( radiation length @xmath182 being 0.56 cm for lead ) . the scintillator s1 in front of ps can work as the anti - coincidence counter for charged particles . the scintillator s2 , located just behind ps , is used for triggering . the electromagnetic calorimeter is divided into two parts , each of which comprises modules with @xmath183 @xmath184 transverse dimensions . the first part ( em1 ) , which is located at 170 cm downstream of ps , consists of 5 layers of lead ( 1@xmath182 ) and scintillators ( 1 cm ) . the second part ( em2 ) , which is located at 220 cm downstream of em1 , consists of 20 layers of lead ( 1@xmath182 ) and scintillators ( 1 cm ) . total radiation lengths of em1 and em2 are 5.1@xmath182 and 20.4@xmath182 , respectively . the thick scintillator s3 , located between em1 and em2 , is used not only for triggering but also for the measurement of the arrival time . the hadron calorimeter ( had ) contains 15 layers of 5 cm thick iron and 2 cm thick scintillators . total thickness is @xmath185 nuclear interaction lengths . hadronic showers will deposit much of its energy in had . between em2 and had , the lead absorber l1 of 20@xmath182 in thickness is inserted to totally absorb electromagnetic showers . a coincidence of two planes of scintillators , _ i.e. _  s2 and s3 , constitutes the first trigger . we also require the signals from em1 and em2 to exceed a threshold , which leads to the rejection of ( i )  muons going through the detector as minimum ionizing particles , and ( ii )  hadronic showers initiated by high - energy neutrinos in had .    for this detector configuration , we have performed monte carlo simulations using geant 3.21 @xcite . a typical event for 100 gev photon incident on the shower detector is shown in fig . [ fig : event ] . we can see that the electromagnetic shower starts to evolve in ps , reaches its maximum after passing em1 , and is mostly absorbed in em2 . figure  [ fig : pid ] shows the distributions of energy deposited in active layers of ( a )  s2 , ( b )  em1 , ( c )  em2 , and ( d )  had , by 100 gev photons and charged pions which are incident at @xmath186 on the shower detector . it can be seen that electromagnetic showers ( initiated by photons ) can clearly be separated from hadronic showers ( initiated by pions ) using the deposit energy of each component . the energy of incident photons can be determined from the sum of deposit energy in active layers of em1 and em2 , denoted as @xmath187 , whose distributions are shown in fig . [ fig : eneres](a ) for photons incident at @xmath186 with energy @xmath188 , 50 , 100 and 200 gev . the inefficiency concerning the scintillation light collection is not included . figure  [ fig : eneres](b ) shows the relation between @xmath189 and @xmath187 for @xmath186 and @xmath190 incidence . it can be seen that good linearity is realized for @xmath188200 gev . the resultant energy resolution of the shower detector as a function of incident photon energy is shown in fig . [ fig : eneres](c ) . the fit result for @xmath186 data is @xmath191 for @xmath188200 gev .    the shower direction is obtained from the reconstructed position of the shower in ps and that in em2 . the position of the shower in ps can be determined from the pad signal of mwpcs , whose spatial resolution is assumed to be 5 mm . the shower center in em2 can be estimated from the observed division of energy within a local cluster of modules . we find that good spatial resolution ( @xmath192 cm ) in comparison with the size of the module ( @xmath183 @xmath184 ) can be obtained owing to the large gap between em1 and em2 , which makes the shower spread widely before entering em2 . the resultant angular resolution averaged over various incident positions is shown in fig . [ fig : angres ] . it is found to be @xmath193 for photons with @xmath194200 gev . the angular resolution could be improved if tracking chambers are used as active layers of em1 and em2 instead of scintillators . although a large number of particles will be produced at the lhc , most of them ( hadrons , @xmath195 and @xmath116 ) will be dumped in our setup by the iron shield with thickness of @xmath196 nuclear interaction lengths . however , high - energy neutrinos and muons can go through the shield and might interact with the material of the detector . the main source of high - energy neutrinos and muons is expected to be `` prompt '' , _ i.e. _ , come from semileptonic decays of bottom and charm hadrons @xcite , while the contribution from the decay of @xmath197 and @xmath198 mesons is negligible at least in our setup . in order to estimate the rates of these prompt neutrinos and muons , we have performed monte carlo simulations using isajet 7.13 @xcite for @xmath41 collisions at @xmath21 tev , by taking the total cross section of the bottom plus charm production to be 2 mb . total @xmath199 events are generated , and the neutrinos and muons which point to the detector covering a polar angle of @xmath200 and an elevation angle of @xmath71 are recorded . we consider four cases , _ i.e. _ , @xmath201 , @xmath202 , @xmath203 and @xmath190 . the energy spectra of the prompt neutrinos are shown in fig . [ fig : nu ] . the spectra have a long high - energy tail when @xmath204 is small . the neutrino could mimic the @xmath27 or @xmath28 signal if it interacts in the preshower detector and deposits enough energy ( see appendix  [ sec : dete ] for the detailed design for the shower detector ) . as a simple estimate of such background , we calculate the number of neutrinos which have energy @xmath205 gev and interact with @xmath206 g/@xmath184 lead . the interaction cross section is taken to be @xmath207 @xmath184/nucleon . the estimated numbers are @xmath208 , @xmath209 , @xmath210 and @xmath211 per 100 fb@xmath24 for @xmath201 , @xmath202 , @xmath203 and @xmath190 , respectively . thus the background induced by the prompt neutrinos is negligibly small . figure  [ fig : mu ] shows the energy spectra of the prompt muons . only the muons with @xmath212 gev can go through the shield because of the ionization energy loss . the resultant rates of muons entering the tunnel are then estimated to be @xmath185 khz , @xmath213 hz , @xmath214 hz and @xmath215 hz for @xmath201 , @xmath202 , @xmath203 and @xmath190 , respectively , with luminosity of @xmath216 @xmath23s@xmath24 . the single rate of the prompt muons will thus be comfortably small if we take @xmath217 . high - energy muons can deposit a significant portion of their energy by bremsstrahlung or direct @xmath218 pair production , both of which could lead to the electromagnetic shower . when combined with inefficiencies in the anti - coincidence counters , these muons might in principle mimic the @xmath27 or @xmath28 signal . folding the simulated spectra by the showering probability @xcite of muons , we estimate the numbers of muon - induced high - energy ( @xmath219 gev ) showers starting to evolve in the preshower detector to be @xmath220 , @xmath221 , @xmath222 and @xmath223 per 100 fb@xmath24 for @xmath201 , @xmath202 , @xmath203 and @xmath190 , respectively . assuming a veto inefficiency of @xmath224 by the staggered layers of anti - coincidence scintillators , the muon - induced background is expected to be negligibly small for @xmath217 .    even if the rate of such muon - induced background turns out to be non - negligible , off - line analysis will eliminate such background based on the information on the arrival time as well as on the off angle @xmath126 . 99 for a review , see , _ e.g. _ , j.f . gunion , report no .  hep - ph/9704349 ( unpublished ) . h.  baer , c - h . chen , f.  paige and x.  tata , phys . d * 52 * , 2746 ( 1995 ) ; 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prospects are examined for the detection of a slow decay of the lightest neutralino ( or any other longlived particles ) at the cern lhc and at very large hadron collider ( vlhc ) . 
 we first point out that such hadron colliders will become the `` neutralino factory '' producing @xmath0@xmath1 neutralinos / yr , if gluinos and/or squarks actually exist below @xmath2 tev . 
 the lightest neutralino ( @xmath3 ) , usually assumed to be stable , will be unstable if lighter superparticles such as the gravitino ( @xmath4 ) or axino ( @xmath5 ) exist , or @xmath6-parity is not conserved . 
 the decay signal would , however , be missed in usual collider experiments , particularly when the decay mostly occurs outside the detector . in order to search for such a slow decay of @xmath3 , 
 we propose a dedicated experiment where the collision products are dumped by a thick shield , which is followed by a long decay tunnel . 
 the decay product of @xmath3 can be detected by a detector located at the end of the tunnel . 
 the slow arrival time and the large off angle ( to the direction of the interaction point ) of the decay product will provide a clear signature of slowly decaying @xmath3 s . 
 one can explore the decay length ( @xmath7 ) in a wide range , _ 
 i.e. _ , 0.2 m to @xmath8 km for @xmath9 gev and 1 m to 2 km for @xmath10 gev at the lhc . 
 this corresponds to the range of the susy breaking scale @xmath11 to @xmath12 gev in case of the @xmath13 decay predicted in gauge - mediated susy breaking models . at vlhc 
 , one can extend the explorable range of @xmath14 up to @xmath15 gev , and that of @xmath16 up to @xmath17 gev . in case of the @xmath18 decay 
 , the peccei - quinn symmetry breaking scale @xmath19 can be explored up to @xmath20 gev . 
 the mass of the decaying particle can be determined by using the correlation between the energy and the arrival time of the decay product . with the setup we propose 
 , one can also search for ( i )  other decay modes of @xmath3 such as @xmath6-parity violating one , ( ii )  slow decays of any other longlived neutral or charged particles , and ( iii )  heavy stable charged particles .    ` 
 ut - icepp 97 - 02 + hep - ph/9706382 + ` june 1997     * hadron colliders as the `` neutralino factory '' : + search for a slow decay of the lightest neutralino at the cern lhc *     k.  maki and s.  orito     _ department of physics , school of science , university of tokyo , tokyo 113 , japan _    5.9 mm