You are an expert at summarizing long articles. Proceed to summarize the following text: 
minimal supersymmetric standard model ( mssm ) is one of the most promising candidates of the physics beyond the standard model ( sm ) that may solve the hierarchy problem in the higgs sector  @xcite . the model predicts a set of superpartners ( sparticles ) whose charges are exactly the same to that of the sm partners but the spins are different by one half . these sparticles will be directly searched at the large hadron collider ( lhc ) at cern , which is a @xmath3 collider with 14  tev center of mass energy . the lhc is scheduled to start in 2007 . one of the interesting features of the mssm model is the conserved r parity , and all sparticles are assigned to have odd r parity . because of the conservation law , the lightest supersymmetric particle ( lsp ) is stable , and is assumed as a good candidate for the dark matter . at collider experiments , sparticles are produced in pairs , and a sparticle decay should produce at least one lsp . susy events at collider experiments therefore have a distinctive missing transverse momentum . if supersymmetry ( susy ) is an exact symmetry , a particle and its superpartner have a same mass . therefore susy must be broken spontaneously . the susy is considered to be broken in `` hidden sector '' , and the susy breaking will be mediated to our sector by mediation fields . the mechanism is already under severe constraints . for example , the mass of the sfermions with same charge must be universal so that they do not cause dangerous fcnc , or sfermion masses must be so heavy that correction from the susy sector is suppressed . this suggests that yet unknown symmetry / dynamics exists in the sector . the origin of the supersymmetry breaking and mediation mechanism may be understood indirectly by measuring masses of the susy particles . therefore both the discovery and mass determination of the susy particle have been studied intensively in recent years  @xcite . if susy is broken at some high energy scale and the boundary conditions are universal at the scale , strongly interacting ( si ) susy particles are heavier than electroweakly interacting ( ewi ) susy particles . for example , gaugino masses follow the relation @xmath4 in the minimal supergravity model , therefore the gluino is six times heavier than the bino - like particles . at the lhc , si susy particles will be copiously produced in @xmath3 collisions , and subsequently decay into lighter ewi susy particles . the gluino and squark decays are associated with jets with high transverse momentum ( @xmath5 ) . the transverse momentum is the order of the gluino and squark masses . moreover , because the lsp is significantly lighter than the gluino , the lsp from the gluino decay also has a high @xmath5 . they would give a large missing transverse momentum to the susy events . in addition , decays of the ewi sparticles may produce high @xmath5 leptons . events from the standard model ( sm ) processes do not have such high @xmath5 particles . motivated by these observations , following cuts are often applied to reduce the sm background events to the susy signal events  @xcite ;    * an event is required to have at least one jet with @xmath6  gev and three jets with @xmath7  gev within @xmath8 , * the effective mass of the event must satisfy @xmath9  gev , where the effective mass is defined using the transverse missing energy ( @xmath2 ) and the transverse momentum of four leading jets as : @xmath10 if the event has hard isolated leptons , the effective mass may be defined as follows : @xmath11 where sum of the lepton @xmath5 can be taken over the leptons with @xmath12  gev and @xmath13  gev . * the missing transverse energy must satisfy the relation : @xmath14 * the transverse sphericity @xmath15 must be greater than 0.2 , where @xmath15 is defined as @xmath16 , with @xmath17 and @xmath18 being the eigenvalues of the @xmath19 sphericity tensor @xmath20 formed by summing over the transverse momentum of all calorimeter cells .    to reduce the background further , hard , isolated lepton(s ) may be required . these cuts are good enough to reduce the sm backgrounds from @xmath21+@xmath22-jets and @xmath23+@xmath22-jets productions down to a manageable level , although the production cross section of the sm processes may be @xmath24 higher than signal cross sections . while the susy production section reduces very quickly as sparticle masses increase beyond 1  tev , but the signature peaks at higher @xmath1 where backgrounds can be ignored . previous studies show that the squark and gluino with mass around 2.5  tev can be found at the lhc in the minimal super gravity model ( msugra ) .    in msugra , the sm background after the cuts can be neglected safely . then , the distribution of accepted events are also useful to determine the mass scale of susy particles . for example , the peak of the @xmath1 distribution is sensitive to the squark and gluino masses . for the events with same flavor opposite sign dileptons , the invariant mass distributions , @xmath25 , @xmath26 , and @xmath27 , are useful to reconstruct the susy particle masses @xmath28 , @xmath29 , @xmath30 and @xmath31 . recently it is pointed out that a string inspired model based on the flux compactification ( kklt models )  @xcite predicts a mass relation different from that of the msugra  @xcite . this is called mixed modulus anomaly mediation ( mmam ) model . this model has a volume modulas @xmath32 and a compensator field of minimum supergravity model @xmath33 as a messenger of the susy breaking . the susy mass spectrum depends on the ratio of the two susy breaking parameters @xmath34 and @xmath35 . the unification scale of the sparticle masses depends on the ratio . it is interesting that the unification scale of the soft susy parameters can be much lower than the gut scale in this model . they may unify even at the weak scale for a special choice of the model parameters . when sparticle masses are degenerated at the weak scale , we expect a reduced probability to have high @xmath5 jets , and smaller @xmath1 and @xmath2 for given squark and gluino masses . this means that the standard susy cuts reduce the signal events as well , and susy discovery is more affected by the sm background . quantitative understanding of the sm background may be required in this case . existing background estimates have large theoretical uncertainty coming from the scale of the strong coupling . recently , several groups has emphasized importance to include the matrix element correction  @xcite in the previous parton shower estimate of the background , which significantly change the background distribution in the signal region . when overlap between the signal and background distribution is large , as it is expected in the degenerated susy spectrum , the uncertainty of the background must be taken seriously , and we also need to reconsider the cuts to reduce the background . the purpose of this paper is to illustrate the phenomenology of the degenerated supersymmetry . we take the mmam model as an example . by changing the ratio @xmath36 , the mass spectrum changes smoothly from msugra - like one to anomaly - mediation - like one . in between , there are regions of parameters where squark , slepton , and gaugino masses are significantly degenerated compared with those expected in msugra . the model therefore provides one dimensional parametrization from the `` transverse signature '' to its non - transverse limit . the investigation of our analysis may easily be extended to other susy / non - susy scenarios with @xmath2 signature , such as the universal extra dimension model or little higgs model with @xmath32 parity . this paper is organized as follows . in section 2 we describe the mmam model and its mass spectrum with an emphasis on the region of parameter space where sparticle masses are degenerated . in section 3 , we describe our monte carlo simulations . in section 4 , we study how susy event distribution depends on sparticle mass degeneracy and compare it with the background . we find that the signal @xmath1 distribution is quite similar to that of the background if @xmath37 . however we find a certain relation among @xmath2 and @xmath1 that is universal for the model with heavy colored particle that decays into the stable neutral particle lhc will miss the susy signature if @xmath38 . section 5 is devoted to discussions and conclusions . in this section , we briefly describe the mmam model following the notation in @xcite . in this model , all shape modulus and dilaton will be fixed by non - zero flux on a cy manifold in the type iib string theory . the low energy @xmath39 lagrangian of this model is given by unfixed volume modulus @xmath32 , compensator field @xmath33 , and gauge and matter fields @xmath40 and @xmath41 as @xmath42 . \end{aligned}\ ] ]    here @xmath43 , @xmath44 is the 4d metric in the super conformal frame . @xmath45 and @xmath46 are the volume modulas and the chiral compensator superfield of @xmath47 sugra , respectively . @xmath48 is the superpotential for @xmath32 and matter . @xmath32 dependent function @xmath49 and @xmath50 may be expressed as @xmath51 where @xmath52 is the modular weights and @xmath53 for matter fields located on d7 ( d3 ) branes , and @xmath54 for matter living at brane intersections  @xcite .    in kklt model , @xmath55 , where the last term of @xmath56 expresses the non - perturbative effect such as the gaugino condensation in d7 brane , which fix the volume modulus , @xmath57 is the contribution of the flux . in addition to the @xmath39 supersymmetric action , there are contributions from anti - d3 branes which break supersymmetry and uplift the potential from ads vacuum to ( nearly minkowski ) de sitter vacuum . the term is expressed by a spurion operator depending on @xmath32 and @xmath33 , and minimum of the potential will be obtained by solving the effective @xmath39 action and the lifting potential . the resulting theory is parametrized by @xmath58 and @xmath59 . the susy breaking terms are obtained by expanding the action by @xmath34 and @xmath35 . here we define the soft terms as @xmath60 where @xmath61 is a canonically normalized yukawa coupling @xmath62 they are explicitly written as functions of @xmath63 and @xmath64 as follows ; @xmath65 where @xmath66 parameter is such that the off - diagonal element of @xmath67 mass matrix is @xmath68 . ] and @xmath69 with @xmath70 , namely for matter in the fundamental representation @xmath71 , @xmath72 , @xmath73 . we only include the effect of the top yukawa coupling @xmath74 , therefore @xmath75 , @xmath76 , @xmath77 and @xmath78 otherwise . the scale dependence of @xmath79 is expressed as @xmath80 where @xmath81 and @xmath82 here , @xmath83 , @xmath84 , @xmath85 , @xmath86 , and @xmath87 , @xmath88 , @xmath89 , @xmath90 .    finally , @xmath91      in eq . ( [ eq : soft ] ) , the highest term in @xmath92 is the contribution of modulas @xmath32 , while the terms independent from @xmath92 is that of pure anomaly mediation . in @xcite , it is pointed out that the mass spectrum in the mmam model shows a special feature if @xmath93 , where @xmath94 this can be seen by investigating the low energy mass parameters as functions of @xmath95 . for example , gaugino masses at the scale @xmath96 may be expressed as @xmath97\ ] ] in one loop level . when @xmath98 , the @xmath99 term in the equation becomes 0 at @xmath100 . namely , if @xmath101 does not depend on the gauge group , the gaugino masses unify at the weak scale , rather than at the gut scale . the mass spectrum in the matter sector depends on @xmath52 . if yukawa couplings @xmath61 are non - vanishing only for the combination @xmath102 satisfying @xmath103 , or if the effect of the yukawa couplings in the rge can be ignored , the scalar masses and trilinear couplings also unify at the same scale of the gaugino mass unification . this relation is satisfied for the choice @xmath104 and @xmath105 and we call this choice of the boundary condition as model a. even if this condition is not satisfied , squark and slepton masses tend to be close with each other at @xmath106 when gaugino masses unify at low energy scale , because the gaugino loop corrections to the sfermion masses are roughly equal .    in table [ table : alphar ] , we show the relation between @xmath107 and @xmath95 for a fixed gluino mass at the gut scale of 450  gev . this corresponds to @xmath108  tev . we can see that the unification of gaugino or squark and slepton masses occurs at @xmath109 . @xmath107 @xmath110 & 0.45 & 0.1 0.30 & 0.50 & 10 0.61 & 0.56 & 20 0.92 & 0.63 & 30 1.25 & 0.73 & 40 1.58 & 0.86 & 50 1.92 & 1.06 & 60    for the following discussion , we calculate the low energy mass spectrum using isajet  @xcite version 7.72 which solves the boundary condition given in section 2.1 . the sparticle mass spectrum for the model a is listed in table [ table : massa ] . as @xmath95 increases , gaugino masses , and slepton and squark masses get closer , and the model shows the mass pattern different from that of msugra . the numerical values roughly agree with those in @xcite . @xmath111 & @xmath96 & @xmath112 & @xmath113 & @xmath114 & @xmath115&@xmath95 0.1 & 1055 & 184 & 350 & 700 & 957 & 435 & 354 & 450 & @xmath110 30&1045 & 436 & 536 & 607 & 913 & 531 & 476 & 631 & 0.92 40&1038 & 573 & 653 & 545 & 879 & 578 & 541 & 729 & 1.24 45&1034 & 657 & 717 & 499 & 852 & 604 & 576 & 790 & 1.41 55&1020 & 882 & 892 & 339 & 765 & 671 & 675 & 951 & 1.74    as can be seen in table [ table : massa ] , the higgsino mass parameter @xmath96 decreases as @xmath95 increases . the @xmath96 is determined by solving the minimization condition of one loop higgs effective potential . in minimal supergravity model ( @xmath116 limit ) , the higgs soft mass square at weak scale is driven to large negative value by stop / top loop , while the correction from gaugino loops is small because @xmath117 . the @xmath96 parameter is chosen to compensate the negative value to get correct gauge symmetry breaking , therefore @xmath96 can be as large as the stop mass in the minimal supergravity model . when @xmath95 is large , @xmath118 at the gut scale . the higgs soft mass parameters get large positive contribution from the gaugino masses . top / stop loop effect is largely compensated by the gaugino corrections at the weak scale . as a result , @xmath119 for @xmath120 , and @xmath121 for larger value of @xmath107 . although @xmath122 and @xmath111 get closer to @xmath123 for @xmath124 , the mass splitting among susy particles increases again . we have seen in the model a that decrease of the @xmath96 parameter limits the mass degeneracy . in our study , we are interested in the model point where the mass splitting among the susy particles are the smallest . the @xmath96 parameter would be largest when the gut scale value of the higgs soft susy breaking mass is the smallest . on the other hand , sfermion masses at gut scale must be large to avoid the @xmath125 or @xmath126 lsp . we therefore also consider the model b , where @xmath127 and @xmath128 as another example of the mmam model . the mass spectrums of the models a and b for @xmath129  gev and @xmath130 are compared in table [ table : massab ] . the mass difference between squark ( gluino ) and lsp hits minimum when @xmath119 at @xmath131 . @xmath132 for the model a and 55 for the model b , where @xmath133 and @xmath134 , respectively . as expected , the model set b has more degenerated mass spectrum at @xmath135 , because the @xmath96 parameter is larger for the same gaugino masses . @xmath136 & @xmath137 & @xmath136 & @xmath138 0 & 995 ( 1055 ) 182 & 961 & 1041 ( 1061 ) 189 & 1007 10 & 986 ( 1053 ) 246 & 924 & 1043 ( 1061 ) 248 & 98420 & 973 ( 1049 ) 326 & 793 & 1044 ( 1060 ) 330&94030 & 951 ( 1045 ) 426 & 726 & 1045 ( 1060 ) 434 & 865 40 & 916 ( 1038 ) 507 & 635 & 1044 ( 1059 ) 569 & 733 50 & 854 ( 1027 ) 426 & 641 & 1038 ( 1057 ) 713 & 548 55 & 803 ( 1021 ) 335 & 663 & 1033 ( 1056 ) 721 & 529 60 & no ewsb & & 1023 ( 1055 ) 700 & 543    in the following sections , we discuss the discovery potential in the mass degenerated susy models . phenomenologically important parameter for the hadron collider is the typical mass scale of the event . this can be expressed by the energy of the jet from @xmath139 decay in the @xmath140 rest frame , which is expressed as @xmath141 because sparticles are pair produced , @xmath138 is the typical order of the effective transverse mass @xmath1 of the susy production process . we list the value of @xmath138 for the model points in table  [ table : massab ] . @xmath142 can be reduced by a factor of @xmath143 to @xmath144 for these models . in the following sections , we find that discovery of susy particles will be non - trivial in this region . it is worth noting that gaugino and higgsino are highly mixed when @xmath145 is minimum . in this case , relatively large nucleon - lsp scattering cross section and smaller dark matter density are expected , possibly consistent with cosmological constraints . another phenomenologically important aspect in terms of collider physics is the branching ratios of the gluino and squark into leptons . the leptons would be produced from the neutralino or chargino decays arising from the squark decays . for the model a , the decay @xmath146 @xmath147 channels are open unless @xmath148 . the chargino and neutralino may decay into ( s)leptons . especially , if the decay channel @xmath149 is open , the large branching ratio into the golden mode @xmath150 is expected . for example , @xmath151 80% and @xmath15214% for the model a , @xmath153  gev , @xmath130 , and @xmath154 . for the model a , @xmath155 if @xmath156 , namely , the decay channel is open especially in the degenerated region . for the model b , the squark and slepton masses are so heavy that the decay into slepton is always closed . here we describe our event simulation method used in the next section . as explained earlier , susy mass spectrum is calculated by isajet  @xcite which is interfaced to the herwig  @xcite event generator using isawig  @xcite . herwig generates hard processes , takes care of initial and final state radiations , and fragments partons into hadrons .    to estimate event distributions to be measured at lhc detectors , we smear particle energies , identify isolated leptons , and reconstruct jets . we independently developed a fast detector simulation program , which takes the following steps ;    1 . * finding isolated leptons : * if a lepton ( @xmath157 or @xmath96 ) with @xmath158  gev and @xmath159 is found in an event record , we take a cone with a size @xmath160 around the lepton . if the sum of @xmath161 of the particles in the cone ( except the lepton at the center of the cone ) is less than 10  gev , we regard it as an isolated lepton candidate . after the jet reconstruction described below , isolated lepton candidates with @xmath162 are accepted as isolated leptons . * reconstruction of jets*. we adopt a simple jet finding algorithm pycell , a subroutine in the pythia package , with minor modification on its treatment of leptons and energy smearing . namely , 1 . we remove isolated lepton candidates for the jet reconstruction . particle energies are measured by the electromagnetic and hadronic calorimeters . we assume that the number of calorimeter cells in @xmath163 direction is 50 within @xmath164 and 50 in @xmath165 direction , respectively . transverse energy deposit @xmath161 in a cell is summed for electrons , photons , and hadrons as @xmath166 which correspond to the hits in the electromagnetic and hadronic calorimeter cells , respectively . transverse energy deposit in each cell is smeared by gaussian energy resolutions @xmath167 } $ ] and @xmath168}$ ] . after the energy smearing , we regard sum of the smeared @xmath169 and @xmath170 as the measured energy deposit in the cell . we take the highest energy cell as the initiator and sum the energy deposits in the cell within @xmath171 . we accept the cluster as a jet if @xmath172   gev . we repeat this procedure after removing the cells which have been already used for the jet reconstruction . the reconstruction process ( 1 and 2 ) is similar to the fast simulation codes used by the atlas and cms groups . note that we do not smear energy of isolated leptons and assume they are identified correctly , because the energy resolution and particle identification are excellent for leptons in both of the lhc detectors . we smear photon and non - isolated electrons energies with better resolution than that for hadrons , however we do not assume fine grained electromagnetic calorimeter in our simulation for simplicity .    our simulation does not take care of other detector effects , such as misidentification of leptons and hadrons , non - uniformity of detector responses ( cracks ) , non - gaussian smearing in the energy measurements . the simulation , however , reproduces the signal distributions of past simulation studies reasonably well . to check the validity of our independently developed simulation program , we compare published distributions of susy signals using the atlfast simulator  @xcite with our simulation results . figure  [ fig : msps1a ] show distributions of the same flavor and opposite sign dilepton invariant mass ( @xmath25 ) and the jet - lepton - antilepton invariant mass ( @xmath173 ) at sps1a  @xcite , where @xmath174 is one of the two highest @xmath5 jets with @xmath175 . the distributions are important to reconstruct the cascade decay @xmath176 . contribution of background events with accidental two leptons can be subtracted using the distributions of @xmath177 events . the plots are produced by applying the same cuts as used in @xcite ;    * @xmath178  gev . * at least 4 jets with @xmath179  gev , @xmath180  gev , and @xmath181  gev . * two and only two leptons with @xmath182  gev and @xmath183  gev . * @xmath184 * @xmath185 . we calculate the sphericity and @xmath2 , based on the smeared energy deposits to the cells in @xmath186 in addition to the momentums of isolated lepton candidates . we find that accepted number of events is consistent with the previous simulation studies . in figure [ fig : msps1a ] we show the @xmath25 and @xmath27 distribution for @xmath187 susy events ( corresponding to @xmath188 1.8  fb@xmath189 ) . the edge and the end point appear at correct positions . the @xmath25 distribution has a sharper edge compared with that in @xcite , because we do not smear lepton energies in our simulation . we find that 445 events remain after the cuts and the background subtraction . in the report @xcite roughly @xmath190 events remain after the cuts for @xmath191 100  fb@xmath189 . the acceptances of the two simulations therefore agree within 1@xmath192 . ( left ) and @xmath27(right ) distribution at the point sps1a by our fast simulation program . we produce @xmath187 susy events for the plot , corresponding to @xmath193 fb@xmath189 . after the cuts and background subtractions , 445 dilepton events remain . , title="fig:",width=226 ]   ( left ) and @xmath27(right ) distribution at the point sps1a by our fast simulation program . we produce @xmath187 susy events for the plot , corresponding to @xmath193 fb@xmath189 . after the cuts and background subtractions , 445 dilepton events remain . , title="fig:",width=226 ] in this sub - section , we study the @xmath1 distributions at the susy model points with degenerated mass spectrum . we first show the @xmath5 distribution of the first jet in the left panel of figure [ fig : ptmeffb ] . here we take the model b , @xmath153  gev , @xmath130 and vary degeneracy by changing @xmath107 from 0 to 55 . as @xmath107 increases , sparticle mass difference gets smaller , resulting in softer @xmath5 distribution . the peak positions are positively correlated with @xmath145 which ranges from @xmath194  gev to @xmath195  gev when we change @xmath107 from @xmath196 to @xmath197 . from the figure , we can read that the acceptance of susy events depends on @xmath107 . for example , events with @xmath198  gev is only 16% for the point with @xmath116 but it is 35% for the point with @xmath199 . this means that about one third of the events are rejected by the requirement on the @xmath5 of the first jet in the previous section for the latter point . distributions of the highest @xmath5 jet for model b , @xmath153  gev and @xmath130 . 50000 events are generated for each points(@xmath200 from right to the left ) . right ) @xmath1 distributions for @xmath201 for model b with @xmath153  gev @xmath202 ( solid histograms from right to left ) and @xmath203  gev @xmath204(dashed histograms from right to left ) respectively . , title="fig:",width=226 ]   distributions of the highest @xmath5 jet for model b , @xmath153  gev and @xmath130 . 50000 events are generated for each points(@xmath200 from right to the left ) . right ) @xmath1 distributions for @xmath201 for model b with @xmath153  gev @xmath202 ( solid histograms from right to left ) and @xmath203  gev @xmath204(dashed histograms from right to left ) respectively . , title="fig:",width=226 ]    the @xmath1 distribution shows a similar behavior . in figure [ fig : ptmeffb ] ( right ) , we show the @xmath1 distributions for the model b , with @xmath153  gev ( solid histograms ) and @xmath203  gev ( dashed histograms ) , respectively . we apply the cut ( a ) and also require one hard isolated lepton with @xmath12  gev and @xmath205 .    here we compare the distributions with @xmath206 ( msugra like ) and @xmath207 to @xmath197 ( degenerated ) . it should be noted that , while the mass spectrums are considerably different , the power low of the distributions beyond their peaks are roughly the same . these high @xmath5 events are originated from the collisions with its center of mass energy @xmath208 much higher than the squark and gluino masses . therefore the power low of the distributions only depends on the dominant luminosity function . the peak position of the @xmath1 distribution has a direct correlation with the produced sparticle mass . in @xcite it is found that the correlation between the susy mass scale defined as @xmath209 where @xmath210 is the lsp mass and @xmath211 . the peak position of @xmath1 is linear for msugra and gauge mediation model . we also find that the linear relation holds for the signal distribution . we do not provide the fit results here , because the existence of the standard model background is very important for this model , as will be discussed in the following subsections . signals . ] we now turn into the relation between @xmath2 and @xmath1 for degenerated points . in figure [ fig : etmissmeffb ] we show the distribution for the model b with @xmath212  gev , @xmath130 and @xmath213 , respectively . the @xmath214- and @xmath74- axes are @xmath1 and @xmath2 , respectively , in figure  [ fig : etmissmeffb ] . we see that the @xmath2 takes a significant part of @xmath1 for degenerated points @xmath215 , and @xmath216 if @xmath1 is higher , while , for @xmath206 the @xmath2 for a fixed @xmath1 is broader in the plot . t     +    this distribution can be understood as follows . suppose we have events with two uncorrelated jets with energy @xmath217 . the dominant part of the cross section is squark / gluino pair production near the threshold for our case , so if they decay directly into two jets and two lsps , the event kinematics are indeed of this type up to the boost to the beam direction . we now calculate missing energy @xmath218 and effective energy @xmath219 of the events . the momentum of the two jets and the missing momentum can be expressed as follows , @xmath220 where we take the direction of the @xmath221 momentum as @xmath222-axis and events are in @xmath214-@xmath222 plane . then the missing energy @xmath218 and effective mass @xmath219 are defined as @xmath223 where @xmath219 ranges from @xmath138 to @xmath224 . the relation between @xmath2 and @xmath1 is somewhat similar to that of @xmath218 and @xmath219 as can be seen in figure  [ fig : etmissmeffb ] . for each plot @xmath2 tends to be small when @xmath225 , where @xmath226  tev for @xmath213 , respectively . it increases linearly as a function of @xmath1 up to @xmath227 , and the number of events reduces quickly beyond @xmath228 . the relation indeed should be true when two particle are pair produced and each of them decays into a visible particle and an invisible particle at hadron collider . on the other hand , for the dominant background coming from @xmath23 + @xmath22-jets or @xmath21 + @xmath22-jets , the @xmath229 should be smaller than those of the signal . this is because the sm events have many other jet activities which are not associated with the missing momentum productions . the background comes from highly boosted events , where @xmath2 is typically a fraction of the missing energy originated from high energy @xmath230 , @xmath231 , and @xmath232 . the canonical cut to reduce the sm background is @xmath233 . if the background distribution in @xmath1 and @xmath2 plane is significantly different from the signal distribution , one can improve the s / n by applying an improved cut in the plane rather than the simple cuts @xmath9 gev and @xmath234 described in section 1 . because there are no background distribution study on the relation between @xmath1 and @xmath2 , we do not attempt to improve the cuts in following sections and use the cut given in section 1 . we now show the signal @xmath1 distributions for the degenerated model . we start our discussion from the @xmath235 distributions of the susy events without high @xmath5 leptons . this channel has been studied in @xcite with an emphasis on the model - independent reconstruction of the susy scale , as discussed in the previous subsection . distributions for non - lepton sample . the thick solid histogram is the background estimated in @xcite . solid and dashed histograms are signal distributions for @xmath153  gev @xmath206 ( msugra ) , and @xmath154 ( degenerate ) in the left panel , and for @xmath203  gev @xmath236 ( msugra ) and @xmath237 ( degenerate ) in the right panel , respectively . all plots are normalized for @xmath238 fb@xmath189 . , title="fig:",width=226 ]   distributions for non - lepton sample . the thick solid histogram is the background estimated in @xcite . solid and dashed histograms are signal distributions for @xmath153  gev @xmath206 ( msugra ) , and @xmath154 ( degenerate ) in the left panel , and for @xmath203  gev @xmath236 ( msugra ) and @xmath237 ( degenerate ) in the right panel , respectively . all plots are normalized for @xmath238 fb@xmath189 . , title="fig:",width=226 ]    in figure [ fig : meffa ] , the signal distributions for the model a , with @xmath153  gev and 650  gev are plotted for @xmath239 and @xmath240 . the signal distributions ( solid and dashed histograms ) are parallel to the background distribution ( bars in the plots ) beyond the peak of @xmath1 distribution . the difference appears only in the overall normalizations . as already discussed , this is because the signal distribution is determined mainly by the luminosity function , once @xmath241 . the background shown in the plots has a large uncertainty . the estimation has been made by the lowest order monte carlo generator isajet . the distribution is subjet to the scale uncertainty which is typically @xmath242(30% ) . we also require at least 4 high @xmath5 jets , while the number of final state parton involved in the tree level diagram is much less than 4 . the number of additional jets is estimated by parton shower ( ps ) approximation . the ps approximation is good to estimate distributions of jets collinear to the leading jets . recently , several groups have emphasized the importance of the matrix element ( me ) correction to the sm background processes . the matrix elements of the diagram involving @xmath243 + @xmath22-partons are calculated by the generator devoted for the process with multi jets  @xcite . experimental groups are also working to take into account the corrections , for example , in the atlas group  @xcite , the backgrounds from @xmath244+@xmath22-jets are calculated up to @xmath245 respectively using alpgen  @xcite . after the inclusion of the me corrections , the sm background is increased by a factor of 2@xmath2464 for @xmath247  tev . even in the highest bin in the plot , the expected background is above 1 . this is caused by the increased high @xmath5 jets in the sm events . the improved background estimation is still preliminary and in the level of the lowest order , and subject of coupling scale uncertainty . we find that the signal rate is the same order of the background rate for the degenerated parameters . if the uncertainty of the overall normalization of the background is 100% , no bound would be obtained from no - lepton channel by looking into @xmath235 distribution only . however , as we noted previously , the structure of the signal distribution may be visible over the background distribution in the @xmath235 and @xmath2 plane . the significant fraction of susy production gives rise to events with isolated leptons ( @xmath248  gev and @xmath13 ) . we show the signal distribution for the model a in figure  [ fig : meffla ] . here , we do not show the background distributions , because they are not given in previous literatures . in @xcite , the distribution of the sm background is given , which is roughly 1/20 of the background of the zero lepton channel with a similar shape . distributions of one lepton events . the solid and dashed histograms correspond to model a , @xmath239 ( msugra - like ) and @xmath240 ( degenerated mass spectrum ) respectively . @xmath249 , 750 , 850  gev from left to right . all plots are normalized for @xmath250fb@xmath189 . , title="fig:",width=170 ]   distributions of one lepton events . the solid and dashed histograms correspond to model a , @xmath239 ( msugra - like ) and @xmath240 ( degenerated mass spectrum ) respectively . @xmath249 , 750 , 850  gev from left to right . all plots are normalized for @xmath250fb@xmath189 . , title="fig:",width=170 ]   distributions of one lepton events . the solid and dashed histograms correspond to model a , @xmath239 ( msugra - like ) and @xmath240 ( degenerated mass spectrum ) respectively . @xmath249 , 750 , 850  gev from left to right . all plots are normalized for @xmath250fb@xmath189 . , title="fig:",width=170 ]     distributions for one lepton signal events for model b , @xmath153  gev ( left panel ) , @xmath203  gev ( right panel ) and @xmath130 . th solid histograms for @xmath206 ( msugra like ) and dashed histograms for @xmath199 and @xmath216 respectively corresponding to degenerated mass spectrum . all plots are normalized for @xmath251fb@xmath189 . , title="fig:",width=226 ]   distributions for one lepton signal events for model b , @xmath153  gev ( left panel ) , @xmath203  gev ( right panel ) and @xmath130 . th solid histograms for @xmath206 ( msugra like ) and dashed histograms for @xmath199 and @xmath216 respectively corresponding to degenerated mass spectrum . all plots are normalized for @xmath251fb@xmath189 . , title="fig:",width=226 ]     and @xmath27 distribution of signal for a degenerated susy point . @xmath252 susy events are generated for model a , @xmath123(gut)@xmath253  gev , @xmath130 and @xmath154 . , title="fig:",width=226 ]   and @xmath27 distribution of signal for a degenerated susy point . @xmath252 susy events are generated for model a , @xmath123(gut)@xmath253  gev , @xmath130 and @xmath154 . , title="fig:",width=226 ]    the histograms in figure  [ fig : meffla ] show signal distributions for @xmath203  gev , @xmath254  gev , @xmath255  gev from left to right , and @xmath239 for solid line and @xmath256 for dashed lines , respectively . as can be seen in table  [ table : massab ] , the minimum mass difference is smaller for the model b than that for the model a , because the higgsino mass @xmath96 is higher . because of the degeneracy , the signal is more suppressed as can be seen in figure [ fig : mefflb ] where we take @xmath153  gev ( left ) and @xmath257  gev ( right ) , @xmath199 and @xmath216 ( dashed histograms ) , respectively . overall normalization of the signal above @xmath258  tev reduces by a factor of 1/10 for for model b @xmath203  gev ( figure [ fig : mefflb ] , right panel ) compared to the model a ( figure [ fig : meffla ] , left panel ) for most degenerate points . we conclude that one lepton signal is not accessible at the most degenerated points by looking into @xmath259 distribution alone , assuming that sm background in the one lepton channel in @xcite , and a factor 2@xmath246 3 uncertainty , even though the susy scale is relatively small for this point , @xmath260  tev the mass reach at the lhc will be revisited again in section 4.5 .      for the model a , there are significant two lepton events in the @xmath261 region because @xmath262 is lighter than the @xmath263-like neutralino . we show the @xmath264 and @xmath27 distribution for the model a , with @xmath129  gev and @xmath154 in figure  [ fig : mlla ] . here we require that one of the two isolated leptons has @xmath12  gev and the other has @xmath265  gev . we also apply the standard cuts described in section  i. the relevant mass spectrum for the most prominent endpoints are @xmath266  gev , @xmath267  gev , @xmath268  gev , @xmath269  gev , and @xmath270  gev . the predicted @xmath25 edge and @xmath27 endpoint for the decay chain @xmath271 is @xmath272  gev and @xmath273  gev , respectively , consistent with figure  [ fig : mlla ] . the edges and endpoints of other cascade decays are also visible in the plots .    to select the jet from @xmath140 decays , we have taken the one of two most highest @xmath5 jets with smaller @xmath27 . if mass difference between @xmath274 and @xmath28 is smaller , we may found the smaller probability to find correct jets that arise from @xmath275 decay . we do not observe such effect in figure  [ fig : mlla ] .    the number of accepted events @xmath276 ( where @xmath277 denotes number of isolated leptons with @xmath12  gev and @xmath278 ) for this point are @xmath279 , @xmath280 , @xmath281 for @xmath252 generated events ( corresponding to @xmath246 20  fb@xmath189 ) . number of two lepton events below the dominant edge is 2933 after the background subtraction . because @xmath1 distribution of the one lepton channel is not very prominent over the background , susy particles may be discovered in the two lepton channel for the degenerate region . note that for the most degenerated susy spectrum , we have @xmath282 so that all neutralinos are highly mixed . in such situation , dominant source of @xmath283 is @xmath284 , because @xmath285 has significant decay branching ratios into charginos . it is worth to point out that the relative weight of the decays @xmath286 may be studied by looking into the charge asymmetry in @xmath26 distributions , @xmath287 @xmath288 @xcite . the charge asymmetry comes from the polarization of @xmath283 arising from @xmath140 , however as discussed in @xcite , the effect tends to be suppressed if sparticle masses are degenerated .    for the model b , the decay of @xmath289 into sleptons are closed for any value of @xmath107 . for @xmath153  gev and @xmath215 , we have @xmath290 , @xmath291 , @xmath292 for @xmath252 generated events . while @xmath293 and @xmath294 is about same as that of the model a , @xmath295 is reduced by a factor of 4 . in addition no significant events with opposite sign same flavor leptons are seen after the subtraction of @xmath296 events .      in msugra , the signal @xmath1 distribution is clearly harder than the background . especially , one can see the increase of the signal towards its peak , where the background is negligible . if the total @xmath1 distribution shows a bump or a clear change in the power behavior , one may claim discovery of susy particles without precise understanding of the background distribution .    on the other hand , when susy mass spectrum is degenerated , the peak of the signal distribution shifts to a lower position where the background may be @xmath24610 times higher . the signal distribution shows a similar power low behavior for @xmath297 as can be seen in figure  [ fig : meffa ] . the bump structure may not be detected and precise understanding of the background would be required . searching edges in @xmath25 distribution from the decay @xmath298 @xmath299 may become more important , however , as we have discussed already , the signal rate is model dependent . we do not consider the possibility to improve s / n ratio by selecting signal region @xmath300 vs @xmath2 in this subsection . table  [ table : meffnum ] shows the number of signal events after the cut for @xmath1 intervals for @xmath252 generated event ( upper row ) and number of events for 10  fb@xmath189 ( lower row ) for both model a and model b. we take a moderate value of @xmath203  gev for the table , which corresponds to @xmath301  tev . @xmath1(tev)&0.8 - 1.2&1.2 - 1.6&1.6 - 2.0&2.0 - 2.4&2.4 - 3.2 & 3.2 - 4.0 & @xmath192&@xmath138(tev ) model a & & & & & & & & @xmath206&448&905&1267&999&568 & 69&0.252pb&1.35 & 22.5 & 45.6&63.9&50.3 & 28.8 & 3.4 & & 10&752&1201&1378&896 & 483&59&0.245pb&1.29 & 36.8 & 58.8 & 67.4 & 43.8 & 23.9 & 2.9 & & 20 & 813 & 1421 & 1319 & 676 & 293&17 & 0.248pb&1.20&40.3&70.5 & 65.4&33.7 & 14.5 & 0.8 & & 30 & 1246&1691&1018&336 & 95 & 9 & 0.267pb & 1.04 & 66.6&90.4 & 54.4 & 18.0&5.1 & 0.5 & & 40 & 2446&2337&758&212&63&9 & 0.314pb&0.87 & 152.3 & 145.5 & 47.2 & 13.2 & 4.0 & 0.6 & & 50 & 882 & 960 & 529 & 198 & 65 & 4 & 0.457pb & 0.90 & 80.7&87.8 & 48.4 & 18.1 & 5.9&0.4 & & 55 & 173 & 249 & 175 & 71&26 & 5 & 0.666pb & 0.94 & 23.0 & 33.2 & 23.2 & 9.5 & 3.5 & 0.7 & & model b & & & & & & & & @xmath206 & 450 & 1108 & 1405&1192 & 784 & 96 & 0.206pb&1.42 & 18.6 & 45.7 & 57.9 & 49.2 & 32.3 & 4.0 & & 10&649 & 1267 & 1585 & 1145 & 654 & 67&0.187pb & 1.38 & 24.3 & 47.4 & 59.3&42.8 & 24.5 & 2.5 & & 20 & 836 & 1528 & 1645 & 962 & 432 & 42 & 0.174pb&1.31 & 29.1 & 53.2 & 57.2 & 33.5 & 15.0 & 1.5 & & 30 & 943&1838&1362&561 & 217 & 26&0.165pb&1.2 & 31.2 & 60.7 & 45.0 & 18.5 & 7.2&0.9 & & 40 & 1711 & 1591 & 711 & 184 & 86 & 4 & 0.158pb & 0.99&54.0 & 50.2 & 22.4 & 5.8 & 2.7 & 0.1 & & 50 & 2428 & 803 & 215 & 67 & 25 & 5 & 0.154pb & 0.73 & 74.9 & 24.8 & 6.6 & 2.1 & 0.8 & 0.2 & &    in the msugra limit @xmath302 , the background rate is negligible in the signal region . the number of events in @xmath303  tev is greater than 10 for @xmath304 , where the number of background events would be around 1 according to @xcite . however , the signal rate is reduced by more than a factor of @xmath305 for @xmath306 compared to that at @xmath239 . another important question is if we have a flatter power spectrum in a certain @xmath1 region . the number of background events is reduced steeply @xmath1 bins in figure [ fig : meffa ] , while we have nearly flat signal distribution between @xmath307-@xmath308  tev for msugra - like ( @xmath239 ) points . the ratio between the signal in the bins @xmath309 and @xmath310 for @xmath311 for the model a and for @xmath312 for the model b , therefore the power law for the signal is similar to that of background in figure [ fig : meffa ] . we can describe the discovery potential in terms of the mass degeneracy rather than @xmath107 . in the table  [ table : meffnum ] , @xmath138 ranges from @xmath313  tev . ( @xmath314  tev ) . once @xmath138 reduces below 1 tev , 70% of @xmath315 , the separation between signal and background are not good in @xmath1 distributions . good understanding of the background distribution and the detector effect is required to exclude the model in early stage of lhc runs @xmath316fb@xmath189 .    a factor 2 decrease of the signal is found for the model a between @xmath317 and @xmath199 . in this model , squark mass decreases as @xmath107 increases . while the production cross section increases as @xmath318 gets lighter , the masses of heavier neutralino and chargino increase . they are heavier than @xmath140 at @xmath199 , so that they would not be produced from @xmath140 decay at all . the lighter neutralinos and charginos are still lighter than @xmath140 but they are degenerated , so that only soft leptons are produced from the decay . the two lepton signal is also suppressed for this model point . this is an example that the rate of signal events with lepton is model dependent . the tendency of the signal reduction is same for the higher mass spectrum . the luminosity needed to discover the susy signal is larger at the degenerated susy points . for example , the production cross section is @xmath319  fb for the model a with @xmath320  gev and @xmath116 , and 15.1 events/10  fb@xmath189 is expected in the region @xmath308  tev @xmath321  tev , which may be enough to claim the discovery . on the other hand , for @xmath154 only 3.8 events/10 fb@xmath189 is expected , excluding the possibility of discovery with low luminosity . in this paper , we study the discovery potential of minimal supersymmetric models with degenerated mass spectrum at the lhc . such parameter regions have not been systematically studied in the past . susy studies have been mainly performed in the models where gluino and squark are significantly heavier than the lsp , i.e. in the msugra model , gauge mediation model , and so on . we do not study the general mssm model here , but take mixed modulas anomaly mediation ( mmam ) models , which are parametrized by @xmath322 , @xmath323 , and @xmath324 . the parameter @xmath107 is the ratio of the @xmath325 terms of the volume modulas @xmath32 in kklt model and the compensator field @xmath33 in @xmath39 msugra . this parameter @xmath107 gives us one parameter description from the msugra - like mass spectrum , where @xmath326 , to ( moderately ) degenerated mass spectrum . the models we have studied include the mssm points where @xmath327 . when sparticle mass spectrum is degenerated , energy of a particle from squark and gluino decays is small relative to the mass scale . this is reflected in the distributions of the first @xmath5 jet , @xmath2 and @xmath1 . they tend to peak at smaller values than msugra prediction for the same gluino and squark masses . the background from the sm processes increases rapidly for such low @xmath5 and low @xmath1 region , therefore , the susy signal has to compete with large background . indeed , the signal and background @xmath1 distributions are quite similar for degenerated parameters we have studied . we find the @xmath328 ratio can be far below 1 for our most degenerated parameter points . nevertheless , we found the signal distribution of degenerated susy mass spectrum show special universal pattern in @xmath1 and @xmath2 plane . this may help to determine the appropriate signal region and discriminate signal from background better . the discovery potential at the degenerated points therefore depends on our knowledge on the background distribution . the main background source to the susy productions is multijet final states involving @xmath230 , @xmath329 and @xmath232 . there are significant improvements in the lowest order estimation of the background recently ; matrix element corrections of the backgrounds are now included . theoretical uncertainty comes from matching between parton shower approximation and matrix corrections , and higher order qcd corrections ( scale uncertainty ) . experimentally backgrounds are partly estimated by the experimental data itself . for example , overall normalization of dominant @xmath21 background can be determined by looking into the events with low @xmath2 , where contamination of the susy events are small . for the degenerated mass spectrum , however , such calibration may also be affected . note that the background estimation in the susy signal region require extrapolation using monte carlo , while there is a contamination in the region for the calibration in non - trivial manner for degenerated susy mass spectrum . we look into @xmath2 distribution and find that the number of events with @xmath330  gev is increased by factor of @xmath331 for our most degenerated point ( the model b with @xmath199 , @xmath153  gev ) from msugra limit ( @xmath206 ) .    even with the uncertainty discussed above , the discovery of supersymmetry in msugra models would not be a problem up to @xmath246 2  tev region . however , as we have discussed in this paper , this is not the case even for moderately degenerated susy parameters in mixed modulas anomaly mediation model . we stress the importance to include the background and its uncertainty to perform susy discovery and parameter studies for degenerated or general mssm mass spectrum , while we find that they tend to be ignored in recent studies @xcite . we would like to thank dr . tasuo kobayashi , dr . shoji asai and dr . junichi kanzaki for discussion . we also thank dr . giacomo polesello for comments to the drafts . this work is supported in part by grant in grant - in - aid for science research , ministry of education , science and culture , japan , 16081207 , 18340060 for mmn and 15340076 , 16081208 for kk . 99 s.  p.  martin , `` a supersymmetry primer , '' arxiv : hep - ph/9709356 . atlas collaboration , _ atlas detector and physics performance technical design report _ , cern / lhcc 99 - 14/15 ( 1999 ) . i.  hinchliffe , f.  e.  paige , m.  d.  shapiro , j.  soderqvist and w.  yao , phys . d * 55 * , 5520 ( 1997 ) [ arxiv : hep - ph/9610544 ] . + h.  bachacou , i.  hinchliffe and f.  e.  paige , phys . d * 62 * , 015009 ( 2000 ) [ arxiv : hep - ph/9907518 ] . arxiv : hep - ph/0410364 . section 5.1.2 " a detailed analysis of the measurement of susy masses with the atlas detector at the lhc s.  kachru , r.  kallosh , a.  linde and s.  p.  trivedi , phys . d * 68 * , 046005 ( 2003 ) [ arxiv : hep - th/0301240 ] . k.  choi , k.  s.  jeong and k.  i.  okumura , jhep * 0509 * , 039 ( 2005 ) [ arxiv : hep - ph/0504037 ] . a.  falkowski , o.  lebedev and y.  mambrini , jhep * 0511 * , 034 ( 2005 ) [ arxiv : hep - ph/0507110 ] . m.  endo , m.  yamaguchi and k.  yoshioka , phys . d * 72 * , 015004 ( 2005 ) [ arxiv : hep - ph/0504036 ] . t.  plehn , d.  rainwater and p.  skands , arxiv : hep - ph/0510144 , s. asai , talk in 4th tev4lhc , oct 20 -22 , 2005 at fermilab . m.  l.  mangano , m.  moretti , f.  piccinini , r.  pittau and a.  d.  polosa , jhep * 0307 * , 001 ( 2003 ) [ arxiv : hep - ph/0206293 ] . see also http://mlm.home.cern.ch/mlm , [ merging matrix element and shower ]      g.  corcella _ et . al . _ _ _ , _ jhep _ * 01 * ( 2001 ) 010 , [ arxiv : hep - ph/0011363 ] . richardn / herwig / isawig/ http://www.physics.ucdavis.edu/  conway / research / software / pgs / pgs4-general.htm e.  richter - was , d.  froidevaux and l.  poggioli , `` atlfast 2.0:a fast simulation package for atlas '' , tech . rep.atl-phys-98-131(1998 ) b.  c.  allanach _ et al . _ , in _ proc . of the aps / dpf / dpb summer study on the future of particle physics ( snowmass 2001 ) _ ed . n.  graf , eur . j.  c * 25 * ( 2002 ) 113 [ econf * c010630 * ( 2001 ) p125 ] [ arxiv : hep - ph/0202233 ] . a.  j.  barr , phys . b * 596 * , 205 ( 2004 ) [ arxiv : hep - ph/0405052 ] . t.  goto , k.  kawagoe and m.  m.  nojiri , at the cern large hadron collider ,  phys . d * 70 * , 075016 ( 2004 ) [ erratum - ibid . d * 71 * , 059902 ( 2005 ) ] [ arxiv : hep - ph/0406317 ] . j.  m.  smillie and b.  r.  webber , jhep * 0510 * , 069 ( 2005 ) [ arxiv : hep - ph/0507170 ] . h.  baer , e.  k.  park , x.  tata and t.  t.  wang , arxiv : hep - ph/0604253 . n.  arkani - hamed , g.  l.  kane , j.  thaler and l.  t.  wang , arxiv : hep - ph/0512190 .
discovery of supersymmetric ( susy ) particles at the large hadron collider ( lhc ) has been studied for the models where squarks and gluino are much heavier than the lightest supersymetric particle ( lsp ) . in this paper 
 , we investigate the susy discovery in the models with degenerated mass spectrum up to @xmath0 . 
 such mass spectrum is predicted in certain parameter region of the mixed modulas anomaly mediation ( mmam ) model . 
 we find that the effective transverse mass of the signal for the degenerated parameters shows the distribution similar to that of the background . experimental sensitivity of the susy particles at the lhc therefore depends on the uncertainty of the background in this class of model . 
 we also find that susy signal shows an interesting correlation between @xmath1 and @xmath2 which may be used to determine the signal region properly to enhance the s / n ratio even if the sparticle masses are rather degenerated . 
 the structure is universal for the models with new heavy colored particles decaying into visible particles and a stable neutral particle , dark matter .