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JHEP08(2000)017 ∗ August 1, 2000 August 15, 2000 , 4000 GeV, with a fine Revised: < 0 Accepted: m May 22, 2000, = 10 (within the focus point region), and 460 GeV. In this region, the mono-leptonic [email protected] , β < 2 / 1 Received: M ) above 2 TeV. We use minimal (mSUGRA) 0 m = 0 and tan , mSUGRA can be discovered through gaugino events, provided 0 0 A m 0, Breaking, Beyond , Supersymmetric We re-analyse the prospects of discovering supersymmetry at the LHC, is of renewed interest because this region has recently been found to µ> [email protected] [email protected] 0 m HYPER VERSION Also at Theory Division, CERN, 1211 23, . ∗ Cavendish Laboratory, University of Cambridge,Cambridge, Madingley CB3 Road 0HE, UK E-mail: DAMTP, University of Cambridge,Cambridge Wilberforce Road CB3 0WA, UK E-mail: [email protected] unification assumptions forat the high SUSY breaking parameters. The discovery reach Standard Model, Hadronic . channel still provides the best reach. Keywords: a top of 174 GeV, all points in mSUGRA with tuning measure up tofine-tuning 210 excludes (includes) (500) the are contributionfor from covered arbitrarily the by high top the Yukawa coupling. search, Even where the definition of Abstract: in order to re-express coverageanalysis in to terms scalar of a ( fine-tuning parameter and to extend the James P.J. Hetherington, M.Andrew Parker and Bryan R. Webber Ben C. Allanach Naturalness reach of theCollider Large in minimal supergravity the gaugino mass parameter have a focusuncertain point, how much leading of the to regionsymmetry can relatively be breaking. ruled low out The due best fine-tuning, towhere fine lack and of tuning for radiative reach electroweak because is found it in remains a mono-leptonic channel, JHEP08(2000)017 , 16 W SUSY M ,andthe SUSY M 1 is expected to be at most around 1 TeV. If the SUSY breaking SUSY M GeV, solving the naturalness problem of the standard model. In addition, the would have masses inconsistent with their measured values. 19 Z Since supersymmetry is not observed amongst the already discovered , would be the typicalmodel mass particles, of and the represents as theConsiderations yet scale undiscovered of at which general this of new newupper the physics bounds becomes standard beyond on relevant. new the physics standardmodels scales model of [2], order [1] a can few result TeV. However, in in supersymmetric it must be a broken . The scale at which supersymmetry is broken, renormalised electromagnetic, weak, andto strong an couplings approximately can common be value at made the to grand converge unification scale. scale is too large,parameters, then, electroweak unless symmetry there breaking are also large will cancellations be of between order SUSY breaking to 10 A possibility for new physicsIf beyond fermionic the generators standard are model addednew is to the supersymmetry space-time bosonic (SUSY). symmetry generators is ofall the supersymmetry. particles Lorentz have group, As a the partner abetween bosonic of result and equal of fermionic mass loops exact but preventmasses radiative supersymmetry, opposite up corrections spin-statistics. to from driving the Cancellations scalar highest scale present, assumed to be the GUT or Planck scale, 10 1. Introduction Contents 1. Introduction2. Fine tuning3. Radiative electroweak symmetry breaking4. Monte-Carlo simulation of LHC discovery5. reach Results6. Summary 5 6 1 3 8 13 and JHEP08(2000)017 2 should be small. SUSY M is at or below the TeV scale, then supersymmetric particles will almost SUSY M The simplest possible SUSY extension of the standard model, with a super- As mentioned above, it is possible to avoid the problem of large electroweak These “naturalness” arguments are often quantified in terms of “fine tuning” [6]. The authors of [8] discuss a more sophisticated measure of fine-tuning and use Since its status as a possible solution of the naturalnessWe therefore problem contend that of fine-tuning is the a stan- relevant way to compare SUSY models, Within mSUGRA, the fundamental SUSY breaking parameters are boundary If partner for each standard modeldoublet, is , called and the the minimalstudied addition supersymmetric sub-category of standard a of model, second or theity, MSSM. Higgs MSSM where scalar The is most supersymmetry minimal supergravity, ismotivated mSUGRA. unification a assumptions Supergrav- local, amongst ratherreducing the MSSM the than SUSY number a breaking of globalfour, parameters, parameters, plus symmetry, from one at the sign. onenot hundred Currently, time supergravity, the or is suppression so the of ofspecified main flavour the by changing motivator MSSM, these neutral for parameters currents, to these together just assumptions. with those The of theory themasses is standard if fully model. there aresituations, where extra the cancellations parameters amongst ofresults, a are the often theory thought SUSY are to masses. carefully beshould unsatisfactory. tuned be Fundamental to However, parameters, independent, avoid it such uncorrelated unphysical is inputs. argued, There are a few different fine-tuningof measures [7] the , degree and all of arefine-tuning cancellation intended above to required be which between measures a fundamental theoryto parameters. becomes support unacceptable the A is argument value often that of advanced, and used certainly be discovered atIndeed, the Large detailed Hadron studies ColliderLHC of (LHC), general-purpose being how experiments built the ATLAS at [3] SUSY CERN. and parameters CMS would [4] be have been measured made by [5]. the it to assessIn the [9] status fine-tuning of motivatedcomplete the one-loop upper MSSM effective bounds potential. if [10] ondifferent superparticles discusses MSSM high- the are use masses supergravity of not scenarios, are fine-tuningnon-minimal found while to obtained supersymmetric compare [11] at using models. uses the a fine-tuning LHC. to compare dard model is onearguments of have the increased main relevance reasons to for studies investigating of supersymmetry, naturalness supersymmetry. experiments, and search channels, andreach. is a As useful experiments measureminimum of push fine-tuning experimental the which discovery lower SUSYuniverse bounds can is on have supersymmetric increases, SUSY at andhigh parameters low fine-tuning our upwards, in confidence falls. the itself that However, can the we be do used not to believeconditions rule that a on a theory the out. running SUSY breaking masses and couplings imposed at a high JHEP08(2000)017 . | 2 H (2.1) m reach of | 0 ). Thus as m Z 0 m M and to present it in 0 m 2 2 TeV [3]. The purpose of µ < − 0 β 2 m 1 tan 2 − 2 H , squarks, sleptons, and the heavy Higgs β 0 is the ratio of Higgs vacuum expectation 2 m . A cancellation is then required between 3 | m β 2 − H tan 1 m 2 H | boson mass is determined to be [2]: m Z = ,maybelarge. GeV. Physical masses of superparticles are obtained 0 2 Z m 16 M is the Higgs mass parameter in the MSSM superpotential. 2 1 µ and has the same origin as the super-partner masses ( 2 2 /v H 1 v m ) cross close to the electroweak scale. 2 2 H m In section 2, we discuss our fine-tuning measure, and which parameters to include Previous predictions of the discovery reach of the LHC in mSUGRA parameter As a result, the electroweak symmetry breaking is insensitive to the GUT scale rises, and consequently so does 0 by minimising the Higgs potential. tan values (VEVs) searches for these particles would be an interesting furtherin study. its definition.breaking We excluded discuss region. in Infor section section use 3 at 4 the the we LHC, discuss matter and16] our SUSY of event simulation search of generator. the the channels discovery electroweak We considered reachand symmetry present using the the in overall HERWIG [15, section fine-tuning 5 reach of the the fine-tuning LHC. reach in each channel, the present investigation is to extend this reach to higher Various measures have been proposed in order to quantify this cancellation [7]. In mSUGRA, terms of asearch naturalness channels measure. perform inthe We this dominant seek SUSY region, to particles. where determine For charginos large how and the neutralinos standard would be SUSY search limits put lowerm bounds upon super-partners’ masses, the lower bound upon space, using ISAJET [14], went only as far as 2. Fine tuning At tree-level, in the MSSM, the scale, usually taken to be 10 particle could avoid detection at the LHC, and the determination of the by evolving the MSSM parametersequations to the (RGEs). weak scale usingpoint” the The behaviour renormalisation [12, RGE group 13]. evolution Awhich relatively of large the region RGE minimal of trajectories GUT converge supergravity scale towardsSpecifically, parameters a shows exists the small for a range renormalisation of “focus group measurabledoublet properties. trajectories ( of the mass squared of a Higgs the terms of equation 2.1 in order to provide the measured value of SUSY breaking parameters [12], andpoint fine-tuning is corresponds smaller to than a expected.by region the This in focus mSUGRA which parameter the scalar SUSY breaking masses, governed JHEP08(2000)017 of DR ) and t (2.2) (2.3) (2.4) m DR ( t ) Z m M employed in ( ) is added to b comparison a m was determined is included. The GUT 2 2 t v M h ( t , + h 2 at this level can make 1

v ) c . p GUT ≡ 1-loop QED. M v GeV ( , the fine-tuning of a particular ⊗ }  i ,B L a 0 ˜ u { . Q

m ,A 2 ) Z  a M ln ), where its scale dependence is small. GUT 2 ln 9ln ˜ t 4 ∂ . M ∂ ( m

1 ˜ t of a “fundamental” parameter ,µ ≡ 2 6+0 m a . / a ( c ). Our initial choice of free, continuously valued, 1 c a p c 119. We will examine the implications of relaxing ,M . was taken into account [18] in order to calculate the 0 = m β ) = 248 Q  Q numerically to one-loop accuracy in soft masses, with two- ( =max( )=0 = v c . Z c } 0 i M a ) into the definition of fine tuning thus increases the naturalness m ( GeV is the GUT scale. It is this selection which gives rise to low { 16 DR Higgs vacuum expectation value MS S GUT by evolving them with 3-loop QCD α 10 M Z ( ∼ t M h were determined by including one-loop SUSY QCD and third family cor- GUT )from DR ) Z M Z M Note that our code does not yet include 2-loop soft terms in the RGEs, finite cor- We also consider the case where the top Yukawa coupling Full one-loop sparticle and QCD corrections were used to determine We have calculated The definition of naturalness ( M ( τ DR S From a choice of a set of fundamental parameters reference [12] is loop accuracy in supersymmetrictions parameters. were added Dominant to one-looppotential the was top/stop minimised Higgs correc- at potential and used to correct eq. (2.1). The Higgs by the approximate formula [19] model is defined to be where m independent and fundamental mSUGRA parameters also follows ref. [12]: the accuracy of the calculation below. rections to the electroweak gaugevacuum expectation couplings, value, a or full tadpole one-loopknown contributions [9] calculation to that of the improving the Higgs the potential. Higgs accuracy It of is the well calculation of a significant difference totation its is numerical obscure value. anyway, this Since factnaturalness is its reaches not in exact in different quantitative conflict channels. interpre- with the proposed reach of the LHC, as our results in section 5 show. inclusion of fine-tuning for large One-loop top, gluinoα and squark corrections were used [19] in order to deduce the list of fundamental parameters in eq.focus (2.3). point In scenario refs. with [12, 13, heavy 20], scalars it has is shown a that large the fine-tuning if [19] and the runningYukawa couplings of from tan runningtermined at masses. Fermion running masses were de- rections [19]. The JHEP08(2000)017 , 0 m . In this region, 2 / 1 M [21]. In the most recent R ˜ t = 10000 GeV (see figure 1). m 0 L ˜ t and small m m 0 ), which must be calculated from t √ m m = ( t Q m plane found in the literature [3, 12, 17] 2 5 / 1 M , 0 m , around 6 TeV for an input pole top mass of 174 GeV, as 0 m which should be investigated. Here and in later versions, the 0 m + 1 TeV was excluded for an input pole top mass of 174 GeV. Here 2 / 1 [21]. M Z 2 M The REWSB exclusion region was also found using our fine-tuning calculation Since the REWSB constraint is so heavily dependent upon the precise values of In version 7.14 of ISASUGRA, which was used in [3, 17] to generate SUSY Between 7.14 and more recent versions [14] such as 7.42, the excluded region ∼ 0 As we shall show,the the version discovery number contour or top inin mass. the the To allowed produce plots region the is of REWSBspecified excluded not our in regions so results, the displayed sensitive captions. we to used our fine-tuning code with the pole top masses mSUGRA does not havetry the breaking (REWSB). required However, properties thespectrum, for REWSB is constraint, radiative very unlike electroweak most sensitive symme- ticularly of to the the details value SUSY of of the the calculation running top and mass input parameters, par- as shown also insparticle in mass figure corrections 1. to the Here, inputs two-loop have corrections been to addedcode, the [21]. RGEs where and the one-loop dependence physics of included the wasfigure exclusion as 2. region described We note on in againof various a the the aspects strong running previous dependence of mass on section. and the the strong top physics coupling. mass, The is andinput on shown the parameters in treatment and detailsthe of exclusion the region calculation, will thereit remain should is stable not no under be reason taken further asinvestigated refinements. to experimentally. a suppose limit Hence Both upon our that we the own believe regionslarge code of corrections. and mSUGRA ISASUGRA We parameter could therefore space be use tosince subject be ISASUGRA7.42 the to to allowed region compute then the extends discovery reach, up to values of show a large excluded triangular region, for large version of ISASUGRA, 7.51, the region has returned once again to low values of Most plots of search reach in the 3. Radiative electroweak symmetry breaking the pole top massship in between the the renormalisationparticles scheme running [18], being and and used. pole hencegated. The masses on precise the depends relation- point on in the the masses SUSY parameter ofmasses space and the being mixings super- investi- andm to obtain the REWSB excluded region, the region above one-loop RGEs were used andscale minimisation of the scalar potential was performed at scalar potential minimisation takes place at shifted to very high shown in figure 1. Theon REWSB the constraint therefore values no of longer provides a useful limit JHEP08(2000)017 0 µ> (SUSY t m / GeV = 10, β = 179 GeV. The 1/2 t M m 10000 (SM)”). Regions to the 1000 800 600 400 200 0 s 9000 α = 179 GeV”) and calcula- t )(“ m 8000 Z (SM) s M α ( S =174 GeV =179 GeV t t 7000 α (SUSY QCD) t m Full m 6000 Full, m v(Q)=246.22 GeV /GeV 0 = 174 GeV”, “ 6 m t 5000 m / TeV DR value of 0 169GeV 174GeV 174GeV 179GeV m 4000 V. 7.51 V. 7.42 3000 = 174 GeV, except for the curve marked t 2000 plane was found through a variety of signals involving hard m 2 1234567 910 / 1 1000 M 200 100 900 800 700 600 500 400 300

08

,

1/2 0 /GeV M m Dependence of the radiative electroweak symmetry breaking excluded region The dependence of the REWSB excluded region in our fine-tuning code on var- =0. 0 A In this study, as in [17], the results of which were used in [3], the SUSY discovery QCD)”), using only aonly constant standard value model of corrections the Higgs to VEV the (“v(Q)=246.22 GeV”), and using isolated leptons, jets and missing transverse momentum. These cuts can be applied curves shown are: the full calculations (“ right of the curves are ruled out by the REWSB constraint. tions leaving out chargino and neutralino corrections to the running top mass (“ 4. Monte-Carlo simulation of LHC discoveryWe reach now turn to the discussion of the LHCreachinthe mSUGRA search. Figure 2: ious approximations for Figure 1: on top mass, according to ISASUGRA versions 7.42 and 7.51, for tan and JHEP08(2000)017 10 (4.1) (4.2) S> 25 GeV, ,usinga > cut T 5and p >E T B> 20 GeV, and lying p , √ > , the sum being taken S/ j T p p i 2, and p . ij 3 100 GeV where , < > 2 2 0and =Σ | / . . being the two-component trans- ) . Or: no jets with 1 η 0 2 | i T ij / p M p S > < · η, φ l 2 | p η λ and 2 | cut is often called the transverse circularity λ 0 + background, as discussed in [22], and the 2 |− 1 T m 7 T λ S / >E W p || = l T / p p T | S background was generated using events with one , and are listed below. The cuts represent typical 2( decay, involving the transverse mass: cut p W E W )leptons,with = e T or M µ space than 0.4 units from the centre of any 15 GeV jet with are transverse two-component momenta, for the lepton and miss- T η, φ / p are the eigenvalues of the matrix , l i λ p , respectively. T p plus jet events. The using the same jet-finding algorithm. Any final state ( cone algorithm with cone-size 0.7 units of Either: at least 2 jets, with pseudo-rapidity Missing transverse momentum ing verse momentum of the particle. where over all detectable final state particles, and where or transverse sphericity. further in cone-size 0.4, and with less than 5Channels GeV with of no energy leptons, within one 0.3and lepton, units three two of leptons the leptons of lepton. were opposite investigated. or the sameIn sign, the one-lepton channel, andue extra to cut standard was model imposed to reduce the background W The search channels used areThe shown mSUGRA in events table were 1. simulated by employing the ISASUSY part of the The discovery limit is set at values of • • • • • where S and B are the expected number of events in the the SUSY signal and total SUSY discovery cuts that mightas be ATLAS used [3] at or a CMS general-purpose [4]. LHC experiment, such with a range of cut energies ISAJET7.42 package [14] toHERWIG6.1 [15, calculate 16] sparticle to simulate masseswas the generated, and events together themselves. branching withand ratios, The the expected and backgrounds SUSY due signal to standard model top anti-top results were rescaled accordingly. of the jets producedThis in produces the an hard underestimate subprocess, of and the the rest in QCD parton cascades. JHEP08(2000)017 , . 1 E − s √ 2 / j0 j1 j3 v2 v3 jss jos − Label cm 33 of data. 1 − 0 1 3 2 3 = 10, pole top mass Leptons β Channels in which the 2(Samesign) 2 (Opposite sign) background with increasing ¯ t t 1 =0,tan 0 0 > Jets Table 1: SUSY discovery reach has been inves- tigated. A 0 . 5 , and with both definitions of fine-tuning 8 > | cut and extending to pseudo-rapidities up to 5.0. ,results η | E E cut E √ / of integrated luminosity. The integrated luminosity 1 − , the minimum final cut level. =10fb E , the Monte Carlo output σ L T S 0and and T / p µ> = 400 GeV, were presented in [23]. The top Yukawa coupling was not included In order to find the hard leptons, and to A low-statistics calculation of the discovery reach with a top mass of 179 GeV Table 2 shows the background for each generated channel, the total background, Calculations were made for mSUGRA with For each value of cut top mass, and a compensating increasewhich in causes the a energy greater of proportion thebackground to resulting could leptons pass safely and the be jets, selection assumed cuts. to Thus be for independent this study of the the top mass. 174 GeV, from the j0 channelcorrection were factors used to to compensate obtain foring linear the underestimate result- of the background. determine electromagnetic resolution of 10% We note that the LHC experiments expect to collect around 300 fb chosen is equivalent to one year of running in the low luminosity mode, 10 was also made, to determine whetheris the a reach small is independent decrease of in the the top mass. production cross There section for 5. Results Preliminary results on theE naturalness reach of the LHC for the j1 channel, with state transverse momentum in the hardcess subpro- was selected to obtainthe some events cuts, passing withinstraints. realistic computer Where time thementum minimum con- had to transverse be mo- increased above background. The former constraint istotal an number approximation of to observed thebackground events requirement at in that the some the 5 experiment will be significantly above the was examined directly, particles with being ignored. For the jetlation count check, and a lepton calorimeter iso- simulation was used, with hadronic resolution of 70% (with/without the top Yukawa coupling). and the resulting expected number of supersymmetry events required to fulfill the These parameters have beenthe LHC. selected to simulate a general-purpose experiment at in the definition ofnels fine-tuning. in Here table we 1, obtain for the several discovery values limit of in all the chan- JHEP08(2000)017 ) ∗ = 174 GeV , as described t cut m 3 3 E 10 10 × × 13 10 10 65 17 11 29 10 30 22 10 10 54 10 10 10 10 431 431 201 579 102 107 6 4 . . 3 1 Required no of greater than SUSY Signal events T p , a plot has been used to determine cut * 5 4 3 3 4 giving the best fine-tuning reach, and E 3 10 10 10 10 10 1 1 10 1* cut 4 1 4 2 5 2 × × × × × 7* 4* 9 451 394 36* 20* < < E × 35 * 12 * 115* < 173 * 3 2 4 6 3 . . . . . 4 . 5 5 7 1 1 7 Total no of background events /GeV 200 300 400 500 200 300 400 500 100 200 300 400 500 100 300 400 500 100 200 300 400 500 100 100 200 cut E 4000 GeV. The values of < j3 j3 j3 j3 j0 j0 j0 j1 j1 j1 j1 j1 j3 j0 j0 jss jss jss jss jss jos jos jos jos jos 0 Total background for SUSY discovery channels. Also shown is the expected m Channel = 179 GeV to calculate the fine-tuning and REWSB exclusion are given. t =100, 200, 300, 400 and 500 GeV were investigated. No results can be presented m For each of the channels, and each value of cut and in section 4. the fine-tuning reach with both definitionslargest of fine fine-tuning. tuning The where fine-tuning reachlimit, the is for fine-tuning the contour is completely within the discovery discovery criteria detailed above. No(v2,v3) discernible was background obtained. in the jet veto channels Table 2: number of SUSY events required for discovery. Backgrounds marked with an asterisk ( have been corrected for the use of a minimum subprocess the corresponding reach, are shown in table 3. The results using E JHEP08(2000)017 t ) = h 2 c / 1 L refers 0 ,M limit c 0 2 350 460 300 350 280 / m 1 M = 174 GeV in t m cut 0, 200 300 200 200 100 E (GeV) 400 300 200 100 700 600 500 0 m µ> are given in GeV. t 0 h 4000 GeV, for each of the 2 c 375 550 270 270 155 / 1 > 0 M = 10, 4000 m cut β 400 400 300 200 100 E and cut t h REWSB E c 375 500 240 240 150 =0,tan 3000 0 A cut 10 =174 GeV 400 400 300 200 100 t reach for large

E

400 210 300 m 2 / 1 2000 0 100 is the fine-tuning limit as defined in the text, and c M 215 130 230 260 190 c cut = 400 GeV j1 channel, as a dashed line in the ( 200 100 300 400 300 E 1000 ,andthe cut

ht

E c c LSP charged = 400 GeV. The excluded region, filled black, along the left hand 70 85 120 210 110 cut and E

c

cut

200 100 1/2 300 400 300 E 800 600 400 200 (GeV) M 1000 Naturalness reach at the LHC for Values of the cut on missing momentum and jet energy which give the best ,andwith j0 j1 j3 jss jos 1 − Figures 3 and 4 show the best obtainable discovery limit using the channel provid- Cut Type to the same quantities for a top mass of 179 GeV. minimal SUGRA. The fine-tuningby is the represented bar by on the the background right.respect density, White to as contours the measured of fine-tuning top areSUSY Yukawa also coupling discovery presented. is contour Fine neglected. tuning in with The the dashed j1 line channel is described the LHC in expectation the text for a luminosity of 10 fb supersymmetry discovery channels. side of the plotparticle is be due neutral, to whilelower the bound that cosmological on along the requirement the charginois that mass. bottom due the The of to excluded lightest lack the region supersymmetric of on plot radiative the is right electroweak hand due symmetry side breaking. to of the the plot experimental for the jet veto channels,reach as in the number these of channels eventsbut in could is these be expected channels is to obtained too be by small. very considering limited. The specific SUSYing the processes, best reach, the Figure 3: Table 3: fine-tuning limits is the same with thea top fine-tuning with mass respect of 174 to GeV the to top calculate Yukawa the coupling REWSB included, excluded using region and fine-tuning. JHEP08(2000)017 used here. β (GeV) 3000 2500 2000 1500 1000 500 0 m = 179. As shown in = 174 GeV ISAJET t t m m increase in the top mass, 4000 σ 2 TeV in the j1 channel with < 3 TeV. However, it is clear that becomes roughly independent of 0 2 ∼

2000 / m 1 0 REWSB M m 3000 11 =174 GeV

t 1000 m 2000 500

1000 charged LSP charged 4000 GeV the discovery reach in

>

1/2 As in figure 3, but with fine tuning with respect to the top Yukawa coupling , being typically a percent around 800 600 400 200 (GeV) M 0 0 1000 m m Also shown in figure 5 is the discovery reach for a 1 For Figure 5 shows consistency of our results for = 179 GeV. Unlike the REWSB exclusion region, the discovery contours are . Here, the SUSY processes involved are dominated by the gauginos, the squark 0 t those obtained using ISAJET 7.14calculated in [17]. with ISAJET7.51 The same (and figurein lower shows statistics). approximation the discovery between We reach see theexclusion, that various as that ISAJET discussed the versions in differences which section shifted 3, the do REWSB not appreciablym alter the discovery reach. table 3 and figure 6, the reach extends to a fine-tuning value of 260. almost identical. We may therefore use our high-statistics m 7.42 discovery contour to calculate the fine-tuning reach for Figure 4: included. plane, and the naturalnesscluded, density respectively. without The and resulting500 fine-tuning with units. limits, the as Excluded top defineddue regions Yukawa above, coupling to due are in- the to 210 experimental cosmological and figures. limits requirement The on that current limit the the onof chargino LSP the mSUGRA mass, light be parameter Higgs and space neutral, mass illustrated, does are due not included to exclude in any the of large the the value region of tan masses being very highalso (larger shows than that 3 scalar TeV),at production, as high illustrated as a in fraction figure of 7. total This SUSY figures processes, decreases JHEP08(2000)017 TV it 2TeV, =174 GeV, t > m 0 m (GeV) 600 500 400 300 200 100 0 m 4000

0, in minimal supergravity. Solid: 400 =179 GeV. Short-dashed: ISAJET t

µ> 260 m =179 GeV t 3000

m 160 = 10, / GeV β 0 12 m Isajet 7.14, mt=170GeV

400 2000 =0,tan 260 0

A 160 1000 = 174 GeV, with ISASUGRA version 7.42 to generate the SUSY

t = 170 GeV). Long-dashed: HERWIG results with

Herwig 6.1 and ISASUGRA 7.42, mt=174GeV Herwig 6.1 and ISASUGRA 7.51, mt=174GeV Herwig 6.1 and ISASUGRA 7.42, mt=179GeV Herwig 6.1 and ISASUGRA t LSP charged m m lower than the SUSY discovery contour but at 2 0 500 1000 1500 2000 2500 3000 3500 4000

/

1

900 800 700 600 500 400 300 200 100 1/2

M 1000 800 600 400 200 (GeV) M 1000 As in figure 3, but with a top mass of 179 GeV used to calculate the fine-tuning Reach at the LHC for 1/2 M / GeV is possible toattempt produce to scalar obtain SUSY a particles limit at on the the LHC. region A of discussion mSUGRA of parameter how to space where the using ISASUGRA version 7.51 to generate the SUSY spectrum and decays. resultsof[14](with HERWIG results with spectrum and decays. Dot-dashed: the same with Figure 6: and REWSB excluded region. at values of Figure 5: JHEP08(2000)017 = 4000 0 m , the standard 4TeV 0 m 1% 50fb 3TeV 250fb Frac. w. scalars 1.25pb 460). Discovery contour Discovery Total cross-section < Up-right squark mass Up-right 10% 2 5% / 1 / GeV M discovery reach gives an adequate repre- 2TeV 20% 2 / . It has been suggested that a focus point 13 1 0 0 m M m remains uncertain, so this region should be ex- 10fb 0 the m 50% 0 6.25pb m 80% 5 sigma discovery 1TeV 0 500 1000 1500 2000 2500 3000 3500 4000 900 800 700 600 500 400 300 200 100 1000 Scalar production in mSUGRA. The contours represent the total SUSY cross- 1/2 M / GeV We have introduced the possibility of using fine-tuning as a quantitative way to We terminate the calculation of the fine-tuning and search-reach at SUSY searches at thegauginos, LHC provided they can are discover not supersymmetry, too through heavy ( events involving gives this region increased naturalness,symmetry and the breaking extent excludes to high which radiative electroweak sentation of the overall SUSY discovery power,This through expression the of gauginos, in the each reach channel. is also shown in table 3. compare the discovery reach ofwith various a channels. Fine-tuning quantitative can measure provide of discomfort with a theory, which increases as the plored thoroughly. We demonstrate that even for arbitrarily high GeV, since for higher values of 6. Summary In this paper,parameter we space, have using obtained theinvestigation the repeats new the discovery supersymmetry calculation reach of routinessistency of [17], in of this the HERWIG. provides the Where a LHCcalculating two useful our into the Monte-Carlos. check mSUGRA on mSUGRA the spectrum Ininto con- updates addition, the the region our old of use results, high of and scalar the allows masses us latest to software move for squarks in particular (rather thanscope SUSY of in this general) paper. can be discovered is beyond the Figure 7: section, the mass ofand a the typical fraction squark, of (the SUSY up-right), processes the involving overall a SUSY squark discovery or contour, slepton. JHEP08(2000)017 ]. < 0, 2 / Phys. . 1 µ> , ]. M (1993) 320 ]. . hep-ph/9809223 B 309 , volume II, Technical hep-ph/9507282 = 174 GeV, all points in t 4000, all values of Probing minimal supergravity m hep-ph/0003170 hep-ph/9306207 > could also be investigated. Phys. Lett. , (1999) 055014 [ 0 , β m (1995) 573 [ D59 About the fine-tuning price of LEP and tan (2000) 035 [ B 357 0 ]; http://cmsinfo.cern.ch/TP/TP.html 14 A 07 , Phys. Rev. Naturalness constraints in supersymmetric theories ), β One loop analysis of the electroweak breaking in su- Phys. Lett. The Higgs mass and new physics scales in the minimal , 4000 GeV and a fine tuning measure up to 210 (500) tan( < 0 hep-ph/9801353 Detector and physics performance TDR m Technical proposal ]. J. High Energy Phys. , (1998) 63 [ Introductory low-energy supersymmetry = 10 (within the focus point region), and plane with β 2 / 1 B 433 M , 0 hep-ph/9303291 standard model Report CERN/LHCC 99-15, (1999) CERN. at the CERN LHC for large with nonuniversal soft terms Lett. [ B. de Carlospersymmetric and models J.A. and Casas, the fine tuning problem This work was funded by the U.K. and Astronomy Research The best fine tuning reach is found in a mono-leptonic channel, where for m =0,tan 0 [1] C. Kolda and H. Murayama, [3] ATLAS collaboration, [2] H.E. Haber, [4] CMS collaboration, [5] H. Baer, C. hao Chen, M. Drees, F. Paige and X. Tata, [6] S. Dimopoulos and G.F. Giudice, [7] See for example R. Barbieri and A. Strumia, the 460 GeV are covered by the search. are covered by the search,contribution where from the definition the of top fine-tuning Yukawa excludes coupling. (includes) the For References Council. Acknowledgments Part of this workComputing was Facility. produced BCA using would theon like Cambridge checks to University of thank High the K. 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