Universal Extra Dimensions

Universal Extra DimensionsAll Standard Model fields propagate into the bulk, typically 1 or 2 extra dimensions.Momentum conservation principle manifests as a conservation of a parity at each vertex KK parityNaturally provides a Dark Matter candidateExcited modes mimic Standard Model zero modes.Minimal number of extra parametersR, and mH

Toy derivation of scalar LagrangianHeuristic derivation showing how mass terms appear infinite tower of KK modes

Dark Matter CandidatesAnalysis by Servant & TaitNeutral Weak Gauge Boson B1Strongest CDM candidate

Neutrinodisfavored by present limits from direct detection experiments

Why B(1)?The mass matrix that governs the mixing between the neutral weak gauge bosons is

The B(1) is mostly photon

Whats involved?If UED theories are incorrect, the LHC will be able to exclude them in their present form.Cosmological constraints place R within the reach of LHC energies.Confirmation of the theory will require more extensive statistics, because SUSY will have the same signature(s) as UEDs within the statistical reach, at the KK1 level.Require higher statistics better angular resolution of decay products spin determinationCorrelation with cosmological experimentsRequire resolution of higher KK modes for model resolution

Servant, TaitPrediction for B(1)h2hep-ph/0206071Graph plotted in 2002 slightly outdatedLower band should span 0.09 to 0.13 corresponding to m = 750 - 950 GeV, using latest WMAP results

Requirements for Dark Matter CandidacyThere must exist a stability mechanismKK Parity conservationElectrically neutralCharged particles could interact with zero mode, and we would have seen themCoannihilation

Lightest Kaluza-Klein Particle (LKP)Stable by virtue of KK parity conservationAll heavier odd-mode particles eventually annihilate/decay into the LKPKK parity conserved at all levels

radiative corrections to massesat lower limit of RWeak gauge boson masses receive almost no correctionLepton mass correction are a few percentGluons & quark masses receive large corrections

Chart1

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Gluon

B

electron

UV Cutoff(TeV)

% mass correction

R=500GeV,mH=280GeV

kkmasses

50010280501.3636141000.584372515.0211281023.091132515.0211281023.091132535.821591048.740791535.4985711048.681544641.67798328.3355970.2727233.004226

50010.15280501.3640751000.582749515.0957821023.24044515.0957821023.24044535.960991049.028106535.6394211048.969238642.30407628.4608150.2728153.019156

50010.3280501.3645181000.581146515.1693411023.387558515.1693411023.387558536.098321049.311134535.7781691049.252634642.92038628.5840770.2729043.033868

50010.45280501.3649431000.579561515.2418361023.532549515.2418361023.532549536.233641049.589998535.9148761049.531858643.52720928.7054420.2729893.048367

50010.6280501.365351000.577995515.3132981023.675473515.3132981023.675473536.3670091049.86482536.04961049.807029644.12482328.8249650.273073.06266

50010.75280501.3657421000.576447515.3837561023.816389515.3837561023.816389536.4984821050.135713536.1823981050.078263644.71349728.9426990.2731483.076751

50010.9280501.3661181000.574917515.4532381023.955352515.4532381023.955352536.628111050.402788536.3133231050.34567645.29348829.0586980.2732243.090648

50011.05280501.3664791000.573404515.521771024.092416515.521771024.092416536.7559451050.666149536.4424281050.609356645.86504229.1730080.2732963.104354

50011.2280501.3668251000.571908515.5893771024.227632515.5893771024.227632536.8820351050.925898536.5697611050.869421646.42839429.2856790.2733653.117875

50011.35280501.3671581000.570429515.6560861024.361048515.6560861024.361048537.0064281051.182131536.6953711051.125963646.9837729.3967540.2734323.131217

50011.5280501.3674781000.568966515.7219181024.492714515.7219181024.492714537.1291671051.434942536.8193031051.379075647.53138729.5062770.2734963.144384

50011.65280501.3677861000.567519515.7868981024.622672515.7868981024.622672537.2502951051.684419536.9416011051.628848648.07145429.6142910.2735573.15738

50011.8280501.3680811000.566087515.8510461024.750969515.8510461024.750969537.3698551051.93065537.0623061051.875367648.6041729.7208340.2736163.170209

50011.95280501.3683651000.564671515.9143841024.877644515.9143841024.877644537.4878861052.173717537.1814611052.118715649.12972829.8259460.2736733.182877

50012.1280501.3686381000.56327515.9769311025.00274515.9769311025.00274537.6044261052.413699537.2991031052.358972649.64831329.9296630.2737283.195386

50012.25280501.36891000.561883516.0387091025.126294516.0387091025.126294537.7195121052.650673537.415271052.596216650.16010330.0320210.273783.207742

50012.4280501.3691521000.560511516.0997341025.248344516.0997341025.248344537.8331791052.884713537.5299991052.830519650.66526830.1330540.273833.219947

50012.55280501.3693941000.559153516.1600251025.368927516.1600251025.368927537.9454631053.115889537.6433241053.061954651.16397530.2327950.2738793.232005

50012.7280501.3696271000.557808516.21961025.488077516.21961025.488077538.0563961053.344272537.755281053.29059651.65638130.3312760.2739253.24392

50012.85280501.3698511000.556478516.2784761025.605828516.2784761025.605828538.1660091053.569926537.8658971053.516492652.1426430.4285280.273973.255695

50013280501.3700661000.55516516.3366681025.722213516.3366681025.722213538.2743351053.792916537.9752091053.739724652.62289930.524580.2740133.267334

50013.15280501.3702721000.553856516.3941931025.837262516.3941931025.837262538.3814011054.013303538.0832451053.960349653.09730230.619460.2740543.278839

50013.3280501.370471000.552564516.4510651025.951006516.4510651025.951006538.4872381054.231148538.1900341054.178427653.56598530.7131970.2740943.290213

50013.45280501.3706611000.551285516.5072991026.063475516.5072991026.063475538.5918721054.446506538.2956051054.394014654.02908230.8058160.2741323.30146

50013.6280501.3708441000.550019516.562911026.174696516.562911026.174696538.6953311054.659435538.3999841054.607166654.48672130.8973440.2741693.312582

50013.75280501.3710191000.548764516.617911026.284698516.617911026.284698538.7976411054.869987538.5031991054.817939654.93902530.9878050.2742043.323582

50013.9280501.3711881000.547521516.6723141026.393505516.6723141026.393505538.8988261055.078215538.6052741055.026383655.38611431.0772230.2742383.334463

50014.05280501.371351000.54629516.7261341026.501145516.7261341026.501145538.9989111055.28417538.7062341055.232549655.82810431.1656210.274273.345227

50014.2280501.3715061000.545071516.7793831026.607642516.7793831026.607642539.0979191055.487899538.8061041055.436486656.26510831.2530220.2743013.355877

50014.35280501.3716551000.543863516.8320711026.71302516.8320711026.71302539.1958731055.68945538.9049061055.638241656.69723431.3394470.2743313.366414

50014.5280501.3717981000.542665516.8842121026.817302516.8842121026.817302539.2927961055.888868539.0026631055.83786657.12458631.4249170.274363.376842

50014.65280501.3719351000.541479516.9358171026.92051516.9358171026.92051539.3887081056.086199539.0993961056.035388657.54726631.5094530.2743873.387163

50014.8280501.3720661000.540303516.9868951027.022667516.9868951027.022667539.483631056.281485539.1951271056.230867657.96537331.5930750.2744133.397379

50014.95280501.3721921000.539138517.0374591027.123795517.0374591027.123795539.5775821056.474767539.2898761056.424339658.37900331.6758010.2744383.407492

50015.1280501.3723131000.537983517.0875181027.223912517.0875181027.223912539.6705841056.666086539.3836621056.615845658.78824731.7576490.2744633.417504

50015.25280501.3724291000.536838517.1370821027.32304517.1370821027.32304539.7626541056.85548539.4765061056.805424659.19319631.8386390.2744863.427416

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50015.55280501.3726451000.534578517.2347631027.518404517.2347631027.518404539.9440731057.228649539.6594371057.178951659.99055131.998110.2745293.446953

50015.7280501.3727461000.533462517.28291027.614676517.28291027.614676540.0334571057.412495539.749561057.362972660.38312432.0766250.2745493.45658

50015.85280501.3728431000.532356517.3305791027.710034517.3305791027.710034540.121981057.594562539.8388121057.545211660.77173532.1543470.2745693.466116

50016280501.3729351000.531259517.3778081027.804493517.3778081027.804493540.2096581057.774885539.9272081057.725704661.15645932.2312920.2745873.475562

50016.15280501.3730231000.530172517.4245971027.898071517.4245971027.898071540.2965061057.953496540.0147651057.904481661.53737432.3074750.2746053.484919

50016.3280501.3731071000.529093517.4709531027.990784517.4709531027.990784540.3825421058.130427540.1014991058.081576661.9145532.382910.2746213.494191

50016.45280501.3731871000.528023517.5168851028.082647517.5168851028.082647540.4677781058.305709540.1874251058.25702662.28805932.4576120.2746373.503377

50016.6280501.3732631000.526962517.56241028.173677517.56241028.173677540.552231058.479372540.2725571058.430842662.65797132.5315940.2746533.51248

50016.75280501.3733361000.525909517.6075051028.263887517.6075051028.263887540.6359131058.651446540.356911058.603072663.02435132.604870.2746673.521501

50016.9280501.3734041000.524865517.6522081028.353294517.6522081028.353294540.7188391058.821959540.4404981058.77374663.38726532.6774530.2746813.530442

50017.05280501.373471000.523829517.6965171028.44191517.6965171028.44191540.8010231058.990938540.5233351058.942872663.74677632.7493550.2746943.539303

50017.2280501.3735321000.522802517.7404371028.52975517.7404371028.52975540.8824771059.158413540.6054331059.110495664.10294632.8205890.2747063.548087

50017.35280501.373591000.521782517.7839751028.616828517.7839751028.616828540.9632141059.324407540.6868071059.276638664.45583532.8911670.2747183.556795

50017.5280501.3736461000.520771517.8271391028.703155517.8271391028.703155541.0432471059.488948540.7674671059.441324664.80550232.96110.2747293.565428

50017.65280501.3736981000.519767517.8699351028.788746517.8699351028.788746541.1225881059.65206540.8474281059.604579665.15200233.03040.274743.573987

50017.8280501.3737481000.518771517.9123681028.873613517.9123681028.873613541.2012481059.813767540.92671059.766428665.49539233.0990780.274753.582474

50017.95280501.3737941000.517782517.9544451028.957768517.9544451028.957768541.2792381059.974094541.0052951059.926895665.83572533.1671450.2747593.590889

50018.1280501.3738371000.516801517.9961721029.041222517.9961721029.041222541.3565721060.133064541.0832251060.086002666.17305533.2346110.2747673.599234

50018.25280501.3738781000.515827518.0375551029.123987518.0375551029.123987541.4332581060.290698541.1605011060.243772666.50743233.3014860.2747763.607511

50018.4280501.3739161000.51486518.0785991029.206075518.0785991029.206075541.5093081060.44702541.2371341060.400228666.83890633.3677810.2747833.61572

50018.55280501.3739521000.513901518.119311029.287496518.119311029.287496541.5847321060.602051541.3131331060.55539667.16752633.4335050.274793.623862

50018.7280501.3739851000.512948518.1596931029.368262518.1596931029.368262541.659541060.755811541.388511060.709281667.4933433.4986680.2747973.631939

50018.85280501.3740151000.512003518.1997531029.448383518.1997531029.448383541.7337421060.908322541.4632741060.86192667.81639433.5632790.2748033.639951

50019280501.3740441000.511064518.2394961029.527868518.2394961029.527868541.8073481061.059602541.5374351061.013327668.13673233.6273460.2748093.647899

50019.15280501.3740691000.510132518.2789261029.606728518.2789261029.606728541.8803681061.209672541.6110041061.163522668.454433.690880.2748143.655785

50019.3280501.3740931000.509207518.3180481029.684973518.3180481029.684973541.952811061.358551541.6839881061.312525668.7694433.7538880.2748193.66361

50019.45280501.3741141000.508288518.3568681029.762612518.3568681029.762612542.0246831061.506258541.7563981061.460353669.08189533.8163790.2748233.671374

50019.6280501.3741341000.507376518.3953891029.839655518.3953891029.839655542.0959971061.652809541.8282411061.607025669.39180533.8783610.2748273.679078

50019.75280501.3741511000.50647518.4336171029.916111518.4336171029.916111542.1667591061.798224541.8995281061.752559669.6992133.9398420.274833.686723

50019.9280501.3741661000.50557518.4715551029.991988518.4715551029.991988542.2369791061.94252541.9702661061.896973670.0041534.000830.2748333.694311

50020.05280501.3741791000.504677518.5092091030.067295518.5092091030.067295542.3066641062.085713542.0404631062.040282670.30666334.0613330.2748363.701842

50020.2280501.374191000.503789518.5465821030.14204518.5465821030.14204542.3758221062.227821542.1101291062.182504670.60678734.1213570.2748383.709316

50020.35280501.37421000.502908518.5836781030.216233518.5836781030.216233542.4444621062.368858542.179271062.323655670.90455734.1809110.274843.716736

50020.5280501.3742071000.502033518.6205021030.289881518.6205021030.289881542.5125911062.508842542.2478951062.46375671.20000934.2400020.2748413.7241

50020.65280501.3742131000.501163518.6570581030.362992518.6570581030.362992542.5802161062.647788542.316011062.602807671.49317934.2986360.2748433.731412

50020.8280501.3742171000.500299518.6933491030.435574518.6933491030.435574542.6473451062.78571542.3836251062.740838671.78410134.356820.2748433.73867

50020.95280501.3742191000.499441518.7293791030.507634518.7293791030.507634542.7139841062.922625542.4507451062.87786672.07280734.4145610.2748443.745876

50021.1280501.374221000.498589518.7651521030.579181518.7651521030.579181542.7801421063.058545542.5173781063.013887672.35933234.4718660.2748443.75303

50021.25280501.3742191000.497742518.8006721030.65022518.8006721030.65022542.8458251063.193486542.5835311063.148934672.64370534.5287410.2748443.760134

50021.4280501.3742171000.496901518.8359421030.72076518.8359421030.72076542.9110391063.327461542.649211063.283013672.9259634.5851920.2748433.767188

50021.55280501.3742131000.496065518.8709651030.790807518.8709651030.790807542.9757911063.460484542.7144231063.416139673.20612634.6412250.2748433.774193

50021.7280501.3742081000.495234518.9057461030.860368518.9057461030.860368543.0400881063.592568542.7791761063.548325673.48423334.6968470.2748423.781149

50021.85280501.3742011000.494409518.9402871030.92945518.9402871030.92945543.1039361063.723727542.8434751063.679584673.7603134.7520620.274843.788057

50022280501.3741931000.493589518.9745911030.998059518.9745911030.998059543.1673411063.853973542.9073271063.80993674.03438734.8068770.2748393.794918

50022.15280501.3741831000.492774519.0086631031.066202519.0086631031.066202543.2303091063.983318542.9707371063.939373674.30649234.8612980.2748373.801733

50022.3280501.3741721000.491964519.0425041031.133885519.0425041031.133885543.2928461064.111775543.0337121064.067928674.57665134.915330.2748343.808501

50022.45280501.374161000.491159519.0761191031.201115519.0761191031.201115543.3549581064.239356543.0962581064.195605674.84489234.9689780.2748323.815224

50022.6280501.3741471000.490359519.109511031.267896519.109511031.267896543.416651064.366072543.158381064.322417675.11124135.0222480.2748293.821902

50022.75280501.3741321000.489564519.142681031.334236519.142681031.334236543.4779291064.491936543.2200841064.448375675.37572435.0751450.2748263.828536

50022.9280501.3741161000.488774519.1756321031.40014519.1756321031.40014543.5387991064.616958543.2813761064.573491675.63836735.1276730.2748233.835126

50023.05280501.3740991000.487988519.2083691031.465614519.2083691031.465614543.5992671064.74115543.3422611064.697775675.89919435.1798390.274823.841674

50023.2280501.3740811000.487208519.2408931031.530663519.2408931031.530663543.6593361064.864522543.4027431064.821239676.15822935.2316460.2748163.848179

50023.35280501.3740621000.486432519.2732081031.595293519.2732081031.595293543.7190131064.987086543.462831064.943892676.41549735.2830990.2748123.854642

50023.5280501.3740411000.48566519.3053161031.659509519.3053161031.659509543.7783031065.108851543.5225251065.065747676.6710235.3342040.2748083.861063

50023.65280501.374021000.484894519.337221031.723316519.337221031.723316543.837211065.229827543.5818341065.186812676.92482235.3849640.2748043.867444

50023.8280501.3739981000.484131519.3689221031.78672519.3689221031.78672543.8957391065.350026543.6407611065.307098677.17692535.4353850.27483.873784

50023.95280501.3739741000.483374519.4004241031.849725519.4004241031.849725543.9538961065.469456543.6993121065.426615677.42735135.485470.2747953.880085

50024.1280501.373951000.48262519.431731031.912338519.431731031.912338544.0116841065.588127543.7574911065.545372677.67612235.5352240.274793.886346

50024.25280501.3739241000.481871519.4628421031.974561519.4628421031.974561544.0691081065.70605543.8153031065.66338677.92325935.5846520.2747853.892568

50024.4280501.3738981000.481126519.4937621032.036401519.4937621032.036401544.1261741065.823232543.8727521065.780647678.16878335.6337570.274783.898752

50024.55280501.3738711000.480386519.5244931032.097862519.5244931032.097862544.1828851065.939684543.9298431065.897182678.41271435.6825430.2747743.904899

50024.7280501.3738431000.479649519.5550361032.158949519.5550361032.158949544.2392451066.055415543.9865811066.012995678.65507235.7310140.2747693.911007

50024.85280501.3738141000.478917519.5853941032.219666519.5853941032.219666544.295261066.170432544.0429691066.128094678.89587835.7791760.2747633.917079

radiative corrections to massesat upper limit of RWeak gauge boson masses receive almost no correctionLepton mass correction are a few percentGluons & quark masses receive large corrections, but smaller than with smaller R

Chart1

18.7320520.0154581.902499

18.8673880.0152691.917429

19.0005870.0150831.932141

19.1317150.0148991.94664

19.2608330.0147181.960933

19.3880.0145391.975024

19.5132720.0143631.988921

19.6367040.0141892.002627

19.7583460.0140172.016149

19.878250.0138472.02949

19.9964610.0136792.042657

20.1130270.0135142.055653

20.227990.013352.068482

20.3413930.0131892.08115

20.4532770.0130292.093659

20.5636810.0128712.106015

20.6726420.0127152.11822

20.7801960.0125612.130278

20.8863780.0124082.142193

20.9912220.0122582.153968

21.0947590.0121082.165607

21.1970230.0119612.177112

21.2980410.0118152.188486

21.3978440.0116712.199733

21.4964590.0115282.210855

21.5939140.0113872.221855

21.6902340.0112472.232736

21.7854460.0111092.2435

21.8795740.0109722.25415

21.9726410.0108362.264687

22.064670.0107022.275116

22.1556840.0105692.285436

22.2457040.0104382.295652

22.3347510.0103082.305765

22.4228450.0101792.315777

22.5100060.0100512.325689

22.5962530.0099242.335505

22.6816040.0097992.345226

22.7660770.0096752.354853

22.849690.0095522.364389

22.9324590.009432.373835

23.01440.0093092.383192

23.0955310.0091892.392464

23.1758650.009072.40165

23.2554190.0089532.410753

23.3342060.0088362.419774

23.4122410.008722.428715

23.4895390.0086062.437576

23.5661110.0084922.44636

23.6419710.0083792.455068

23.7171330.0082682.463701

23.7916080.0081572.47226

23.8654090.0080472.480747

23.9385470.0079382.489162

24.0110330.007832.497508

24.082880.0077222.505784

24.1540970.0076162.513993

24.2246960.007512.522135

24.2946870.0074062.530212

24.3640790.0073022.538224

24.4328840.0071992.546172

24.5011090.0070962.554058

24.5687660.0069952.561883

24.6358620.0068942.569647

24.7024070.0067942.577351

24.768410.0066942.584996

24.8338790.0065962.592584

24.8988220.0064982.600115

24.9632480.0064012.607589

25.0271640.0063042.615009

25.0905790.0062092.622373

25.1534990.0061142.629685

25.2159330.0060192.636943

25.2778880.0059252.644149

25.339370.0058322.651303

25.4003870.005742.658407

25.4609450.0056482.665461

25.5210510.0055572.672466

25.5807120.0054662.679422

25.6399340.0053762.68633

25.6987230.0052872.693191

25.7570860.0051982.700006

25.8150270.005112.706774

25.8725540.0050232.713497

25.9296720.0049352.720175

25.9863870.0048492.726809

26.0427030.0047632.733399

26.0986270.0046782.739947

26.1541630.0045932.746452

26.2093170.0045092.752915

26.2640950.0044252.759336

26.31850.0043422.765717

26.3725380.0042592.772057

26.4262140.0041772.778358

26.4795320.0040952.784619

26.5324960.0040142.790841

26.5851130.0039332.797025

26.6373850.0038532.803172

26.6893170.0037732.80928

26.7409140.0036942.815352

Gluon

B

electron

UV Cutoff(TeV)

% mass correction

R=1500GeV,mH=120GeV

kkmasses

1500101201500.2318722999.8281851528.5374783036.2215861528.5374783036.2215861558.6811283073.3753191558.6591443073.3708581780.98078218.7320520.0154581.902499

150010.151201500.229042999.8222291528.761443036.6695111528.761443036.6695111559.1164713074.2587481559.094663074.2543421783.01081518.8673880.0152691.917429

150010.31201500.2262472999.8163591528.9821173037.1108641528.9821173037.1108641559.5453113075.128971559.5236683075.1246171785.00880819.0005870.0150831.932141

150010.451201500.2234922999.8105731529.1996033037.5458361529.1996033037.5458361559.9678383075.986371559.9463583075.9820681786.97572819.1317150.0148991.94664

150010.61201500.2207742999.8048681529.413993037.9746091529.413993037.9746091560.3842333076.8313171560.3629113076.8270641788.91249819.2608330.0147181.960933

150010.751201500.2180922999.7992411529.6253633038.3973571529.6253633038.3973571560.794673077.6641651560.7735023077.659961790.82000219.3880.0145391.975024

150010.91201500.2154452999.7936921529.8338083038.8142471529.8338083038.8142471561.1993163078.4852521561.1782983078.4810931792.69908519.5132720.0143631.988921

150011.051201500.2128332999.7882181530.0394043039.2254381530.0394043039.2254381561.5983313079.2949031561.5774583079.2907881794.55055819.6367040.0141892.002627

150011.21201500.2102532999.7828171530.2422283039.6310861530.2422283039.6310861561.9918683080.093431561.9711373080.0893581796.37519719.7583460.0140172.016149

150011.351201500.2077072999.7774861530.4423533040.0313361530.4423533040.0313361562.3800733080.8811311562.359483080.87711798.17374619.878250.0138472.02949

150011.51201500.2051912999.7722251530.6398513040.4263311530.6398513040.4263311562.7630883081.6582931562.742633081.6543021799.94691919.9964610.0136792.042657

150011.651201500.2027072999.7670321530.8347893040.8162081530.8347893040.8162081563.141053082.4251921563.1207233082.421241801.69540120.1130270.0135142.055653

150011.81201500.2002532999.7619041531.0272333041.2010971531.0272333041.2010971563.5140883083.1820931563.4938893083.1781791803.41985120.227990.013352.068482

150011.951201500.1978292999.756841531.2172473041.5811231531.2172473041.5811231563.8823283083.9292521563.8622533083.9253741805.12090220.3413930.0131892.08115

150012.11201500.1954332999.7518381531.404893041.956411531.404893041.956411564.245893084.6669141564.2259383084.6630711806.79916220.4532770.0130292.093659

150012.251201500.1930652999.7468981531.5902213042.3270721531.5902213042.3270721564.6048923085.3953141564.5850583085.3915051808.45521620.5636810.0128712.106015

150012.41201500.1907252999.7420171531.7732973042.6932231531.7732973042.6932231564.9594453086.1146811564.9397273086.1109061810.08962720.6726420.0127152.11822

150012.551201500.1884122999.7371941531.9541713043.0549721531.9541713043.0549721565.3096573086.8252341565.2900523086.8214911811.70293720.7801960.0125612.130278

150012.71201500.1861252999.7324281532.1328963043.4124221532.1328963043.4124221565.6556323087.5271851565.6361383087.5234731813.29566920.8863780.0124082.142193

150012.851201500.1838642999.7277181532.3095233043.7656751532.3095233043.7656751565.9974713088.2207371565.9780863088.2170561814.86832520.9912220.0122582.153968

1500131201500.1816272999.7230621532.4840993044.1148291532.4840993044.1148291566.335273088.9060871566.3159913088.9024361816.42139221.0947590.0121082.165607

150013.151201500.1794162999.7184581532.6566733044.4599771532.6566733044.4599771566.6691233089.5834251566.6499483089.5798031817.95533821.1970230.0119612.177112

150013.31201500.1772282999.7139071532.827293044.801211532.827293044.801211566.9991213090.2529361566.9800473090.2493421819.47061321.2980410.0118152.188486

150013.451201500.1750642999.7094061532.9959933045.1386161532.9959933045.1386161567.325353090.9147951567.3063753090.9112291820.96765521.3978440.0116712.199733

150013.61201500.1729232999.7049541533.1628253045.472281533.1628253045.472281567.6478963091.5691761567.6290183091.5656351822.44688321.4964590.0115282.210855

150013.751201500.1708042999.7005511533.3278273045.8022831533.3278273045.8022831567.9668393092.2162421567.9480563092.2127281823.90870621.5939140.0113872.221855

150013.91201500.1687082999.6961961533.4910383046.1287071533.4910383046.1287071568.2822583092.8561541568.2635693092.8526661825.35351621.6902340.0112472.232736

150014.051201500.1666332999.6918871533.6524983046.4516261533.6524983046.4516261568.594233093.4890691568.5756333093.4856051826.78169421.7854460.0111092.2435

150014.21201500.1645792999.6876231533.8122433046.7711171533.8122433046.7711171568.9028293094.1151341568.8843213094.1116941828.19360721.8795740.0109722.25415

150014.351201500.1625462999.6834041533.970313047.087251533.970313047.087251569.2081263094.7344971569.1897063094.7310811829.58961121.9726410.0108362.264687

150014.51201500.1605342999.6792281534.1267333047.4000951534.1267333047.4000951569.5101913095.3472971569.4918573095.3439041830.97005122.064670.0107022.275116

150014.651201500.1585412999.6750951534.2815463047.7097211534.2815463047.7097211569.8090913095.9536711569.7908413095.9503011832.33525922.1556840.0105692.285436

150014.81201500.1565682999.6710041534.4347813048.0161931534.4347813048.0161931570.104893096.5537521570.0867233096.5504031833.68555922.2457040.0104382.295652

150014.951201500.1546142999.6669531534.5864723048.3195741534.5864723048.3195741570.3976523097.1476671570.3795673097.144341835.02126422.3347510.0103082.305765

150015.11201500.1526792999.6629431534.7366483048.6199271534.7366483048.6199271570.6874393097.7355411570.6694333097.7322351836.34267622.4228450.0101792.315777

150015.251201500.1507632999.6589721534.885343048.917311534.885343048.917311570.9743083098.3174941570.9563813098.3142081837.65009122.5100060.0100512.325689

150015.41201500.1488642999.655041535.0325763049.2117831535.0325763049.2117831571.2583193098.8936431571.2404693098.8903781838.94379222.5962530.0099242.335505

150015.551201500.1469832999.6511461535.1783863049.5034011535.1783863049.5034011571.5395273099.4641021571.5217533099.4608571840.22405822.6816040.0097992.345226

150015.71201500.145122999.6472891535.3227953049.792221535.3227953049.792221571.8179863100.0289821571.8002863100.0257561841.49115522.7660770.0096752.354853

150015.851201500.1432742999.6434681535.4658313050.0782921535.4658313050.0782921572.093753100.5883891572.0761233100.5851811842.74534422.849690.0095522.364389

1500161201500.1414452999.6396841535.607523050.361671535.607523050.361671572.3668693101.1424271572.3493133101.1392381843.98687922.9324590.009432.373835

150016.151201500.1396322999.6359341535.7478873050.6424041535.7478873050.6424041572.6373933101.6911991572.6199083101.6880281845.21600523.01440.0093092.383192

150016.31201500.1378352999.6322191535.8869563050.9205421535.8869563050.9205421572.905373102.2348011572.8879543102.2316471846.43296123.0955310.0091892.392464

150016.451201500.1360552999.6285371536.0247513051.1961321536.0247513051.1961321573.1708483102.7733291573.1535013102.7701941847.63797823.1758650.009072.40165

150016.61201500.134292999.6248891536.1612953051.4692211536.1612953051.4692211573.4338733103.3068781573.4165933103.3037591848.83128223.2554190.0089532.410753

150016.751201500.132542999.6212731536.2966113051.7398531536.2966113051.7398531573.6944893103.8355361573.6772743103.8324341850.01309323.3342060.0088362.419774

150016.91201500.1308062999.617691536.4307213052.0080721536.4307213052.0080721573.9527393104.3593931573.9355893104.3563071851.18362223.4122410.008722.428715

150017.051201500.1290862999.6141381536.5636453052.2739211536.5636453052.2739211574.2086653104.8785331574.191583104.8754641852.34307823.4895390.0086062.437576

150017.21201500.1273812999.6106171536.6954063052.5374411536.6954063052.5374411574.462313105.3930411574.4452873105.3899871853.49166323.5661110.0084922.44636

150017.351201500.1256912999.6071261536.8260223052.7986731536.8260223052.7986731574.7137123105.9029971574.6967513105.8999591854.62957223.6419710.0083792.455068

150017.51201500.1240142999.6036651536.9555133053.0576571536.9555133053.0576571574.962913106.408481574.946013106.4054571855.75699623.7171330.0082682.463701

150017.651201500.1223522999.6002341537.08393053.314431537.08393053.314431575.2099433106.9095691575.1931033106.9065611856.87412223.7916080.0081572.47226

150017.81201500.1207032999.5968321537.21123053.569031537.21123053.569031575.4548483107.4063371575.4380673107.4033441857.98113223.8654090.0080472.480747

150017.951201500.1190672999.5934581537.3374323053.8214931537.3374323053.8214931575.697663107.8988581575.6809383107.8958791859.078223.9385470.0079382.489162

150018.11201500.1174452999.5901111537.4626133054.0718561537.4626133054.0718561575.9384163108.3872031575.921753108.3842391860.165524.0110330.007832.497508

150018.251201500.1158362999.5867931537.5867613054.3201521537.5867613054.3201521576.1771483108.8714431576.1605393108.8684921861.24319924.082880.0077222.505784

150018.41201500.1142392999.5835011537.7098933054.5664161537.7098933054.5664161576.413893109.3516441576.3973373109.3487071862.3114624.1540970.0076162.513993

150018.551201500.1126552999.5802361537.8320253054.810681537.8320253054.810681576.6486763109.8278731576.6321783109.824951863.37044324.2246960.007512.522135

150018.71201500.1110842999.5769971537.9531733055.0529771537.9531733055.0529771576.8815363110.3001951576.8650923110.2972851864.42030324.2946870.0074062.530212

150018.851201500.1095252999.5737841538.0733543055.2933381538.0733543055.2933381577.1125033110.7686731577.0961123110.7657751865.46119124.3640790.0073022.538224

1500191201500.1079782999.5705971538.1925823055.5317941538.1925823055.5317941577.3416063111.2333681577.3252673111.2304831866.49325624.4328840.0071992.546172

150019.151201500.1064422999.5674341538.3108733055.7683751538.3108733055.7683751577.5688743111.694341577.5525873111.6914681867.5166424.5011090.0070962.554058

150019.31201500.1049192999.5642961538.428243056.003111538.428243056.003111577.7943373112.1516481577.7781023112.1487881868.53148624.5687660.0069952.561883

150019.451201500.1034072999.5611821538.5446993056.2360281538.5446993056.2360281578.0180233112.6053491578.0018383112.6025011869.53793124.6358620.0068942.569647

150019.61201500.1019062999.5580921538.6602633056.4671561538.6602633056.4671561578.239963113.0554991578.2238253113.0526641870.53610824.7024070.0067942.577351

150019.751201500.1004162999.5550251538.7749463056.6965231538.7749463056.6965231578.4601743113.5021531578.4440883113.4993291871.52614924.768410.0066942.584996

150019.91201500.0989372999.5519811538.8887623056.9241531538.8887623056.9241531578.6786923113.9453651578.6626543113.9425521872.50818124.8338790.0065962.592584

150020.051201500.0974692999.548961539.0017223057.1500751539.0017223057.1500751578.8955393114.3851861578.8795483114.3823851873.4823324.8988220.0064982.600115

150020.21201500.0960122999.5459621539.1138413057.3743121539.1138413057.3743121579.110743114.8216671579.0947973114.8188771874.44871824.9632480.0064012.607589

150020.351201500.0945662999.5429861539.225133057.5968911539.225133057.5968911579.3243213115.2548591579.3084243115.252081875.40746325.0271640.0063042.615009

150020.51201500.0931292999.5400311539.3356023057.8178341539.3356023057.8178341579.5363053115.6848091579.5204543115.6820421876.35868325.0905790.0062092.622373

150020.651201500.0917032999.5370981539.4452693058.0371681539.4452693058.0371681579.7467153116.1115671579.730913116.108811877.30249125.1534990.0061142.629685

150020.81201500.0902872999.5341861539.5541413058.2549131539.5541413058.2549131579.9555753116.5351781579.9398153116.5324321878.23899925.2159330.0060192.636943

150020.951201500.0888812999.5312951539.6622323058.4710941539.6622323058.4710941580.1629083116.9556891580.1471913116.9529531879.16831625.2778880.0059252.644149

150021.11201500.0874852999.5284241539.7695513058.6857331539.7695513058.6857331580.3687343117.3731431580.3530613117.3704181880.09054925.339370.0058322.651303

150021.251201500.0860982999.5255741539.876113058.8988511539.876113058.8988511580.5730763117.7875851580.5574473117.784871881.00580125.4003870.005742.658407

150021.41201500.0847212999.5227441539.981923059.110471539.981923059.110471580.7759553118.1990571580.7603683118.1963521881.91417425.4609450.0056482.665461

150021.551201500.0833532999.5199331540.086993059.3206111540.086993059.3206111580.9773913118.6076011580.9618463118.6049061882.8157725.5210510.0055572.672466

150021.71201500.0819952999.5171421540.1913323059.5292941540.1913323059.5292941581.1774043119.0132591581.1619013119.0105731883.71068425.5807120.0054662.679422

150021.851201500.0806462999.514371540.2949553059.736541540.2949553059.736541581.3760153119.416071581.3605533119.4133941884.59901225.6399340.0053762.68633

1500221201500.0793052999.5116171540.3978693059.9423681540.3978693059.9423681581.5732433119.8160741581.5578223119.8134071885.48084925.6987230.0052872.693191

150022.151201500.0779742999.5088821540.5000833060.1467971540.5000833060.1467971581.7691063120.2133091581.7537253120.2106521886.35628625.7570860.0051982.700006

150022.31201500.0766522999.5061661540.6016083060.3498461540.6016083060.3498461581.9636243120.6078131581.9482823120.6051651887.22541225.8150270.005112.706774

150022.451201500.0753382999.5034681540.7024523060.5515351540.7024523060.5515351582.1568143120.9996231582.1415123120.9969841888.08831625.8725540.0050232.713497

150022.61201500.0740322999.5007881540.8026253060.751881540.8026253060.751881582.3486953121.3887751582.3334313121.3861451888.94508325.9296720.0049352.720175

150022.751201500.0727352999.4981261540.9021353060.95091540.9021353060.95091582.5392833121.7753051582.5240573121.7726841889.79579825.9863870.0048492.726809

150022.91201500.0714472999.4954811541.0009913061.1486121541.0009913061.1486121582.7285963122.1592471582.7134083122.1566351890.64054326.0427030.0047632.733399

150023.051201500.0701672999.4928531541.0992013061.3450331541.0992013061.3450331582.9166513122.5406361582.9015013122.5380331891.47939926.0986270.0046782.739947

150023.21201500.0688942999.4902421541.1967753061.540181541.1967753061.540181583.1034643122.9195051583.0883513122.916911892.31244626.1541630.0045932.746452

150023.351201500.067632999.4876481541.2937193061.7340691541.2937193061.7340691583.2890513123.2958871583.2739753123.29331893.1397626.2093170.0045092.752915

150023.51201500.0663742999.4850711541.3900433061.9267171541.3900433061.9267171583.4734293123.6698141583.4583893123.6672361893.9614226.2640950.0044252.759336

150023.651201500.0651262999.482511541.4857543062.1181391541.4857543062.1181391583.6566123124.0413171583.6416083124.0387471894.77749826.31850.0043422.765717

150023.81201500.0638852999.4799651541.580863062.308351541.580863062.308351583.8386173124.4104281583.8236483124.4078661895.58806926.3725380.0042592.772057

150023.951201500.0626522999.4774361541.6753683062.4973671541.6753683062.4973671584.0194573124.7771771584.0045233124.7746231896.39320426.4262140.0041772.778358

150024.11201500.0614262999.4749221541.7692873062.6852041541.7692873062.6852041584.1991483125.1415931584.1842493125.1390471897.19297326.4795320.0040952.784619

150024.251201500.0602082999.4724251541.8626223062.8718751541.8626223062.8718751584.3777043125.5037061584.3628393125.5011671897.98744626.5324960.0040142.790841

150024.41201500.0589982999.4699421541.9553823063.0573951541.9553823063.0573951584.5551393125.8635441584.5403083125.8610141898.77669126.5851130.0039332.797025

150024.551201500.0577942999.4674751542.0475743063.2417771542.0475743063.2417771584.7314673126.2211361584.716673126.2186131899.56077426.6373850.0038532.803172

150024.71201500.0565982999.4650231542.1392043063.4250371542.1392043063.4250371584.9067023126.576511584.8919383126.5739941900.3397626.6893170.0037732.80928

150024.851201500.0554092999.4625861542.2302793063.6071871542.2302793063.6071871585.0808573126.9296921585.0661253126.9271841901.11371326.7409140.0036942.815352

Chart1

18.7320520.0154581.902499

18.8673880.0152691.917429

19.0005870.0150831.932141

19.1317150.0148991.94664

19.2608330.0147181.960933

19.3880.0145391.975024

19.5132720.0143631.988921

19.6367040.0141892.002627

19.7583460.0140172.016149

19.878250.0138472.02949

19.9964610.0136792.042657

20.1130270.0135142.055653

20.227990.013352.068482

20.3413930.0131892.08115

20.4532770.0130292.093659

20.5636810.0128712.106015

20.6726420.0127152.11822

20.7801960.0125612.130278

20.8863780.0124082.142193

20.9912220.0122582.153968

21.0947590.0121082.165607

21.1970230.0119612.177112

21.2980410.0118152.188486

21.3978440.0116712.199733

21.4964590.0115282.210855

21.5939140.0113872.221855

21.6902340.0112472.232736

21.7854460.0111092.2435

21.8795740.0109722.25415

21.9726410.0108362.264687

22.064670.0107022.275116

22.1556840.0105692.285436

22.2457040.0104382.295652

22.3347510.0103082.305765

22.4228450.0101792.315777

22.5100060.0100512.325689

22.5962530.0099242.335505

22.6816040.0097992.345226

22.7660770.0096752.354853

22.849690.0095522.364389

22.9324590.009432.373835

23.01440.0093092.383192

23.0955310.0091892.392464

23.1758650.009072.40165

23.2554190.0089532.410753

23.3342060.0088362.419774

23.4122410.008722.428715

23.4895390.0086062.437576

23.5661110.0084922.44636

23.6419710.0083792.455068

23.7171330.0082682.463701

23.7916080.0081572.47226

23.8654090.0080472.480747

23.9385470.0079382.489162

24.0110330.007832.497508

24.082880.0077222.505784

24.1540970.0076162.513993

24.2246960.007512.522135

24.2946870.0074062.530212

24.3640790.0073022.538224

24.4328840.0071992.546172

24.5011090.0070962.554058

24.5687660.0069952.561883

24.6358620.0068942.569647

24.7024070.0067942.577351

24.768410.0066942.584996

24.8338790.0065962.592584

24.8988220.0064982.600115

24.9632480.0064012.607589

25.0271640.0063042.615009

25.0905790.0062092.622373

25.1534990.0061142.629685

25.2159330.0060192.636943

25.2778880.0059252.644149

25.339370.0058322.651303

25.4003870.005742.658407

25.4609450.0056482.665461

25.5210510.0055572.672466

25.5807120.0054662.679422

25.6399340.0053762.68633

25.6987230.0052872.693191

25.7570860.0051982.700006

25.8150270.005112.706774

25.8725540.0050232.713497

25.9296720.0049352.720175

25.9863870.0048492.726809

26.0427030.0047632.733399

26.0986270.0046782.739947

26.1541630.0045932.746452

26.2093170.0045092.752915

26.2640950.0044252.759336

26.31850.0043422.765717

26.3725380.0042592.772057

26.4262140.0041772.778358

26.4795320.0040952.784619

26.5324960.0040142.790841

26.5851130.0039332.797025

26.6373850.0038532.803172

26.6893170.0037732.80928

26.7409140.0036942.815352

Gluon

B

electron

UV Cutoff(TeV)

% mass correction

R=1500GeV,mH=280GeV

kkmasses

1500102801500.2318722999.8281851528.5374783036.2215861528.5374783036.2215861558.6811283073.3753191558.6591443073.3708581780.98078218.7320520.0154581.902499

150010.152801500.229042999.8222291528.761443036.6695111528.761443036.6695111559.1164713074.2587481559.094663074.2543421783.01081518.8673880.0152691.917429

150010.32801500.2262472999.8163591528.9821173037.1108641528.9821173037.1108641559.5453113075.128971559.5236683075.1246171785.00880819.0005870.0150831.932141

150010.452801500.2234922999.8105731529.1996033037.5458361529.1996033037.5458361559.9678383075.986371559.9463583075.9820681786.97572819.1317150.0148991.94664

150010.62801500.2207742999.8048681529.413993037.9746091529.413993037.9746091560.3842333076.8313171560.3629113076.8270641788.91249819.2608330.0147181.960933

150010.752801500.2180922999.7992411529.6253633038.3973571529.6253633038.3973571560.794673077.6641651560.7735023077.659961790.82000219.3880.0145391.975024

150010.92801500.2154452999.7936921529.8338083038.8142471529.8338083038.8142471561.1993163078.4852521561.1782983078.4810931792.69908519.5132720.0143631.988921

150011.052801500.2128332999.7882181530.0394043039.2254381530.0394043039.2254381561.5983313079.2949031561.5774583079.2907881794.55055819.6367040.0141892.002627

150011.22801500.2102532999.7828171530.2422283039.6310861530.2422283039.6310861561.9918683080.093431561.9711373080.0893581796.37519719.7583460.0140172.016149

150011.352801500.2077072999.7774861530.4423533040.0313361530.4423533040.0313361562.3800733080.8811311562.359483080.87711798.17374619.878250.0138472.02949

150011.52801500.2051912999.7722251530.6398513040.4263311530.6398513040.4263311562.7630883081.6582931562.742633081.6543021799.94691919.9964610.0136792.042657

150011.652801500.2027072999.7670321530.8347893040.8162081530.8347893040.8162081563.141053082.4251921563.1207233082.421241801.69540120.1130270.0135142.055653

150011.82801500.2002532999.7619041531.0272333041.2010971531.0272333041.2010971563.5140883083.1820931563.4938893083.1781791803.41985120.227990.013352.068482

150011.952801500.1978292999.756841531.2172473041.5811231531.2172473041.5811231563.8823283083.9292521563.8622533083.9253741805.12090220.3413930.0131892.08115

150012.12801500.1954332999.7518381531.404893041.956411531.404893041.956411564.245893084.6669141564.2259383084.6630711806.79916220.4532770.0130292.093659

150012.252801500.1930652999.7468981531.5902213042.3270721531.5902213042.3270721564.6048923085.3953141564.5850583085.3915051808.45521620.5636810.0128712.106015

150012.42801500.1907252999.7420171531.7732973042.6932231531.7732973042.6932231564.9594453086.1146811564.9397273086.1109061810.08962720.6726420.0127152.11822

150012.552801500.1884122999.7371941531.9541713043.0549721531.9541713043.0549721565.3096573086.8252341565.2900523086.8214911811.70293720.7801960.0125612.130278

150012.72801500.1861252999.7324281532.1328963043.4124221532.1328963043.4124221565.6556323087.5271851565.6361383087.5234731813.29566920.8863780.0124082.142193

150012.852801500.1838642999.7277181532.3095233043.7656751532.3095233043.7656751565.9974713088.2207371565.9780863088.2170561814.86832520.9912220.0122582.153968

1500132801500.1816272999.7230621532.4840993044.1148291532.4840993044.1148291566.335273088.9060871566.3159913088.9024361816.42139221.0947590.0121082.165607

150013.152801500.1794162999.7184581532.6566733044.4599771532.6566733044.4599771566.6691233089.5834251566.6499483089.5798031817.95533821.1970230.0119612.177112

150013.32801500.1772282999.7139071532.827293044.801211532.827293044.801211566.9991213090.2529361566.9800473090.2493421819.47061321.2980410.0118152.188486

150013.452801500.1750642999.7094061532.9959933045.1386161532.9959933045.1386161567.325353090.9147951567.3063753090.9112291820.96765521.3978440.0116712.199733

150013.62801500.1729232999.7049541533.1628253045.472281533.1628253045.472281567.6478963091.5691761567.6290183091.5656351822.44688321.4964590.0115282.210855

150013.752801500.1708042999.7005511533.3278273045.8022831533.3278273045.8022831567.9668393092.2162421567.9480563092.2127281823.90870621.5939140.0113872.221855

150013.92801500.1687082999.6961961533.4910383046.1287071533.4910383046.1287071568.2822583092.8561541568.2635693092.8526661825.35351621.6902340.0112472.232736

150014.052801500.1666332999.6918871533.6524983046.4516261533.6524983046.4516261568.594233093.4890691568.5756333093.4856051826.78169421.7854460.0111092.2435

150014.22801500.1645792999.6876231533.8122433046.7711171533.8122433046.7711171568.9028293094.1151341568.8843213094.1116941828.19360721.8795740.0109722.25415

150014.352801500.1625462999.6834041533.970313047.087251533.970313047.087251569.2081263094.7344971569.1897063094.7310811829.58961121.9726410.0108362.264687

150014.52801500.1605342999.6792281534.1267333047.4000951534.1267333047.4000951569.5101913095.3472971569.4918573095.3439041830.97005122.064670.0107022.275116

150014.652801500.1585412999.6750951534.2815463047.7097211534.2815463047.7097211569.8090913095.9536711569.7908413095.9503011832.33525922.1556840.0105692.285436

150014.82801500.1565682999.6710041534.4347813048.0161931534.4347813048.0161931570.104893096.5537521570.0867233096.5504031833.68555922.2457040.0104382.295652

150014.952801500.1546142999.6669531534.5864723048.3195741534.5864723048.3195741570.3976523097.1476671570.3795673097.144341835.02126422.3347510.0103082.305765

150015.12801500.1526792999.6629431534.7366483048.6199271534.7366483048.6199271570.6874393097.7355411570.6694333097.7322351836.34267622.4228450.0101792.315777

150015.252801500.1507632999.6589721534.885343048.917311534.885343048.917311570.9743083098.3174941570.9563813098.3142081837.65009122.5100060.0100512.325689

150015.42801500.1488642999.655041535.0325763049.2117831535.0325763049.2117831571.2583193098.8936431571.2404693098.8903781838.94379222.5962530.0099242.335505

150015.552801500.1469832999.6511461535.1783863049.5034011535.1783863049.5034011571.5395273099.4641021571.5217533099.4608571840.22405822.6816040.0097992.345226

150015.72801500.145122999.6472891535.3227953049.792221535.3227953049.792221571.8179863100.0289821571.8002863100.0257561841.49115522.7660770.0096752.354853

150015.852801500.1432742999.6434681535.4658313050.0782921535.4658313050.0782921572.093753100.5883891572.0761233100.5851811842.74534422.849690.0095522.364389

1500162801500.1414452999.6396841535.607523050.361671535.607523050.361671572.3668693101.1424271572.3493133101.1392381843.98687922.9324590.009432.373835

150016.152801500.1396322999.6359341535.7478873050.6424041535.7478873050.6424041572.6373933101.6911991572.6199083101.6880281845.21600523.01440.0093092.383192

150016.32801500.1378352999.6322191535.8869563050.9205421535.8869563050.9205421572.905373102.2348011572.8879543102.2316471846.43296123.0955310.0091892.392464

150016.452801500.1360552999.6285371536.0247513051.1961321536.0247513051.1961321573.1708483102.7733291573.1535013102.7701941847.63797823.1758650.009072.40165

150016.62801500.134292999.6248891536.1612953051.4692211536.1612953051.4692211573.4338733103.3068781573.4165933103.3037591848.83128223.2554190.0089532.410753

150016.752801500.132542999.6212731536.2966113051.7398531536.2966113051.7398531573.6944893103.8355361573.6772743103.8324341850.01309323.3342060.0088362.419774

150016.92801500.1308062999.617691536.4307213052.0080721536.4307213052.0080721573.9527393104.3593931573.9355893104.3563071851.18362223.4122410.008722.428715

150017.052801500.1290862999.6141381536.5636453052.2739211536.5636453052.2739211574.2086653104.8785331574.191583104.8754641852.34307823.4895390.0086062.437576

150017.22801500.1273812999.6106171536.6954063052.5374411536.6954063052.5374411574.462313105.3930411574.4452873105.3899871853.49166323.5661110.0084922.44636

150017.352801500.1256912999.6071261536.8260223052.7986731536.8260223052.7986731574.7137123105.9029971574.6967513105.8999591854.62957223.6419710.0083792.455068

150017.52801500.1240142999.6036651536.9555133053.0576571536.9555133053.0576571574.962913106.408481574.946013106.4054571855.75699623.7171330.0082682.463701

150017.652801500.1223522999.6002341537.08393053.314431537.08393053.314431575.2099433106.9095691575.1931033106.9065611856.87412223.7916080.0081572.47226

150017.82801500.1207032999.5968321537.21123053.569031537.21123053.569031575.4548483107.4063371575.4380673107.4033441857.98113223.8654090.0080472.480747

150017.952801500.1190672999.5934581537.3374323053.8214931537.3374323053.8214931575.697663107.8988581575.6809383107.8958791859.078223.9385470.0079382.489162

150018.12801500.1174452999.5901111537.4626133054.0718561537.4626133054.0718561575.9384163108.3872031575.921753108.3842391860.165524.0110330.007832.497508

150018.252801500.1158362999.5867931537.5867613054.3201521537.5867613054.3201521576.1771483108.8714431576.1605393108.8684921861.24319924.082880.0077222.505784

150018.42801500.1142392999.5835011537.7098933054.5664161537.7098933054.5664161576.413893109.3516441576.3973373109.3487071862.3114624.1540970.0076162.513993

150018.552801500.1126552999.5802361537.8320253054.810681537.8320253054.810681576.6486763109.8278731576.6321783109.824951863.37044324.2246960.007512.522135

150018.72801500.1110842999.5769971537.9531733055.0529771537.9531733055.0529771576.8815363110.3001951576.8650923110.2972851864.42030324.2946870.0074062.530212

150018.852801500.1095252999.5737841538.0733543055.2933381538.0733543055.2933381577.1125033110.7686731577.0961123110.7657751865.46119124.3640790.0073022.538224

1500192801500.1079782999.5705971538.1925823055.5317941538.1925823055.5317941577.3416063111.2333681577.3252673111.2304831866.49325624.4328840.0071992.546172

150019.152801500.1064422999.5674341538.3108733055.7683751538.3108733055.7683751577.5688743111.694341577.5525873111.6914681867.5166424.5011090.0070962.554058

150019.32801500.1049192999.5642961538.428243056.003111538.428243056.003111577.7943373112.1516481577.7781023112.1487881868.53148624.5687660.0069952.561883

150019.452801500.1034072999.5611821538.5446993056.2360281538.5446993056.2360281578.0180233112.6053491578.0018383112.6025011869.53793124.6358620.0068942.569647

150019.62801500.1019062999.5580921538.6602633056.4671561538.6602633056.4671561578.239963113.0554991578.2238253113.0526641870.53610824.7024070.0067942.577351

150019.752801500.1004162999.5550251538.7749463056.6965231538.7749463056.6965231578.4601743113.5021531578.4440883113.4993291871.52614924.768410.0066942.584996

150019.92801500.0989372999.5519811538.8887623056.9241531538.8887623056.9241531578.6786923113.9453651578.6626543113.9425521872.50818124.8338790.0065962.592584

150020.052801500.0974692999.548961539.0017223057.1500751539.0017223057.1500751578.8955393114.3851861578.8795483114.3823851873.4823324.8988220.0064982.600115

150020.22801500.0960122999.5459621539.1138413057.3743121539.1138413057.3743121579.110743114.8216671579.0947973114.8188771874.44871824.9632480.0064012.607589

150020.352801500.0945662999.5429861539.225133057.5968911539.225133057.5968911579.3243213115.2548591579.3084243115.252081875.40746325.0271640.0063042.615009

150020.52801500.0931292999.5400311539.3356023057.8178341539.3356023057.8178341579.5363053115.6848091579.5204543115.6820421876.35868325.0905790.0062092.622373

150020.652801500.0917032999.5370981539.4452693058.0371681539.4452693058.0371681579.7467153116.1115671579.730913116.108811877.30249125.1534990.0061142.629685

150020.82801500.0902872999.5341861539.5541413058.2549131539.5541413058.2549131579.9555753116.5351781579.9398153116.5324321878.23899925.2159330.0060192.636943

150020.952801500.0888812999.5312951539.6622323058.4710941539.6622323058.4710941580.1629083116.9556891580.1471913116.9529531879.16831625.2778880.0059252.644149

150021.12801500.0874852999.5284241539.7695513058.6857331539.7695513058.6857331580.3687343117.3731431580.3530613117.3704181880.09054925.339370.0058322.651303

150021.252801500.0860982999.5255741539.876113058.8988511539.876113058.8988511580.5730763117.7875851580.5574473117.784871881.00580125.4003870.005742.658407

150021.42801500.0847212999.5227441539.981923059.110471539.981923059.110471580.7759553118.1990571580.7603683118.1963521881.91417425.4609450.0056482.665461

150021.552801500.0833532999.5199331540.086993059.3206111540.086993059.3206111580.9773913118.6076011580.9618463118.6049061882.8157725.5210510.0055572.672466

150021.72801500.0819952999.5171421540.1913323059.5292941540.1913323059.5292941581.1774043119.0132591581.1619013119.0105731883.71068425.5807120.0054662.679422

150021.852801500.0806462999.514371540.2949553059.736541540.2949553059.736541581.3760153119.416071581.3605533119.4133941884.59901225.6399340.0053762.68633

1500222801500.0793052999.5116171540.3978693059.9423681540.3978693059.9423681581.5732433119.8160741581.5578223119.8134071885.48084925.6987230.0052872.693191

150022.152801500.0779742999.5088821540.5000833060.1467971540.5000833060.1467971581.7691063120.2133091581.7537253120.2106521886.35628625.7570860.0051982.700006

150022.32801500.0766522999.5061661540.6016083060.3498461540.6016083060.3498461581.9636243120.6078131581.9482823120.6051651887.22541225.8150270.005112.706774

150022.452801500.0753382999.5034681540.7024523060.5515351540.7024523060.5515351582.1568143120.9996231582.1415123120.9969841888.08831625.8725540.0050232.713497

150022.62801500.0740322999.5007881540.8026253060.751881540.8026253060.751881582.3486953121.3887751582.3334313121.3861451888.94508325.9296720.0049352.720175

150022.752801500.0727352999.4981261540.9021353060.95091540.9021353060.95091582.5392833121.7753051582.5240573121.7726841889.79579825.9863870.0048492.726809

150022.92801500.0714472999.4954811541.0009913061.1486121541.0009913061.1486121582.7285963122.1592471582.7134083122.1566351890.64054326.0427030.0047632.733399

150023.052801500.0701672999.4928531541.0992013061.3450331541.0992013061.3450331582.9166513122.5406361582.9015013122.5380331891.47939926.0986270.0046782.739947

150023.22801500.0688942999.4902421541.1967753061.540181541.1967753061.540181583.1034643122.9195051583.0883513122.916911892.31244626.1541630.0045932.746452

150023.352801500.067632999.4876481541.2937193061.7340691541.2937193061.7340691583.2890513123.2958871583.2739753123.29331893.1397626.2093170.0045092.752915

150023.52801500.0663742999.4850711541.3900433061.9267171541.3900433061.9267171583.4734293123.6698141583.4583893123.6672361893.9614226.2640950.0044252.759336

150023.652801500.0651262999.482511541.4857543062.1181391541.4857543062.1181391583.6566123124.0413171583.6416083124.0387471894.77749826.31850.0043422.765717

150023.82801500.0638852999.4799651541.580863062.308351541.580863062.308351583.8386173124.4104281583.8236483124.4078661895.58806926.3725380.0042592.772057

150023.952801500.0626522999.4774361541.6753683062.4973671541.6753683062.4973671584.0194573124.7771771584.0045233124.7746231896.39320426.4262140.0041772.778358

150024.12801500.0614262999.4749221541.7692873062.6852041541.7692873062.6852041584.1991483125.1415931584.1842493125.1390471897.19297326.4795320.0040952.784619

150024.252801500.0602082999.4724251541.8626223062.8718751541.8626223062.8718751584.3777043125.5037061584.3628393125.5011671897.98744626.5324960.0040142.790841

150024.42801500.0589982999.4699421541.9553823063.0573951541.9553823063.0573951584.5551393125.8635441584.5403083125.8610141898.77669126.5851130.0039332.797025

150024.552801500.0577942999.4674751542.0475743063.2417771542.0475743063.2417771584.7314673126.2211361584.716673126.2186131899.56077426.6373850.0038532.803172

150024.72801500.0565982999.4650231542.1392043063.4250371542.1392043063.4250371584.9067023126.576511584.8919383126.5739941900.3397626.6893170.0037732.80928

150024.852801500.0554092999.4625861542.2302793063.6071871542.2302793063.6071871585.0808573126.9296921585.0661253126.9271841901.11371326.7409140.0036942.815352