Our Cosmic Roots Recreating the Universe in the Laboratory

Recreating the Universe in the LaboratoryBrijesh K SrivastavaDepartment of PhysicsPurdue UniversityUSAOur Cosmic RootsRadiochemistry Division,B.A.R.C, Trombay, MumbaiDec. 16, 2010

1

An Old (and Fundamental!) Question:

What is the Structure of Matter in the Universe?

2Both disciplines physics and astronomy have seen stunning progress with in their own realms of study in the past two decades . The advances made by physicists in understanding the deepest inner workings of matter, space and time and by astronomers in understanding the universe as a whole as well as the objects within it have bought these scientists together in new ways.

The questions now being asked about the universe at its two extremes

The very large ---- Astrophysics The very small ---- Physics MOTIVATION3Why do so many things in this world share the same characteristics? People have come to realize that the matter of the world is made from a few fundamental building blocks of nature. The word "fundamental" is key here. By fundamental building blocks we mean objects that are simple and structureless -- not made of anything smaller. 4

Even in ancient times, people sought to organize the world around them into fundamental elements, such as earth, air, fire, and water.

Ancient Greeks: Earth, Air, Fire and WaterBy 1900, nearly 100 elementsBy 1936, back to three particles: proton, neutron, electron5

6

7baryonmesonhadronsParticlesLeptons

pionudForce carriersGluons

Glue the quark together8

9

Phase TransitionsEveryone knows that ice is frozen water, and that steam is water vapor. To put it another way: ice, water and steam are three different forms of the same thing. We call those three forms solid, liquid and gas. And we know that one form can turn into another form, if the conditions are right. 10How to Liberate Quarks and Gluons

Increase Temperature and/or PressureBayon(pressure)

Water molecule is liberated with high T and PLibrated Quarks and Gluons1,500,000,000,000 K~100,000 times higher temperature than the center of our sun.11

One Way to Increase Temperature or PressureSmall BangHeavy alien object hits the heavy earthTremendous kinetic energy converted into tremendous heat and pressure.12

13

STARPHENIXPHOBOSBRAHMSRHICThe Relativistic Heavy Ion Collider14

15Facts about RHICRHIC's beam travels at 99.995% the speed of light (186,000 miles per second, or 300,000,000 meters per second).

RHIC's beam is not continuous -- instead, it's made up of 57 separate "bunches", each containing billions of ions.

When the machine runs, thousands of subatomic collisions take place each second.

Each collision sends out a shower of thousands of subatomic particles.

16If quark-gluon plasma is formed in a RHIC collision, it will last less than 0.00000000000000000000001 seconds.

The temperature inside a RHIC collision is over trillion degrees, far hotter than the center of the sun.

RHIC ions are so small that, even at high speed, the force of their impact is about the same as the impact of two mosquitoes colliding.

In 20 years of running, RHIC will use less than one gram of gold.Facts about RHIC

17

Initial statePre-equilibriumQGPand expansionHaronization and mixed phase

Hadronic interactionand chemical freeze-outElastic scatteringand kinetic freeze-outParticle ratioFreeze-out temp.To study the QCD under extreeme conditions heavy ion collisions are investigated at relativistic energies.

A new state of matter is expected to form, reflecting the early Universe, few s after the Big Bang.

Phase Diagram of Nuclear Matter18

The Large Detectors PHENIX and STAR19

20

The STAR Detector

MagnetCoils

Central TriggerBarrel (CTB)

ZCal

Time Projection Chamber(TPC)

Barrel EM Cal (BEMC)Silicon Vertex Tracker (SVT)Silicon Strip Detector (SSD)

FTPCEndcap EM CalFPDTOFp, TOFr

21

p+p@200 GeVAu+Au@200 GeVSTAR Time Projection ChamberA Central Event Typically 1000 to 2000 tracks per event into the TPCVery few tracks per event22Different Stage after the Collision Right before the collision. Instantly (< 1 fm/c) after the collision. Highest energy density (15GeV/fm3). After ~1fm, system thermalized, i.e. thermal equilibrium. Temperature is the same everywhere.Hadron continue to interact with each other elastically. Hadron is not changed but the momentum distribution does. At Kinetic freezout, the elastic interaction between hadrons stop. Hadron spree out and detected by the experimentSystem continue the expension and cool down. Quarks and gluons start to fragment into hadrons. The particle ratio kept on changing due to the chemical reactions. At the point of Chemical Freezout, the chemical reaction ceased

23What are the probes. soft hadron: Pions, kions, protons, etc coming from the fragmentation process after chemical freezout. To study their behavior (cross section, correlation, suppression, etc) can leads to the estimation of the QGP properties, e.g. temperature, pressure, energy density.

Penetrating probes: direct photons, jet, heavy flavor, etcComing from the QGP, i.e. before the chemical freezout. Directly bring the information of the QGP properties.

24

Nomenclature: Rapidity vs xfxf = pz / pmax A natural variable to describe physics at forward scattering anglesRapidity is different. It is a measure of velocity but it stretches the region around v = c to avoid the relativistic scrunch

Rapidity and pT are the natural kinematic variable for HI collisions( y is approximately the lab angle where y = 0 at 90 degrees )When the mass of the particle is unknown, then y

25

Centrality Definition : Impact Parameter Important for A+A CollisionsNo. of charged particles in|| < 0.5

2.5 for pp collisions

550 for Au+Au collisionsb ~ 1b ~ 8-100-10%10-20%20-30%First thing to look at is the total no ofcharged particles 26

Particle identificationdE/dx method

2728Bulk Properties Temperature and Pressure29

Identified Mesons and Baryons: Au+Au @ 200 GeVChemical Freeze-out

30Chem Fit

Elliptic FlowNonzero impact parameter b > 0:Spatial anisotropy in the initial stateMomentum anisotropy in the final statecoordinate space momentum space Fourier analysis=> v2 = elliptic flow

xyz

Jets and Energy Loss in the Medium

32Lets look at some collision systems in detail Final stateInitial stateAu + Aud + Aup + p3333Evidence for Parton Energy Loss in High Density Matter

Nuclear Modification Factor

34Jet QuenchingAway-side jets vanishTrigger on a high pT hadron and look for associated hadron as a function of relative azimuthal angle and rapidity

The away side jet is absorbed in the medium Conclusions About Nuclear Matter at RHIC RHIC has produced wealth of results :

1. Temperature and particle ratios --------- Thermometer

Collectivity ( Flow) ---------- Barometer

3. Suppression of high pT particle yields relative to p-p -------- Opaque

Dense Matter has been created

There is plenty of work for theorists (and experimentalists)!

36Could we establish the connection between Astrophysics & Nuclear Physics ??37

CGCGlasmaInitial SingularitysQGPHadron Gaswith some artistic interpretation38What is the Future ? 39

hSTAR

Dedicated Facilities for QGP search

SPS Layout

AGS LayoutAGS: Fixed TargetAu at 11.7GeV/A (Ec.m.=4.86GeV)LHC: ColliderPb+Pb @5500GeV/A SPS: Fixed TargetPb at 158GeV/A (Ec.m.=17.3GeV)RHIC: ColliderAu+Au @ 200GeV/A

BevalacBevalac: Fixed Target Au at 1GeV/A 40

LARGE HADRON COLLIDER (LHC)ATLASALICECMSLHC-BPt-1Pt-2Pt-5Pt-8pp: s = 14 TeVpA: s = 8.8 TeVAA: sNN = 5.5 TeV41

http://public.web.cern.ch/public/42

LHC Energies pp at 900 GeV and 14 TeVAlice 43

The ALICE detectorSize: 16 x 26 metersWeight: 10,000 tonsCentral Detectors:Inner Tracking SystemTime Projection Chamber Time-of-Flight Transition Radiation DetectorMultiplicity Detectors:Photon Multiplicity (PMD)Forward Multiplicity (FMD)Calorimeters:Zero Degree CalorimeterEM Calorimeter

Trigger:Trigger DetectorsHigh-Level-TriggerSpectrometers:HMPIDPhoton SpectrometerMuon Spectrometer44

TPCStrong2010: Nayak4546

Pb+Pb at 2.76 TeV

O Omnipresent, the embodiment of all virtues, the creator of this cosmic universe, the king of dancers, who dances the Ananda Tandava in the twilight, I salute thee. ( Source: Verse No. 56, Sivanandalahiri, by Sri Adi Sankara).

Presented by: The Department of Atomic Energy, Government of India.

O Omnipresent, the embodiment of all virtues, the creator of this cosmic universe,the king of dancers, who dances the Ananda Tandava in the twilight, I salute thee. ( Source: Verse No. 56, Sivanandalahiri, by Sri Adi Sankara).

Presented by: The Department of Atomic Energy, Government of India.4747Chart50.08839967720.33924363120.73105857860.93503083090.98704627250.99752737680.99953204330.99991158080.99998329860.99999684550.99999940420.99999988750.99999997870.99999988750.99999940420.99999684550.99998329860.99991158080.99953204330.99752737680.98704627250.93503083090.73105857860.33924363120.0883996772

y

Simple PictureMpsi3.1124.8188909590024.818890959Mpsip3.71.118.38076606110018.3807660611NormPsi51.213.6127178910013.612717891NormPsiP0.021.310.08152150810010.0815215081NormB5.00E+021.47.4663323469007.4663323469Resln0.151.55.5295342741005.5295342741Slope0.3331.64.0951497827004.09514978271.73.0328506727003.03285067271.82.2461164282002.24611642821.91.663464362001.66346436221.2319546969001.23195469692.10.91238045720.000000001100.91238045832.20.6757051220.000000076100.67570519812.30.5004243660.000003329200.50042769522.40.37061217680.000093322300.37070549912.50.27447381640.001677313100.27615112952.60.20327415180.019329600700.22260375252.70.15054398030.142827503900.29337148422.80.11149223740.67667641620.00000000030.78816865392.90.08257068122.05556145250.00000001332.138132147130.06115149864.00368701460.00000037334.06483888643.10.045288542250.00000670935.04529525143.20.03354050354.00368701460.00007731844.03730483653.30.02483995552.05556145250.000571312.08097271813.40.01839636640.67667641620.00270670570.69777948833.50.01362427140.14282750390.00822224580.16467402123.60.0100900780.01932960070.01601474810.04543442683.70.00747266930.00167731310.020.02914998243.80.00553422740.00009332230.01601474810.02164229783.90.00409862550.00000332920.00822224580.012324200540.00303542480.00000007610.00270670570.00574220664.10.00224802280.00000000110.000571310.00281933394.20.001664876200.00007731840.00174219464.30.001233000300.00000670930.00123970954.40.000913154800.00000037330.00091352814.50.000676278600.00000001330.00067629194.60.000500849100.00000000030.00050084944.70.0003709267000.00037092674.80.0002747068000.00027470684.90.0002034467000.000203446750.0001506718000.0001506718

Simple Picture

Summed ContributionsJ/PsiPsi PrimeMmm (GeV)Counts"Typical" Di-Muon Spectrum

Sheet1SchulerJunkD-YPsi/D-Y01.00E-091.00E-0921.00E-091.00E-09-0.000076466240.00000001681.00E-090.00000000632.6929163225mJPsi3.160.00016254031.00E-090.00015408211.0548938407mDY2.980.00278787381.00E-090.00356393510.782245965nDY17100.01164632991.00E-090.01591451760.7318054005120.02770161741.00E-090.03708960160.7468836614140.04961140741.00E-090.06273696860.7907842616160.0754460891.00E-090.08867350960.8508300776180.10350591281.00E-090.11232290060.9215032041200.13251971931.00E-090.13251971931220.161610465110.14898728241.0847265788240.190204388410.16191807011.1746952534260.217944348810.17171106081.2692504943280.244622155710.17882623621.3679321388300.270129679610.18371147461.4704017819320.294424789510.18677027761.5764006631340.317508055710.18835111641.6857243102360.339406977410.1887474881.7982065932380.360165379210.18820276211.9137093162400.379836327310.18691672992.0321151964420.398477433110.18505232842.1533229904440.416147776210.18274184592.2772440228460.432905921210.18009234672.4037996572480.448808675810.17719027042.5329194129500.463910348610.17410525982.6645395387520.478262341610.17089330912.798601912540.491912966210.16759933692.9350531765560.504907405310.16425927793.0738440575580.517287769910.16090178063.2149288102600.529093214910.15754958323.3582647703620.540360087710.15422062893.5038119839640.551122096410.15092896923.6515328992660.561410484410.14768549743.8013921076680.571254203910.1444985443.9533561244700.580680086810.14137436044.1073932014720.589713005410.13831751314.2634731651740.598376026410.13533120474.4215672776760.60669055310.13241753584.5816481139780.614676458110.12957771884.7436894555800.622352206610.12681225294.9076661956820.629734968610.12412106725.073554256840.636840722810.12150363765.2413305119860.643684352210.11895908275.4109727256880.650279730610.11648624275.5824594865900.656639802510.11408374285.755770157920.66277665610.11175004675.930884824940.668701589410.10948349876.1077842538960.674425172110.10728235946.2864498522980.679957300210.10514483366.46686362731000.685307247310.10306909416.64900815571020.690483711510.10105329976.83286655131040.695494857710.09909561077.01842243681060.700348356710.09719420087.20565991721080.705051421410.09534726647.39456355521100.709610839110.09355303467.5851183491120.714033002110.09180976827.77730971051140.718323935210.0901157717.97112344641160.722489321210.08846939028.16654573961180.726534524610.0868690198.36356313241200.730464612610.08531309848.56216251031220.734284375810.08380011768.76233108711240.737998345810.08232861488.96405639121260.741610812710.08089717689.16732625231280.745125840510.07950443899.37212878871300.748547281510.07814908419.57845239651320.751878789910.07682984239.78628573771340.755123834210.07554548959.99561773041360.758285708510.074294846310.20643753911380.761367543510.073076777110.41873456511400.764372316110.071890188410.63249843791420.767302858710.070734027910.84771900711440.77016186810.069607282711.06438633441460.772951912510.068508978611.28249068581480.775675440410.067438177811.50202252511500.778334786110.066393978611.72297250681520.780932177210.065375513411.945331471540.783469739910.064381947412.16909043161560.785949504910.063412477712.39424058121580.788373412810.062466331912.62077327551600.790743318910.061542766812.84868003221620.793060997610.060641067213.07795252611640.79532814710.059760544913.30858258331660.79754639310.058900537713.54056217711680.799717292610.058060408113.77388342341700.801842337910.057239542414.00853857641720.803922959410.056437349814.24452002461740.80596052910.055653261314.4818202871760.807956362910.05488672914.72043200921780.809911724610.054137225114.96034795991800.811827827310.053404240915.20156102761820.813705836310.052687286515.44406421691840.815546871710.051985889615.68785064561860.817352010310.051299594915.93291354171880.819122287410.050627963516.17924624031900.820858699310.04997057216.4268421811920.822562204810.049327012116.67569490461940.82423372710.048696890116.92579805131960.82587415510.048079825717.17714535751980.827484345110.047475452217.42973065362000.82906512310.046883415617.6835478622020.830617284410.046303373817.93859099392040.832141596710.045734996818.19485414832060.833638800410.045177965718.45233150882080.835109609810.044631972418.71101734232100.836554714710.044096719218.97090599672120.837974780910.043571918419.2319918992140.839370451710.043057291819.49426955362160.840742348310.042552570419.75773354022180.842091071510.042057494420.02237851262200.843417201710.041571811920.28819919662220.844721300310.041095279820.55519038832240.846003910410.040627662420.82334695292260.847265557310.040168731921.09266382312280.848506749410.039718267521.36313599732300.849727978810.039276055621.63475853862320.850929722110.038841889321.90752657322340.852112440910.038415568222.18143528892360.853276582210.037996898222.45647993432380.854422579310.037585691122.73265581682400.85555085210.037181764623.00995830222420.856661807510.036784941923.28838281272440.857755840610.036395051623.56792482652460.85883333410.036011927723.8485798762480.859894659210.035635408924.1303435473

Sheet1

RHICSPSJ/YD-YE(CM) in GeVJ/Psi relative cross section

NA50 Actual DataA15Chi^220.2530151985B50NDF12Slope20Data1st Derivative2nd DerivativeE_TRatioErrorE_Td(Ratio)/dE_TErrorE_Td^2(Ratio)/dE_T^2ErrorFunctionChi^21435.82.639.82926518962.401623959719-0.760.34058772732428.22.223.50.05388888890.054066859630.05971059560.71457097128-0.2750.347535969432261.732.250.00882352940.050004538625.09482589970.28350870336.5-0.20.24469683944124.21.440.75-0.05882352940.038325963721.43674517943.895702654945-0.70.21505813174918.6148.750.08190476190.039342671619.3146793250.510766537552.5-0.08571428570.20203050895618156-0.01428571430.040816326518.04050313130.001640503659.5-0.18571428570.20203050896316.71630.05306122450.040816326517.14260634340.195900375266.50.18571428570.20203050897018170-0.05306122450.040816326516.50986917112.220489887273.5-0.18571428570.20203050897716.7176.75-0.05347985350.049183923716.06398682190.404512762780-0.53333333330.24776781258313.51.183.250.10183150180.049282035515.78822082424.327235157486.50.12857142860.20303814869014.40.9900.01632653060.041019900515.55544982691.64822753493.50.24285714290.20303814869716.11.196.75-0.02454212450.053687688915.39141887750.41494810511000.08333333330.283823106110316.61.3103.25-0.06776556780.057510324115.28997023631.01548993106.5-0.35714285710.243276948111014.11.1110.50.03908730160.038524777515.20433857191.007903869114.5-0.04444444440.189215404111913.71.357.25-0.0003881611-0.001652536315.13029202591.2104942482

Bill Zajc:"Fitting" to Angelis et al, Phys. Lett 87B, 398,

I get

s^{3/2} d\sigma/{dm dy} ~ (1 - m/\sqrt{s})^{16}

The integral yield beyond some mDY goes as one powerhigher, I.e, 16 --> 17.

NA50 Actual Data0.05406685960.05406685960.05000453860.05000453860.03832596370.03832596370.03934267160.03934267160.04081632650.04081632650.04081632650.04081632650.04081632650.04081632650.04918392370.04918392370.04928203550.04928203550.04101990050.04101990050.05368768890.05368768890.05751032410.05751032410.03852477750.0385247775-0.0016525363-0.0016525363

E_T (GeV)d^2(Ratio)/dE_T^22nd Derivatives

Sheet20.34058772730.34058772730.34753596940.34753596940.24469683940.24469683940.21505813170.21505813170.20203050890.20203050890.20203050890.20203050890.20203050890.20203050890.20203050890.20203050890.24776781250.24776781250.20303814860.20303814860.20303814860.20303814860.28382310610.28382310610.24327694810.24327694810.18921540410.1892154041

E_T (GeV)d(Ratio)/dE_T1st Derivatives

NA50 MB Analysis2.62.62.22.2001.71.71.41.411111111111.11.10.90.91.11.11.31.31.11.11.31.3

DataE_T (GeV)RatioData

yBEAM5.3Spread0.3-1-60.0883996772-0.98-2.297559925125.2525252525-5.50.3392436312-0.96-1.945910149112.7551020408-50.7310585786-0.94-1.73804934498.5910652921-4.50.9350308309-0.92-1.58902691526.5104166667-40.9870462725-0.9-1.47221948965.2631578947-3.50.9975273768-0.88-1.37576765654.4326241135-30.9995320433-0.86-1.2933446723.8402457757-2.50.9999115808-0.84-1.22117351773.3967391304-20.9999832986-0.82-1.15681746463.0525030525-1.50.9999968455-0.8-1.09861228872.7777777778-10.9999994042-0.78-1.04537054852.5536261491-0.50.9999998875-0.76-0.99621508232.367424242400.9999999787-0.74-0.95047938062.21043324490.50.9999998875-0.72-0.90764498332.076411960110.9999994042-0.7-0.86730052771.96078431371.50.9999968455-0.68-0.82911403831.860119047620.9999832986-0.66-0.79281363191.77179305462.50.9999115808-0.64-0.75817374471.693766937730.9995320433-0.62-0.72500508781.6244314493.50.9975273768-0.6-0.69314718061.562540.9870462725-0.58-0.66246270741.50693188674.50.9350308309-0.56-0.63283318671.456876456950.7310585786-0.54-0.6041556031.41163184645.50.3392436312-0.52-0.5763397551.370614035160.0883996772-0.5-0.54930614431.3333333333-0.48-0.52298427761.2993762994-0.46-0.49731128761.2683916794-0.44-0.47223080441.2400793651-0.42-0.44769202351.2141816416-0.4-0.42364893021.1904761905-0.38-0.40005965011.1687704535-0.36-0.37688590121.1488970588-0.34-0.3540925291.1307100859-0.32-0.33164710871.1140819964-0.3-0.30951960421.0989010989-0.28-0.28768207251.0850694444-0.26-0.26610840691.0725010725-0.24-0.24477411271.0611205433-0.22-0.2236561091.0508617066-0.2-0.20273255411.0416666667-0.18-0.18198268861.0334849111-0.16-0.16138669611.026272578-0.14-0.14092557611.0199918401-0.12-0.12058102841.0146103896-0.1-0.10033534771.0101010101-0.08-0.0801713251.0064412238-0.06-0.06007215591.0036130068-0.04-0.04002135381.0016025641-0.02-0.02000266731.00040016010010.020.02000266731.00040016010.040.04002135381.00160256410.060.06007215591.00361300680.080.0801713251.00644122380.10.10033534771.01010101010.120.12058102841.01461038960.140.14092557611.01999184010.160.16138669611.0262725780.180.18198268861.03348491110.20.20273255411.04166666670.220.2236561091.05086170660.240.24477411271.06112054330.260.26610840691.07250107250.280.28768207251.08506944440.30.30951960421.09890109890.320.33164710871.11408199640.340.3540925291.13071008590.360.37688590121.14889705880.380.40005965011.16877045350.40.42364893021.19047619050.420.44769202351.21418164160.440.47223080441.24007936510.460.49731128761.26839167940.480.52298427761.29937629940.50.54930614431.33333333330.520.5763397551.37061403510.540.6041556031.41163184640.560.63283318671.45687645690.580.66246270741.50693188670.60.69314718061.56250.620.72500508781.6244314490.640.75817374471.69376693770.660.79281363191.77179305460.680.82911403831.86011904760.70.86730052771.96078431370.720.90764498332.07641196010.740.95047938062.21043324490.760.99621508232.36742424240.781.04537054852.55362614910.81.09861228872.77777777780.821.15681746463.05250305250.841.22117351773.39673913040.861.2933446723.84024577570.881.37576765654.43262411350.91.47221948965.26315789470.921.58902691526.51041666670.941.73804934498.59106529210.961.945910149112.75510204080.982.297559925125.252525252511.02111

y

cosq

Alpha13Chi^241.6061249153Beta50NDF23Gamma25Data1st Derivative2nd DerivativeE_TRatioErrorE_Td(Ratio)/dE_TErrorE_Td^2(Ratio)/dE_T^2ErrorFunctionChi^228.128.11.329.24886411030.780999256829.95-0.24324324320.427334818931.827.20.931.825-0.09653864390.136922356827.01352599120.042929081433.7-0.60526315790.284648784935.624.90.635.5750.06770981510.094500512325.03745459830.05248268537.45-0.35135135140.211087829139.323.60.539.325-0.03963963960.072025389823.38147539030.191012020241.2-0.50.168503269443.121.70.443.0750.01081081080.057599294221.9175656970.295842703344.95-0.45945945950.135135135146.8200.346.8250.05936462780.046744224120.69078612675.302060808948.7-0.23684210530.111648439150.619.10.350.5750.04153627310.042678046319.60629515252.848164238252.45-0.08108108110.114665964554.318.80.354.325-0.02048364150.042678046318.6974744940.116794215356.2-0.15789473680.111648439158.118.20.358.075-0.00834518730.042678046317.89406382021.039966068159.95-0.18918918920.114665964561.817.50.361.825-0.00568990040.042678046317.2207929170.866184390963.7-0.21052631580.111648439165.616.70.365.5750.07776197250.042678046316.62561165120.061484738367.450.08108108110.114665964569.3170.369.325-0.08477951640.042678046316.12684029878.471198489471.2-0.23684210530.111648439173.116.10.373.0750.05595068750.042678046315.68591917231.905143687574.95-0.0270270270.114665964576.8160.376.825-0.04893314370.042678046315.31642026645.192013913178.7-0.21052631580.111648439180.615.20.380.5750.05614035090.042678046314.98977786210.491037191782.4500.114665964584.315.20.384.325-0.03508771930.042678046314.71604634012.602346054786.2-0.13157894740.111648439188.114.70.388.0750.00625889050.042678046314.47406369540.567191263989.95-0.10810810810.114665964591.814.30.391.8250.00075865340.039688613314.27127839630.009165894793.7-0.10526315790.094882928395.613.90.295.5750.02086296820.036269365114.0920132440.921727146597.45-0.0270270270.097447331899.313.80.399.325-0.04893314370.039518305313.94178619950.2233702931101.2-0.21052631580.1116484391103.1130.3103.0750.07776197250.042678046313.80898330847.2717110356104.950.08108108110.1146659645106.813.30.3106.825-0.01460407780.042678046313.69769237661.7573247378108.70.02631578950.1116484391110.613.40.3110.5750.00739687060.046744224113.59930957510.4413811857112.450.05405405410.1351351351114.313.60.4114.325-0.01441441440.057599294213.5168632250.043198271116.200.1685032694118.113.60.5118.075-0.02162162160.076569750213.4439794530.0973696443119.95-0.08108108110.2324952775121.813.30.713.38290169470.0140259

0.42733481890.42733481890.28464878490.28464878490.21108782910.21108782910.16850326940.16850326940.13513513510.13513513510.11164843910.11164843910.11466596450.11466596450.11164843910.11164843910.11466596450.11466596450.11164843910.11164843910.11466596450.11466596450.11164843910.11164843910.11466596450.11466596450.11164843910.11164843910.11466596450.11466596450.11164843910.11164843910.11466596450.11466596450.09488292830.09488292830.09744733180.09744733180.11164843910.11164843910.11466596450.11466596450.11164843910.11164843910.13513513510.13513513510.16850326940.16850326940.23249527750.2324952775

E_T (GeV)d(Ratio)/dE_T1st Derivatives

0.13692235680.13692235680.13692235680.13692235680.09450051230.09450051230.09450051230.09450051230.07202538980.07202538980.07202538980.07202538980.05759929420.05759929420.05759929420.05759929420.04674422410.04674422410.04674422410.04674422410.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.03968861330.03968861330.03968861330.03968861330.03626936510.03626936510.03626936510.03626936510.03951830530.03951830530.03951830530.03951830530.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04267804630.04674422410.04674422410.04674422410.04674422410.05759929420.05759929420.05759929420.05759929420.07656975020.07656975020.07656975020.0765697502

E_T (GeV)d^2(Ratio)/dE_T^22nd Derivatives

1.31.30.90.9000.60.60.50.50.40.40.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.30.20.20.30.30.30.30.30.30.30.30.40.40.50.50.70.7

DataE_T (GeV)RatioData