The ALICE ITS upgrade - CERN Document Server

188 Pages·2012·12.75 MB·English

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
ALICE-UG-001 CERN-LHCC-2012-012/LHCC-I-022
September8,2012
Upgrade of the ALICE Experiment
Letter Of Intent
TheALICECollaboration
∗
CopyrightCERN,forthebenefitoftheALICECollaboration.
ThisarticleisdistributedunderthetermsofCreativeCommenceAttributionLicense(CC-BY-3.0),which
permitsanyuseprovidedtheoriginalauthor(s)andsourcearecredited.
SeeAppendixAforthelistofcollaborationmembers
∗

Contents
1 Introduction 1
1.1 StudyofQuark–GluonPlasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ProposedPhysicsProgramme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Heavy-FlavourProduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 ProductionofQuarkonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Low-MassDileptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.4 JetMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.5 HeavyNuclearStates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.6 ComparisonofPhysicsReach . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.7 ComparisonwithOtherLHCExperiments. . . . . . . . . . . . . . . . . . . . . 9
1.3 ALICEDetectorUpgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Runningscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 PhysicsMotivation 15
2.1 HeavyFlavour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Heavy-flavourThermalization,Coalescence,andPossibleThermalProduction . 16
2.1.2 Heavy-flavourEnergyLoss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.1.3 Proton–ProtonRunningRequirementsforHeavy-flavourReferenceData . . . . 39
2.2 Quarkonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.2 InputsforSimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.3 J/ψ YieldandtheNuclearModificationFactor . . . . . . . . . . . . . . . . . . 48
2.2.4 J/ψ EllipticFlow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.5 J/ψ Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.6 ElectromagneticJ/ψ Production . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.7 ψ(2S)Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
i
ii TheALICECollaboration
2.3 Low-MassDileptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.1 ScientificObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.2 ExperimentalChallenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3.3 PhysicsPerformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.4.1 JetMeasurementsinALICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.4.2 JetStructureModifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.4.3 Photon–JetMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.4.4 HeavyFlavourJets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.4.5 ReferenceData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.5 HeavyNuclearStates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3 DetectorsandReadoutElectronics 85
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2 Beampipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3 ITSUpgrade. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.1 CurrentITSPerformanceandLimitations . . . . . . . . . . . . . . . . . . . . . 87
3.3.2 ITSUpgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3.3 TechnicalImplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4 TPCUpgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4.1 StatusandLimitationsofthePresentTPC . . . . . . . . . . . . . . . . . . . . . 95
3.4.2 UpgradeConcept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4.3 ExpectedPerformanceoftheUpgradedTPC . . . . . . . . . . . . . . . . . . . 96
3.4.4 TechnicalImplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.5 R&D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.4.6 PrototypeTest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.4.7 Front-EndandReadoutElectronics . . . . . . . . . . . . . . . . . . . . . . . . 102
3.5 UpgradeofTOFReadoutElectronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.6 UpgradeofTRDReadoutElectronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.7 MuonSpectrometerUpgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.1 MuonTriggerUpgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.2 MuonTrackingUpgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.8 OtherUpgradeItems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
ALICEUpgradeLOI iii
4 DataCollectionandProcessing 113
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2.1 EventRates,EventSizesandDataThroughput . . . . . . . . . . . . . . . . . . 114
4.2.2 OnlineDataReduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.2.3 OnlineDataProcessingRequirements . . . . . . . . . . . . . . . . . . . . . . . 116
4.2.4 OfflineDataProcessingandStorageRequirements . . . . . . . . . . . . . . . . 117
4.3 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.1 FastTriggerProcessor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.2 Dataflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.3 FarmLayout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.4 PlatformIndependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.5 DetectorControlSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.6 Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4 Research,PrototypingandDevelopment . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.1 DDLandRORC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.2 High-LevelProgrammingofFPGAs . . . . . . . . . . . . . . . . . . . . . . . . 123
4.4.3 FLPandEPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4.4 FarmNetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.4.5 ReconstructionSoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.4.6 ParallelHLTReconstructiononGPUandCPU . . . . . . . . . . . . . . . . . . 131
4.4.7 AnalysisofCurrentAliRootPerformance . . . . . . . . . . . . . . . . . . . . . 132
4.4.8 PlansfortheDevelopmentofParallelAliRoot. . . . . . . . . . . . . . . . . . . 133
5 Schedule,CostEstimateandOrganization 135
5.1 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.2 CostEstimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.3 Organization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
ListofFigures 155
ListofTables 164
References 167
A TheALICECollaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
iv TheALICECollaboration
Chapter 1
Introduction
QuantumChromoDynamics(QCD)iswell-establishedasthegaugetheoryofstronginteractions. How-
ever,severalofitsfundamentalaspectsarenotwell-understoodatpresent. Thereremainimportantopen
questionsabouttheparton–hadrontransitionandthenatureofconfinement,andaboutthenatureofQCD
matter at high temperature. A much deeper insight into the mechanisms underlying chiral-symmetry
breakingandtheoriginoflight-quarkmassisnecessary.
This Letter of Intent (LoI) presents the plans of the ALICE (A Large Ion Collider Experiment [1]) col-
laborationtoextenditsphysicsprogramme,inordertofullyexploitthescientificpotentialoftheLarge
Hadron Collider (LHC) for fundamental studies of QCD, with the main emphasis on heavy-ion colli-
sions. TheproposedenhancementoftheALICEdetectorperformancewillenabledetailedandquantita-
tivecharacterizationofthehighdensity, hightemperaturephaseofstronglyinteractingmatter, together
withtheexplorationofnewphenomenainQCD.Inthefollowingweoutlinethephysicsmotivationfor
running the LHC with heavy ions at high luminosities and summarize the performance gains expected
withtheupgradedALICEdetector. Withtheproposedtimelineofinitiatinghigh-rateoperationafterthe
2018LongShutdown(LS2),theobjectivesofourupgradeplanswillbeachievedbycollectingdatainto
themid-2020’s.
1.1 StudyofQuark–GluonPlasma
Strongly-interacting matter at very high temperature and density is expected to exist in a state called
the Quark–Gluon Plasma (QGP), in which quark and gluon degrees of freedom are liberated, and with
properties very different from the hadronic matter we ordinarily find around us. Such conditions of
high temperature and density prevailed in the early Universe, a few microseconds after its formation.
However, the cosmological QGP epoch is effectively shielded from astronomical observations by the
subsequent evolution of the Universe, and the only means to study this fundamental state of matter is
via the collision of heavy nuclei in the laboratory. In heavy-ion collisions at ultra-relativistic energies,
nuclearmatterisheatedandbroughttovaluesoftemperatureanddensitywellbeyondthoserequiredfor
the creation of QGP, and the same kind of medium that filled the very early Universe is generated for a
fleetinginstant.
To reach the QGP state, matter has to undergo a QCD phase transition, and that reflects breaking of
a fundamental symmetry in the theory. Below the corresponding critical temperature, matter is best
described in terms of hadronic degrees of freedom, with quarks and gluons confined in colour-neutral
objects. As the temperature rises the hadrons melt (deconfinement phase transition) and quarks and
gluonsarenolongerboundintohadrons. Thedeconfinementphasetransitioniscausedbythebreakingof
theZ -symmetry(exactsymmetryinthelimitofpure-gaugeQCD)athightemperature,andisillustrated
3
1
2 TheALICECollaboration
inFigure2.46(left)byamarkedchangeofthecorrespondingorderparameter,theexpectationvalueof
Polyakovloop.
A second phase transition is connected with the generation of hadronic mass, as a consequence of the
presence of a quark–antiquark condensate in the vacuum at low temperature. At high temperatures, the
vacuumcondensatedecreases,andthemassesofquarksdroptotheirbarevaluesduringthechiralphase
transition. This can be seen in Figure 2.46 (right): the expectation value for the density of vacuum
quark–antiquark condensate, i.e. the order parameter of the chiral transition, exhibits a sudden drop in
thevicinityofthecriticaltemperature. Theunderlyingreasonforthisphasetransitionistherestoration
oftheapproximatechiralsymmetry(exactsymmetryinthelimitofzerobarequarkmasses)oftheQCD
Lagrangian.
Lattice-QCDcalculationspredictthatthetransitionbetweentheQGPandhadronicmatteratzerobaryo-
chemical potential is not a sharp phase transition, but rather a smooth cross-over occurring over a wide
temperature range (see Figure 2.46). Recent calculations also suggest that the two phase transitions
may occur at different critical temperatures [2]. Lattice QCD further predicts that even at several times
the transition temperature, the energy density is still about 15% below that expected for the Stefan–
Boltzmannlawforanidealgasofnon-interactingquarksandgluons,withveryslowconvergencetothis
limit. This indicates that the effective degrees of freedom in a QGP at finite temperature are not bare
quarksandgluons,butrathermorecomplexformationswhosenaturehasnotyetbeenunderstood. The
crucial question of effective degrees of freedom in the QGP is also addressed experimentally, and is an
area ofintenseactivity inthe fieldat present. However, it remains aprofound challengefor experiment
andtheory,andmayhaveadeepconnectiontootherareasofphysicsandcosmology.
The experimental demonstration of these phase transitions, the verification of the lattice QCD predic-
tions reflecting the fundamental symmetries of the theory, and a detailed investigation of the properties
of strongly interacting matter at high temperature, are the principal aims of the ALICE scientific pro-
gramme. Precise determination of the QGP properties, including critical temperature, degrees of free-
dom,speedofsound,and,ingeneral,transportcoefficientsandequationofstate,istheultimategoalin
the field. This would go a long way towards a better understanding of QCD as a genuine multi-particle
theory,sheddinglightonthecomplexissuesofdeconfinementandchiral-symmetryrestoration.
ThetheoreticalexpectationformanyyearswasthattheQGPathightemperatureisaweakly-interacting
gas of quarks and gluons, with the constituents traveling long distances between interactions, relative
to the size of a proton. Heavy-ion experiments indicate instead fundamentally different and surprising
behaviour of the created matter: the formation of a strongly-coupled plasma with very short mean free
path, which exhibits a high degree of collectivity and flows, and which absorbs a significant fraction
of high-energy partons propagating through it. Over time, the image of the QGP as an almost-perfect,
inviscid liquid emerged from the experimental investigation at both, CERN SPS and BNL RHIC. With
thefirsttwoyearsofLHCrunning,theALICEcollaborationhasconfirmedthisbasicpicture,observing
thecreationofhothadronicmatteratunprecedentedvaluesoftemperatures,densitiesandvolumes. The
firstresultsextendedtheprecisionandkinematicreachofallsignificantprobesoftheQGPthathadbeen
measured over the past decade, and new and intriguing phenomena were observed with charm mesons
andcharmonia.
The observation that the QGP is a near-perfect liquid is based on measurements of inclusive spectra
(radialflow)andazimuthalanisotropyofparticleproduction(ellipticflow)foridentifiedhadronsatsoft
transverse momenta (p ), up to about 3 GeV/c. This is further confirmed by comparison to model cal-
T
culationsbasedonviscousrelativistichydrodynamics. Hydrodynamicsisageneralapproachtofluiddy-
namics,describingthelong-wavelengthbehaviourofacomplexsysteminquasi-equilibrium,andserves
as a powerful tool to determine the QGP properties. The good agreement of hydrodynamic calculation
with ALICE and other experiments flow measurements provides strong evidence for the formation of a
ALICEUpgradeLOI 3
quasi-equilibratedQGPinheavy-ioncollisionsatLHCenergies. Theverylowratioofshear-viscosityto
entropy-densityoftheQGP,inferredfromthecomparisonofmodelcalculationsandexperimentalmea-
surements, demonstrates very short mean free path inside this medium composed of strongly-coupled
quasi-particlemodes,whoseoriginisthesubjectoffurtherexperimentalstudy.
1.2 ProposedPhysicsProgramme
TheLHCprovidestheoptimalexperimentalconditionstostudytheQGP,duetothefollowing:
– the net baryon density in the central (mid-rapidity) region is very small, corresponding to the
conditionsoftheearlyUniverse;
– theinitialtemperatureandenergydensityarethehighestachievableinthelaboratory;
– thelargecollisionenergyensuresanabundanceofperturbativelycalculablehardQCDprocesses.
Thestudyofthestrongly-interactingstateofmatterinthesecondgenerationofLHCheavy-ionstudies
followingLS2willfocusonrareprobes,andthestudyoftheircouplingwiththemediumandhadroniza-
tion processes. These include heavy-flavour particles, quarkonium states, real and virtual photons, jets
andtheircorrelationswithotherprobes. Thecrosssectionsofalltheseprocessesaresignificantlylarger
at LHC than at previous accelerators. In addition, the interaction with the medium of heavy-flavour
probes is better controlled theoretically than the propagation of light partons. All these investigations
should involve soft momentum scales, and thus benefit from the ALICE detector strengths: excellent
tracking performance in high-multiplicity environment and particle identification over a large momen-
tumrange. Inmostofthesestudies,theazimuthalanisotropyofdifferentprobeswillbemeasured. Major
highlightsoftheproposedprogrammefocusonthefollowingphysicsquestions:
– Study of the thermalization of partons in the QGP, with focus on the massive charm and beauty
quarks. Heavy-quarkazimuthal-flowanisotropyisespeciallysensitivetothepartonicequationof
state. Ultimately, heavy quarks might fully equilibrate and become part of the strongly-coupled
medium.
– Study of the low-momentum quarkonium dissociation and, possibly, regeneration pattern, as a
probeofdeconfinement,andanevaluationofthemediumtemperature.
– Study of the production of thermal photons and low-mass dileptons emitted by the QGP. This
should allow to assess the initial temperature and the equation of state of the medium, as well as
toshedlightonthechiralnatureofthephasetransition.
– Studyofthein-mediumpartonenergy-lossmechanismthatprovidesbothatestinggroundforthe
multi-particle aspects of QCD and a probe of the QGP density. The relevant observables are: jet
structure, jet–jetandphoton–jetcorrelations, andjetcorrelationswithhigh-momentumidentified
hadrons and heavy-flavour particle production in jets. In particular, it is crucial to characterize
the dependencies of energy loss on the parton colour-charge, mass, and energy, as well as on the
densityofthemedium.
– Search for heavy nuclear states such as light multi-Λ hyper-nuclei 5H, bound states of (ΛΛ)
ΛΛ
or the H dibaryon, (Λn) bound state, as well as bound states involving multi-strange baryons; a
systematicstudyoflightnucleiandanti-nucleiproduction.
Belowweoutlinethebasicphysicsmotivationforthesemeasurements;thedetailsandthecorresponding
performancestudiesaredescribedinChapter2.
4 TheALICECollaboration
1.2.1 Heavy-FlavourProduction
High-precisionmeasurementsofcharmandbeautyproductioninheavy-ioncollisionsattheLHCisone
oftheprincipalphysicsmotivationsfortheupgradeoftheALICEdetectorandthehigh-luminosityrun-
ningoftheexperiment. Theenvisagedmeasurementsofopenheavy-flavourproductionwillmakepossi-
bletopreciselydetermineimportantparametersofthestronglyinteractingmatterthatarenotaccessible
withthepresentexperimentalsetup,seeSection2.1fordetails. Twotopicsthatneedhigh-precisionand
high-statisticsmeasurementsareproposedtostudy:
– thermalizationofheavyquarksinthemedium,bydeterminationofthebaryon-to-mesonratiofor
charmandforbeautyparticles,theazimuthal-flowanisotropyforcharmmesonsandbaryonsand
beautyparticles,andthepossiblein-mediumthermalproductionofcharmquarks;
– parton mass and colour-charge dependence of in-medium energy loss, by measuring the p -
T
dependencies of the nuclear modification factors separately for D and B mesons, and comparing
themwiththoseforlight-flavourparticles.
Thesetwotopicsarecloselyconnected: thein-mediumheavy-quarkenergylosslowersthemomentaof
heavy quarks, they may thermalize in the system, and thus participate in the collective flow dynamics.
Thesimultaneousobservationofthetwophenomenaopensthepossibilityfordeterminationoftheheavy-
flavour transport coefficients. Heavy-flavour production plays a special role in heavy-ion physics: it
provides a calibrated probe (input p spectra calculable from perturbative QCD), and, in addition, this
T
probe is well-tagged (identified), from production till observation, which enables a unique access to its
interactionsintheQGP,alsointhelow-andintermediate-p regime.
T
The ALICE collaboration already presented the first results on D-meson production in heavy-ion colli-
sions. To address the physics questions mentioned above, these measurements have to be extended to a
lower p ,includecharmbaryons(possiblyalsocharm–strangebaryons)andbeautyparticles. Thecapa-
T
bilityofstudyingyieldsandspectraofparticlescontainingheavyquarksisgivenbytheperformanceof
secondary-vertexisolationclosetotheprimary-interactionvertex. Charmproductionismeasuredbythe
reconstruction of exclusive hadronic decays using topological selection of a secondary vertex. Particle
identificationforchargedhadronsisneededtoreducetheverylargebackgroundsinheavy-ioncollisions,
especially at low transverse momentum. In addition, charm and beauty can be tagged in semi-leptonic
decays, detecting electrons and muons. Therefore, the excellent particle-identification capabilities of
the ALICE detector have to be preserved. However, important physics topics, such as the study of
heavy-flavourbaryonsorofopenheavy-flavourhadronswithmorethanoneheavyquark,arebeyondthe
capabilityofthepresentdetector.
Preliminarymeasurementsoftheelliptic-flowcoefficientv (theamplitudeofsecondorderharmonicof
2
theazimuthaldistribution)fordifferentDmesonsin30–50%centralPb-Pbcollisionswereobtainedby
the ALICE experiment; the result is very intriguing, because it suggests that D mesons in the p range
T
2–6GeV/cmayindeedtakepartinthecollectiveflow. Modelstakingintoaccountheavy-quarktransport
inthemedium, withvariousimplementationsofthequark–mediuminteraction, predictalargev forD
2
mesons at low transverse momenta that should become accessible with the upgraded ALICE detector.
Thelow-p Bmesonsv ,notinthereachofpresentexperiments,ispredictedtobesubstantiallysmaller
T 2
than that for D mesons. Such difference in the azimuthal anisotropy at intermediate p is inherent to
T
theQCDinteractionmechanisms,andwouldthusserveasanimportanttestofourunderstandingofthe
natureofmatterformedinheavy-ioncollisions.
The study of heavy-flavour energy loss has a particular interest, because gluon radiation from heavy
quarksatsmallanglesispredictedtobesuppressed,incomparisontothecaseoflightpartons. Moreover,
at LHC energies, high-p light-flavour hadrons are dominantly produced in gluon fragmentation, and
T