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Physics at the Electron Ion Collider 3

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Physics at the Electron Ion Collider 3 Unpolarized quark distributions: valence quarks and sea quarks x X here is x-bjorken. In DIS it can be measured explicitly event by event In p-p scattering it is not possible to use it, but can be inferenced from MC events generation. 7/15/2019 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 80 Deep Inelastic Scattering: Precision and control Kinematics: Q2 = −q2 = −(k − k" )2 Measure of µ µ resolution 2 power Q = 2Ee Ee"(1 − cosΘe ' ) pq E" %θ" ( y 1 e cos2 e Measure of = = − ' * inelasticity pk Ee & 2 ) Q2 Q2 Measure of High lumi & acceptance x = = momentum Exclusive DIS 2 pq sy fraction of detect & identify everything e+p/A à e’+h(p,K,p,jet)+… struck quark Hadron : Semi-inclusive events: e+p/A à e’+h(p,K,p,jet)+X Eh detect the scattered lepton in coincidence with identified hadrons/jets z = ; pt E*/"$.#,=#-/$/%$g* ν Inclusive events: e+p/A à e’+X s = 4 Eh Ee Low lumi & acceptance detect only the scattered lepton in the detector 6/24/21 NNPSS 2021 EIC Lecture 3 81 The x-Q2 Plane y = 0.95 Energy s y = const 2 2 Q s x y ⇡ · · log Q The x-Q2 y = 0.01 plane… y = const log x 1 • Low-x reach requires large √s • Large-Q2 reach requires large √s • y at colliders typically limited to 0.95 < y < 0.01 !18 7/15/2019 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 82 Kinematic coverage as a function of energy of collisions 5 x 50 10 x 100 As beam energies increase, so does the x, Q2 coverage of the collider: 5, 10 20 x 250 and 20 GeV electrons colliding with 50, 100 and 250 GeV protons y = 0.95 and 0.01 are shown on all plots (they too shift as function of energy of collisions) 7/15/2019 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 83 7/04/2014 Questions in Hadron Physics: RHIC Spin 25 Monte Carlo Generated events: for a pT range of pions produced what is the x of the leading parton that created the pion p+p à pi + X Principle LimitationsStart with any polarized gluon distribution and• Limited produce P_T distribution x-range of pions or gamma distribution. • Need to widen it… See bottom. • Higher and lower Center of Mass For any pTOperationrange, one see one sees the x distribution of the originating partons associated• PHENIX with it. measured at 62 GeV CM There is a large overlap. The lowest pT distribution end at 10^{-2}. Any thingExtendsignificantly less to than pT of 2 is going to be difficult to measure and identify inlower detectors. x at √s = 500 GeV 7/15/2019 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 84 • Overlapping x for p bins T • Need more exclusive π measurements (Luminosity) x • γ-Jet (PHENIX VTX upgrade) √ • Jet-Jet (STAR ready) Abhay Deshpande Center for Frontiers in Nuclear Science Electron Ion Collider The Electron Ion Collider Abhay Deshpande Lecture 3 of 3 Lecture 1 of 3 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 85 Abhay Deshpande Overview of these lectures: Understanding the structure of matter Lecture 3: Electron Ion Collider: Frontiers in investigations of QCD • Solving the spin puzzle è 3D imaging of the nucleon • Gluons in nuclei: what role in nuclei? Do they saturate? • Designing an EIC detector and Interaction Region (IR) • EIC: Status and prospects • What can you do for the US EIC? 7/15/2019 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 86 Center for Frontiers in Nuclear Science Electron Ion Collider: Science, Status & Prospects 2018 2015 2016 2019 2019 - future Realization Physics of EIC Evaluation 6/24/21 NNPSSAbhay 2021 Deshpande EIC Lecture 3 87 On the menu today: • Highlights of the Electron Ion Collider science • The EIC project setup • Machine, detector & call for proposal • EIC Users Group aspirations & recent developments • Proto-CollaBorations/consortia… • Realization and the path forward (particularly for experiments) 6/24/21 NNPSS 2021 EIC Lecture 3 88 Deep Inelastic Scattering: Precision and control Kinematics: Q2 = −q2 = −(k − k" )2 Measure of µ µ resolution 2 power Q = 2Ee Ee"(1 − cosΘe ' ) pq E" %θ" ( y 1 e cos2 e Measure of = = − ' * inelasticity pk Ee & 2 ) Q2 Q2 Measure of High lumi & acceptance x = = momentum Exclusive DIS 2 pq sy fraction of detect & identify everything e+p/A à e’+h(p,K,p,jet)+… struck quark Hadron : Semi-inclusive events: e+p/A à e’+h(p,K,p,jet)+X Eh detect the scattered lepton in coincidence with identified hadrons/jets z = ; pt E*/"$.#,=#-/$/%$g* ν Inclusive events: e+p/A à e’+X s = 4 Eh Ee Low lumi & acceptance detect only the scattered lepton in the detector 6/24/21 NNPSS 2021 EIC Lecture 3 89 Ep proton beam energy Ee electron beam energy p =(0, 0,Ep,Ep) four momentum of incoming proton with mass mp e =(0, 0, °Ee,Ee) four momentum of incoming electron 0 0 0 0 0 0 e =(Eesinµe, 0,Eecosµe,Ee) four momentum of scattered electron 2 s =(e + p) =4EpEe square of total ep c.m. energy q2 =(e ° e0)2 = °Q2 mass squared of exchanged current J = square of four momentum transfer ∫ = q · p/mp energy transfer by J in p rest system ∫max = s/(2mp)maximumenergytransfer y =(q · p)/(e · p)=∫/∫max fraction of energy transfer x = Q2/(2q · p)=Q2/(ys) Bjorken scaling variable 0 qc = x · p +(e ° e ) four momentum of current quark 2 0 2 M =(e + qc) = x · s mass squared of electron - current quark system. 0 The electron and proton masses (me,mp) have been neglected. The angle µe of the scattered electron is measured with respect to the incoming proton (see Fig. 1b). For simplicity, the scattered electron has been assumed to have zero azimuthal angle. For p fixed c.m. energy s,theinclusiveprocessep ! eX is described by two Lorentz- invariant variables which can be determined from the electron or the hadronic system. The electron side yields: 0 Ee 0 y =1° (1 ° cosµe) 2Ee 2 0 0 Q =2EeEe(1 + cosµe) 0 0 x = Ee(1 + cosµe)/(2yEp) 0 Ee =(1° y)Ee + xyEp xyE E°j (1 ° y)E cosµ0 x = p (1 + cosµej)/(1 ° y) Some times scatterede =electron2Ep can’t be measured…. xyEp +(1° y)Ee 0 2 2 0 Ej = yEe + x(1 ° y)Ep Ee sin µe =4xy(1 ° y)EeEp . (3) Reason: ° yEe +(1° y)xEp cospµj = 1) ScatteringWith theangle help so of small the relation that it isM too= closex · stothe theyE variable beame +(1 pipe°x ycan)xE bep replaced by the mass 2 2 2 2) RadiativeM of correction the electron too current large, quark i.e. Eelectronj system.sin µj lost=4 itsxy (1energy° y)E edueEp = toQ Initial(1 ° yState) . Radiation or(4) BrehmstrahlungNeglectingthrough the proton material remnant, -- So the the hadron kinematic system reconstructionj,withenergy unreliable.E and production Using the method of Jacquet-Blondel [8] the hadron variablesj can be determined What toangle do? µThen,yields: see if we can reconstruct the hadronic final state? j approximately by summing the energies (E ) and transverseEj (p ) and longitudinal h x = (1Th + cosµj)/(1 ° y) momenta (p ) of all final state particles. The method2 restsEp on the assumption Zh Ej that the total transversey = momentum(1 ° cos carriedµj) by thoseEj hadrons= yE whiche + x(1 escape° y)E detectionp 2Ee through the beam hole in the proton direction as well as the energy° yEe carried+(1° byy)xE particlesp 2 2 2 cosµ Q = E sin µj/(1 ° y) j = escaping through the beamj hole in the electron direction canyE be neglected.e +(1° y) ThexEp result is: E2sin2µ xy y E E Q2 y . 3 j j =4 (1 ° ) e p = (1 ° ) (4) 1 yJB = (Eh ° pZh) Using the2E methode of Jacquet-Blondel [8] the hadron variables can be determined Xh approximately by summing2 the energies2 (Eh) and transverse (pTh) and longitudinal 2 ( h pXh) +( h pYh) QmomentaJB = (pZh) of all final state particles. The method rests on the assumption P 1 ° yJBP that the total2 transverse momentum carried by those hadrons which escape detection xthroughJB = theQJB beam/(yJB holes) in the proton direction as well as the (5) energy carried by particles escaping through the beam hole in the electron direction can be neglected. The result 7/15/2019 NNPSS 2021: UNAM/IU: Lectures on the Electron Ion Collider 90 The double-angle (DA) methodis: of [1] uses the electron scattering angle and the angle ∞h which characterizes the longitudinal and transverse momentum1 flow of the hadronic system (in the naive quark-parton model y∞JBis= the scattering(Eh ° anglepZh) of the h 2Ee struck quark): Xh ( p )2 +( p )2 Q2 = h Xh h Yh 2 2 JB 2 y ( h pXh) +( h pYh) ° ( h(Eh ° pZhP)) 1 ° JBP cos∞ = 2 (6) h 2 2 x = Q /2(y s) (5) (Ph pXh) +(Ph pYh) +(PhJB(Eh ° pZhJB)) JB P P P leading to The double-angle (DA) method of [1] uses the electron scattering angle and the angle ∞h which characterizes the longitudinal and transverse momentum flow of the 2 0 hadronic4E systemsin∞h (in(1 +thecos naiveµ ) quark-parton model ∞ is the scattering angle of the Q2 e e h DA = 0 0 strucksin∞ quark):h + sinµe ° sin(∞h + µe) 0 0 Ee sin∞h + sinµe + sin(∞2h + µe) 2 2 xDA = · ( h pXh) +( h pYh) ° ( h(Eh ° pZh)) E sin∞ cos+∞hsin=µ0 ° sin(∞ + µ0 ) (6) p h (e p )2h +(e p )2 +( (E ° p ))2 Ph0 Xh Ph Yh Ph h Zh sin∞h (1 + cosµe) y = P P P DA sin∞ sinµ0 sin ∞ µ0 leading toh + e + ( h + e) (1 ° cos∞ ) sinµ0 = h e 0 0 4E2sin∞ (1 + cosµ0 ) sin∞h + sinµe °Q2sin(∞h + µe) e h e DA = 0 0 2 sin∞h + sinµe ° sin(∞h + µe) = QDA/(xDAs) .
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