Collectivity and manifestations of minimum-bias jets in high-energy nuclear collisions Tom Trainor University of Washington ISMD 2017 Tlaxcala, Mexico
Agenda • What is collectivity? • The two-component (soft + hard) model (TCM) • p-p jets, spectra, correlations and the TCM • p-p 𝑞 𝑢 TCM • p- Pb 𝑞 𝑢 TCM arXiv:1708.09412 • Pb-Pb 𝑞 𝑢 TCM • Naïve Glauber model of p -Pb collisions • PYTHIA – p-p model assumptions vs reality 2
What is Collectivity? collectivity countable collection, any correlations collectivity e.g. dijets = collective phenomenon! several mechanisms may produce correlations our task is to identify them via data analysis 3
Two-component Model – TCM hadron production in p-p collisions near midrapidity 𝝇 𝟏 = 𝝇 𝒕 + 𝝇 𝒊 charge densities: soft + hard soft component SC: projectile-nucleon dissociation participant low- x gluons 𝝇 𝒕 log(√s/10 GeV) hard component HC: large- angle scattered gluons → dijets 𝝇 𝒊 ≈ a a = O (0.01) 𝟑 MB jet fragments: 𝝇 𝒕 (noneikonal) hadron production in A-B collisions follows suite: 𝑸 𝒖 = (𝑶 𝒒𝒃𝒔𝒖 /𝟑) 𝒐 𝒕𝑶𝑶 𝒒 𝒖𝒕𝑶𝑶 + 𝑶 𝒄𝒋𝒐 𝒐 𝒊𝑶𝑶 𝒒 𝒖𝒊𝑶𝑶 extensive 𝑸 𝒖 𝒐 𝒕 = 𝒒 𝒖𝒕 + 𝒚 𝒐 𝒕 𝝃 𝒐 𝒕 𝒒 𝒖𝒊𝑶𝑶 ( 𝒐 𝒕 ) 4
QCD Jets and p - p p t Spectra 𝑸 𝑭 𝑸 𝒒|𝑭 p-p e-e 𝑸 𝑭 𝑸 𝒒 = p-p ∞ 𝑸 𝒒|𝑭 𝑸(𝑭) dE 𝑭 𝒏𝒋𝒐 3 GeV universal form FF – fragmentation functions JS – jet spectra PRD 89, 094011 (2014) PRD 74, 034012 (2006) noneikonal UA1 𝝇 𝒊 ≈ a 𝟑 𝝇 𝒕 𝑸 𝒒 : NSD PYTHIA 200 GeV 200 GeV JS FF = H hard components 200 GeV dijet production PRD 93, 014031(2016) JPHYSG 42, 085105 (2015) 5
p - p Angular Correlations – 2D Model Fits two-particle correlations PRD 93, 014031 (2016) PoS CFRNC2006, 004 (2006) no p t cuts n = 6 H S H ∆𝛓/ 𝛓 𝐬𝐟𝐠 ∆𝛓/ 𝛓 𝐬𝐟𝐠 y t y t p t ≈ 0.6 GeV/c high multiplicity dijets + quad per-participant (per low- x gluon) model-parameter trends S H H Q AS 1D peak LPHD SS 2D peak A Q0 𝝇 𝒕 = soft hard (dijets) 𝟑 quadrupole 𝟒 𝝇 𝒕 𝝇 𝒕 𝝇 𝒕 6
p-p p t Spectrum Hard Component HC energy dependence lower p t cut JPHYSG 44, 44, 0750 5008 08 (201 017) 7) 𝒒 𝒖𝒊𝟏 QCD jets 𝝄 ′ 𝒒 𝒖𝒕 𝝇 𝒕 ≈ 𝟑 𝝇 𝒕𝑶𝑻𝑬 𝜷 ′ / 𝒐 𝒕 𝑸 𝒖𝒕 𝝇 𝒊 ≈ a 𝟑 𝝇 𝒕 ′ = 𝒒 𝒖𝒊𝟏 𝒒 𝒖𝒕 𝒒 𝒖𝒕 /𝝄 spectrum HCs 1 HC n ch 6 dependence 1 SC density: spectrum HCs 𝝇 𝒕 = 𝒐 𝒕 /𝚬𝜽 HC model parameters vs n ch PRD 93, 014031(2016) (biased jet spectra) 7
p-p 𝑞 𝑢 TCM 𝒒 𝒖𝒊𝟏 ALICE: PLB 727, 371(2013) arXiv:1708.09412 ALICE 𝒒 𝒖 ′ 𝒒 𝒖𝒊 𝒒 𝒖𝒊 𝒒 𝒖 ′ ALICE ′ 𝒒 𝒖𝒕 UA1 200 GeV STAR 𝒒 𝒖𝒕 𝒒 𝒖𝒕 STAR 𝝇 𝟏 = 𝝇 𝒕 = ′ / 𝒐 𝒕 = 𝝄 + 𝒚(𝒐 𝒕 ) 𝒒 𝒖𝒊 (𝒐 𝒕 , √s ) 𝒒 𝒖𝒊 𝒐 𝒕 : n ch 𝒐 𝒅𝒊 𝝄 ≈ 0.76 -0.80 dependence, (takeaway 𝒚 𝒐 𝒕 , √s ≡ 𝒐 𝒊 / 𝒐 𝒕 ≈ 𝜷( √s ) 𝝇 𝒕 spectrum HC from p-p ) 𝒒 𝒖𝒕 +𝒚(𝒐 𝒕 ) ′ ≈ 𝒒 𝒖𝒊 (𝒐 𝒕 ) ′ ′ / 𝒐 𝒅𝒊 = 𝑸 𝒖 𝒒 𝒖 direct correspondence: 𝝄+𝒚(𝒐 𝒕 ) 𝒒 𝒖𝒊 vs spectrum HC ′ 𝒐 𝒅𝒊 ′ ≈ 𝒒 𝒖𝒕 + 𝒚(𝒐 𝒕 , √s ) 𝒒 𝒖𝒊 (𝒐 𝒕 , √s ) 𝒒 𝒖 𝒐 𝒕 vs isolated QCD jets 8
p- Pb 𝑞 𝑢 TCM a [ 𝝇 𝒕𝟏 + 𝒏 𝟏 ( 𝝇 𝒕 − 𝝇 𝒕𝟏 ) ] PLB 727, 371(2013) arXiv:1708.09412 𝒒 𝒖 ′ 𝒒 𝒖 ′ 𝒏 𝟏 ≈ 0.1 𝝇 𝒕𝟏 , 𝒏 𝟏 ) ( 𝝇 𝒕𝟏 ≈ 15 𝑸 𝒖 𝒐 𝒕 /𝒐 𝒕 ′ 𝒒 𝒖𝒕 𝒒 𝒖𝒕 𝝇 𝒕 = 𝝇 𝟏 = ′ / 𝒐 𝒕 = 𝝄 + 𝒚(𝒐 𝒕 )𝝃(𝒐 𝒕 ) 𝒐 𝒅𝒊 ′ = 𝒒 𝒖𝒕 +𝒚(𝒐 𝒕 )𝝃(𝒐 𝒕 ) 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) ′ ′ / 𝒐 𝒅𝒊 𝑸 𝒖 = 𝒒 𝒖 𝝄+𝒚(𝒐 𝒕 )𝝃(𝒐 𝒕 ) 𝝇 𝒕 = (𝑶 𝒒𝒃𝒔𝒖 /𝟑) 𝝇 𝒕𝑶𝑶 (𝒐 𝒕 ) * 𝑸 𝒖 𝒐 𝒕 /𝒐 𝒕 = ′ 𝒐 𝒅𝒊 𝒚 𝒐 𝒕 ≡ 𝝇 𝒊𝑶𝑶 𝒐 𝒕 / 𝝇 𝒕𝑶𝑶 (𝒐 𝒕 ) ′ = 𝒒 𝒖 𝒒 𝒖𝒕 + 𝒚(𝒐 𝒕 )𝝃(𝒐 𝒕 ) 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) ≈ 𝜷 𝝇 𝒕𝑶𝑶 𝒐 𝒕 𝒐 𝒕 assume: 𝑶 𝒒𝒃𝒔𝒖 /𝟑 = 𝜷 𝝇 𝒕 / 𝒚 𝒐 𝒕 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) ≈ 𝒒 𝒖𝒊𝟏 p-p value 𝑶 𝒒𝒃𝒔𝒖 = 𝑶 𝒄𝒋𝒐 + 𝟐 𝝃 ≡ 𝟑𝑶 𝒄𝒋𝒐 /𝑶 𝒒𝒃𝒔𝒖 no jet modification 9
𝑞 𝑢 TCM – I Pb-Pb fluctuations PRC 91, 044905(2015) ST: sharp transition 𝝇 𝟏 𝝇 𝒕 = 𝝇 𝒕 = x pp ? PRL 106, 032301(2011) x pp ? ST: PRC 86, 064902(2012) Glauber: 𝝇 𝒕𝑶𝑶 ) 𝟐/𝟒 𝝃 ( 𝒐 𝒕 ) ≈ ( TCM for A-A yield vs centrality: 𝝇 𝒕 / (𝑶 𝒒𝒃𝒔𝒖 /𝟑) 𝝇 𝟏 = 𝝇 𝒕𝑶𝑶 [𝟐 + 𝒚 𝝃 𝝃] 𝒚 ( 𝒐 𝒕 ) = 𝒚 [ 𝝃 ( 𝒐 𝒕 )] obtain from data above: peripheral Pb-Pb follows p-p 𝒚 𝝃 = 𝒚 𝒒𝒒 + 𝟏. 𝟐𝟓𝟑 − 𝒚 𝒒𝒒 × more-central Pb-Pb shows ST: jet modification 𝟐 + tanh[ 𝝃 − 𝟑. 𝟒 /𝟏. 𝟔] /2 PRC 86, 064902(2012) 10
𝑞 𝑢 TCM – II Pb-Pb 𝒒 𝒖𝒊𝟏 PLB 727, 371(2013) arXiv:1708.09412 𝒒 𝒖 ′ 𝒒 ′ 𝒒 ′ 𝒒 ′ ′ 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) 𝒒 𝒖𝒕 x pp ? ′ = 𝒒 𝒖𝒕 +𝒚(𝒐 𝒕 )𝝃(𝒐 𝒕 ) 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) ′ ′ / 𝒐 𝒅𝒊 = new information from Pb-Pb: 𝑸 𝒖 𝒒 𝒖 𝝄+𝒚(𝒐 𝒕 )𝝃(𝒐 𝒕 ) 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) follows p-p trend given Glauber 𝝃 ( 𝒐 𝒕 ) solve for: for peripheral, 𝒒 𝒖𝒊𝑶𝑶 𝒐 𝒕 ≈ 𝒚 𝒐 𝒕 𝑸 𝒖𝒊𝑶𝑶 /𝒐 𝒕𝑶𝑶 falls to saturation value for central given 𝒚 ( 𝒐 𝒕 ) solve for: minimum is 73% of maximum 𝒒 𝒖𝒊𝑶𝑶 (𝒐 𝒕 ) 11
𝑞 𝑢 Data Lessons from three successive collision systems • p-p 𝒒 𝒖𝒊 (𝒐 𝒕 , √s ) trends agree with spectrum HC and MB dijets • p-p dijet production is noneikonal, centrality not relevant • p -Pb 𝒒 𝒖 (𝒐 𝒕 ) establishes factorization of A-B Glauber and N-N noneikonal • p -Pb 𝒒 𝒖 data confirm MB dijets dominate 𝒒 𝒖 (𝒐 𝒕 ) trends • Pb-Pb 𝒒 𝒖 data confirm that naïve Glauber dominates A-A collisions, but peripheral A-A collisions follow p-p trends • Pb-Pb 𝒒 𝒖𝒊𝑶𝑶 𝒐 𝒕 trend confirms jets are modified above ST • Jets still dominate structure in more-central Pb-Pb collisions arXiv:1708.09412 12
Naïve Glauber Model for p -Pb 𝒆𝑸/𝒆𝒐 𝒚 uncertainty? 𝟐 − 𝝉 𝝉 𝟏 100 𝑶 𝒒𝒃𝒔𝒖 = 𝑶 𝒄𝒋𝒐 + 𝟐 𝐣𝐨 𝒒 − 𝐁 PLB 727, 371(2013) n x “[ n ch ] at mid-rapidity scales linearly with [N part ]” 𝒆𝑸/𝒆𝒐 𝒚 → (𝟐/𝝉 𝟏 ) 𝒆𝝉/𝒆𝒐 𝒚 assumes: PLB 727, 371(2013) black points derived from n ch , N part , N bin , b Glauber values in b 0 ≈ 8 fm 𝝇 𝟏 𝒒 𝒖 ′ ? ′ 𝒒 𝒖𝒕 →x ( n ch ) ≈TCM 𝒒 𝒖𝒊𝟏 =1.3 GeV/c 𝒄 𝒄 𝟏 𝟑 𝝉 𝝉 𝟏 = 13
PYTHIA (and Other Monte Carlos) arXiv: 1706.02166 MPI = multiple parton interactions CR 𝒐 𝒅𝒊 ∝ 𝒐 𝑵𝑸𝑱 PLB 727, 371(2013) no jet spectrum cutoff 𝒒 𝟏 → 𝟑 GeV 𝒐 𝑵𝑸𝑱 (𝒄) depends on centrality eikonal model 𝒒 𝒖 (𝒐 𝒅𝒊 ) trend requires color reconnection (CR) 14
PYTHIA (and Other Monte Carlos) arXiv: 1706.02166 MPI = multiple parton interactions CR (HC 3) 𝒐 𝒅𝒊 ∝ 𝒐 𝑵𝑸𝑱 PLB 727, 371(2013) eikonal no jet spectrum cutoff ′ 𝒒 𝒖𝒕 𝒒 𝟏 → 𝟑 GeV 𝒐 𝑵𝑸𝑱 (𝒄) depends on centrality eikonal model 𝒒 𝒖 (𝒐 𝒅𝒊 ) trend requires color reconnection (CR) those assumptions conflict with MB dijets and the p-p TCM see also HIJING, AMPT 15
Conclusions • TCM provides accurate, comprehensive description • Soft component S(y t ) is universal: 𝝇 𝒕 ~ low- x gluons • Jets dominate 𝒒 𝒖𝒊 (𝒐 𝒕 , √s ) structure in all systems • Centrality not relevant for p-p collisions (noneikonal) • A-B systems evolve from isolated N-N to Glauber • Naïve Glauber model applied to p -A system fails • p-p TCM is opposite to PYTHIA basic assumptions • A- B “collectivity” is jet manifestations, not flows 16
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