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Alternative to the two-component ansatz and implications for small collision systems

Alternative to the two-component ansatz and implications for small collision systems

Correlations and Fluctuations in p-A and A-A collisions, Institute for Nuclear Theory, Seattle, Washington

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J. Scott Moreland

July 06, 2015
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  1. Alternative to the two-component ansatz and implications for small collision

    systems Supported by NNSA Stewardship Science Graduate Fellowship J.S. Moreland, J.E. Bernhard, S.A. Bass | April 6, 2017 Correlations and Fluctuations in p+A and A+A Collisions April 6, 2017 1 / 15
  2. Thinking of initial conditions as a mapping Side view ?

    m n Beam view nucl A nucl B ? 1. Consider all combinations of m-on-n nucleon collisions, how many particles does each system produce at mid-rapidity? April 6, 2017 2 / 15
  3. Thinking of initial conditions as a mapping Side view ?

    m n Beam view nucl A nucl B ? 1. Consider all combinations of m-on-n nucleon collisions, how many particles does each system produce at mid-rapidity? 2. Treat larger systems as amalgamation of m-on-n collisions April 6, 2017 2 / 15
  4. Thinking of initial conditions as a mapping Side view ?

    m n Beam view nucl A nucl B ? 1. Consider all combinations of m-on-n nucleon collisions, how many particles does each system produce at mid-rapidity? 2. Treat larger systems as amalgamation of m-on-n collisions Fundamental assumption There exists a single (possibly energy dependent) mapping from nuclear thickness to entropy density: dS/dy|y=0 ∝ f (TA, TB) April 6, 2017 2 / 15
  5. Continuous function of two variables... where to begin? For all

    its shortcomings, the wounded nucleon model is remarkably successful at describing soft particle production Mapping must respect basic physical constraints, e.g. symmetric and monotonic in TA, TB April 6, 2017 3 / 15
  6. Continuous function of two variables... where to begin? For all

    its shortcomings, the wounded nucleon model is remarkably successful at describing soft particle production Mapping must respect basic physical constraints, e.g. symmetric and monotonic in TA, TB Could start by making wild guesses .... TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 April 6, 2017 3 / 15
  7. Continuous function of two variables... where to begin? For all

    its shortcomings, the wounded nucleon model is remarkably successful at describing soft particle production Mapping must respect basic physical constraints, e.g. symmetric and monotonic in TA, TB Could start by making wild guesses .... TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 non-symmetric April 6, 2017 3 / 15
  8. Continuous function of two variables... where to begin? For all

    its shortcomings, the wounded nucleon model is remarkably successful at describing soft particle production Mapping must respect basic physical constraints, e.g. symmetric and monotonic in TA, TB Could start by making wild guesses .... TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 non-symmetric non-monotonic April 6, 2017 3 / 15
  9. Continuous function of two variables... where to begin? For all

    its shortcomings, the wounded nucleon model is remarkably successful at describing soft particle production Mapping must respect basic physical constraints, e.g. symmetric and monotonic in TA, TB Could start by making wild guesses .... TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 non-symmetric non-monotonic plausible April 6, 2017 3 / 15
  10. Parameterizing entropy deposition Historically started with wounded nucleon model, dS/dy|y=0

    ∼ TA + TB 2 April 6, 2017 4 / 15
  11. Parameterizing entropy deposition Historically started with wounded nucleon model, dS/dy|y=0

    ∼ TA + TB 2 Binary collision term later postulated to boost particle production in central A+A collisions dS/dy|y=0 ∼ (1 − α) TA + TB 2 + α σNNTATB April 6, 2017 4 / 15
  12. Parameterizing entropy deposition Historically started with wounded nucleon model, dS/dy|y=0

    ∼ TA + TB 2 Binary collision term later postulated to boost particle production in central A+A collisions dS/dy|y=0 ∼ (1 − α) TA + TB 2 + α σNNTATB In this work we replace the arithmetic mean with a generalized mean, dS/dy|y=0 ∝ Tp A + Tp B 2 1/p p = −∞ min −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 4 / 15
  13. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates −10 −5 0 5 10 x [fm] −10 −5 0 5 10 y [fm] April 6, 2017 5 / 15
  14. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) −10 −5 0 5 10 x [fm] −10 −5 0 5 10 y [fm] April 6, 2017 5 / 15
  15. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw −10 −5 0 5 10 x [fm] −10 −5 0 5 10 y [fm] TA April 6, 2017 5 / 15
  16. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw −10 −5 0 5 10 x [fm] −10 −5 0 5 10 y [fm] TB April 6, 2017 5 / 15
  17. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw 4. Take generalized mean of TA, TB , dS/dy|y=0 ∝ TR ≡ Tp A +Tp B 2 1/p −10 −5 0 5 10 x [fm] −10 −5 0 5 10 y [fm] dS/dy April 6, 2017 5 / 15
  18. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw 4. Take generalized mean of TA, TB , dS/dy|y=0 ∝ TR ≡ Tp A +Tp B 2 1/p −10 −5 0 5 10 x [fm] −10 −5 0 5 10 y [fm] dS/dy April 6, 2017 5 / 15
  19. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw 4. Take generalized mean of TA, TB , dS/dy|y=0 ∝ TR ≡ Tp A +Tp B 2 1/p −10 −5 0 5 10 x [fm] 0 1 2 3 4 Thickness [fm−2 ] Generalized Mean p=-10 TA TB TR April 6, 2017 5 / 15
  20. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw 4. Take generalized mean of TA, TB , dS/dy|y=0 ∝ TR ≡ Tp A +Tp B 2 1/p −10 −5 0 5 10 x [fm] 0 1 2 3 4 Thickness [fm−2 ] Generalized Mean p=1 TA TB TR April 6, 2017 5 / 15
  21. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw 4. Take generalized mean of TA, TB , dS/dy|y=0 ∝ TR ≡ Tp A +Tp B 2 1/p −10 −5 0 5 10 x [fm] 0 1 2 3 4 Thickness [fm−2 ] Generalized Mean p=10 TA TB TR April 6, 2017 5 / 15
  22. TRENTo – new parametric model for entropy deposition 1. Sample

    nucleon coordinates 2. Determine nucleon participants, Pcoll = 1 − exp(−σgg Tpp ) 3. Define participant thickness, T = Npart i=1 wi Tp (x − xi , y − yi ) Sample wi from Gamma dist, Pk (w) = kk Γ(k) wk−1e−kw 4. Take generalized mean of TA, TB , dS/dy|y=0 ∝ TR ≡ Tp A +Tp B 2 1/p “Thickness Reduced Event-by-event Nuclear Topology” −10 −5 0 5 10 x [fm] 0 1 2 3 4 Thickness [fm−2 ] Generalized Mean p=1 TA TB TR April 6, 2017 5 / 15
  23. Demonstrating the flexibility of the ansatz For p = 1

    model reduces to a wounded nucleon model (exact) for p = −0.65 model replicates the KLN mapping to O(1%) dNg d2r⊥dy ∼ Q2 s,min 2 + log Q2 s,max Q2 s,min , Q2 s ∼ T Drescher, Nara Phys. Rev. C 75, 034905 (2007) KLN mapping TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 Generalized mean p=-0.65 TA 0 2 4 6 8 10 TB 0 2 4 6 8 10 f(TA ,TB ) 0 2 4 6 8 10 April 6, 2017 6 / 15
  24. Demonstrating the flexibility of the ansatz p ≈ 0 mimics

    the IP-Glasma model Similar harmonics and multiplicities right: eccentricity vs impact param. More on this later in the talk ... 0 2 4 6 8 10 12 14 b [fm] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 εn Au-Au @ 200 GeV Eccentricities KLN IP-Glasma Npart Trento p=0, k=1.4 Schenke, Tribedy, Venugopalan Phys. Rev. Lett. 108, 252301 (2012) Opportunity: Constrain the generalized mean parameter p via systematic model-to-data comparison to simultaneously extract the QGP viscosity and initial conditions April 6, 2017 7 / 15
  25. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 TRENTo model plotted against LHC multiplicity distributions April 6, 2017 8 / 15
  26. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 TRENTo model plotted against LHC multiplicity distributions Lines indicate different values of the generalized mean (annotated) April 6, 2017 8 / 15
  27. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 TRENTo model plotted against LHC multiplicity distributions Lines indicate different values of the generalized mean (annotated) Bands indicate ±30% variation in optimal fluctuation parameter April 6, 2017 8 / 15
  28. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 TRENTo model plotted against LHC multiplicity distributions Lines indicate different values of the generalized mean (annotated) Bands indicate ±30% variation in optimal fluctuation parameter Norm is varied to account for differences in energy and kinematic cuts April 6, 2017 8 / 15
  29. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 All means fit p+p, p+Pb with suitably chosen norm and fluctuations April 6, 2017 8 / 15
  30. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 All means fit p+p, p+Pb with suitably chosen norm and fluctuations Only geometric mean describes shape of Pb+Pb data April 6, 2017 8 / 15
  31. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 All means fit p+p, p+Pb with suitably chosen norm and fluctuations Only geometric mean describes shape of Pb+Pb data Normalizations provide further constraints on allowable parameters: p k p+p norm p+Pb norm Pb+Pb norm +1 0.8 9.7 7.0 13. 0 1.4 19. 17. 16. −1 2.2 24. 26. 18. April 6, 2017 8 / 15
  32. Testing parameterization against measured multiplicities 0 10 20 30 40

    50 Nch 10−4 10−3 10−2 10−1 100 101 P(Nch ) p=1 p=0 p=−1 ALICE 2.36 TeV NSD |η| <1, pT corrected p+p ×102 ×101 ×100 0 50 100 150 200 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 5.02 TeV |η| <1, 0.2<pT <3.0 GeV p+Pb ×104 ×102 ×100 0 1000 2000 3000 Nch 10−6 10−4 10−2 100 102 p=1 p=0 p=−1 ALICE 2.76 TeV |η| <1, 0.2<pT <3.0 GeV Pb+Pb ×104 ×102 ×100 All means fit p+p, p+Pb with suitably chosen norm and fluctuations Only geometric mean describes shape of Pb+Pb data Normalizations provide further constraints on allowable parameters: p k p+p norm p+Pb norm Pb+Pb norm +1 0.8 9.7 7.0 13. 0 1.4 19. 17. 16. −1 2.2 24. 26. 18. April 6, 2017 8 / 15
  33. Testing parameterization against flow constraints 0 25 50 75 100

    Centrality % 0.0 0.2 0.4 0.6 εn ε2 0 25 50 75 100 Centrality % 0.0 0.2 0.4 0.6 ε3 Arithmetic: p=1 Geometric: p=0 Harmonic: p=−1 0 10 20 30 40 Centrality % 0.3 0.6 0.9 1.2 Ratio IP-Glasma Gray band: PRC 89 014902 (2014) TRENTo Pb+Pb eccentricity harmonics: εneinφ = − dx dy rneinφs(x, y) dx dy rns(x, y) April 6, 2017 9 / 15
  34. Testing parameterization against flow constraints 0 25 50 75 100

    Centrality % 0.0 0.2 0.4 0.6 εn ε2 0 25 50 75 100 Centrality % 0.0 0.2 0.4 0.6 ε3 Arithmetic: p=1 Geometric: p=0 Harmonic: p=−1 0 10 20 30 40 Centrality % 0.3 0.6 0.9 1.2 Ratio IP-Glasma Gray band: PRC 89 014902 (2014) TRENTo Pb+Pb eccentricity harmonics: εneinφ = − dx dy rneinφs(x, y) dx dy rns(x, y) Generalized mean parameter strongly affects fireball ellipticity, April 6, 2017 9 / 15
  35. Testing parameterization against flow constraints 0 25 50 75 100

    Centrality % 0.0 0.2 0.4 0.6 εn ε2 0 25 50 75 100 Centrality % 0.0 0.2 0.4 0.6 ε3 Arithmetic: p=1 Geometric: p=0 Harmonic: p=−1 0 10 20 30 40 Centrality % 0.3 0.6 0.9 1.2 Ratio IP-Glasma Gray band: PRC 89 014902 (2014) TRENTo Pb+Pb eccentricity harmonics: εneinφ = − dx dy rneinφs(x, y) dx dy rns(x, y) Generalized mean parameter strongly affects fireball ellipticity, but only weakly affects triangularity April 6, 2017 9 / 15
  36. Testing parameterization against flow constraints 0 25 50 75 100

    Centrality % 0.0 0.2 0.4 0.6 εn ε2 0 25 50 75 100 Centrality % 0.0 0.2 0.4 0.6 ε3 Arithmetic: p=1 Geometric: p=0 Harmonic: p=−1 0 10 20 30 40 Centrality % 0.3 0.6 0.9 1.2 Ratio IP-Glasma Gray band: PRC 89 014902 (2014) TRENTo Pb+Pb eccentricity harmonics: εneinφ = − dx dy rneinφs(x, y) dx dy rns(x, y) Generalized mean parameter strongly affects fireball ellipticity, but only weakly affects triangularity Varying fluctuation parameter by ±30% has negligible effect on eccentricity harmonics, i.e. p+p fluctuations are sub-leading effect. April 6, 2017 9 / 15
  37. Testing parameterization against flow constraints 0 25 50 75 100

    Centrality % 0.0 0.2 0.4 0.6 εn ε2 0 25 50 75 100 Centrality % 0.0 0.2 0.4 0.6 ε3 Arithmetic: p=1 Geometric: p=0 Harmonic: p=−1 0 10 20 30 40 Centrality % 0.3 0.6 0.9 1.2 Ratio IP-Glasma Gray band: PRC 89 014902 (2014) Ratio of ε2/ε3 strong discriminator for initial condition models. Easy to fit v2 by varying η/s... hard to fit v2 and v3 simultaneously. April 6, 2017 9 / 15
  38. Testing parameterization against flow constraints 0 25 50 75 100

    Centrality % 0.0 0.2 0.4 0.6 εn ε2 0 25 50 75 100 Centrality % 0.0 0.2 0.4 0.6 ε3 Arithmetic: p=1 Geometric: p=0 Harmonic: p=−1 0 10 20 30 40 Centrality % 0.3 0.6 0.9 1.2 Ratio IP-Glasma Gray band: PRC 89 014902 (2014) Ratio of ε2/ε3 strong discriminator for initial condition models. Easy to fit v2 by varying η/s... hard to fit v2 and v3 simultaneously. Gray band from Retinskaya, Luzum, Ollitrault, allowed region for eccentricity ratio ε2 2 / ε2 3 0.6 determined using measured flows and linear response vn ∝ εn. Eccentricity ratio prefers geometric mean and mimics IP-Glasma Both multiplicities and flows in agreement, prefer p ∼ 0 at LHC April 6, 2017 9 / 15
  39. Event-by-event flow distributions Top: IP-Glasma ε2/ ε2 , and IP-Glasma+Music

    v2/ v2 (Bjorn’s QM14 talk) Bottom: TRENTo ε2/ ε2 for different values of the generalized mean 0.0 0.5 1.0 1.5 2.0 2.5 3.0 v2 / ­ v2 ® , ε2 / ­ ε2 ® 10−2 10−1 100 P(v2 / ­ v2 ® ), P(ε2 / ­ ε2 ® ) 0-5% ATLAS p=0 p=1 p=−1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 v2 / ­ v2 ® , ε2 / ­ ε2 ® 10−2 10−1 100 P(v2 / ­ v2 ® ), P(ε2 / ­ ε2 ® ) 15-20% ATLAS p=0 p=1 p=−1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 v2 / ­ v2 ® , ε2 / ­ ε2 ® 10−2 10−1 100 P(v2 / ­ v2 ® ), P(ε2 / ­ ε2 ® ) 40-45% ATLAS p=0 p=1 p=−1 April 6, 2017 10 / 15
  40. Event-by-event flow distributions Top: IP-Glasma ε2/ ε2 , and IP-Glasma+Music

    v2/ v2 (Bjorn’s QM14 talk) Bottom: TRENTo ε2/ ε2 for different values of the generalized mean 0.0 0.5 1.0 1.5 2.0 2.5 3.0 v2 / ­ v2 ® , ε2 / ­ ε2 ® 10−2 10−1 100 P(v2 / ­ v2 ® ), P(ε2 / ­ ε2 ® ) 0-5% ATLAS p=0 p=1 p=−1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 v2 / ­ v2 ® , ε2 / ­ ε2 ® 10−2 10−1 100 P(v2 / ­ v2 ® ), P(ε2 / ­ ε2 ® ) 15-20% ATLAS p=0 p=1 p=−1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 v2 / ­ v2 ® , ε2 / ­ ε2 ® 10−2 10−1 100 P(v2 / ­ v2 ® ), P(ε2 / ­ ε2 ® ) 40-45% ATLAS p=0 p=1 p=−1 Generalized mean parameter strongly affects eccentricity distribution shape. Preliminary results (no hydro) consistent with p ≈ 0. Consistent with harmonic ratio and multiplicity constraints shown previously. April 6, 2017 10 / 15
  41. Implications for small collision systems

  42. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p=−1.0 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  43. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p=−0.8 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  44. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p=−0.6 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  45. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p=−0.4 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  46. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p=−0.2 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  47. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p= +0.0 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  48. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p= +0.2 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  49. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p= +0.4 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  50. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p= +0.6 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  51. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p= +0.8 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  52. Mapping effect on p+p entropy deposition Bzdak, Schenke, Tribedy, Venugopalan,

    Phys. Rev. C 87, no. 6, 064906 (2013) Generalized Mean p+p collision −2 −1 0 1 2 x [fm] −1 0 1 y [fm] p= +1.0 Generalized mean interpolates between distinct deposition schemes April 6, 2017 12 / 15
  53. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  54. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  55. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  56. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  57. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  58. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  59. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  60. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  61. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  62. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  63. p+Pb @ 2.76 TeV d+Au @ 200 GeV −∞ min

    −1 harmonic 0 geometric 1 arithmetic ∞ max April 6, 2017 13 / 15
  64. Constraining entropy deposition with multiple systems 100 101 102 103

    dNch /dη p+p d+Au Cu+Cu Cu+Au Au+Au U+U (× 2) TRENTO p=0.3, k=1.3 PHOBOS Au+Au, |η|< 1 STAR Au+Au, |η|< 0.5 PHOBOS Cu+Cu, |η|< 1 STAR d+Au, |η|< 0.5 UA5 p+p, |η|< 1.5 0 20 40 60 80 100 Centrality % 0.7 1.0 1.3 Ratio April 6, 2017 14 / 15
  65. Constraining entropy deposition with multiple systems 100 101 102 103

    dNch /dη p+p d+Au Cu+Cu Cu+Au Au+Au U+U (× 2) TRENTO p=1.0, k=1.0 PHOBOS Au+Au, |η|< 1 STAR Au+Au, |η|< 0.5 PHOBOS Cu+Cu, |η|< 1 STAR d+Au, |η|< 0.5 UA5 p+p, |η|< 1.5 0 20 40 60 80 100 Centrality % 0.7 1.0 1.3 Ratio April 6, 2017 14 / 15
  66. Summary Introduce TRENTo , a new parametric model which deposits

    entropy proportional to the generalized mean of participant matter. Model can mimic behaviour of well known initial conditions models such as KLN and IP-Glasma. Preliminary results (no hydro!) indicate that the LHC prefers p ≈ 0 which closely mimics IP-Glasma scaling. RHIC prefers p ≈ 0.3. Model prefers entropy deposition in p+p and p+A collisions which is more eikonal, i.e. localized in p+p overlap region. Currently working on embedding model in systematic Bayesian analysis to extract QGP medium and initial state properties simultaneously. Model available at: https://github.com/Duke-QCD/trento April 6, 2017 15 / 15