(1) ncteq nuclear parton distributions and (2) nlo parton 2014-01-13آ  (1) ncteq nuclear parton...

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  • (1) nCTEQ Nuclear Parton Distributions and

    (2) NLO Parton Shower Monte Carlo

    A. Kusina

    Southern Methodist University, Dallas, TX 75275, USA

    Collaborators: F. I. Olness, K. Kovařı́k, I. Schienbein, S. Jadach, M. Skrzypek

    10 January 2014

    1 / 45

  • Education/Employment

    Master’s studies: Jagiellonian University, Krakow, Poland; supervisor: Stanislaw Jadach; thesis: “Evolution of parton distributions in QCD as a two-level Markovian process and its Monte Carlo simulation”

    PhD studies: Institute of Nuclear Physics PAN in Krakow, Poland; supervisor: Stanislaw Jadach; thesis: “Exclusive Kernels for NLO QCD Non-singlet Evolution”

    Postdoc position: Southern Methodist University, Dallas, TX; working with Fred Olness

    2 / 45

  • Topics/projects I have been working on

    During PhD:

    Evolution equations: DGLAP, CCFM

    NLO parton shower Monte Carlo During postdoc at SMU:

    nCTEQ parton distribution functions N3LO heavy quark production in DIS We combined the full massive NLO result with the N3LO massless calculation to obtain an approximate N3LO DIS structure functions with heavy quark mass effects. This is being implemented in HeraFitter and QCDNUM programs.

    W/Z production at LHC We investigated theoretical uncertainties related with W/Z production originating form the strange quark PDF, and observed how W/Z measurements at LHC can be used to constrain strange PDF.

    Hybrid Variable Flavor Number Scheme: generalization of the variable-flavor-number scheme for heavy quarks

    3 / 45

  • nCTEQ PDFs

    nCTEQ nuclear PDFs in collaboration with: F. Olness, K. Kovařı́k, I. Schienbein and T. Ježo

    4 / 45

  • Motivations

    What are PDFs of bound protons/neutrons?

    Heavy ion collisions in LHC and RHIC

    Differentiate flavors in free-proton PDFs (e.g. strange) charged lepton DIS

    Fl ±

    2 ∼ (

    1 3

    )2 [d + s] +

    ( 2 3

    )2 [u + c]

    neutrino DIS

    Fν2 ∼ [ d + s + ū + c̄

    ] Fν̄2 ∼

    [ d̄ + s̄ + u + c

    ] Fν3 ∼ 2

    [ d + s − ū − c̄]

    Fν̄3 ∼ 2 [ u + c − d̄ − s̄]

    5 / 45

  • Assumptions entering the nuclear PDF analysis

    1 Factorization & DGLAP evolution

    allow for definition of universal PDFs make the formalism predictive needed even if it is broken

    2 Isospin symmetry { un/A(x) = dp/A(x)

    dn/A(x) = up/A(x)

    3 The bound proton PDFs have the same evolution equations and sum rules as the free proton PDFs provided we neglect any contributions from the region x > 1 (it is expected to have negligible contribution [PRC 73, 045206 (2006), arXiv:hep-ph/0509241] )

    Then observables OA can be calculated as:

    OA = Z Op/A + (A − Z)On/A

    With the above assumptions we can use the free proton framework to analyze nuclear data

    6 / 45

    http://arxiv.org/abs/0709.3038

  • Schematics of Global Analysis

    1 Parametrize PDFs at low initial scale µ = Q0 = 1.3GeV:

    f (x,Q0) = f (x; a0, a1, . . . ) = a0xa1 (1 − x)a2 P(x; a3, . . . )

    2 Use DGLAP equation to evolve f (x, µ) from µ = Q0 to µ = Q.

    3 Define and minimize appropriate χ2 function (with respect to parameters a0, a1, . . . )

    χ2({ai}) = ∑

    experiments

    wnχ2n({ai})

    χ2n({ai}) = ∑

    data points

    ( data − theory({ai})

    uncertainty

    )2

    (by default wn = 1)

    7 / 45

  • Uncertainties in global analysis

    Experimental errors (included in PDFs error analysis) Theoretical uncertainties (not included) “Details” of Global Fits (e.g. parametrization, HF schemes; hard to estimate not included)

    Propagating experimental errors to PDFs:

    Hessian Method Eigenvector PDFs Quadratic approximation Simple computation of correlations

    Lagrange Multipliers

    Monte Carlo Methods

    8 / 45

  • Hessian method [JHEP 07 (2002) 012, arXiv:hep-ph/0201195]

    Expand χ2 function around minimum, {a0i }, and diagonalize

    χ2 = χ20 + ∑

    ij

    1 2

    (ai − a0i )(aj − a0j ) ( ∂2χ2

    ∂yi∂yj

    ) 0

    = χ20 + ∑

    i

    z2i

    Choose ∆χ2 = χ2 − χ20 value (defining 1-σ uncertainty), ideal case ∆χ2 = 1 realistic global analysis ∆χ2 ∼ 10 − 100

    Construct error PDFs corresponding to each eigenvector direction:

    f ±i = f ({zi}) = f (0, . . . , zi = ± √

    ∆χ2, . . . , 0)

    zi = ± √

    ∆χ2

    Calculate errors of observable X:

    ∆X = 1 2

    √∑ i

    [ X(f +i ) − X(f −i )

    ]2 9 / 45

    http://arxiv.org/abs/hep-ph/0201195

  • Available nuclear PDFs

    Multiplicative nuclear correction factors

    f p/Ai (xN , µ0) = Ri(xN , µ0,A,Z) f free proton i (xN , µ0)

    Hirai, Kumano, Nagai [PRC 76, 065207 (2007), arXiv:0709.3038] Eskola, Paukkunen, Salgado [JHEP 04 (2009) 065, arXiv:0902.4154] de Florian, Sassot, Stratmann, Zurita [PRD 85, 074028 (2012), arXiv:1112.6324]

    Native nuclear PDFs nCTEQ [PRD 80, 094004 (2009), arXiv:0907.2357]

    f p/Ai (xN , µ0) = fi(xN ,A, µ0)

    fi(xN ,A = 1, µ0) ≡ f free protoni (xN , µ0)

    10 / 45

    http://arxiv.org/abs/0709.3038 http://arxiv.org/abs/0902.4154 http://arxiv.org/abs/1112.6324 http://arxiv.org/abs/0907.2357

  • nCTEQ framework [PRD 80, 094004 (2009), arXiv:0907.2357]

    Functional form of the bound proton PDF same as for the free proton (CTEQ6M, x restricted to 0 < x < 1)

    xf p/Ai (x,Q0) = c0x c1 (1 − x)c2 ec3x(1 + ec4 x)c5 , i = uv, dv, g, . . .

    d̄(x,Q0)/ū(x,Q0) = c0xc1 (1 − x)c2 + (1 + c3x)(1 − x)c4

    A-dependent fit parameters (reduces to free proton for A = 1)

    ck → ck(A) ≡ ck,0 + ck,1 ( 1 − A−ck,2), k = {1, . . . , 5}

    PDFs for nucleus (A,Z)

    f (A,Z)i (x,Q) = Z A

    f p/Ai (x,Q) + A − Z

    A f n/Ai (x,Q)

    (bound neutron PDF f n/Ai by isospin symmetry)

    11 / 45

  • Data sets

    NC DIS & DY CERN BCDMS & EMC & NMC N = (D, Al, Be, C, Ca, Cu, Fe, Li, Pb, Sn, W) FNAL E-665 N = (D, C, Ca, Pb, Xe) DESY Hermes N = (D, He, N, Kr) SLAC E-139 & E-049 N = (D, Ag, Al, Au, Be,C, Ca, Fe, He) FNAL E-772 & E-886 N = (D, C, Ca, Fe,W)

    Single pion production (not yet included)

    RHIC - PHENIX & STAR

    N = Au

    Neutrino (to be included later)

    CHORUS CCFR & NuTeV

    N = Pb N = Fe

    12 / 45

  • nCTEQ fits

    Fit properties:

    fit @NLO

    using ACOT heavy quark scheme

    kinematical cuts: Q > 2GeV, W > 3.5GeV

    708 (1233) data points after (before) cuts

    17 free parameters

    7 gluon 8 valence 2 sea

    χ2/dof = 0.87

    Error analysis:

    use Hessian method

    χ2 = χ20 + 1 2

    Hij(ai − a0i )(aj − a0j )

    Hij = ∂2χ2

    ∂ai∂aj

    tolerance ∆χ2 = 35 (every nuclear target within 90% C.L.)

    eigenvalues span 10 orders of magnitude→ require numerical precision

    use noise reducing derivatives

    13 / 45

  • nCTEQ results

    A-dependence of bound proton PDFs

    x f Ai (x,Q) A = (1, 2, 4, 9, 12, 27, 56, 108, 207)

    PR EL

    IM INA

    RY

    uval dval

    u g

    14 / 45

  • nCTEQ results

    Nuclear correction factors (Q = 10GeV)

    Ri(Pb) = f Pbi (x,Q)

    f pi (x,Q)

    different solution for d-valence & u-valence compared to EPS09 & DSSZ

    sea quark nuclear correction factors similar to EPS09

    nuclear correction factors depend largely on underlying proton baseline

    10 3 10 2 10 1 1

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4 ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4 ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4 ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    1.4 ( , )

    nCTEQ EPS09 DSSZ

    10 3 10 2 10 1 1

    ( , )

    nCTEQ EPS09 DSSZ

    PR EL

    IM INA

    RY

    15 / 45

  • nCTEQ results

    Nuclear PDFs (Q = 10GeV)

    x f Pbi (x,Q)

    nCTEQ dval & uval solution between HKN07 & EPS09

    nCTEQ features larger uncertainties than previous nPDFs

    better agreement between different groups (nPDFs don’t depend on proton baseline)

    in EPS09 and DSSZ analysis uval & dval are tied together whereas in nCTEQ they are treated as independent

    10 3 10 2 10 1 1 0.0

    0.1

    0.2

    0.3

    0.4

    0.5

    ( , )nCTEQ HKN07 EPS09 DSSZ

    10 3 10 2 10 1 1 0.0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    ( , )nCTEQ HKN07 EPS09 DSSZ

    10 3 10 2 10 1 1 0

    5

    10

    15

    20

    ( , )

    nCTEQ HKN07 EPS09 DSSZ

    10 3 10 2 10 1 1 0.1

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