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  • Electromagnetic Emission

    (and energy loss) in the QGP

    Guy D. Moore (McGill University)

    P. Arnold, L. Yaffe, S. Jeon,

    P. Aurenche, F. Gelis, H. Zaraket,

    and of course many others

    1

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    2

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    3

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    5

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    9

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    16

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    Decay photons: decays in flight of π0 and η

    17

  • Cartoon of yields of each processL

    og(N

    umbe

    r)

    Log(Energy)

    Prompt

    QGPHadronic

    Prompt: power law hard

    tail

    QGP: thermal (exp. tail)

    plus small powerlaw tail

    Hadronic: like QGP but

    softer

    18

  • The bad news isL

    og(N

    umbe

    r)

    Log(Energy)

    Prompt

    QGPHadronic

    Decay Photons

    Probably more Decay pho-

    tons than Direct photons at

    every energy!

    Why? direct photons have

    no αEM suppression

    19

  • Seeing the prompt photons

    Prompt photon yield should be calculable

    • Perturbative calculation

    Not easy: relatively small x, scale dependence

    • Measurement in pp collisions

    May be visible above the backgrounds!

    • Main background: π0 decays

    • π0 rate is measurable (with errors)

    • π0 production is suppressed (Jet Quenching)

    20

  • Direct photons: Already observed?

    (GeV)Tp

    0 1 2 3 4 5 60

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8

    2

    0 1 2 3 4 5 60

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8

    2

    (GeV)Tp

    0 1 2 3 4 5 60

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8

    2

    0 1 2 3 4 5 60

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8

    2

    PbGl, peripheral (60-80%)

    PHENIX preliminary PHENIX preliminary

    = 200 GeV Au+Au NNs

    PbGl, central (0-10%)

    = 200 GeV Au+Au NNs

    (γ / π0) m

    easured / (

    γ / π0) sim

    (γ / π0) m

    easured / (

    γ / π0) sim

    Phenix observation can be interpreted as seeing photon

    excess in central collisions at high pT .

    At pT ∼ 5 GeV, probably “direct” photons.

    21

  • Direct photons: Already observed!

    Eγ(GeV)

    QM2004 data, most central bin

    22

  • Thermal Photons: an Interesting Theoretical

    Problem

    • Approximate/Assume QGP to be in equilibrium

    • Compute dNγ(k, T )/d3kd4x by Thermal Field Theory

    • Insert into hydrodynamic evolution of the QGP

    +

    Leading order diagrams.

    Parametrically O(αsαEM).

    Logarithmically enhanced.

    Problem believed solved in

    1989

    23

  • That treatment is incomplete!

    Aurenche, Gelis, Kobes, Zaraket

    and

    naively O(α2sαEM)

    actually O(αsαEM)

    Bremsstrahlung, inelastic annihilation: collinear

    enhancements

    Thermal QFT diagrams, summing all lines but γ:

    24

  • Treatment STILL incomplete!

    Loop diagrams like

    corresponding to the interference between diagrams,

    are also αsαEM! (Double collinear enhancement)

    25

  • Physical reason

    Opening angle ∼ gsT/E ¿ 1, and vquark ' c.

    Wave packet transverse size ∼ 1/gsT .

    Approaching quark

    wide transverseScattering

    site

    Outgoing quark

    Wave packets overlap overa long distance (Formation length)

    Outgoing photonwave packet

    26

  • Second scattering while wave packets still overlap:

    Approaching quark

    Emissions from scatterings overlap and interfere in

    amplitude.

    For E ∼ T , τ−1form∼ g2sT , and scattering width Γ ∼ g

    2sT .

    Some–incomplete–interference expected. LPM effect!

    27

  • Diagrammatic Analysis

    Lengthy power counting analysis (Arnold, GM, Yaffe)

    One must include

    diagrams of form

    corresponding roughly to

    *

    But no other diagrams needed

    28

  • Resummation of Diagrams

    Diagrams may be resummed by defining a dressed vertex,

    +=

    + + . . . =

    determined by an integral equation (second line).

    29

  • Emission rate from thermal QGP (3 light flavors) is AMY

    dNγd3kd4x

    =2αEM4π2k

    ∫ ∞

    −∞

    dp

    ∫ d2p⊥(2π)2

    nf (k+p) [1−nf (p)]

    2[p (p+k)]2×

    ×

    [

    p2 + (p+k)2]

    Re{

    2p⊥ · f(p⊥; p, k)}

    (1)

    2p⊥ = iδE f(p⊥; p, k) +2π

    3g2s

    ∫ d2q⊥(2π)2

    m2D T

    q2⊥(m2D+q

    2⊥)×

    ×

    [

    f(p⊥; p, k)− f(q+p⊥; p, k)]

    , (2)

    δE =p2⊥ +m

    2∞

    2

    k

    p(k+p)(3)

    Note, (2) is implicit and must be solved numerically.

    30

  • Result

    Brem/pair type and 2↔ 2 production rates are comparable.

    31

  • Folding into a hydro code:

    Hydro model dependence À rate uncertainty!

    Ruuskanen et. al.

    Thermal γ ∼ γ(π0)/10.

    Challenging but not im-

    possible experimentally

    32

  • Jet quenching

    A few hard partons are produced when the primaries collide.

    They must escape through the QGP.

    Lose energy on the way, mostly

    to gluon brem.

    33

  • Jet quenching, γ production similar: brem, LPM...

    Emission rate, per dk of gluon energy and dt of time:

    dΓ(p, k)

    dkdt=

    Csg2s

    16πp71

    1± e−k/T1

    1± e−(p−k)/T×

    ×

    1+(1−x)2

    x3(1−x)2q → qg

    Nfx2+(1−x)2

    x2(1−x)2g → qq

    1+x4+(1−x)4

    x3(1−x)3g → gg

    ×

    ×

    d2h

    (2π)22h · Re F(h, p, k) ,

    (p: parton energy; x ≡ k/p; h: measure of non-collinearity)

    34

  • Here F is given by

    2h = iδE(h, p, k)F(h) + g2∫

    d2q⊥(2π)2

    C(q⊥)×

    ×

    {

    (Cs − CA/2)[F(h)− F(h−k q⊥)]

    +(CA/2)[F(h)− F(h+pq⊥)]

    +(CA/2)[F(h)− F(h−(p−k)q⊥)]}

    ,

    δE(h, p, k) =h2

    2pk(p−k)+m2k2k

    +m2p−k2(p−k)

    −m2p2p

    .

    with C(q⊥) =m2

    D

    q2⊥

    (q2⊥

    +m2D

    ), m2D =

    g2s T2

    6 (2Nc+Nf) .

    35

  • Jet quenching has been observed!

    0 2 (GeV/c)Tp

    4 6 8 100

    0.5

    1

    1.5

    2d+Au FTPC-Au 0-20%

    d+Au Minimum Bias

    pT (GeV/c)

    Au+Au Central

    RAB (pT)

    STAR data: charged yield (scaled to pp), AA vs. DA.

    36

  • A calculation of γ production and jet quenching using the

    same formalism and hydro model should inter-relate them.

    There are also γ produced as secondaries off the jets as they

    quench (the bremsstrahlung is sometimes a γ not a gluon).

    Work in progress S. Jeon, GM

    preliminary results of γ production from hard jets not

    promising: γ yield 10−3 of energetic partons–but see Gale’s

    talk.

    37

  • Conclusions• Direct γ’s are intrinsically interesting

    • Decay γ’s should outnumber direct γ’s, making

    observation of direct γ’s challenging

    • Computing γ production from QGP is Challenging

    due to LPM, but is nevertheless broadly under control

    • uncertainties in QGP γ dominated by Hydro, not QFT

    • Connection between γ production and jet quenching

    deserves more attention, and may help constrain hydro

    (and other) uncertainties.

    38