String Balls in Application to QCD in Heavy Ion
Collisions
Kristina Krylova
Johns Hopkins University
[email protected]
April 14, 2015
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Application of Strings to QCD
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Outline
Introduction to string balls
Relevance to Black Holes
Self-interaction of strings
Lattice gauge theory - birth of QCD flux tube
Holographic extension
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Application of Strings to QCD
2/14
Relevance to experimental collisions at RHIC and LHC
QGP
↓
Mixed phase/Formation of string balls
↓
Final hadrons/Deconfinement
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Application of Strings to QCD
3/14
String balls - facts
Initial states for high multiplicity in pp collisions
Temperature is space dependent in models: T(x)
Entropy-rich at certain string coupling constants
(phase dependent)
Additional phases include jet quenching and study of angular
deformations
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Application of Strings to QCD
4/14
Self-interactions of strings → string balls
Excited states of bosonic strings in 26-dim (lack ground state)
Short strings interact and at Hagedorn temperature TH
become excited (long strings)
QCD strings at T ≈ Tc numerically close to TH
Well described by thermal lattice models
Massive strings result in collapse of the string ball
(classically a Black Hole)
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Application of Strings to QCD
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Some relevance to black holes
Given dilaton field φ string couplings are then:
closed string
gs = e φ
open string
gs = e φ/2
String ball generation√from ”random walk” as a function of
string mass Ms ∼ 1/ α0 leads to entropies
M
Sball ∼ M
s
d−1
SBekenstein ∼ M d−2
Including self-interaction asa function
of radius
R
1
R2
S(M, R) ∼ M 1 − R 2 1 − M 2 1 +
Kristina Krylova
Application of Strings to QCD
g 2M
R d−2
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Tube string as dipole-dipole scattering
Impact parameter b is the dipole transverse separation.
Polar coordinate: Matsubara time τ = 1/T
Logitudinal coordinate: σW ∈ (0, 1)
T (σW ) =
1
χ
2πb cosh(χ(σW − 21 ))
χ = ln( ss0 ) is rapidity of colliding dipoles or string diffusion
time
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Application of Strings to QCD
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Tube scattering as a nuclear process
large b: ”cold string” Pomerons
↓
Mixed phase/Formation of string balls
↓
small b: Final hadrons/Deconfinement (black hole)
Even when the system is minimally stretched, or maximally
superimposed strings, and corresponds to ∆x = 0 along the
beam direction, one can think of it as extending
holographically into a z-axis for the purpose of AdS/QCD
calculations
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Application of Strings to QCD
8/14
More relevance to nuclear collisions
Assume a lightest scalar state: σ meson with mass in vacuum
mσ = 0.6GeV
Its binding in nucleon N (Yukawa potential):
VNN (r ) =
Kristina Krylova
2
gσNN
e −mσ r
4π
r
Application of Strings to QCD
9/14
Color diagrams for σ meson exchange
left: suppressed Ncolor → ∞
upper limit on self-interaction of QCD strings
gNmax =
2
gσNN
≈ 13GeV −2
2
4πmN
right: suppressed Ncolor → ∞
Nflavor → ∞
(Veneziano limit)
Kristina Krylova
Application of Strings to QCD
10/14
Spaghetti state
Definition: confined phase excitation of multiple color charges
(in relativistic motion) connected by parallel QCD strings
String interactions mediated by σ meson (activity around flux
tubes)
Chiral condensate correlated with the Wilson line < qq >
creating correlation between flux tubes is discussed on the
next slide
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Application of Strings to QCD
11/14
Interactions between QCD strings in spaghetti state
C = 0.21, sstring = 0.11fm
C = 0.26, sstring = 0.176fm
Plots of chiral condensate as a function of transverse distance
(C is a constant, sstring is intrinsic width of string/lattice
spacing)
Chiral condensate:
< qq(r⊥ )W >
= 1 − CK0 (mσ r̃⊥ )
< W >< qq >
Regularized transverse distance:
q
2
r̃⊥ = r⊥2 + sstring
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Application of Strings to QCD
12/14
Holographic strings
”Quenched” quarks (lattice guage theories) Nc → ∞
Nf = finite
Dynamical quarks Nc → ∞
Nf → ∞
(Veneziano limit)
Calculation is done with massless fields in the bulk (flux tube);
”soft walls” quantize the motion;
outside the bulk mass spectrum of hadrons is then generated
String fluctuations vanish in time and longitudinal coordinate,
finite in ”transverse” coordinate
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Application of Strings to QCD
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References
Shuryak, E and Kalaydzhyan, T
Self-interacting QCD strings and string balls
arXiv:1402.7363
Shuryak, E
Heavy Ion Collisions: Achievements and Challenges
arXiv:1412.8393
Kristina Krylova
Application of Strings to QCD
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