Hot Dense Matter & Random Fluctuation Walk
G.KozlovJINR,Dubna
14.11.2018 G Kozlov qnp2018 1
14.11.2018 G Kozlov qnp2018
Spontaneous Breaking Symmetry
↙ ↘ PP Major role Cosmology Phase Transitions (High #, %, %&, … ) Extreme conditions
CP corresponds to initial state / invariant G conformal
↓ non-trivial expansion other states (physical matter states) do not possess invariance under G but, invariant under * symmetry group H triggered by G Ø CP/PT Soluble Model
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14.11.2018 G Kozlov qnp2018
Early Universe • Light massive / Massless states
o Critical phenomena through Phase Transitions (PT) ↘ Single-mode BE condensation Ø Light scalar dilaton in ideal Bose gas
Condensation single zero mode
suggests breaking of conformal symmetry
All scales in PP & Cosmology are subjects of dilatons Quarks & gluon properties
↘ ↙ scalar condensate @ High #, %, %&, … ↓ keys Universe evolution → HI experiments CP &PT 3
CP & Critical Phenomena
Collider Fixed targetstrong interacting matter @ high T & µB
• Freeze-out point in PP is referred to as CP
In the proximity of CP: • Matter becomes weakly coupled ! Color is no more confined ! Chiral symmetry is restored
" Important:
Phase transition & CP are associated with breaking of symmetry - CP clarified through µB −T( ) plane
scanning of µB −T( ) phase diagram
G Kozlov qnp201814.11.2018 4
CP & Critical Phenomena
A few questions do arise: Ø CP meaning? Ø Basic observables to be measured when CP approached? Ø New knowledge if CP approached?
Answer: in terms of QCDT @ large distances N/Perturbative phenomena: χSB & Confinement of color ↓ ?relations? ↓ Phase transition of χS Restoration Deconfinement ↓ correlations ↓ important issue NO correct solution (massless quarks in the theory) Effective models, e.g., with topological defects
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CP • Fluctuation measure • Observables
visible ↓ through Fluctuations of characteristic length ξ of a “critical” mode
Test 1. Excitations above vacuum: narrow flux tubes, rs ~ ξ ~ m
−1 (in the center, rs → 0 , scalar condensate vanishes) Ensemble of a single flux tube system, N R( ) configurations of f.t.’s Partition function Z flux = N R( )exp −β E m,R( )"# $%D
x ,β;M( )R∑
β
∑
Effective energy: E m,R( ) ~ m2R a+ b ln µR( )!" #$ GK, 2010
! Gauge field is the “critical” mode with mass m
- Particles: Bound states in terms of flux tubes
G Kozlov qnp201814.11.2018 6
TPCF At large distances for any correlator (observables) O τ , x( )O τ , 0( ) ~ A
x c D x ,β;M( ) as x →∞
D x ,β;M( ) = exp −M β( )
x"# $%, Dx ,β;M( ) ≠ 0 even at β = βc
M −1 β( ) (LO & N/P contr’s) is the measure of screening effect of color electric field
At high T, g <<1, c= - 4; gξ / π <!x <M −1, m2 β( ) ~ g2 β( )δ 2( ) 0( ) ,δ 2( ) 0( ) ~ πrs
2( )−1
O τ , !x( )O τ , 0( ) ~ LW−4 −TVσ 0 β( )ξ 2 1
ξ8πσ 0
− N ln ξ 2πσ 0( )+...⎡
⎣⎢
⎤
⎦⎥ GK, 2014
Large fluctuations ξ , - TPCF’s singularity (CP does approach) Swell of strings with rs ~ ξ→∞
G Kozlov qnp201814.11.2018 7
SU(3) gluodynamics vacuum
kGL =ξl
~mφ
m<1 (type I vacuum, flux tubes attracted)>1 (type II vacuum, flux tubes repel)
Scalar fields, dilatons φ (condensate) remain massive up to the CP (1st order PT) ! kGL →∞ Deconfinement! ! If kGL =1 parallel strings (carry the same flux) do not interact
each other. Tc ≈172 MeV, Nc = 3 pions GK 2014
Singularity of Z flux ⇒ kGL ≥34α β( )ξmqq
1+ 43
ξ 2
α β( )βM β( ) LW
R
⎡
⎣⎢⎢
⎤
⎦⎥⎥
↓ ↓
low bound
Type-I vac Type-II vac →∞ as ξ→∞ To an experiment: Observation of correlations between two bound states (strings) is rather useful & instructive to check the CP is approached!
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Test 2. Primary photons
Ø Origin: Conformal invariance breaking/dilatons
Primary photons (not produced in decays of hadrons): ü Soft interaction with medium ü Indicator of CP
High T . Conformal sector has no direct couplings to SM L = χ
fχθµtreeµ +θµanom
µ( )
θµtreeµ = − mq +γm g( )⎡⎣ ⎤⎦q
q∑ q− 1
2m2χ 2 +∂µχ∂
µχ
In contrast to SM, χ couples to γ and g even before running any SM in the loop
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QCD & QED in CS QCDQED
⎫⎬⎪
⎭⎪∈Conformal Sector
bo +
light∑ b0 = 0⇒
heavy∑ bo = −
light∑ bo
heavy∑ above the scale Λ (UV)
Mass of χ splits light and heavy sectors αs
8πb0lightGµν
a Gµνa →β g( )2g
Gµνa Gµνa, αs
8πb0lightGµν
a Gµνab0light = −11+ 2
3nL
The only nL particles lighter than χ are contributed to β -function For mχ ~O Λ( )→ nL = 3 light quark sector ! About 14 times increase of the χgg (production)
coupling strength to that of the SM Higgs boson 14.11.2018 G Kozlov qnp2018 10
Primary photons escape
Γ χ→ γγ( ) ≈ αFanom4π
⎛
⎝⎜
⎞
⎠⎟2 mχ
3
16π fχ2
ü Conformal anomaly contributes only through
Fanom = −2nL
3⎛
⎝⎜
⎞
⎠⎟bEMb0light
⎛
⎝⎜
⎞
⎠⎟, bEM = −4 eq
2 = −83q:u,d,s
∑
IRFP: mχ ≈ 1− N f / N f
cΛ, N fc →α f
c Chiral symmetry breaking
Fanom decreases because of increasing of b0light as nL → 0 Close to CP: Fluctuation rate of the primary photons /observable(s) Ø CP: Fluctuations grow in the IR to become large
Scheme independence in terms of confinement scale Non-monotonous increase of fluctuations of primary photons 14.11.2018 G Kozlov qnp2018 11
Test 3. Particle Correlations: Size of the particle source • Possible approach to CP study through spatial correlations
of final state particles • Size effect of space composed of “hot” particles ⇒ derive
theoretical formulas for 2− , ...,n − particle distribution-correlation functions (stochastic, chaotic behavior)
ü Stochastic scale (size) Lst in c’s Bose-Einstein GK (2008-2010)
C 2 q ,λ( ) ≈ η n( ) 1+λ ν( )e −q2Lst2&
'()*+, η n( ) =
n n −1( )n
2
event-to-event fluctuations Particle coherence function:
λ ν( ) =1 / 1+ ν( )2
, 0 < ν <∞ , n ~ V d ω m 2 1
e ω−µ( )β −1∫
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v OBSERVABLES? The scaling form C 2 is important to predict behavior of observables @ CP
Observable, e.g., kT2 =
1ν n( ) T 3 Lst
5, kT =
pT1 +pT2 GK’2016
Lst →∞ as T →Tc , µ→µ c indicate the vicinity of CP Ø Coherence λ measured.
0 < λ ν n( )#
$%&≤ 1
⇓ ⇓
fully coherent phase chaotic (critical behavior: BM to AM, cross-over walk)
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Спасибо за внимание!
Anomaly Matter
Baryonic Matter
Random Fluctuation Walk (cross-over BM to AM)
14.11.2018 G Kozlov qnp2018
Random Fluctuation Walk (cross-over BM ⇒ AM) Model 1D x-oriented (0 < x <∞)
P x ; λ ,µc( ) = p λ( ) λ j 12 πt
e − y−2 j / 4t +e − y+
2 j / 4t$%&
'()
j =0
∞
∑
y±j = xµc ±a
j , a = µ / µc( ) >1, t = lµc (lattice spacing)
liml→0µc ≠0
P x ; λ ,µc( ) = p λ( ) λ j δ xµc −aj( )+δ xµc +a j( )&
'()
j =0
∞
∑
p λ( ) = 0.5 1−λ( ) , 0 < λ ≤1, NC: 2 p +λp + ...+λ j p + ...( ) =1 The limit λ→1⇒ broad behavior of P: vicinity of CP is approached
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BM & AM mixed phases
§ Infinite # of divergent (singular) terms in F.T. G k ; λ ,µc( ) § Not suitable to describe an arbitrary phase of excited matter
Why? Because wide range of λ , µ ; singularity @ k <<µc k → 0( ) § To find non-analytical part @ k ≈ 0 (large distances)
G k ; λ ,µc( ) =GBM k ; λ ,µc( )+GAM ak ; λ ,µc( ) linear non-homog. eq.
BM GBM k ; λ ,µc( ) = 2 p λ( )cos k / µc( ) regular if k ≈ 0, for all λ
AM GAM k ; λ ,µc( ) = λG ak ; λ ,µc( ), for a −2 < λ <1 GAM k ; λ ,µc( )→ 0 , if λ→ 0 The phase with BM does exist only
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Solution for AM phase
Probability for Anomaly Matter phase
GAM k ; λ ,µc( ) ~ i α−2
Γ α−1( )ξ
α−2( )2 λ( ) k
µc
α
1log a
bm cos 2πmlog k( )log a
+ϑm
(
)
**
+
,
--m=0
∞
∑
Grows up very sharply/ divergent if a) random fluctuation weight λ→1 (because of ξ as the series of λ ) b) a = µ /µc( )→1 from above The AM disappears if λ→ 0
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Conclusions
1. Theoretical search for CP, cross-over between BM & AM 2. CP Tests 1,2,3 - Narrow flux tubes/swell of string with - Particle correlations/ particle size at CP - Primary photons fluctuations close to CP 3. Solution: mixed phase BM (regular) + AM (singular). 4. Smooth λ ν( )⇒ BM λ ν( )→1 (strong particle chaoticity) ⇒ AM asymp. behavior at k → 0 (IR), large x is approached ⇓ infinite size of particle source. CP (cross-over) kGL →∞ at µ =µc . No dependence on particle n .
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14.11.2018 G Kozlov qnp2018
Thank you
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