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

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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

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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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