Hadrons in a hot and dense medium: a holographic study€¦ · Vector mesons in medium G. Brown, M....

Hadrons in a hot and dense medium:

a holographic study

Floriana Giannuzzi

University of Bari

In collaboration with: Pietro Colangelo, Fulvia De Fazio, F. Jugeau, Stefano Nicotri, Juan Jose Sanz-Cillero, Fen Zuo

2F. GiannuzziF. Giannuzzi Hadrons in a hot and dense medium: a holographic studyHadrons in a hot and dense medium: a holographic study

What happens to hadrons?

supposed to melt in plasma

IntroductionIntroduction


Heavy Quarkonium:

Potential models EFTMEM on the latticeSum Rules

….

Some techniques developed so far for spectral functions at finite temperature:

Difficult task! QCD is non-perturbative!

Light mesons:

Sum Rules (P)NJL ….

In next slides, some examples and results (not exhaustive, only an idea)

Spectral function is a key quantity to look at


Also studies at finite density, see discussion in concluding remarks


MEM on lattice

J/ψ

M. Asakawa, T. HatsudaPRL 92 012001 (2004)

M. Asakawa, T. HatsudaPRL 92 012001 (2004)

G. Aarts, C. Allton, S. Kim, M.P. Lombardo, M.B. Oktay, S.M. Ryan, D.K. Sinclair, J.I. Skullerud

JHEP 1111 (2011) 103

G. Aarts, C. Allton, S. Kim, M.P. Lombardo, M.B. Oktay, S.M. Ryan, D.K. Sinclair, J.I. Skullerud

JHEP 1111 (2011) 103

Lattice (1)



EFT

M. LaineJHEP 0705, 028 (2007)

M. LaineJHEP 0705, 028 (2007) M.A. Escobedo, FG, M. Mannarelli, J. Soto

PRD 87, 114005 (2013)

M.A. Escobedo, FG, M. Mannarelli, J. SotoPRD 87, 114005 (2013)

J/ψ



Lattice (2)

charmonium

Only real part of the potential Including imaginary part

Through quark-antiquark potential

P. Petreczky, C. Miao, A. MocsyNPA 855, 125 (2011)

P. Petreczky, C. Miao, A. MocsyNPA 855, 125 (2011)



QCD Sum Rules (1)

P. Gubler, K. Morita, M. OkaPRL 107, 092003 (2011)

P. Gubler, K. Morita, M. OkaPRL 107, 092003 (2011)

J/ψ



QCD Sum Rules (2)

T. Hatsuda, Y. Koike, S.H. LeeNPB 394, 221 (1993)

T. Hatsuda, Y. Koike, S.H. LeeNPB 394, 221 (1993)

ρ

A. Ayala, C.A. Dominguez, M. Loewe, Y. Zhang PRD 86, 114036 (2012)

A. Ayala, C.A. Dominguez, M. Loewe, Y. Zhang PRD 86, 114036 (2012)



PNJL ( )σ


H. Hansen, W.M. Alberico, A. Beraudo, A. Molinari, M. Nardi, C. Ratti PRD 75, 065004 (2007)

H. Hansen, W.M. Alberico, A. Beraudo, A. Molinari, M. Nardi, C. Ratti PRD 75, 065004 (2007)


Present talk: Soft wall


Scalar light mesons


‣ Introduction on AdS/CFT

‣ The AdS/QCD correspondence

‣ The soft-wall model

‣ The finite temperature case

‣ The finite density case

OutlineOutline


IIB string theory in AdS

5 x S5

N=4 SYM, SU(N) in M

4

anti-de Sitter space:constant and negative curvature

Why interesting for us?

J.M. MaldacenaAdv.Theor.Math.Phys. 2, 231 (1998)

J.M. MaldacenaAdv.Theor.Math.Phys. 2, 231 (1998)

AdS/CFT correspondenceAdS/CFT correspondence



E. WittenAdv.Theor.Math.Phys. 2, 253 (1998)


S.S. Gubser, I.R. Klebanov, A.M. Polyakov PLB 428, 105 (1998)

S.S. Gubser, I.R. Klebanov, A.M. Polyakov PLB 428, 105 (1998)

How can the two theories be linked?

Holographic description + dictionary

AdS space has a boundary:

Minkowski space + point at infinity

Build gauge theory on

Minkowski space at boundary,

i.e.


How can the two theories be linked?


Example: 0-form scalar➢ kind of field fixed by operator

➢ mass is related to conformal dimension of operator

➢ boundary value identified with source of operator

Holographic description + dictionary

Bulk-to-boundary propagator


Apply to QCD!

QCD is not:

1. supersymmetric

2. conformal (running coupling constant)

Introduce:

1. independent bosonic and fermionic states

2. mass scale

Break!

Investigate the NP regime of QCD through a perturbative theory in a curved space with d>4

Two approaches:

AdS/QCD correspondenceAdS/QCD correspondence


Our studies in the Soft-Wall model:

Regge trajectories:

Vector mesons:

Scalar mesons:

Scalar glueballs:

Hybrid vector mesons:

c=388 MeVm

ρ=776 MeV

➢ Scalar glueballs➢ Scalar mesons➢ Finte temperature spectral functions for scalar glueballs and mesons➢ Finite temperature free energy➢ AVV vertex➢ Chiral condensate at finite temperature and density➢ Spectral functions at finite density➢ Gluon condensate at finite temperature and density

Suggestion: J/Ψ in the same scheme, by fitting cΨ

=mΨ

/2=1.55 GeV

M. Fujita, K. Fukushima, T. Misumi, M. MurataPRD 80, 035001 (2009)

M. Fujita, K. Fukushima, T. Misumi, M. MurataPRD 80, 035001 (2009)

mn2=c2(4 n+4)

Bottom-up: soft wallBottom-up: soft wallTo break conformal invariance, introduce a mass scale

Soft wall: insert in the action

mass scalemn2=c2(4 n+6)

mn2=c2(4 n+8)

mn2=c2(4 n+8)


scalar mesonsvev axial vector vector

Soft wall, vector and scalar mesonsSoft wall, vector and scalar mesonsA. Karch, E. Katz, D.T. Son, M.A. Stephanov

PRD 74, 015005 (2006)

A. Karch, E. Katz, D.T. Son, M.A. StephanovPRD 74, 015005 (2006)

Next slides: scalar mesons in vacuum and finite T vector mesons at finite density


Eigenfunctions:

Spectrum:

e.o.m.

Bogoliubov transformation

Scalar mesonsScalar mesonsP. Colangelo, F. De Fazio, FG, F. Jugeau, S. Nicotri

PRD 78, 055009 (2008)

P. Colangelo, F. De Fazio, FG, F. Jugeau, S. NicotriPRD 78, 055009 (2008)

close to f0(980)


Two-point correlation function:

Scalar mesonsScalar mesons

on-shell action

digamma function

poles


Scalar mesonsScalar mesons


AdS space + black hole E. WittenAdv.Theor.Math.Phys. 2, 505 (1998)


Hawking temperature

Application: spectral functions at finite temperatureApplication: spectral functions at finite temperature

Example: scalar mesonsExample: scalar mesons

Finite temperatureFinite temperature

Same action, but different metric! Eom reads:

P. Colangelo, FG, S. NicotriPRD 80, 094019 (2009)

P. Colangelo, FG, S. NicotriPRD 80, 094019 (2009)

rest frame


Low temperatures (high )

BH horizon far, does not affect eigenfunctions

Eigenfunctions can be found by solving a Schroedinger-type eq., as at T=0

Scalar mesons at finite temperatureScalar mesons at finite temperature


High temperatures compute spectral functions

masses = position of peaksfinite width appears

BTBP is the solution of the eom, with boundary conditions:

“falling-in” solution, to get the retarded Green's function

Spectral function:

Green's function:



Masses and widths from fit with modified Breit-Wigner function:


ground state

1st excited state

from Sch.-type eq


Glueballs in the AdS-BH model with

peaks shift towards higher q02 and become broader

T=30 MeV

Finite temperatureFinite temperature


AdS + Charged Black Hole AdS/RN metric

dual to

outer horizon of BH BH charge

Temperature and chemical potential are related to BH parameters by:

from

Finite temperature and densityFinite temperature and density


Vector meson spectral functions

Vector mesons in mediumVector mesons in medium

P. Colangelo, FG, S. NicotriJHEP 1205, 076 (2012)

P. Colangelo, FG, S. NicotriJHEP 1205, 076 (2012)


✔

? Peaks move towards lower masses

✔ Broadening of peaks

✔ Melting (earlier for excited states)



Masses and widths from fit with modified Breit-Wigner function:

Mass decrease effect:

13% at T=0 (25% for squared mass)

8% at T=0.1c (16% for squared mass)



Comparison with other models and experiments:

✔ Width Increases with temperature and chemical potential, in agreement with other models and experiments

? Mass

➔ in SW decreases with temperature and chemical potential

➔ Models suggest a mass increase or decrease

➔ In experiments found a small decrease or no effect

In particular:

• Brown-Rho dropping: mass decrease related to chiral symmetry breaking parameters

• Hatsuda-Lee:

Assuming this scaling we find


G. Brown, M. RhoPRL 66, 2720 (1991)

G. Brown, M. RhoPRL 66, 2720 (1991)

T. Hatsuda, S.H. LeePRC 46, 34 (1992)

T. Hatsuda, S.H. LeePRC 46, 34 (1992)


Little analytical and numerical effort to compute spectral functions

Reproduce key feature, in spite of the simplicity of the model

Able to reach finite density

Need to improve the model! i.e. fixing the mass scale

There are many indications that AdS/QCD can help in studying QCD, however the holographic description still needs some efforts

Concluding remarksConcluding remarks

About hadrons' fate:

Broadening of peaks in the spectral functions, as in models and experiments

Downward mass shift at finite density, debated issue!

Very small mass decrease at nuclear density, in agreement with experiments

About soft wall:

Hadrons in a hot and dense medium: a holographic study€¦ · Vector mesons in medium G. Brown, M....

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