Hadrons in a hot and dense medium: a holographic study€¦ · Vector mesons in medium G. Brown, M....
Transcript of 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
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What happens to hadrons?
supposed to melt in plasma
IntroductionIntroduction
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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
IntroductionIntroduction
Also studies at finite density, see discussion in concluding remarks
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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)
IntroductionIntroduction
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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
IntroductionIntroduction
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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)
IntroductionIntroduction
7F. GiannuzziF. Giannuzzi Hadrons in a hot and dense medium: a holographic studyHadrons in a hot and dense medium: a holographic study
QCD Sum Rules (1)
P. Gubler, K. Morita, M. OkaPRL 107, 092003 (2011)
P. Gubler, K. Morita, M. OkaPRL 107, 092003 (2011)
J/ψ
IntroductionIntroduction
8F. GiannuzziF. Giannuzzi Hadrons in a hot and dense medium: a holographic studyHadrons in a hot and dense medium: a holographic study
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)
IntroductionIntroduction
9F. GiannuzziF. Giannuzzi Hadrons in a hot and dense medium: a holographic studyHadrons in a hot and dense medium: a holographic study
PNJL ( )σ
IntroductionIntroduction
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)
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Present talk: Soft wall
IntroductionIntroduction
Scalar light mesons
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‣ Introduction on AdS/CFT
‣ The AdS/QCD correspondence
‣ The soft-wall model
‣ The finite temperature case
‣ The finite density case
OutlineOutline
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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
13F. GiannuzziF. Giannuzzi Hadrons in a hot and dense medium: a holographic studyHadrons in a hot and dense medium: a holographic study
AdS/CFT correspondenceAdS/CFT correspondence
E. WittenAdv.Theor.Math.Phys. 2, 253 (1998)
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.
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How can the two theories be linked?
AdS/CFT correspondenceAdS/CFT correspondence
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
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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
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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)
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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
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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)
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Two-point correlation function:
Scalar mesonsScalar mesons
on-shell action
digamma function
poles
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Scalar mesonsScalar mesons
21F. GiannuzziF. Giannuzzi Hadrons in a hot and dense medium: a holographic studyHadrons in a hot and dense medium: a holographic study
AdS space + black hole E. WittenAdv.Theor.Math.Phys. 2, 505 (1998)
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
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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
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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:
Scalar mesons at finite temperatureScalar mesons at finite temperature
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Masses and widths from fit with modified Breit-Wigner function:
Scalar mesons at finite temperatureScalar mesons at finite temperature
ground state
1st excited state
from Sch.-type eq
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Glueballs in the AdS-BH model with
peaks shift towards higher q02 and become broader
T=30 MeV
Finite temperatureFinite temperature
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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
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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)
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✔
? Peaks move towards lower masses
✔ Broadening of peaks
✔ Melting (earlier for excited states)
Vector mesons in mediumVector mesons in medium
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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)
Vector mesons in mediumVector mesons in medium
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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
Vector mesons in mediumVector mesons in medium
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)
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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: