Sabyasachi Ghosh Outline of the talk Motivation meaning of spectral function RTF essence calculations Results of inmedium spectral function ID: 374617
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Slide1
Vector Meson Spectral Functions in Medium
Sabyasachi
Ghosh
Outline of the talk ………………
Motivation + meaning of spectral function
RTF (essence + calculations)
Results of in-medium spectral function ( + )
Application on dileptonSlide2
Experimental motivation :
In-medium modification
of light vector mesons (specially
ρ
).
D
Slide3
Fourier
transform
Probabilistic amplitude of Unstable particle
time axis
energy axis
3
QFT definition of spectral function
Propagator
spectral
function
:Slide4
-
∞
+
∞t-axis
- i
b
0
-∞
(+∞
,-
ib/2)+∞
t-plane
Time evolution
operator
~
density matrix
Essence of RTF
Field Theory of vacuum
Field Theory at finite temperature
Vacuum interacting propagator
thermal propagator
Thermal self-energy
Vacuum free propagator
DiagonalizationSlide5
Mass shift
Width enhancement
Spectral function =
Im
[propagator]Slide6
Self Energy of
ρ for mesonic loops :
(k)
(q)
(q)
(p=q – k)
Landau cuts
Unitary cuts
Unitary cutsSlide7
ρ
p
p
ρ
Mesonic
collision rate
ρ
ρ
k
k
p
p
Bose enhancement of decay rate Slide8
+
o
Unitary cut
Self Energy of
ρ
for
baryonic loops :
ρ
ρ
Pauli blocking of decay rate
Landau cut
ρ
ρ
Bosonic
collision rate Slide9
9
o
Unitary cut
Landau cut
=(0.94-0.94)
GeV
= 0
GeV
[min]
=(
1.72-0.94)
GeV = 0.78 GeV [max]
N*(1520)
N*(1650)
N*(1720)
=(0.94+0.94)
GeV
= 1.88
GeV
[min]
=(
1.72+0.94)
GeV
= 2.66
GeV
[max]
Unitary cut
Landau cutSlide10
----------------------------
vacuum part of loop (unitary cut )
-------------------------thermal part of loops (unitary cut)
----------------------------
loops (Landau cut )
----------------------------loops (Landau cut)Slide11
Physical interpretation of imaginary part
of in-medium self-energy :
rate at which
ρ
try to be thermalized with the thermal bath
Thermalized
Hadronic
matter with
mesons(H) and baryons(B)
N*(1520)
N*(1650)
N*(1720)
ρ
H
H
ρ
ρ
ρ
ρ
ρ
H
HSlide12
Real part
of self-energy
Baryonic loops
Mesonic
loopsSlide13
Effect of
various loops on low mass invariant mass space in
ρ spectral function :Slide14
Effect of
baryonic chemical potential on ρ
spectral function in low mass region:Slide15
Effect of
temperature on ρ
spectral function in low mass region:Slide16
Effect of
momentum of ρ in off mass shell on its
spectral function in low mass region:Slide17
Self Energy of
for mesonic
loops :
Landau cut
Unitary
cutSlide18
S.
Ghosh
& S.
Sarkar
Eur. Phys. J. A 49 (2013) 97
Self Energy of
for
baryonic loops :Slide19
ρ
meson spectral function
ω meson spectral function
Formalism of
dilepton
:Slide20
Contribution of
ω
is down by a factor ~ 10Slide21
Effect of mesonic as well as baryonic medium modification of
ρ on dilepton rate in low mass region :Slide22
Transverse momentum spectra
22
Dilepton
production in
transverse momentum and
invariant mass space :
Invariant mass spectra
Fluid elementSlide23
contribution
Understanding low
mass
enhancement in the language of Thermal Field Theory :
Mesonic collision rate
(Landau cuts of H loops)
Baryonic collision rateBose enhancement of decay rate (
)Vacuum decay rate()
+
+
+
Hdronic Matter
Quark MatterTotal
+
+
Baryon part from
Eltesky
et. al. [Phys. Rev. C 64, (2001) 035202 ]
contributionSlide24
Low mass
enhancement at SPS :
Phys.Rev. C85 (2012) 064906
J K
Nayak, J
Alam, T Hirano, S Sarkar and B Sinha
S. Sarkar & S. Ghosh
J.Phys.Conf.Ser. 374 (2012) 012010
Meson (
S.Ghosh, S.Mallik. S.Sarkar
Eur. Phys. C 70, (2010) 251) + Bayon
(S.Ghosh, S.Sarkar
Nucl
. Phys. A 870, (2011) 94)
-loop self-energies
Meson loop self-energies
(
S.Ghosh
,
S.Mallik
.
S.Sarkar
Eur. Phys. C 70, (2010) 251)
+
Baryon part from
Eltesky
et. al.
(Phys. Rev. C 64, (2001) 035202) Slide25
Analytic structure of ρ meson propagator at finite temperature
Eur. Phys. J. C 70, 251 (2010)
.
S.Ghosh
, Sourav
Sarkar
, (VECC
) , S. Mallik
, (SINP)
ρ self-energy at finite temperature and density in the real-time formalism
Nucl
. Phys. A 870, 94 (2011)
S.
Ghosh
,
Sourav
Sarkar
, (
VECC
)
Observing many-body effects on lepton pair production from low
mass enhancement and flow at RHIC and LHC energies
Eur. Phys. J. C 71, 1760 (2011).
S.
Ghosh
,
Sourav
Sarkar
,
Jan-e
Alam
, (
VECC
)
Analysis of
self-energy at finite temperature and density
in the real-time formalism
Eur. Phys. J. A 49, 97 (2013).
S.
Ghosh
,
Sourav
Sarkar
,
Jan-e
Alam
, (
VECC
)
In-medium vector mesons and low mass lepton pairs from heavy ion collisions
J.Phys.Conf.Ser
. 374 (2012) 012010
Sourav
Sarkar
,
S.
Ghosh
, (
VECC
)
Elliptic flow of thermal
dileptons
as a probe of QCD matter
Phys.Rev
. C (R) 85 (2012) 031903
Payal
Mohanty
,
Victor Roy
,
S.
Ghosh
,
Santosh
K. Das
,
Bedangadas
Mohanty
,
Sourav
Sarkar
,
Jane
Alam
,
Asis
K.
Chaudhuri
, (
VECC
)
Collaborators at VECC (
India
)
S.
Mallik
S.
Sarkar
J.
Alam
S.K. Das
P.
Mohanty
B.
Mohanty
A.K.
Chaudhuri
V. Roy
Thank u…