the nature of the sigma meson and the soft modes of the qcd critical points teiji kunihiro (kyoto)...
TRANSCRIPT
The nature of the sigma meson and
the soft modes of the QCD critical points
Teiji Kunihiro (Kyoto)
HHIQCD2015, YITP Feb.16 --- 20 March, 2015
Based on the works done in collaboration with
・ SCALAR collaboration+M. Wakayama,・ Y.Minami,・ T.Yokota and K. Morita
Contents● Introduction● Lattice simulations of the sigma
meson● The sigma mode at finite
temperature● The sigma mode at QCD critical point● On-going FRG analysis● Summary
Introduction continued
A condensed matter physics of vacuum (Y. Nambu; 1960)
Chiral Transition = a phase transition of QCD vacuum,
being the order parameter. Lattice QCD;eg. F. Karsch, Nucl. Phys. Proc. Suppl. 83, 14 (2000).
The wisdom of many-body theory tells us:If a phase transition is of 2nd order or weak 1st order,9 soft modes » the fluctuations of the order parameter
For chiral transition,
Eg. The meson becomes the soft mode of chiral transition at
T. Hatsuda and T. K. , Phys. Rev. Lett.; Prog. Theor. Phys (1985):
It was also shown that hadronic excitations (para pion and sigma) exisit even in the ``QGP” phase.
1. Then what is the sigma?2. What about at hot and dense matter?
The significance of the meson in low energy hadron physics and QCD
1. The pole in this mass range observed in the pi-pi S-matrix. As a compilation of the pole positions of the obatined in the modern analyses: Significance of respecting chiral symmetry,unitarity and crossing symmetry to reproduce the phase shifts both in the (s)- and , (t)-channels with a low mass pole;(Igi and Hikasa(1999)).
– re-identification of the : “f0(600) of ” in PDG2002 2. Seen in decay processes from heavy particles; E. M. Aitala et al, Phys. Rev. Lett. (86), 770 (2001) 3. Responsible for the intermediate range attraction in the nuclear force.
4. Accounts for I=1/2 enhancement in K 2 compared with K+ . E.P. Shabalin (1988); T. Morozumi, C.S. Lim and I. Sanda (1990).
-N sigma term 40-60 MeV (naively » 15 MeV) enhanced by the collectiveness of the (.T.Hatsuda and T.K.(1990))
6. Coupled to the quantum fluctuation of the chiral order parameter. The Higgs particle in the WSG model
S. Sakai and T.K., PTEP (’15) 013D03
Significance of the final-state int.
Some issues to understand the sigma in QCD
● In the constituent quark model;
the mass in the 1.2 --- 1.6 GeV region.
Some mechanism needed to down the mass;● (i) Color magnetic interaction between the di-quarks?
(Jaffe; 1977, Maiani, ‘tHooft ….)
● (ii) The collectiveness of the scalar mode as the ps mode; a superposition of states. Chiral symmetry (NJL)
● (iii) The - molecule as suggested in scatt.
What would the Lattice tell us about the sigma?
The Scalar mesons on the Lattice
The Scalar Collaboration:S. Muroya,A. Nakamura,C. Nonaka,M. Sekiguchi,H. Wada,T. K.
(Phys. Rev. D70, 034504(2004))
---- A full QCD calculation -----
Scalar Mesons in Lattice QCDScalar Mesons in Lattice QCD
2004
DeTar and Kogut, PRD36(1987)28281987 screening mass
Alford and Jaffe, NPB578(2000)367
quench
Lee and Weingarten, PRD61(2000)014015
SCALAR ,NPProc.Suppl.106(2002)272
McNeile and Michael, PRD63(2001)114503
Prelovsek and Orginos, NPProc.Suppl.119(2003)822
2000
2001
2002
2003
mixing with glueball
disconnected diagram
+glueball
domain wall fermion, propagators in quench
disconnected diagram SCALAR,PRD70 (2004)034504
dynamical
mesonas
• Operator (two flavor)
• Propagator
SCALAR, Phys. Rev. D70 (2004)034504
Quark modelcolor Dirac
Disconnected diagram
- Vacuum contribution
connected
disconnected
Simulation SetupSimulation Setup• Full QCD, Hybrid Monte Carlo Plaquette gauge action, Wilson Fermion•
• Lattice size • Disconnected diagrams Z2 noise method (number of noise: 1000)
CP-PACS, Phys. Rev. D60 (1999)114508
CP-PACS
our results
SCALAR, Phys. Rev. D70 (2004)034504
Disconnected DiagramsDisconnected Diagrams• Propagators
• Due to the existence of disconnected diagram, m becomes smaller.
SCALAR, Phys. Rev. D70 (2004)034504
connected
disconnected
Light Scalar MesonLight Scalar MesonSCALAR,Phys. Rev. D70 (2004)034504
• Only connected diagrams
• Disconnected diagrams
• At chiral limit
Possible tetra/molecular property of the sigma Possible tetra/molecular property of the sigma
With not only connected but also disconnected diagrams
Use of tetra and molecular operators as the interpolationOperators to see the overlap with the physical sigma fromThe signal of the propagators.
Various diagrams including disconnected ones and hence
Very time-consuming!
CautionCaution• “Molecule” contains mixing with tetra and two quark state• “Tetra” contains mixing with molecule and two quark state• Application of the variational method for the possible interpolators is needed.
Results:•Molecular op: Singly disconnected diagram is dominant.•Slopes (~masses) of them are almost the same.•Due to the singly disconnected diagram, the mass of tetra becomes smaller.
arXiv1412.3909[hep-lat]
How does the sigma mode manifest itself or modify its properties at finite temperature, density, magnetic field and so on?
How does the sigma mode manifest itself or modify its properties at finite temperature, density, magnetic field and so on?
The nature of the sigma may be revealedby seeing possible change of its propertiesat varying environment.
The sigma in the hot and dense medium
Chiral Transition and the sigma mode (meson)
0
c.f. Higgs particle in WS model
; Higgs fieldHiggs particle
para sigmapara pion
the softening ofthe with increasing T
and
:Screening masses
The poles of the S matrix in the complex mass plane forthe sigma meson channel: complied in Z. Xiao and H.Z. Zheng (2001)
G.Colangero, J. Gasser and Leutwyler (2001)
Softening !
T.Hatsuda and TK, Prog. Theor. Phys. 74 (1985) 765; PRL55 (1985) 158.
cf. K. Yokokawa et al, PRC 66 (2002), 022201. T. Hyodo, D. Jido and TK, NPA848 (2010). Possible spectral change depending on the strength of the exotic components.
Finite T and with finite quark mass--- soft modes at QCD critical point ----
The same universality class; Z2
Density fluctuation is the soft mode of QCD critical point!The sigma mode is a slaving mode of the density.
H. Fujii, PRD 67 (03) 094018;H. Fujii and M.Ohtani,Phys.Rev.D70(2004)Dam. T. Son and M. A. Stephanov, PRD70 (’04) 056001
T
P
SolidLiq.
Classical Liq.-Gas
Critical point
Triple.P
gas
Plausible QCD phase diagram:
What is the soft mode at CP?What is the soft mode at CP?Sigma meson has still a non-zero mass at CP. This is because the chiral symmetry is explicitly broken.
What is the soft mode at CP?
T-dependence (=CP )
-mode
Space-like region
(the soft modes)
T>Tc
(non-soft mode)
Phonon mode in the space-like region softens at CP.
H. Fujii (2003)H. Fujii and M.Ohtani(2004)
Spectral function of the chiral condensate
It couples to hydrodynamicalmodes,
See also, D. T. Son and M. Stephanov (2004)
does not affect particlecreation in the time-like region.
leading to interesting dynamical criticalphenomena.
At finite density, scalar-vector mixing is present.
p
p P=40 MeV
Spectral function of density fluctuations in the Landau frame
In the long-wave length limit, k→0
/p nc c t
Long. Dynamical :: specific heatratio
: sound velocity
thermal expansion rate :
Rel. effects appearonly in the sound mode.
Rel. effects appear only in the width of the peaks.
rate of isothermal exp.
Notice:
As approaching the critical point, the ratio of specific heats diverges!
P
The strength of the sound modes vanishes out at the critical point.
enthalpy
sound modesthermal mode
20 0
1( / 2 )
2 s Pc T w
Y.Minami and TK, Prog. Theor. Phys.122 (2010),881
Spectral function of density fluctuation at CP
( ) /c cT T T
( ) /c ct T T T
The sound mode (Brillouin) disappearsOnly an enhanced thermal mode remains. Furthermore, the Rayleigh peak is enhanced, meaning the large energy dissipation.
Suggesting interesting criticalphenomena related to sound mode/density fluctuation.
Spectral function at CP
0.4
0. 1t
The soft mode around QCD CP is thermally induced density fluctuations,but not the usual sound mode.
Y. Minami and T.K., (2009)
Mach cone?
FRG analysis of spectral function of collective excitations
Based on the pioneering work byR-A. Tripolt et al, PRD89 (2014), 034010; PRD90 (2014), 074031andT.Yokota, K. Morita andTK, in progress.
Model:
Taken from R-A. Tripolt et al, PRD89 (2014), 034010; PRD90 (2014), 074031
T.Yokota et al
T_c=10 MeV
c= 293 MeV
Collective excitations around the CP
p-h excitation due to Fermi sphere is seen in the sigma channel!
T. Yokota et al
Slightly different from the previous results, probably due to the difference in the treatment of thermally excited modes. More works are needed.
Preliminary!
Summary• The sigma meson (scalar mesons) is an interesting hadron(s)
reflecting the non-pert. Dynamics of QCD, such as chiral symmetry and its SSB, possible significance of tetra/molecular/diquark correlations in hadron
dynamics.
• Exploring the possible change of the spectral properties may reveal the
nature of the sigma and the roles of the above-mentioned dynamics.
• The soft mode around the QCD CP is the hydrodynamic modes coupled
to the sigma mode, which may be analyzed by the application of FRG
(combined with fluid dynamics/dynamical RG.)
Applicable to find unexpected collectiveexcitations in the hot and dense medium(even under magnetic field?) to reveal the rich physics of such a medium as condensed matter.
BACK-UPS
The numbers in ( , ) are those in the naive quark model.(T.K. and T. Hatsuda, Phys. Lett. B240 (1990) 209)
The quark content (or the scalar charge of the quarks) isenhanced by the collective mode in the scalar channel!
C.f.
The empirical value of -N Sigma term is reproduced due to the enhancement of the scalar charge due to the -mesonic collective mode!
Scalar Mesons in the Di-quark picture
(Jaffe(1977), Alford and Jaffe (2000))
Extrapolation
5.1410±0.0747 c = 0.1945±0.0029
( CP-PACS c = 0.19286(14) )
0.8093
a = 0.207±0.009 fm
CP-PACSa = 0.197(2) fm
0.270
334.08093.0
270.0
m
m
mσ=257MeV
Propagators of Molecule
Connected diagrams
Singly disconnected diagram
• Singly disconnected diagram is dominant.• Slopes (~masses) of them are almost the same.
total
arXiv1412.3909[hep-lat]
Propagators of Tetra
totalConnected diagram
Singly disconnected diagram
• Singly disconnected diagram is dominant.• Due to the singly disconnected diagram, the mass of tetra becomes smaller.
arXiv1412.3909[hep-lat]
Experimental results for meson
● It is remarked that the with I=1/2 is reported to exist with a mass m ~ 800MeV.
● The is supposed to constitute the nonet scalar states of chiral SU(3) X SU(3) symmetry together with . Fermilab E791, E. Aitala et al,. Phys. Rev. Lett. 89 (2002) 121801.
Scalar Mesons in Lattice QCDScalar Mesons in Lattice QCD2004 Full QCDSCALAR, PRD70(2004)034504
SCALAR, PLB652(2007)250
UKQCD,PRD74(2006)114505
UKQCD,PRD74(2006)014508
BGR,PRD85(2012)034508
ETM,JHEP1304(2013)137
S.Prelovsek et al, PRD79(2009)014503
S.Prelovsek et al, PRD82(2010)094507
2006
20092010
2013
2014 SCALAR(+Wakayama), arXiv1412.3909[hep-lat]
2007
2012 a
a
a
aG
connected diagrams
connected + singly disconnected diagrams
Extrapolation ( hop_s = 0.1845 fix)
Chiral limit
527 MeV
846 MeV
1.729 GeV
SCALAR, PLB652(2007)250
Summary on
m ~ 800MeV is not reproduced but twice of it.
P.D.G. による m K/m K*
Possible disappearance or strong suppression of Mach cone at the QCD critical point
Mach cone sound mode as the density fluctuationdeveloped from
Around the CP;
However,
(i) Attenuation of the sound mode; the dynamical density fluctuation is hardly developed.(ii) The enhancement of the Rayleigh peak suggests that the energy dissipation is so large that the possible density fluctuation gets dissipated rapidly.
Possible disappearance or strong suppression of Mach cone at the QCD critical point!
Thus, if the identification of the Mach cone in the RHIC experiment is confirmed, possible disappearance or suppression along with the variation of the incident energy can bea signal of the existence of the critical point belonging to the same universality class as liq.-gas transition.
scvsc
M si n sM
c
v