Thermal modification of bottomonium spectral functions from QCD sum rules with the maximum entropy method Kei Suzuki (Tokyo Institute of Technology) Philipp Gubler (RIKEN) Kenji Morita (YITP) Makoto Oka (TITech, KEK) Thank you for the introduction and the opportunity to make today’s this presentation . I’d like to talk about quarkonium suppression and QCD sum rules. My collaborators are Mr. Gubler and Mr. Moirita and Mr. Oka. P. Gubler, K. Morita, and M. Oka, Phys. Rev. Lett. 107, 092003 (2011) K. Suzuki, P. Gubler, K. Morita, and M. Oka, arxiv:1204.1173, to be published in NPA

Xth Quark Confinement and the Hadron Spectrum Outline of Our Work ・Background Quarkonium melts in quark gluon plasma (QGP) ー ・Purpose 　To investigate melting temperature First, I’ll overview our research. As a background knowledge, it is well known that the quarkonium melts in the quark gluon plasma. This famous phenomena are called “quarkonium suppression’’. And Our purpose is to investigate about quarkonium melting temperatures. Then, as a method to achieve this purpose, we use QCD sum rules and MEM. ・Method 　QCD sum rules with MEM 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Outline of Today’s Talk Introduction 1-1. Quarkonium suppression 1-2. Previous work 2. Methods Results 3-1. Charmonium 3-2. Bottomonium 3-3. Bottomonium excited states 4. Summary T=? ー T=? ー I’d like to outline of today’s talk. First, I will introduce quakonium suppression and its previous work . And, Secondly, as a method, I explain QCD sum ruled for quyarkonium. And thirdly, I’ll report about results for charmonium and bottomonimu and bottomoinumu excited states. Finally, I’ll summarize. 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum 1. Introduction 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Quarkonium suppression T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986), T. Hashimoto et al. , Phys. Rev. Lett. 57, 2123 (1986) Quarkonium suppression Quarkonium (J/Ψ,Υ etc.) dissociates in QGP ⇒A signal of QGP matter? ー Quarkonium suppression is the famous phenomenon in QGP. This phenomenon is well known as a signal of QGP. And, then, it is interesting that a variety of quarkonium have different melting temperatures . Therefore, by comparing with different melting temperature,s this phenomona are expected as a thermometer for QGP. Different melting temperatures between a variety of quarkonium (J/Ψ,ηc,Υ…） ⇒Thermometer for QGP!! Taken from K. Fukushima and T. Hatsuda, Rept. Prog. Phys. 74, 014001 (2011) 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Previous work (Theory) M. Asakawa and T. Hatsuda, Phys. Rev. Lett. 92, 012001 (2004) Lattice QCD with MEM J/Ψ ηc J/Ψ ⇒J/Ψ and ηc melt at 1.6Tc 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Previous work (Theory) G. Aarts et al., JHEP 1111 (2011) 103 Lattice QCD + NRQCD with MEM Υ First peak survives and second peak disappears. This behavior shows that~ ⇒Excited state Υ(2S) melts at lower temperature than ground state Υ(1S) 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Previous work (Experiment) S. Chatrchyan et al. [CMS Collaboration], arxiv:1208.2826 Heavy ion collisions at the LHC (CERN) Υ(1S) Υ(2S,3S) ⇒Excited states Υ(2S), Υ(3S) melt at lower temperature than ground state Υ(1S) 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum 2. Methods 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Theoretical approach for quarkonium suppression How can we describe quarkonium suppression from QCD? ⇒We study temperature dependence of spectral function Quarkonium correlation function Spectral function of hadron state Non-perturbative QCD approach T-dependence input T-dependence output latticeQCD, QCD sum rule etc. m t ρ(t) First, As theoretical approach for quarkonium suppression, we study temperature dependence of spectral functions. Generaly speaking, if one calculate quarkonium correlation function, then, by using non-perturbative QCD approach, one can obtain spectral functions of hadrons. And, we input temperature depedence into left side, and we can output temperature dependence of spectral functions. Namely, at zero temperature, we should get the peak of spectral functions, and at finite temperature, we will investigate the behavior of peaks. In the next slide, I’ll explane QCD sum rules. 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum QCD sum rule M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov, Nucl. Phys. B147, 385 (1979); B147, 448 (1979) QCD sum rule Relation between operator product expansion (OPE) of correlation function and spectral function of hadron m t ρ(t) Borel transformation QCD sum rules is relation between hadron~ However, because in the left side, OPE lost some information, so, in the right side, we need some assumption. In the Conventional QCD sum rules approaches, we assume phenomenological assumption, namely “pole+continuum’’. In this time, we don’t use these assumption. Instead, in order to estimate possible functional form, we used MEM. Output spectral function with MEM Input OPE One hadron state 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum Quarkonium OPE A. Bertlmann, Nucl. Phys. B204, 387 (1982） Temperature dependence ・1st term → Free correlator ・2nd term → αs correction ・3rd term → Scalar gluon condensate ・4th term → Twist-2 gluon condensate ー This expression is quarkonium OPE. This OPE consists of four terms. Attractive Repulsive at finite T ー 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum OPE ＋ ＋ ＋ ＋ ＋ ＋ ・3rd-term＋4th-term (Gluon condensates) Especially, 3rd term and 4th term, namely gluon condensate terms, these coefficients of gluon condensate are inversely proportional to 4th power of quark mass. So, these coefficients generate different melting temperatures between charmonium and bottomonium. ⇒Coefficients of gluon condensates are inversely proportional to m4 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Temperature dependence of gluon condensates Gluon condensates at finite temperature are expressed as energy density ε and pressure p We Input ε and p from quenched lattice QCD So, these behaviors of gluon condensates cause the quarkonium suppression. ⇒Gluon condensates decrease 　with increasing temperature K. Morita and S.H. Lee, Phys. Rev. Lett. 100, 022301 (2008); Phys. Rev. C 77, 064904 (2008) 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum 3. Results 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Charmonium at zero temperature Υ ηb J/Ψ ηc Mass=3.06GeV exp.)3.10GeV Mass=3.02GeV exp.)2.98GeV The obtained masses are consistent with experimental values of ground state mass. χc0 χc1 Mass=3.36GeV exp.)3.42GeV Mass=3.50GeV exp.)3.51GeV 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Charmonium at finite temperature ー J/Ψ ηc disappear at T=1.2Tc disappear at T=1.1-1.2Tc χc0 χc1 The peak of spectral function gradually decrease and disappear at about 1.2Tc. disappear at T=1.0-1.1Tc disappear at T=1.0-1.1Tc 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Bottomonium at zero temperature Υ ηb Mass=9.63GeV exp.)9.46GeV Mass=9.55GeV exp.)9.39GeV Obtained masses is higher than the experimental values of the ground state masses. So, these gaps are due to contributions of the excited states. Namely, these peaks contain ground and excited states. χb0 χb1 Mass=10.18GeV exp.)9.86GeV Mass=10.44GeV exp.)9.89GeV 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Bottomonium at finite temperature ー Υ ηb survive up to T>2.5Tc survive up to T>2.5Tc χb0 χb1 At the finite temperature, in the case of upsilon and eta_b, these peaks survive up to 2.5T_c. On the other hand, x_c0 and x_c1 are disappear at T=2.0-2.5T_c. disappear at T=2.0-2.5Tc disappear at T=2.0-2.5Tc 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Bottomonium excited states The obtained bottomonium spectral functions include contributions of excited states To investigate behavior of the excited states, we analyzed “residue’’ (integral value) of peak We used least squares fitting to exclude contributions of continuum (one peak + continuum as Breit-Wigner + step-like function) Υ(1S,2S,3S) states are mixed Υ ・Our method cannot separate these states Next, we will discuss about bottomonium excited states. As I have mentioned before, the obtained bottomonium spectral functions contain contributions of excited states. This result is the next slide. 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Temperature dependence of residue Υ(1S+2S+3S) Υ(1S) only? This analyze And at 1.5Tc to 2.0Tc, the residue suddenly decrease Finally, at 3.0Tc, the some residue survive. And, this residue corresponds to upsilon(1S) only. Obtained residue of Υ peak decreases with increasing temperature ⇒Excited states(2S, 3S) melt at 1.5-2.0Tc and ground state(1S) survives? 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum Summary We extracted melting temperature of quarkonia from QCD sum rules with MEM Melting temperatures of quarkonia Our results suggested that bottomonium excited states Υ(2S,3S) melt at lower temperature than ground state Υ(1S) J/Ψ ηc χc0 χc1 1.2Tc 1.1-1.2Tc 1.0-1.1Tc Υ ηb χb0 χb1 >2.5Tc 2.0-2.5Tc 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Xth Quark Confinement and the Hadron Spectrum Outlook We will investigate contribution of 2nd order αs correction ⇒These change melting temperatures? As a next outlook, we will investigate contributions of 2nd order alpha_s corrections like these diagrams. And, we will discuss whether or not these corrections change melting temperature. This calculation is in preparation and coming soon. That’s all. Thank you for your kind attention. Coming Soon! 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Previous Work (Theory） Potential model 　⇒Υ(1s) survive at T>4.0Tc 　⇒Υ(2s) melts at T～1.60Tc 　⇒Υ(3s) melts at T～1.17Tc 　⇒Υ(1s) melts at T～4.10Tc 　⇒Υ(2s) melts at T～1.38Tc 　⇒χb melt at T～1.18Tc Spectral function with complex potential 　⇒Υ(1s) melts at T～2.2Tc H. Satz, J. Phys. G32 (2006) R25 S. Digal, O. Kaczmarek, F. Karsch, H. Satz, Eur. Phys. J. C43 (2005) 71 C.-Y.Wong Phys. Rev. C72 (2005) 034906 P. Petreczky, C. Miao, and A. Mocsy, Nucl.Phys. A855 (2011) 125 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

MEM analysis of mock data To confirm reproducibility of MEM, We input δ function and exp. value mass shift Information of excited states remain as residue or mass shift 3 peaks are combined into a single peak ⇒This method cannot separate multiple states 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Charmonium at finite temperature P. Gubler, K. Morita, and M. Oka, Phys. Rev. Lett. 107, 092003 (2011) T=1.2Tc T=1.1Tc T=1.0Tc T=0.9Tc J/Ψ ⇒J/Ψ melts at 1.2Tc 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum

Residue analysis (least squares fitting) Continuum intrude peak at finite temperature ⇒Fitting function is ①Breit-Wigner + continuum 　　　　　　　　　②Gaussian + continuum 09/Oct/2012 Xth Quark Confinement and the Hadron Spectrum