Quarkonia at finite T from QCD sum rules and MEM and light vector mesons at finite density Quarkonia at finite T from QCD sum rules and MEM P. Gubler and M. Oka, Prog. Theor. Phys. 124, 995 (2010). P. Gubler, K. Morita and M. Oka, Phys. Rev. Lett. 107, 092003 (2011). K. Ohtani, P. Gubler and M. Oka, Eur. Phys. J. A 47, 114 (2011). K. Ohtani, P. Gubler and M. Oka, Phys. Rev. D 87, 034027 (2013). K. Suzuki, P. Gubler、K. Morita and M. Oka, Nucl. Phys. A897, 28 (2013). NFQCD @ YITP, Kyoto University 12.12.2013 Philipp Gubler (RIKEN, Nishina Center) Collaborators: Makoto Oka (TokyoTech), Kenji Morita (YITP), Keisuke Ohtani (TokyoTech), Kei Suzuki (TokyoTech)

Contents Introduction, Motivation The method: QCD sum rules and the maximum entropy method Quarkonia at finite temperature Light vector mesons in nuclear matter Conclusions

Introduction: Hadrons in hot or dense matter General Motivation: Understanding the behavior of matter at high T and μ. QGP (T>Tc) ↔ confining phase (T<Tc) Quarkonium suppression Partial restoration of chiral symmetry in nuclear matter Mass shift of light vector mesons ? Broadening ?

QCD sum rules M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Nucl. Phys. B147, 385 (1979); B147, 448 (1979). In this method the properties of the two point correlation function is fully exploited: is calculated “perturbatively”, using OPE spectral function of the operator χ After the Borel transformation:

More on the OPE in matter non-perturbative condensates perturbative Wilson coefficients Change in hot or dense matter!

The basic problem to be solved given ? “Kernel” (but only incomplete and with error) This is an ill-posed problem. But, one may have additional information on ρ(ω), which can help to constrain the problem: - Positivity: - Asymptotic values:

The Maximum Entropy Method How can one include this additional information and find the most probable image of ρ(ω)? → Bayes’ Theorem likelihood function prior probability

likelihood function prior probability (Shannon-Jaynes entropy) Corresponds to ordinary χ2-fitting. “default model” M. Jarrel and J.E. Gubernatis, Phys. Rep. 269, 133 (1996). M.Asakawa, T.Hatsuda and Y.Nakahara, Prog. Part. Nucl. Phys. 46, 459 (2001).

A first test: mock data analysis When only free c-quarks contribute to the spectral function, this should be reproduced in the MEM analysis. Both J/ψ and ψ’ are included into the mock data, but we can only reproduce J/ψ.

First applications in the light quark sector ρ-meson channel Nucleon channel + 970 MeV - 1570 MeV Experiment: mρ= 0.77 GeV Fρ= 0.141 GeV Experiment: mN+= 0.94 GeV mN- = 1.54 GeV PG and M. Oka, Prog. Theor. Phys. 124, 995 (2010). K. Ohtani, PG and M. Oka, Eur. Phys. J. A 47, 114 (2011). K. Ohtani, PG and M. Oka, Phys. Rev. D 87, 034027 (2013).

Quarkonium at finite T

The quarkonium sum rules at finite T The application of QCD sum rules has been developed in: A.I. Bochkarev and M.E. Shaposhnikov, Nucl. Phys. B 268, 220 (1986). T. Hatsuda, Y. Koike and S.H. Lee, Nucl. Phys. B 394, 221 (1993). depend on T

The T-dependence of the condensates K. Morita and S.H. Lee, Phys. Rev. Lett. 100, 022301 (2008). Considering the trace and the traceless part of the energy momentum tensor, one can show that in tht quenched approximation, the T-dependent parts of the gluon condensates by thermodynamic quantities such as energy density ε(T) and pressure p(T). The values of ε(T) and p(T) are obtained from quenched lattice calculations: G. Boyd et al, Nucl. Phys. B 469, 419 (1996). O. Kaczmarek et al, Phys. Rev. D 70, 074505 (2004). taken from: K. Morita and S.H. Lee, Phys. Rev. D82, 054008 (2010).

Results for charmonium at T=0 S-wave P-wave mJ/ψ=3.06 GeV (Exp: 3.10 GeV) mχ0=3.36 GeV (Exp: 3.41 GeV) mηｃ=3.02 GeV (Exp: 2.98 GeV) mχ1=3.50 GeV (Exp: 3.51 GeV) PG, K. Morita and M. Oka, Phys. Rev. Lett. 107, 092003 (2011).

Results for charmonium at finite T S-wave P-wave PG, K. Morita and M. Oka, Phys. Rev. Lett. 107, 092003 (2011).

Comparison with lattice results Imaginary time correlator ratio: Lattice data are taken from: A. Jakovác, P. Petreczky, K. Petrov and A. Velytsky, Phys. Rev. D 75, 014506 (2007).

Results for bottomonium at finite T S-wave P-wave K. Suzuki, PG, K. Morita and M. Oka, Nucl. Phys. A897, 28 (2013).

The φ meson in dense matter

Light vector mesons at finite density Important early study: T. Hatsuda and S.H. Lee, Phys. Rev. C 46, R34 (1992). Vector meson masses mainly drop due to changes of the quark condensates. The most important condensates are: for for Important assumption: Might be wrong!

What has changed since 1992? Vacuum No fundamental changes since 1992

What has changed since 1992? Finite density effects May have changed a bit Finite density effects Has changed a lot!! Has changed a little New term Has changed a little

What has changed since 1992? A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Eur. Phys. J. C 63, 189 (2009). 1992 2013 Some changes, but no big effect. non-negligible

What has changed since 1992? The strangeness content of the nucleon: Taken from M. Gong et al. (χQCD Collaboration), arXiv:1304.1194 [hep-ph]. y ~ 0.04 Value used by Hatsuda and Lee: y=0.22 Too big!! The value of y has shrinked by a factor of about 5: a new analysis is necessary!

First results (vacuum) Analysis of the sum rule is done using the maximum entropy method (MEM), which allows to extract the spectral function from the sum rules without any phenomenological ansatz. mφ=1.05 GeV (Exp: 1.02 GeV) mρ=0.75 GeV (Exp: 0.77 GeV) Used input parameters:

φ meson at finite density ruled out !? The φ meson mass shift strongly depends on the strange sigma term.

What happened? Let us examine the OPE at finite density more closely: Measuring the φ meson mass shift in nuclear matter provides a strong constraint to the strange sigma term!

Relation between the φ meson mass shift and the strange sigma term

However… Experiments seem to suggest something else: Result of the E325 experiment at KEK 35 MeV mass reduction of the φ meson at nuclear matter density! R. Muto et al, Phys. Rev. Lett. 98, 042501 (2007).

What could be wrong? 1. So far neglected condensates Terms containing higher orders of ms and other so far neglected terms could have a non-negligible effect. Effects of these terms are small 2. αs corrections These corrections seem to be small 3. Underestimated density dependence of four-quark condensates Does not seem to have a large effect.

Conclusions We have shown that MEM can be applied to QCD sum rules We could observe the melting of the S-wave and P-wave quarkonia using finite temperature QCD sum rules and MEM Using recent lattice results on the strange sigma term, we have shown that the φ-meson mass presumably experiences a smaller shift than thought before.

Backup slides

What about the excited states? S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. 107, 052302 (2011). Exciting results from LHC! Is it possible to reproduce this result with our method? Our resolution might not be good enough.

Extracting information on the excited states However, we can at least investigate the behavior of the residue as a function of T. Fit using a Breit-Wigner peak + continuum Fit using a Gaussian peak + continuum A clear reduction of the residue independent on the details of the fit is observed. Consistent with melting of Y(3S) and Y(2S) states ?

What has changed since 1992? Value used by Hatsuda and Lee: 45 MeV Taken from G.S. Bali et al., Nucl. Phys. B866, 1 (2013). Value used by Hatsuda and Lee: 45 MeV Recent lattice results are mostly consistent with the old values. The latest trend might point to a somewhat smaller value.

First results (ρ meson at finite density) 200 MeV 0.12 ~ 0.19 Consistent with the result of Hatsuda-Lee. Used input parameters: A. Semke and M.F.M. Lutz, Phys. Lett. B 717, 242 (2012). M. Procura, T.R. Hemmert and W. Weise, Phys. Rev. D 69, 034505 (2004).