Koichi Hattori, RBRC Hadron and Hadron Interactions in QCD Mar. 9th, 2015 Charmonium spectroscopy in strong magnetic fields by QCD sum rules S.Cho, KH, S.H.Lee, K.Morita, S.Ozaki, PRL 113 (2014); PRD 91 (2015)

Phase diagram of QCD matter Asymptotic freedom Quark-gluon plasma Light-meson spectra in B-fields Hidaka and A.Yamamoto Quark and gluon condensates at zero and finite temperatures Bali et al. Results from lattice QCD in magnetic fields

PSR Extremely strong magnetic fields UrHIC NS/Magnetar Lienard-Wiechert potential Z = 79(Au), 82(Pb) Lighthouse in the sky Event-by-event analysis, Deng, Huang (2012) Au-Au 200AGeV b=10fm Impact parameter (b)

Strong magnetic fields in nature and laboratories Magnet in Lab. Magnetar Heavy ion collisions

Light meson spectra in strong B-fields Chernodub Hidaka, A.Yamamoto Landau levels for charged mesons Bali et al. Effective masses in the strong-field limit: The Lowest Landau Level ( n = 0 ) Similar to “Nielsen-Olesen instability” In hadronic degrees (will not be reliable when eB > Λ 2 QCD ~ 0.05 GeV 2 ) From lattice QCD Chiral condensate in B-fields from lattice QCD Magnetic catalysis

Mixing btw η c and J/psi in B-fields Equation of motions Mass spectra with level repulsion Coupling among 1 PS and 2 Vector fields Longitudinal J/psi ηcηc Mixing only with Longitudinal J/psi

Operator product expansions (OPE) and dispersion relations ? Current correlators QCD sum rules Spectral function: Shifman, Vainshtein, Zakharov

Conventional spectral ansatz: “pole + continuum” Borel transformation QCD sum rules work well for the isolated lowest states. Dispersion relation is INSENSITIVE to detail structures of the continuum.

+ Direct couplings with Bethe-Salpeter amplitudes in HQ limit nd -order perturbation Spectral ansatz with magnetically induced mixing effects + Bohr radius a 0 = 0.16 fm in Coulombic wave function

On-shell J/psi created through off-shell ηc Intermediate state as an off-shell J/psi Close look at mixing effects The same calculation applied to the vector channel Needed for maintaining the normalization of ρ

+ 2 Perturbative part + dim.-4 gluon condensates OPE for charmonium in B-fields NB) The resummed vector current correlator can be applied in the strong field limit. KH, Itakura, 2013 Preferred orientation  Polarization and momentum dependences

Results: η c and J/psi spectra

Roles of magnetically induced terms on the phenomenological side

Stability of the Borel curves ηc J/psi Less 10 MeV

Summary We obtained charmonium spectra in magnetic fields by QCD sum rules with a careful treatment of the phenomenological side as well as OPE. Application to lighter mesons (D and D* mesons) P.Gubler, KH, S.H.Lee, S.Ozaki, K.Suzuki Phenomenological side + Landau levels of charged D ±, D* ± + Mixing effects OPE for open flavors + Effects of B-fields on condensate D ± and longitudinal D* ± spectra Landau levels + mixing effects c.f.) B and B* by Machado, Finazzo, Matheus, Noronha QCD sum rules relate modification of QCD vacuum properties to hadron spectrum in B-fields.

Prompt formation of charmonia Kharzeev, Thew

Borel transform Borel-transformed dispersion relation: Spectral ansatz: Mass formula in “pole+continuum” ansatz

Conventional spectral ansatz: “pole + continuum” Borel transformation QCD sum rules work well for the isolated lowest states. Dispersion relation is INSENSITIVE to detail structures of the continuum.

Discussion 2: Mixing with continuum ~ Combined w/ mixing effects Effects of a ccbar loop