XI ｔｈ International Conference on Quark Confinement and the Hadron Petersburg, Russia Philipp Gubler (RIKEN, Nishina Center) Collaborator: Keisuke Ohtani (Tokyo Institute of Technology) P. Gubler and K. Ohtani, arXiv: [hep-ph]. Relating the strangeness content of the nucleon to the mass shift of the φ meson in nuclear matter

Introduction: Vector mesons at finite density Understanding the behavior of matter under extreme conditions - To be investigated at J-PARC - Vector mesons: clean probe for experiment - Firm theoretical understanding is necessary for interpreting the experimental results! Basic Motivation: Understanding the origin of mass and its relation to chiral symmetry of QCD

The E325 experiment at KEK p e e p e e   outside decayinside decay Slowly moving φ mesons are produced in 12 GeV p+A reactions and are measured through di-leptons. No effect (only vacuum) Di-lepton spectrum reflects the modified φ-meson

Results from E325 A large negative mass shift? R. Muto et al, Phys. Rev. Lett. 98, (2007). 35±7 MeV mass reduction of the φ meson at nuclear matter density.

The strangeness content of the nucleon: Governs the leading order behavior of the strange quark condensate: Provides a measure of the strangeness content of the nucleon: strange quarks and anti-quarks It is an important parameter for dark-matter searches: Adapted from: W. Freeman and D. Toussaint (MILC Collaboration), Phys. Rev. D 88, (2013). Neutralino: Linear superposition of the Super-partners of the Higgs, the photon and the Z-boson

The strangeness content of the nucleon: recent developments from lattice QCD Taken from M. Gong et al. (χQCD Collaboration), arXiv: [hep-ph]. y ~ 0.04 Taken from C. Alexandrou et al. (ETM Collaboration), arXiv: [hep-ph]. Still large systematic uncertainties?

QCD sum rules 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: M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Nucl. Phys. B147, 385 (1979); B147, 448 (1979).

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

Strangeness content of nucleon and the φ meson in dense matter can be related by QCD sum rules 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 Too big? A more general analysis is needed,

Structure of QCD sum rules for the light vector mesons VacuumDense matter (leading order in ρ)

Structure of QCD sum rules for the light vector mesons VacuumDense matter (leading order in ρ) Gluonic twist 2 term: non-negligible!

Structure of QCD sum rules for the light vector mesons Vacuum Dense matter (leading order in ρ) Terms of higher order in m s : small

Structure of QCD sum rules for the light vector mesons Vacuum Dense matter (leading order in ρ) α s -corrections: small

φ meson at finite density Measuring the φ meson mass shift in nuclear matter constrains the strangeness content of the nucleon. P. Gubler and K. Ohtani, arXiv: [hep-ph].

Relation between the φ meson mass shift and the strange sigma term P. Gubler and K. Ohtani, arXiv: [hep-ph].

What do the experimental results of E325 hence tell us? Will be remeasured at the E16 experiment at J-PARC with 10 times increased statistics.

What are the main uncertainties? 1. Higher order m s terms Terms containing higher orders of m s and other so far neglected terms could have a non-negligible effect. 3. Four-quark condensates Gives the biggest contribution to the error! 2. α s corrections The effects of these terms are small These corrections are small Better constraints on their density dependence are needed.

Conclusions The φ-meson mass shift in nuclear matter constrains the strangeness content of the nucleon Most recent lattice calculation give a small σ sN -value  → increasing φ-meson mass in nuclear matter?? The E325 experiment at KEK measured a negative mass shift of -35 MeV at normal nuclear matter density  → a σ sN -value of > 100 MeV?? Outlook Momentum dependence of the φ-meson mass shift Density dependence of the four-quark condensates

Backup slides

Contents Introduction, Motivation  Vector mesons at finite density  The strange quark content of the nucleon Why interesting? Why important? Our method  QCD sum rules at finite density Results  Implications for the KEK E325 experiment and for the future E16 experiment to be done at J-PARC Conclusions and Outlook

Estimation of the error of G(M) Gaussianly distributed values for the various parameters are randomly generated. The error is extracted from the resulting distribution of G OPE (M). D.B. Leinweber, Annals Phys. 322, 1949 (1996). PG, M. Oka, Prog. Theor. Phys. 124, 995 (2010).

First results (ρ meson at finite density) 200 MeV 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, (2004).