xi th international conference on quark confinement and the hadron spectrum @st. petersburg,...
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XI th International Conference on Quark Confinement and the Hadron Spectrum@St. Petersburg, Russia8.9.2014Philipp Gubler (RIKEN, Nishina Center)
Collaborator:Keisuke Ohtani (Tokyo Institute of Technology)
P. Gubler and K. Ohtani, arXiv:1404.7701 [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 probefor 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 decay inside 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 E325A large negative mass shift?
R. Muto et al, Phys. Rev. Lett. 98, 042501 (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, 054503 (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:1304.1194 [hep-ph].
y ~ 0.04
Taken from C. Alexandrou et al. (ETM Collaboration), arXiv:1309.7768 [hep-ph].
Still large systematic uncertainties?
QCD sum rules
In this method the properties of the two point correlation function isfully 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 coefficientsnon-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
for
Too big?
A more general analysis is needed,
Structure of QCD sum rules for the light vector mesons
Vacuum Dense matter (leading order in ρ)
Structure of QCD sum rules for the light vector mesons
Vacuum Dense matter (leading order in ρ)
Gluonic twist 2 term: non-negligible!
Structure of QCD sum rules for the light vector mesons
VacuumDense matter (leading order in ρ)
Terms of higher order in ms: small
Structure of QCD sum rules for the light vector mesons
VacuumDense matter (leading order in ρ)
αs-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:1404.7701 [hep-ph].
Relation between the φ meson mass shift and the strange sigma term
P. Gubler and K. Ohtani, arXiv:1404.7701 [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 ms terms
Terms containing higher orders of ms and other so far neglected terms could have a non-negligible effect.
3. Four-quark condensates
Gives the biggest contribution to the error!
2. αs 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 σsN-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 σsN-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 GOPE(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, 034505 (2004).
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