Talk at ECT Workshop New perspectives on Photons and Dileptons in Ultrarelativistic HeavyIon Collisions at RHIC and LHC 4 December 2015 P Gubler and K Ohtani Phys Rev D ID: 788602
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Slide1
The phi meson in nuclear matter - recent result from theory -
Talk at ECT* Workshop “New perspectives on Photons and Dileptons in Ultrarelativistic Heavy-Ion Collisions at RHIC and LHC” 4. December, 2015
P. Gubler and K. Ohtani, Phys. Rev. D 90, 094002 (2014). P. Gubler and W. Weise, Phys. Lett. B 751, 396 (2015).
Collaborators:
Keisuke
Ohtani
(
Tokyo Tech
)
Wolfram Weise (ECT*, TUM)
Slide2Introduction
φ mesonmφ = 1019 MeV
Γφ = 4.3 MeVObject of study:
Interest:
Slide3Previous developmentsThe E325 Experiment (KEK)
Slowly moving
φ mesons are produced in 12 GeV p+A reactions and are measured through di-leptons.
p
e
e
p
e
e
f
f
outside decay
inside decay
No effect
(
only vacuum)
Di-lepton spectrum reflects the modified
φ
-meson
Slide44
bg
<1.25 (Slow)
1.25<
bg
<1.75
1.75<
bg
(Fast)
Large Nucleus
Small Nucleus
Fitting Results
Slide5Experimental Conclusions
Pole mass:
Pole width:
35 MeV negative mass shift at normal nuclear matter density
Increased width to 15 MeV at normal nuclear matter density
R. Muto et al, Phys. Rev. Lett.
98
, 042501 (2007).
Slide6QCD 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).
q
2
Slide7perturbative Wilson coefficients
non-perturbative condensates
More on the OPE in matter
Change in hot or dense matter!
Slide8Structure of QCD sum rules for the phi meson
Dim. 0:
Dim. 2:
Dim. 4:
Dim. 6:
In Vacuum
Slide9In Nuclear Matter
Structure of QCD sum rules for the phi meson
Dim. 0:
Dim. 2:
Dim. 4:
Dim. 6:
Slide10The strangeness content of the nucleon: results from lattice QCD
Taken from M. Gong et al. (
χQCD Collaboration), arXiv:1304.1194 [hep-ph].
y ~ 0.04
Still large systematic uncertainties?
Slide11Results of test-analysis (using MEM)
P. Gubler and K.
Ohtani, Phys. Rev. D 90, 094002 (2014). Peak position can be extracted, but not the width!
Slide12Results for the φ
meson mass
P. Gubler and K. Ohtani, Phys. Rev. D 90, 094002 (2014).
Most important parameter, that
determines the behavior of the
φ
meson mass at finite density:
Strangeness content of the nucleon
Slide13Compare Theory with Experiment
Experiment
Sum Rules + Experiment
Lattice QCD
Not consistent?
Slide14However…
slope = σsN
Slide15Experiment
Sum Rules + Experiment
Lattice QCD
Therefore…
?
Slide16However…
Slide17Experiment
Sum Rules + Experiment
Lattice QCD
Therefore…
??
Slide18Issues of Borel sum rules
Details of the spectral function cannot be studied (e.g. width)Higher order OPE terms are always present (e.g. four-quark condensates at dimension 6)Use a model to compute the complete spectral function
Use moments to probe specific condensates
Slide19Method
Vector meson dominance model:
Kaon
-loops introduce self-energy corrections to the
φ
-meson propagator
Slide20Starting point:
Rewrite using hadronic degrees of freedom
Kaon
loops
Slide21Vacuum spectrum
Data fromJ.P. Lees et al. (BABAR Collaboration), Phys. Rev. D
88, 032013 (2013).
(Vacuum)
How
is this spectrum modified in nuclear matter?
Is the (modified) spectral function consistent with QCD sum rules?
Slide22What happens in nuclear matter?
Forward KN (or KN) scattering amplitude
If working at linear order in density, the free scattering amplitudes can be used
Slide23More on the free KN and KN scattering amplitudes
For KN: Approximate by a real constant (↔ repulsion) T. Waas, N. Kaiser and W. Weise, Phys. Lett. B
379, 34 (1996). For KN: Use the latest fit based on SU(3) chiral effective field theory, coupled channels and recent experimental results (
↔ attraction)
Y. Ikeda, T.
Hyodo
and W. Weise,
Nucl
. Phys. A
881
, 98 (2012).
K
-
p scattering length obtained from
kaonic
hydrogen (SIDDHARTA Collaboration)
Slide24Results (Spectral Density)
Takes into account further KN-interactions with intermediate hyperons, such as:
Asymmetric modification of the spectrum.
→
Not necessarily
parametrizable
by a simple
Breit
-Wigner peak!
→
Important message for future E16 experiment at J-PARC
Slide25Moment analysis of obtained spectral functions
Starting point: Borel-type QCD sum rules
Large M limitFinite-energy sum rules
Slide26Consistency check
(Vacuum) Are the zeroth and first momentum sum rules consistent with our phenomenological spectral density?Zeroth MomentFirst Moment
Consistent!
Slide27Consistency check
(Nuclear matter) Are the zeroth and first momentum sum rules consistent with our phenomenological spectral density?Zeroth MomentFirst Moment
Consistent!
Slide28Dependence on continuum onset?
Ansatz used so far:However, experiments give us a different picture:
Slide29New trial: ramp function
Mimics the experimental behavior of the 2K + n
π
states
Will this new
ansatz
significantly change the behavior of our results?
Slide30New trial: ramp function
→ modified sum rules
Slide31Results of ramp-function analysis
(Vacuum) → Consistent, if W’ is not too small
Slide32Results of ramp-function analysis
(Nuclear matter) → Also consistent, if W’ is not too small
Slide33Ratios of moments
Vacuum: Nuclear Matter: (S-Wave) (S- and P-Wave)
Interesting to measure in actual experiments?
Slide34Second moment sum rule
Factorization hypothesis Strongly violated?
Slide35Summary and Conclusions
The φ-meson mass shift in nuclear matter constrains the strangeness content of the nucleon: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??Most lattice calculations give a small σsN
-value
decreasing
φ
-meson mass in nuclear matter??
One recent lattice calculates obtains a large
σ
sN
-value (
σ
sN
= 105 MeV)
Slide36Summary and Conclusions
We have computed the φ meson spectral density in vacuum and nuclear matter based on an effective vector dominance model and the latest experimental constraints Accurate description of the spectral function in vacuumNon-symmetric behavior of peak in nuclear matter
We have carried out a moment analysis of the obtained spectral functionsSpectral functions are consistent with lowest two momentum sum rules
Moments provide direct links between QCD condensates and experimentally measurable quantities
Slide37Outlook
Further improve the sum rule computationComplete OPE up to operators of mass dimension 6Accurate evaluation of four-quark condensates (on the lattice?)
Consider finite momentumUse both QCD sum rules and effective theory
Make predictions for the E16 experiment at J-PARC
Slide38Backup slides
Slide39In-nucleus decay fractions for E325 kinematics
Taken from: R.S. Hayano and T. Hatsuda, Rev. Mod. Phys. 82, 2949 (2010).
Slide40Other experimental results
There are some more experimental results on the φ-meson width in nuclear matter, based on the measurement of the transparency ratio T:
T. Ishikawa et al, Phys. Lett. B
608
, 215 (2005).
Measured at SPring-8 (LEPS)
A.
Polyanskiy
et al, Phys. Lett. B
695
, 74 (2011).
Measured at COSY-ANKE
Slide41Results of test-analysis (using MEM)
P. Gubler and K. Ohtani, Phys. Rev. D
90, 094002 (2014).
Slide42Results of ramp-function analysis
(Nuclear matter) → Also consistent, if W’ is not too small