QCD sum rules for nucleons in nuclear matter II

The proton matrix element of the isovector-scalar density, p|uu−dd|p /2M p , is calculated by evaluating the nucleon current correlation function in an external isovector-scalar field using the QCD sum-rule method. In addition to the usual chiral and gluon condensates of the QCD vacuum, the response of the chiral condensates to the external isovector field enters the calculation. The latter is determined by two independent methods. One relates it to the difference between the up and down quark chiral condensates and the other uses the chiral perturbation theory. To first order in the quark mass difference δm = m d − m u , the non-electromagnetic part of the neutron-proton mass difference is given by the product δm p|uu − dd|p /2M p ; the resulting value is in reasonable agreement with the experimental value.

show abstract

“…To first order in the external field S V , the propagators in the fixed-point gauge [19][20][21] take the form…”

Section: Sum-rule Calculationmentioning

confidence: 99%

Calculation of 〈p‖u¯u-d¯d‖p〉 from QCD sum rules and the neutron-proton mass difference

1995

Self Cite

View full text Add to dashboard Cite

show abstract

“…The correlation function is evaluated in the ground state of nuclear matter instead of the QCD vacuum. The appearance of an additional four-vector at finite density, the four-velocity of the nuclear medium, leads to additional invariant functions relative to the vacuum case [2][3][4][5][6]14]. In the rest frame of the medium, the analytic properties of the various invariant functions can be studied through Lehman representations in energy.…”

mentioning

confidence: 99%

“…To obtain the finite-density sum rules from this mixed correlator, we follow the procedures established in Ref. [2][3][4][5][6]. The correlator Π 12 µν (q) contains nine distinct structures at finite density.…”

mentioning

confidence: 99%

“…The correlator of χ 1 µ and χ 1 ν gives the sum rules discussed extensively in Refs. [2][3][4][5][6]. In particular, the sum rule at the structure, γ µ / qγ ν , strongly depends on the even-chirality fourquark condensates, q Γ i q q Γ i q ρ N and q Γ i λ a q q Γ i λ a q ρ N , where λ a are the Gell-Mann matrices and Γ i are any of the 16 Dirac matrices.…”

mentioning

confidence: 99%

“…The QCD sum-rule approach [1] is a particularly useful method for connecting the properties of QCD to observed nuclear phenomena [2][3][4][5][6][7][8][9][10]. Recent progress in understanding the origin of the large and canceling isoscalar Lorentz-scalar and -vector self-energies for propagating nucleons in nuclear matter has been made via the analysis of QCD sum rules generalized to finite nucleon density [2][3][4][5][6].…”

mentioning

confidence: 99%

See 2 more Smart Citations

New QCD sum rules for nucleons in nuclear matter

1996

Self Cite

View full text Add to dashboard Cite

Two new QCD sum rules for nucleons in nuclear matter are obtained from a mixed correlator of spin-1/2 and spin-3/2 interpolating fields. These new sum rules, which are insensitive to the poorly known four-quark condensates, provide additional information on the nucleon scalar self-energy. These new sum rules are analyzed along with previous spin-1/2 interpolator-based sum rules which are also insensitive to the poorly known four-quark condensates. The analysis indicates consistency with the expectations of relativistic nuclear phenomenology at nuclear matter saturation density. However, a weaker density dependence near saturation is suggested. Using previous estimates of in-medium condensate uncertainties, we find M * = 0.64 +0.13 −0.09 GeV and Σ v = 0.29 +0.06 −0.10 GeV at nuclear matter saturation density.

show abstract

In-medium Chiral Perturbation Theory beyond the Mean-Field Approximation

2002

View full text Add to dashboard Cite

An explicit expression for the generating functional of two-flavor low-energy QCD with external sources in the presence of nonvanishing nucleon densities was derived recently (J. A. Oller, Phys. Rev. C 65 (2002) 025204). Within this approach we derive power counting rules for the calculation of in-medium pion properties. We develop the so-called standard rules for residual nucleon energies of the order of the pion mass and a modified scheme (nonstandard counting) for vanishing residual nucleon energies. We also establish the different scales for the range of applicability of this perturbative expansion, which are √ 6π f π 0.7 GeV for standard and 6π 2 f 2 π /2m N 0.27 GeV for nonstandard counting, respectively. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses, and couplings of the axial-vector, vector, and pseudoscalar currents to pions. In particular, we find a mass shift for negatively charged pions in heavy nuclei, M π − = (18 ± 5) MeV, that agrees with recent determinations from deeply bound pionic 207 Pb. We have also established the absence of in-medium renormalization in the π 0 → γ γ decay amplitude up to the same order. The study of ππ scattering requires the use of the nonstandard counting and the calculation is done at leading order. Even at that order we establish new contributions not considered so far. We also point toward further possible improvements of this scheme and touch upon its relation to more conventional many-body approaches. C 2002 Elsevier Science (USA)

show abstract

QCD sum rules for nucleons in nuclear matter II

Cited by 94 publications

References 45 publications

Calculation of 〈p‖u¯u-d¯d‖p〉 from QCD sum rules and the neutron-proton mass difference

Calculation of 〈p‖u¯u-d¯d‖p〉 from QCD sum rules and the neutron-proton mass difference

New QCD sum rules for nucleons in nuclear matter

In-medium Chiral Perturbation Theory beyond the Mean-Field Approximation

Contact Info

Product

Resources

About