Algebraic quantization of the SU(3) skyrmion

The algebraic quantization of the SU(3) skyrmion is presented. We discuss the role of the number of colors (N_c) in QCD and the Wess-Zumino term in the quantization. Two distinct dynamical group chains are shown to correspond to different methods of semiclassical quantization. We obtain most of the SU(6) quark model predictions for the skyrmion quantized with N_c=3.     

Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm _d—m _u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m _d—m _u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN _c counting and furthermore provides an alternative interpretation of the Borel mass.     

Comments on a Minimal Quasiparticle Approach for the QGP and Its Large-N c Limits

A minimal quasiparticle approach for describing QGP at temperatures much higher than the critical one is discussed. It involves an ideal-gas framework in which quark and gluon masses depend on temperature. This model is able to reproduce the recent equations of state computed in lattice QCD for temperatures typically higher than 2 T _c , in a range in which it is reasonable to neglect interactions between quasiparticles. In addition, the equations of state for a generic gauge theory with gauge groups SU(N _c ) and quarks in an arbitrary representation are studied. The gauge independence in the pure glue sector and the large-N _c equivalence between the gauge groups SU(N _c ) and SO(2N _c ) in a full plasma is finally shown for normalized thermodynamic quantities.     

Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses

The meson spectrum of QCD is studied in the framework of nonperturbative QCD as a function of varying quark masses m _q . It is shown that the total spectrum consists of two branches: 1) the standard one, which may be called the flux-tube spectrum, depending approximately linearly on m _q , and 2) the chiral symmetry breaking (CSB) spectrum for pseudoscalar (PS) flavor nonsinglet mesons with mass dependence √m _q . The formalism for PS mesons is derived from the QCD Lagrangian with m _q corrections, and a unified form of the PS propagator was derived. It is shown that the CSB branch of PS mesons joins to the flux-tube branch at around m _q = 200 MeV. All these results are in close correspondence with recent numerical data on large lattices.     

On the bare pomeron graph in two-dimensional QCD

We present a detailed study of the bare pomeron graph in two-dimensional QCD in the 1/N_c approximation. The absence of a new singularity unrelated to quark parameters is derived. The “cylinder” graph is shown to induce renormalization of the vertex and intercept associated with quark andti-quark exchange in the vacuum channel.     

Coupled Channel Approach to S-Wave Hyperonic Interactions from Lattice QCD

We studied hyperonic interactions by lattice QCD simulation throuth coupled channel formalism. Our approach to baryon-baryon interactions is deriving a potential from inverting Schrödinger equation using Nambu-Bethe-Salpeter (NBS) wave function simulated on the lattice. The quark mass dependences and flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with results of gauge configurations with different quark masses. Our numerical results are obtained from three ensembles of 2+1 flavor QCD gauge configurations, which corresponds to m _π ~ 700, 570 and 410 MeV, provided by the PACS-CS Collaboration.     

Instantons and meson correlation functions in QCD

Various QCD correlators are calculated in the instanton liquid model in zeromode approximation and 1/N _c expansion. Previous works are extended by including dynamical quark loops. In contrast to the original “perturbative” 1/N _c approximation, not all quark loops are suppressed. Renormalization of the instanton density allows the identification of the density with the gluon condensate even in presence of dynamical quark loops. In the flavor singlet meson correlators a chain of quark bubbles survives the N _c → ∞ limit causing a massive η′ in the pseudoscalar correlator while keeping massless pions in the triplet correlator. The correlators are plotted and meson masses and couplings are obtained from a spectral fit. They are compared to the values obtained from numerical studies of the instanton liquid and to experimental results.     

Quark masses and their hierarchies

Electroweak symmetry breaking is attributed to dynamical generation of quark masses. Quarksq (and leptonsl) are assumed to be produced by hypercolor confinement of preons at an intermediate scaleΛ _hc. Hierarchies observed in theq mass spectra can be explained by a BCS mechanism if the color interaction is enough asymptotically free and if residual ones emerging by the confinement are medium strong. The former assumption claims thatN≦4, whereN is the family number ofq andl. Dynamical equations to determineq masses and mixings are given, but they require knowledge on the physics atΛ _hc. A phenomenological approach is also made on the basis of anSU(7)×SU(7) chiral preon model withN=4. The mass ratiom _t/mb is related to (m _c/m _s)^ηB withη _B?1.1 andm _t'/mb' to (m _u/m _d)^ηA withη _A?1.4. In this scheme the fourth down quark is the heaviest (～ 110 GeV) and contributes dominantly toF ², whereF is the Fermi scale.     

QCD sum rules for heavy quark systems

In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2⁺⁺. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the ¹P₁ level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-η_b splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p² = ?m_q²: m_c = 1.28 GeV and m_b = 4.25 GeV.     

A new slant on hadron structure

Rather than regarding the restriction of current lattice QCD simulations to quark masses that are 5–10 times larger than those observed as a problem, we note that this presents a wonderful opportunity to deepen our understanding of QCD. Just as it has been possible to learn a great deal about QCD by treating N _c as a variable, so the study of hadron properties as a function of quark mass is leading us to a deeper appreciation of hadron structure. As examples we cite progress in using the chiral properties of QCD to connect hadron masses, magnetic moments, charge radii and structure functions calculated at large quark masses within lattice QCD with the values observed physically.     

One-loop corrections to the baryon axial vector current

The symmetry breaking corrections to the pion?Cbaryon couplings vanish to first order in 1/N _c, where N _c is the number of colours. Loop graphs with octet and decuplet intermediate states cancel to various orders in N _c as a consequence of the large-N _c spin-flavour symmetry of QCD baryons. The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large N _c limit. 1/N _c corrections in the case of g _A in QCD are presented here.     

Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory

Chiral perturbation theory in the two-flavour sector allows one to analyse Green functions in QCD in the limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses m _u and m _d . In this framework, the low-energy constants of SU(2) _R × SU(2) _L depend on the value of the heavy quark masses. For the coupling constants which occur at order p ² and p ⁴ in the chiral expansion, we worked out in [1] the dependence on the strange quark mass at two-loop accuracy, and provided in [2] analogous relations for some of the couplings c _i which are relevant at order p ₆. This talk comments on the methods used, and illustrates implications of the results obtained.     

Renormalized Wick expansion for a modified PQCD

The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m_q and m_g associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m_q and m_g is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum.     

Pseudoscalars and vector mesons in a unitary and self-consistently broken SU(6) W scheme

We estimate hadronic self-energy effects to “bare” pseudoscalar (P) and vector (V) meson states due to theP→PV→P, P→VV→P, V→ PP→V, V→PV→V andV→VV→V loops. We simulate higher order diagrams by consistently requiring external and internal particles to have the same mass. We find good agreement with all the experimental masses (exceptm _π), widths and mixing angles. The “bare”P andV states are heavy (≈1.26 GeV) and degenerate up to a smallm _s?m_u quark mass difference term. The “bare” coupling constants for thePPV, PVV andVVV vertices obey exact OZI rule and almost exact SU(6) _W symmetry. We use a common cut-off ofk _cm?0.7 GeV/c corresponding to a harmonic oscillator radius of ?0.7 fm for all SU(6) _W related thresholds except for the pion.     

Quen's gambit: Decuplet quarks and composite axions

Exotic quarks transforming as decuplets under SU(3)_c (quens) qith zero bare (current) mass plausibly condense at a scale exponentially removed from the ordinary triplet quark chiral symmetry breaking scale. The pseudoscalar pseudo-Goldstone boson remaining after the breaking of the quentic global chiral U(1)_A in the presence of QCD instantons is a likely composite invisible axion (CIA) candidate.     

Radiative corrections to high-energy neutrino scattering

Motivated by precise neutrino experiments, we reconsider the electromagnetic radiative corrections to the data. We investigate the usefulness and demonstrate the simplicity of the “leading log” approximation: the calculation to order α ln (Q/μ), α ln (Q/m_q). Here Q is an energy scale of the overall process, μ is the lepton mass and m_q is a hadronic mass, the effective quark mass in a parton model. We identify those questions the answers to which do not depend on unknown hadron parameters like quark masses. The leading log radiative corrections to dδ/dy distributions and to suitably interpreted dδ/dx distributions are quark-mass independent. We improve upon the conventional leading log approximation and compute explicitly the largest terms that lie beyond the leading log level. In practice this means that our model-independent formulae, though approximate, are likely to be excellent estimates everywhere except at low energy or very large y. We point out that radiative corrections to measurements of deviations from the Callan-Gross relation and to measurements of the “sea” constituency of nucleons are gigantic. The QCD inspired study of deviations from scaling is of particular interest. We compute, beyond the leading log level, the radiative corrections to the QCD predictions.     

Glueball spectrum from N_f=2 lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using N_f = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ～938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67)GeV at mπ～938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of ∈_ijkTrB_iD_jB_k, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter(around 1 GeV) and compatible with the expected masses of the flavor singlet qq meson. This indicates that the operator ∈ijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and qq mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.     

Calculation of the pseudoscalar masses from a QCD effective potential

We calculate the effective two-loop potential of QCD with massive quarks in the CJT composite operator formalism. To perform the wave-function renormalization of composite operators we are lead to a condition which corresponds to the Adler-Dashen requirement in the limit of vanishing quark masses. The condition also assures absence of spontaneous breaking of parity. Pseudoscalar masses are calculated from the second derivatives of the effective potential, and a fit is obtained for quark masses m_u = 3.6 MeV, m_d = 7 MeV, m_s = 152 MeV. We also comment on consistuent quark masses and on the effect of heavy quarks.     

The spatial string tension and dimensional reduction in QCD

The spatial string tension is calculated in 2+1 flavor QCD with a physical strange quark mass and almost physical light quark masses on lattices with N_t=4,6 and 8. The results are compared with predictions of dimensionally reduced QCD. They suggest that dimensional reduction works also in the presence of light dynamical quarks down to temperatures of about 1.5T_c.