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.     

Mass spectrum in SQCD and problems with the Seiberg duality. Another scenario

The N = 1 SQCD with SU(N _c ) colors and N _F flavors of light quarks is considered within the dynamical scenario that assumes that quarks can be in the two different phases only: the heavy-quark phase, where they are confined, and the phase of higgsed quarks, at the appropriate values of the Lagrangian parameters. The mass spectra of this (direct) theory and its Seiberg dual are obtained and compared for quarks of small equal or unequal masses. It is shown that in those regions of the parameter space where an additional small parameter exists (it is < [`(b)]₀ /N_F = (3N_c - N_F )/N_F << 1< \bar b_0 /N_F = (3N_c - N_F )/N_F \ll 1 at the right end of the conformal window, where the direct theory is weakly coupled in the vicinity of its IR fixed point, or its analog 0 < b ₀/N _F = (2N _F − 3N _c )/N _F ≪ 1 for the dual theory at the left end of the conformal window), the mass spectra of the direct and dual theories are parametrically different. A number of other regimes are also considered.     

Hadron masses in QCD with one quark flavour

One-flavour QCD – a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation – is studied by Monte Carlo simulations. The mass spectrum of the hadronic bound states is investigated in a volume with extensions of L≃4.4r₀ (≃ 2.2 fm) at two different lattice spacings: a≃0.37r₀ (≃ 0.19 fm) and a≃0.27r₀ (≃ 0.13 fm). The lattice action is a Symanzik tree-level improved Wilson action for the gauge field and an (unimproved) Wilson action for the fermion.     

On mass spectrum in SQCD. Unequal quark masses

The N = 1 SQCD with N _c colors and two types of light quarks, N _l flavors with the smaller mass m _l and N _h = N _F − N _l flavors with the larger mass m _h , N _c < N _F < 3N _c , 0 < m _l ≤ m _h ≪ Λ _Q , is considered within the dynamical scenario in which quarks can form a coherent colorless diquark condensate 〈$ \bar Q $ \bar Q Q〉. There are several phase states at different values of the parameters r = m _l /m _h . N _l , and N _F . Properties of these phases and their mass spectra are described.     

Hadronic corrections to QCD sum rules and light quark masses

A parametrization of theJ ^p =0^? hadronic continuum, in the framework of Extended PCAC, is discussed with emphasis on finite-width effects and on the constraints imposed by the correct threshold behavior of the pion spectral function. As an application light quark masses are calculated using both Hilbert and Laplace transform QCD sum rules. The results for the runing quark masses are: \((\bar m_u + \bar m_d )|_{1 Gev} = 16 \pm 2 MeV,(\bar m_u + \bar m_s )|_{1 Gev} = 199 \pm 27 MeV\) , and a ratio \(R \equiv 2(\bar m_u + \bar m_s )/(\bar m_u + \bar m_d )_{1 Gev} = 25 \pm 4\) .     

QCD equation of state: Physical quark masses and asymptotic temperatures

Within a phenomenological quasiparticle model, the quark mass and temperature dependence of the QCD equation of state is discussed and compared with lattice QCD results. Different approximations for the quasiparticle dispersion relations are employed, scaling properties of the equation of state with quark mass and deconfinement temperature are investigated and a continuation to asymptotically large temperatures is presented.     

Dynamical quark effects on the hadronic spectrum and qq-potential in lattice QCD

The results of a calculation which incorporates virtual quark-antiquark pairs at a coupling of β=5.7 and quark mass of 0.05 are compared with those of two quenched simulations at β=5.895 and 6. The inclusion of the dynamical quark produces no effects in the hadron mass spectrum besides an overall shift in the coupling. In contrast, the Wilson lopp factors show a non-trivial effect, in the form of a flattening of the heavy quark potential. All three studies were carried out on a 10³·32 lattice.     

On QCD sum rules of the Laplace transform type and light quark masses

We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in QCD. Two specific examples corresponding to the ?-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.     

The β-function for effective quark masses to two loops in QCD

We calculate the evolution equation for effective masses in QCD to two loops in the minimal subtraction scheme of 't Hooft. We compare our result with two other recent calculations and make some comments on the gauge independence and regularization dependence of the β-functions.     

On the choice of quark currents in the QCD sum rules for baryon masses

The cryteria for the choice of the most suitable quark currents in the QCD sum rules for baryon masses are discussed. The currents used in [1, 2] are preferable comparing with those adopted in [3, 4] since the latters result in large power corrections.     

The effect of quark masses on the running of the QCD coupling constant

The presence of thresholds for finite quark masses alters the behavior of the QCD coupling constant. While the alterations are small they can have significant influence on the determination of the scale parameter Λ. Part of the discrepancy between recent highQ ² determinations of Λ and older lowQ ² determinations can be attributed to charm and bottom thresholds. We present simple, analytic expressions for the mass dependence of α(Q ²) and exploit these to discuss Λ determinations, scale breaking and the phenomenon of temporary freedom when more than 17 quark flavors exist.     

Meson decay constants and bare quark masses from duality for current two-point functions

Duality is applied in a quasi-local form to the SU(4) × SU(4) current two-point functions. Interpolating functions for some of their space-time components are assumed to be given by the free quark model. Mass intervals in the finite energy sum rules are taken to be approximately SU(3) × SU(3) invariant and a linear dependence of the hadronic mass spectrum upon the radial quantum number is assumed. The correct order of magnitude of various meson decay constants is reproduced provided the color gauge group is SU(3). The bare uncharmed quark masses are given by the formulae: $\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ M}{}_{\mathrm{\pi }}\text{F}{}_{\mathrm{\pi }}\text{/F}{}_{\mathrm{\pi }}\text{√6 ≌ 40}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ 1 = 6}$. The η-η mixing problem is discussed. Predictions are made for the masses and decay constants of the vector mesons of the first L = 2 level of SU(6) × O(3), as well as for the decay constants of the radially excited pseudoscalar mesons; estimates of corrections to PCAC in Goldberger-Treiman relations are presented. The bare charmed quark mass is found to be of the order of 1.1–1.2 GeV. Some decay constants of charmed mesons are evaluated.