Constituent quarks, chiral symmetry, and chiral point of the constituent quark model

We construct the full axial current of the constituent quarks by a summation of the infinite number of diagrams describing constituent-quark soft interactions. By requiring that the conservation of this current is violated only by terms of order $O(M_\pi^2)$, where $M_\pi$ is the mass of the lowest pseudoscalar $\bar QQ$ bound state, we derive important constraints on (i) the axial coupling $g_A$ of the constituent quark and (ii) the $\bar QQ$ potential at large distances. We define the chiral point of the constituent quark model as those values of the parameters, such as the masses of the constituent quarks and the couplings in the $\bar QQ$ potential, for which $M_\pi$ vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current of the constituent quarks is conserved, the leptonic decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.Comment: 10 pages, typo in eq. (46) of the published version is correcte

Accuracy of the pion elastic form factor extracted from a local-duality sum rule

We analyze the accuracy of the pion elastic form factor predicted by a local-duality (LD) version of dispersive sum rules. To probe the precision of this theoretical approach, we adopt potential models with interactions that involve both Coulomb and confining terms. In this case, the exact form factor may be obtained from the solution of the Schroedinger equation and confronted with the LD sum rule results. We use parameter values appropriate for hadron physics and observe that, independently of the details of the confining interaction, the deviation of the LD form factor from the exact form factor culminates in the region Q^2~4-6 GeV^2. For larger Q^2, the accuracy of the LD description increases rather fast with Q^2. A similar picture is expected for QCD. For the pion form factor, existing data suggest that the LD limit may be reached already at the relatively low values Q^2=4-10 GeV^2. Thus, large deviations of the pion form factor from the behaviour predicted by LD QCD sum rules for higher values of Q^2, as found by some recent analyses, appear to us quite improbable. New accurate data on the pion form factor at Q^2=4-10 GeV^2 expected soon from JLab will have important implications for the behaviour of the pion form factor in a broad Q^2 range up to asymptotically large values of Q^2.Comment: 12 pages, extended version, conclusions remain unchange

The γ∗γ∗→ηc\gamma^* \gamma^*\to\eta_c transition form factor

We study the $\gamma^* \gamma^*\to\eta_c$ transition form factor, $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2),$ with the local-duality (LD) version of QCD sum rules. We analyse the extraction of this quantity from two different correlators, and $,$ with $P,$ $A,$ and $V$ being the pseudoscalar, axial-vector, and vector currents, respectively. The QCD factorization theorem for $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2)$ allows us to fix the effective continuum thresholds for the and $$ correlators at large values of $Q^2=Q_2^2$ and some fixed value of $\beta\equiv Q_1^2/Q_2^2$. We give arguments that, in the region $Q^2\ge10$--$15 GeV^2$, the effective threshold should be close to its asymptotic value such that the LD sum rule provides reliable predictions for $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2).$ We show that, for the experimentally relevant kinematics of one real and one virtual photon, the result of the LD sum rule for $F_{\eta_c\gamma}(Q^2)\equiv F_{\eta_c\gamma\gamma}(0,Q^2)$ may be well approximated by the simple monopole formula $F_{\eta_c\gamma}(Q^2)={2e_c^2N_cf_P}(M_V^2+Q^2)^{-1},$ where $f_P$ is the $\eta_c$ decay constant, $e^2_c$ is the $c$-quark charge, and the parameter $M_V$ lies in the mass range of the lowest $\bar cc$ vector states.Comment: 9 page

Dispersion representations and anomalous singularities of the triangle diagram

We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations. For the double dispersion representation in $p_1^2$ and $p_2^2$, the appearance of the anomalous cut in the region $q^2>0$ is demonstrated, and a new derivation of the anomalous double spectral density is given. We point out that the double spectral representation is particularly suitable for applications in the region of $p_1^2$ and/or $p_2^2$ above the two-particle thresholds. The dispersion representations for the triangle diagram in the nonrelativistic limit are studied and compared with the triangle diagram of the nonrelativistic field theory.Comment: 10 pages, revtex, added a reference, version to be published in Phys. Rev.

Pressure Waves due to Rapid Evaporation of Water Droplet in Liquid Lead Coolant

Flash evaporation of a superheated water droplet in heavy liquid metal coolant (lead) is considered, in application to the analysis of a lead-cooled fast reactor steam generator tube rupture accident. The model is based on thermodynamic equilibrium formulation for the expanding water-steam mixture and inviscid compressible formulation for the surrounding liquid lead, with the interface conditions determined from the solution of the Riemann problem. Numerical solution is performed in the spherically symmetric geometry using a conservative numerical scheme with a moving sharp interface. Transient pressure and velocity profiles in each phase are presented for the parameters typical of the steam generator tube rupture accidents, demonstrating the process of boiling water expansion and pressure wave formation in the coolant. The results obtained are compared with a simplified model which considers the volume-averaged parameters of boiling water droplets and considers coolant as an incompressible liquid. Good agreement between the full and simplified models is demonstrated. Impacts of coolant flow on structures caused by pressure wave propagation and subsequent coolant flow are discussed

One Interesting New Sum Rule Extending Bjorken's to order {1/m_Q}

We explicitly check quark-hadron duality to order $(m_b-m_c)\Lambda/m_b^2$ for $b \to c l\nu$ decays in the limit $m_b-m_c \ll m_b$ including ground state and orbitally excited hadrons. Duality occurs thanks to a new sum rule which expresses the subleading HQET form factor $\xi_3$ or, in other notations, $a_+^{(1)}$ in terms of the infinite mass limit form factors and some level splittings. We also demonstrate the sum rule, which is not restricted to the condition $m_b-m_c \ll m_b$, applying OPE to the longitudinal axial component of the hadronic tensor without neglecting the $1/m_b$ subleading contributions to the form factors. We argue that this method should produce a new class of sum rules, depending on the current, beyond Bjorken, Voloshin and the known tower of higher moments. Applying OPE to the vector currents we find another derivation of the Voloshin sum rule. From independent results on $\xi_3$ we derive a sum rule which involves only the $\tau_{1/2}^{(n)}$ and $\tau_{3/2}^{(n)}$ form factors and the corresponding level splittings. The latter strongly supports a theoretical evidence that the $B$ semileptonic decay into narrow orbitally-excited resonances dominates over the decay into the broad ones, in apparent contradiction with some recent experiments. We discuss this issue.Comment: 9 page

Non-local anomaly of the axial-vector current for bound states

We demonstrate that the amplitude $<\rho\gamma|\partial_\nu (\bar q\gamma_\nu \gamma_5 q)|0>$ does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet-finite as guaranteed by the presence of the bound-state wave function. As a result, the amplitude behaves like $\sim 1/p^2$ in the limit of a large momentum $p$ of the current. This is to be compared with the amplitude $$ which remains finite in the limit $p^2\to\infty$. The observed effect leads to the modification of the classical equation of motion of the axial-vector current in terms of the non-local operator and can be formulated as a non-local axial anomaly for bound states.Comment: revtex, 4 pages, numerical value for $\kappa$ in Eq. (19) is corrected, Eqs. (22) and (23) are modified. New references added. Results remain unchange