Narrow Results

We study the spectra of quantum graphs with the method of trace identities (sum rules), which are used to derive inequalities of Lieb–Thirring, Payne–Pólya–Weinberger, and Yang types, among others. We show that the sharp constants of these inequalities and even their forms depend on the topology of the graph. Conditions are identified under which the sharp constants are the same as for the classical inequalities. In particular, this is true in the case of trees. We also provide some counterexamples where the classical form of the inequalities is false.

The nucleon has been used as a laboratory to investigate its own spin structure and quantum chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov–Drell–Hearn, Bjorken and Burkhardt–Cottingham). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher-twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT.

We give sum rules for tetraquark decay coupling constants, taking into account the SU(3) symmetry breaking interactions to first order.

For tetraquarks of the form we give sum rules for their decay coupling constants, taking into account the SU(3) symmetry breaking interactions to first-order.

The SU(3) classification of baryon number B = 2, that is dibaryon sextaquarks, is considered. It is noted that the deuteron belongs to the 10* representation. Sum rules in broken SU(3) are given for the 10* and 10 dibaryons into B(8)+B(8). Finally, the possibility of observing the dibaryons in low energy pp- and e⁺e^--collisions is discussed.

The SU(3) octet states with baryon number B = 2, hexaquark dibaryons, are considered. We extend previous work and determine strong decay coupling constants sum rules with first-order SU(3) symmetry breaking for dibaryon octet into two ordinary baryon octets and into a baryon octet plus a baryon decuplet. Possibilities for the experimental observation of multibaryon and anti-multibaryon states are pointed out.

10 and 27 SU(3) multiplets of hexaquarks states with baryon number $B=2$, known as dibaryons, are considered. Previous analyses are complemented and sum rules for strong decay amplitudes with SU(3) symmetry violation up to the first order are determined for the 10 and 27 dibaryon multiplets into a baryon octet plus a baryon decuplet and for the dibaryon 27 into two baryon octets.

The energy-weighted sum rule for an electric dipole transition operator of a Schiff type differs from the Thomas–Reiche–Kuhn (TRK) sum rule by several corrective terms which depend on the number of system components, . For illustration the formalism was applied to the case of Na clusters. One concludes that the random phase approximation (RPA) results for Na clusters obey the modified TRK sum rule.

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight into some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e., the Bjorken, Burkhardt–Cottingham, Gerasimov–Drell–Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g₁ at low momentum transfer of 0.05–0.1 GeV² but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability δ_LT. The Burkhardt–Cottingham sum rule has been verified with good accuracy in a wide range of Q² assuming that no singular behavior of the structure functions is present at very high excitation energies.

This paper deals with a microscopic approach for the description of the pygmy dipole resonance (PDR) as well as of the giant dipole resonance (GDR). The formalism is based on a Hamiltonian which is summing a mean field term, the pairing for alike nucleons and the dipole–dipole interaction. Two features are specific for our description: (a) The use of a projected spherical single particle basis and (b) the involved dipole operator is a Schif-like operator including a corrective term which is cubic in the radial coordinate. The dipole strength distribution with energy is plotted for the PDR region, i.e., [0,10] MeV. The dominant transitions have an isovector character for three isotopes and isoscalar for another three. The PDR states carry only 0.4–1.8$\%$ of the total EWSR. The dependence of the dipole strength on nuclear deformation is evidenced. For the whole interval of [0,20] MeV the dipole strength was first folded by Lorentzian of 1MeV width and then plotted as function of the QRPA energies. The peaks belonging to each of the two ranges are analyzed in detail and their nature, isovector/isoscalar, was pointed out. The r-cubic term and the nuclear deformation have opposite effects on the dipole strength. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new EWSR is very well satisfied. The photoabsorbtion cross-section is calculated and compared with experimental data in a figure showing its dependence on energy. The total cross-section, ${\sigma }_0$, the moments of the integrated cross-sections, ${\sigma }_{-1}$, ${\sigma }_{-2}$, the dipole polarizability and the thickness of the neutron crust are also calculated. The main features of PDR and GDR are realistically described.

The LHCb experiment has measured CP violation (CPV) across the Dalitz plot of charmless decays of B+ mesons to 3 charged tracks, namely in Kππ, KKK, πππ and πKK final states, with strikingly large CPV that vary strongly with Dalitz variables. Identifying these processes with b → sqq, sss and b → dqq, dss, where q = u, d, then the “sum rule” that requires two-loop absorptive parts by unitarity works well for inclusive b → s CPV, but less well for inclusive b → d case. We elucidate the situation, and argue that the 30 year old unitarity/CPT argument is valid to this day, while affirming quark-hadron duality.

The nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent experimental data on nucleon spin structure at low to intermediate momentum transfers provide new information in the confinement regime and the transition region from the confinement regime to the asymptotic freedom regime. New insight is gained by exploring moments of spin structure functions and their corresponding sum rules (i.e. the generalized Gerasimov-Drell-Hearn, Burkhardt-Cottingham and Bjorken). The Burkhardt-Cottingham sum rule is verified to good accuracy. The spin structure moments data are compared with Chiral Perturbation Theory calculations at low momentum transfers. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.05 to 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT (the δ_LT puzzle). New data have been taken on the neutron (³He), the proton and the deuteron at very low Q² down to 0.02 GeV². They will provide benchmark tests of Chiral dynamics in the kinematic region where the Chiral Perturbation theory is expected to work.

We explain the origin of the controversy about the existence of a transverse angular momentum sum rule, and show that it stems from utilizing an incorrect result in the literature, concerning the expression for the expectation values of the angular momentum operators. We demonstrate a new, short and direct way of obtaining correct expressions for these expectation values, from which a perfectly good transverse angular momentum sum rule can be deduced. We also introduce a new classification of sum rules into primary and secondary types. In the former all terms occurring in the sum rule can be measured experimentally; in the latter some terms cannot be measured experimentally.

The three site Higgsless model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this talk, we present how well the three site Higgsless model performs as a general representative of Higgsless models, in describing W_LW_L scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein (KK) modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. After comparing the three site Higgsless model to flat and warped continuum Higgsless models, we analyze an extensions of the three site Higgsless model, namely, the Hidden Local Symmetry (HLS) Higgsless model. We demonstrate that W_LW_L scattering in the HLS Higgsless model can very closely approximate scattering in the continuum models, provided that the parameter 'a' is chosen to mimic ρ-meson dominance of ππ scattering in QCD.