Heavy and heavy to light quark expansions

We analyze the phenomenon of heavy quark condensation within the framework of the QCD sum rule approach. We discuss two alternative expansions for massive quark condensates. The first one (heavy to light quark expansion), introduced by Broadhurst and Generalis, establishes a connection between the heavy and light quark worlds. The other one (heavy quark expansion) is valid when only heavy quark systems are considered. As a byproduct we have obtained the coefficients of \(\left\langle {\bar qq} \right\rangle \) , \(\left\langle {\bar qGq} \right\rangle \) , 〈G ²〉 and 〈G ³〉 for all bilinear currents.     

Meson spectra and mass splitting of \eta_{c}^{} - J/ \psi calculated with a regularized quark potential

The complete Breit potential contains the terms of spin-spin, spin-orbit, orbit-orbit, and tensor force interactions which become singular at short distance. Most of previous calculations of the non-relativistic potential quark model considered only the spin-spin interaction and substituted the $ \delta$ (r) -function by the Gaussian or Yukawa potential in coordinate space. Recently, a method to regularize the Breit potential consists of subtracting terms that cancel the singularity at the origin but leave the intermediate- and long-distance behavior unchanged. Motivated by this work we regularize the Breit potential by multiplying the singular terms in momentum space identically by the form factor [ $ \mu^{2}_{}$ /(q ² + $ \mu^{2}_{}$ )]² of the momentum transfer q , where the screened mass μ increases with the reduced mass of the meson. With the regularized Breit potential we calculate the masses of 30 common mesons and the new $ \eta_{b}^{}$ meson. We find that the calculated masses from light to heavy mesons agree well with experimental data. The inclusion of such a dependence of the reduced mass in the potential regularization improves the spin-spin splittings of $ \eta_{c}^{}$ -J/ $ \psi$ and $ \eta_{b}^{}$ - $ \Upsilon$ (1S) . The spin-orbit and tensor force interactions in the Breit potential lead to the splittings of $ \chi_{{c0}}^{}$ , $ \chi_{{c1}}^{}$ , and $ \chi_{{c2}}^{}$ .     

Ultraheavy Yukawa-bound states of fourth-generation at Large Hadron Collider

A study of bound states of the fourth-generation quarks in the range of 500?C700 GeV is presented, where the binding energies are expected to be mainly of Yukawa origin, with QCD subdominant. Near degeneracy of their masses exhibits a new ??isospin??. The production of a colour-octet, isosinglet vector meson via $q\bar q \to \omega_8$ is the most interesting. Its leading decay modes are $\pi_8^\pm W^\mp$ , $\pi_8^0Z^0$ , and constituent quark decay, with $q\bar q$ and $t\bar t'$ and $b\bar b'$ subdominant. The colour octet, isovector pseudoscalar ?? ₈ meson decays via constituent quark decay, or to Wg. This work calls for more detailed study of fourth-generation phenomena at LHC.     

The correlation between charge and energy flow within cascade models for quark and hadron jets

We consider the ratio \(\frac{{\Delta Q}}{{\Delta \varepsilon }}\) of the charge and energy fraction carried by particles in the angular interval ΔΩ with respect to the jet axis, where we assume a recursive scheme for the hadron cascade. A measurement of this ratio inep andvp collisions determines the quark chargeQ _q at any angle ΔΩ and ine ⁺ e ^?-annihilations alsoQ _q ⁴ can be obtained. In hadron hadron collisions this ratio discriminates in a very direct way between different production models. We consider the “stopping quark” model, the “two dual sheet” model, and finally a leading cluster model. More data on \(\frac{{\Delta Q}}{{\Delta \varepsilon }}\) would be desirable at higher energies in particular for meson beams.     

Energy andx dependence of inclusive particle production in annihilation and non-annihilation reactions in the quark recombination model

Existing data are used to show that the structure functions of meson production in \(\bar p\) p annihilation are characterized by (1?x)^α distributions with α consistently less than in \(\bar p\) p non-annihilation orpp interactions. The energy dependence of \(\bar p\) p annihilation is interpreted as being given by the probability of at least one valence quark of \(\bar p\) andp being in the wee region. The annihilation is attributed to the recombination of a sea antiquark with a quark of the dismembered spectator valence di-quark system. This model can describe the existing annihilation data. Other models are briefly reviewed with respect to features of annihilation data.     

Exclusive semi-leptonic decays of bottom mesons in the spectator quark model

We calculate the exclusive semileptonic bottom meson decays \(B \to D(D*) + l^ - + \bar v_l \) in the spectator quark model. The helicity structure of the mesonic current transitionsB→D(D ^*) is matched to the helicity structure of the free quark current transitionsb→c at minimum momentum transferq ²=0. The results are continued toq ²≠=0 by pole-dominated form factors. Our results are compared to recent calculations that use quark model dynamics at maximum momentum transferq _max ² = (M ₁ ?M ₂)². We find agreement atq _max ² . Atq ²=0 there are significant differences between the predictions of the two approaches leading to marked differences in the predictions for the shape of the lepton energy spectrum, the shape of theq ²-distribution, and the helicity composition of the transition measurable in the angular distributions of the decaysD ^*→Dπ and \(W_{virtual}^ - \to l^ - + \bar v_l \) .     

Top and bottom quark condensates

It is possible that electroweak symmetry might be broken dynamically by a condensate of top quarks. We extend a previous study of top quark dynamics to include the bottom quark. The simultaneous gap equations in dressed ladder approximation for∑ _t (p),∑ _b (p) are studied numerically and analytically in various regions of parameter space, and the solutions are used to determine \(\langle \bar tt\rangle ,\langle \bar bb\rangle \) and the decay constantsF _±,F ₀, as well as the top and bottom masses. We discuss the question of fine-tuning, and show how our approach can be extended to other quark and lepton masses.     

Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid ³He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ～ 325 GeV. They together satisfy the Nambu sum rule M ₁ ² + M ₂ ² = 4M _t ² , where M _t ～ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ～210 GeV. In this case the Nambu sum rule is 2M ₁ ² + 2M ₂ ² = 4M _t ² . In addition, the properties of the Higgs modes in superfluid ³He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M ₊ ² + M _? ² = 4M _t ² .     

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 \(R \equiv 2(\bar m_u + \bar m_s )/(\bar m_u + \bar m_d )_{1 Gev} = 25 \pm 4\) .     

Spectra and hadronic couplings of light hermaphrodite mesons

We clarify the discrepancies of previous results for the masses and decay amplitudes of hermaphrodite mesons obtained from QCD sum rules. We study the case of the strange quark within a light quark expansion formalism. We find tht the hermaphrodite masses are much higher than the ones of their ordinary meson partners. Our values of the set of masses and continuum thresholds are compared with some other sum rule results. We analyze the hadronic couplings of the isovector 1^?+ exotic hermaprodite \(\tilde \rho \) using a three-point function sum rule evaluated at the symmetric euclidean point. We find that the \(\tilde \rho \) can be very broad and prefers to decay into ρπ andK ^* K. Its most characteristic decays are the ones into πγ, ηπ and μ′π. The former and the latter are of the order of (3～8) MeV.     

On the semileptonic decay distributions from the next heavy quark

Motivated by the discovery of λ(9.4), we study the semileptonic decay correlations of the next heavy quark, and their consequences for thee ⁺ e ^? colliding beam and neutrino experiments. A detailed comparison is made with the corresponding correlations from the production and decay of charm and heavy leptons, τ^±. Some tests of the \({\rm B}^0 - \bar {\rm B}^0 \) mixing ( \(B = b\bar q\) withbaQ=?1/3 heavy quark) are suggested fore ⁺ e ^? colliding beam experiments.     

Some comments on heavy quark bound states,production and decay

We suggest that mixed heavy quark bound states like \(b\bar c\) may offer very good testing ground for Q.C.D. We make a prediction within ≈0.3% for the \(b\bar c\) ground state mass and discuss its possible production in weak decays. Various general features of non leptonic decays of heavey flavors and in particular the prediction of absence ofK _* ⁰ resonance inD ⁰→K ^-→⁺→⁰ arte discussed, and finally we close by commenting on the importance of associated heavy flavor production as a crucial test for the recently advanced preconfinment notion.     

Relativistic effects and the constituent quark model of heavy quarkonia

Charmonium \(c\bar c\) and bottomonium \(b\bar b\) are investigated in the framework of a constituent quark model. A scalar confining and a one-gluon exchange (OGE) potential are used in a nonrelativistic reduction to order (p/m)². Therefore the model includes spin dependent as well as spin independent terms. Their influence on the meson mass spectra and decay widths is analysed. We find that the experimental spectra can be reproduced by using a full model as well as by using a reduced version neglecting the spin independent terms. For both versions we calculate leptonic and radiative decay widths including relativistic corrections for the current operators. We find that for leptonic decays inclusion of all terms of the OGE potential gives better results than the non-relativistic formulas. For radiative transitions relativistic corrections are important.     

ψψ production at collider energies

We estimate ψψ production at collider energies in the framework of perturbative QCD. TheO(α _s ² )?(α _s ⁴ ) parton cross-sections, with the non-relativistic approximation for the heavy quark bound states, are used. This first insight into the characteristics of the kinematical distributions allows predictions on the predominance of the quark, gluon orB meson production mechanisms in particular kinematical regions.     

Covariant trace formalism for heavy mesons-wave top-wave transitions

Heavy meson,s- top-wave, weakb→c transitions are studied in the context of the heavy quark effective theory using covariant meson wave functions. We use the trace formalism to evaluate the weak transitions. As expected from heavy quark symmetry, the eight transitions betweens- andp-wave states are described in terms of only two universal form factors which are given in terms of explicit wave function overlap integrals. We present our results in terms of both invariant and helicity amplitudes. Using our helicity amplitude expressions we discuss rate formulae, helicity structure functions and joint angular decay distributions in the decays \(\bar B \to D^{**} ( \to (D,D^* ) + \pi ) + W^ - ( \to l^ - \bar v_l )\) . The heavy quark symmetry predictions for the one pion transitionsD ^**→(D,D ^*)+π are similarly worked out by using trace techniques.     

Coherent versus incoherent quark fragmentation picture

We study the helicity density matrix of vector mesons produced ine ⁺ e ^? interactions at high energies through the two step process \(e^ + e^ - \to q\bar q \to VX\) . Whereas in the usual incoherent fragmentation picture in which each quark decays independently, ρ(V) is predicted to be diagonal, we find that final state interactions (coherent fragmentation) give rise to a non-vanishing ρ_1-1(V). Various corrections to the standard picture such as, e.g., gluon bremsstrahlung, quark masses, transverse momenta, are shown to be small. Therefore, any significant non-zero value of ρ_1-1(V) found experimentally can be considered as a clear measurement of coherence effects.     

Exotic Mesons with Hidden Bottom Near Thresholds

We discuss exotic meson spectroscopy near open bottom thresholds. Assuming the exotic mesons as ${B^{(\ast)}\bar{B}^{(\ast)}}$ molecular states, we study the interaction among two heavy mesons in terms of the one boson exchange potential model. It is shown that masses of Z _b (10610) and Z _b (10650) are reproduced as ${B^{(\ast)}\bar{B}^{(\ast)}}$ bound and resonance states. Besides, we also show that ${B^{(\ast)}\bar{B}^{(\ast)}}$ molecular states having various exotic quantum numbers can exist around the thresholds. By contrast, there are no ${D^{(\ast)}\bar{D}^{(\ast)}}$ molecular states having exotic quantum numbers.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.