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We show that the sum rule recently proved by Uraltsev in the heavy quark limit of QCD holds in relativistic quark models \`a la Bakamjian and Thomas, that were already shown to satisfy Isgur-Wise scaling and Bjorken sum rule. This new sum rule provides a {\it rationale} for the lower bound of the slope of the elastic IW function $\rho^2 \geq {3 \over 4}$ obtained within the BT formalism some years ago. Uraltsev sum rule suggests an inequality $|\tau_{3/2}(1)| > |\tau_{1/2}(1)|$. This difference is interpreted in the BT formalism as due to the Wigner rotation of the light quark spin, independently of a possible LS force. In BT models, the sum rule convergence is very fast, the $n = 0$ state giving the essential contribution in most of the phenomenological potential models. We underline that there is a serious problem, in the heavy quark limit of QCD, between theory and experiment for the decays $B \to D^*_{0,1}(broad) \ell \nu$, independently of any model calculation., Comment: 16 pages, Latex

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 pages

We study CP-violation in resonant three-body Bd→DPP decays, where PP stands for either D π , D K S , ππ or πKS. Analogously to the Bd→3π channel and the extraction of 2α, the first three channels are shown to measure cos2β in addition to sin2β, thus allowing to resolve the β→ π 2 −β ambiguity, while the DπKS final state leads to a measurement of 2β+γ. As cos2β and cos(2β+γ) are CP-conserving quantities, their determination is possible without tagging the flavor of the Bd meson. The Bd0(t)→D+D−π0 channel via the interference between D ∗∗ orbitally excited resonances is taken as an example, although this Cabibbo-suppressed decay suffers from irreducible penguin uncertainties. Then two penguin-free and Cabibbo-dominant modes are proposed: Bd0(t)→D+D−KS with the D s ∗∗ resonances, and Bd0(t)→D0CPπ+π− with the D ∗∗ plus the ρ. Finally, the Bd0(t)→D±π∓KS channel with the D s ∗∗ and K ∗ resonances provides a new clean method to measure the unusual angle 2β+γ. We present in all cases a crude estimate of the number of cos2β (respectively 2β+γ) sensitive events. We show that this number is an increasing function of the resonance mass, a favorable situation compared to the more extensively studied three-pion Dalitz plot. However, the poor detection efficiency of the D mesons could pose a problem. As an annex and speculative application of these Dalitz plot based methods, the penguin-dominated Bd0(t)→KSKSKL decay also measures 2β.

The heavy mass limit of quark models based on the Bakamjian-Thomas cons\-truction reveals remarkable features. In addition to previously demonstrated properties of covariance and Isgur-Wise scaling, exact duality, leading to the Bjorken-Isgur-Wise sum rule, is proven, for the first time to our knowledge in relativistic quark models. Inelastic as well as elastic contributions to the sum rule are then discussed in terms of ground state averages of a few number of operators corresponding to the nonrelativistic dipole operator and various relativistic corrections., Comment: 14 pages

We consider the dominant $c\bar{c}$ contribution to $\Delta \Gamma$ for the $B_s^0$-$\bar{B}_s^0$ system in the heavy quark limit for both $b$ and $c$ quarks. In analogy with the Bjorken-Isgur-Wise sum rule in semileptonic heavy hadron decay, we impose duality between the parton model calculation of $\Delta \Gamma$ and its estimation by a sum over heavy mesons. Varying the mass ratio $m_c/m_b$ and assuming factorization and saturation by narrow resonances $(N_c \to \infty$), we obtain new sum rules that involve the Isgur-Wise functions $\xi^{(n)}(w)$ and $\tau^{(n)}_{1/2}(w)$ and the decay constants $f^{(n)}$, $f^{(n)}_{1/2}$ ($n$ stands for any radial excitation). Alternatively, we deduce the sum rules with another method free of the factorization hypothesis, from the saturation of the expectation value of a product of two currents by heavy hadrons and by the corresponding free quarks. The sum rules read $\sum\limits_{n}{f^{(n)} \over f^{(0)}} \xi^{(n)}(w) = 2 \sum\limits_{n}{f^{(n)}_{1/2} \over f^{(0)}} \tau^{(n)}_{1/2}(w) = 1$, valid for all $w$. Moreover, we obtain, in the heavy quark limit, $f^{(n)}_{3/2} = 0$. As a consequence, unlike the BIW sum rule, the slope of the elastic function $\xi (w)$ is related to radial excitations alone. These are generalizations, rigorous for QCD in the heavy quark limit, of results that have an easy understanding in the non-relativistic quark model., Comment: 15 pages

Once chosen the dynamics in one frame, for example the rest frame, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the heavy quark limit, fully covariant current form factors as matrix elements of the quark current operator. They also verify the Isgur-Wise scaling and give a slope parameter $\rho^2>3/4$ for all the possible choices of the dynamics. In this paper we study the $L=1$ excited states and derive the general formula, valid for any dynamics, for the scaling invariant form factors $\tau_{1/2}^{(n)}(w)$ and $\tau_{3/2}^{(n)}(w)$. We also check the Bjorken-Isgur-Wise sum rule already demonstrated elsewhere in this class of models.

A major problem in the determination of the the CP angle $\alpha$, that should be measured through modes of the type $B_d, \bar{B}_d \to \pi \pi , \cdots ,$ is the uncertainty coming from Penguin diagrams. We consider the different ground state modes $\pi \pi$, $\pi \rho$, $\rho \rho$, and, assuming the FSI phases to be negligible, we investigate the amount of uncertainty coming from Penguins that can be parametrized by a dilution factor $D$ and an angle shift $\Delta \alpha$. The parameter $D$ is either 1 or very close to 1 in all these modes, and it can be measured independently, up to a sign ambiguity, by the $t$ dependence. Assuming factorization, we show that $\Delta \alpha$ is much smaller for the modes $\rho \pi$ and $\rho \rho$ than for $\pi \pi$, and we plot their allowed region as a function of $\alpha$ itself. Moreover, we show that most of the modes contribute to the asymmetry with the same sign, and define for their sum an effective $D_{eff}$ and an effective $\Delta \alpha_{eff}$, an average of $\Delta \alpha$ for the different modes. It turns out that $D_{eff}$ is of the order of 0.9, $\Delta \alpha_{eff}$ is between 5 $\%$ and 10 $\%$ and, relative to $\pi \pi$, the statistical gain for the sum is of about a factor 10. Finally, we compute the ratios $K\pi /\pi \pi , \cdots$ that test the strength of the Penguins and depend on the CP angles, as emphasized by Silva and Wolfenstein and by Deandrea et al., Comment: 18 pages

We present new accurate lower bounds on the ground state of the Hamiltonian p2+m2−αr. From these, we obtain a lower bound on the maximum mass of a boson star in the semirelativistic framework, and we compare it to a variational upper bound. We get 0.846 (Gm)−1 < Mmax < 1.439(Gm)−1, where G is Newton's constant and m the boson mass.

We consider the decay modes D s D s ∗ + D s D s ∗ for the B s − B s or D + D ∗+ for the B d − B d systems in the heavy quark limit. The quantum states (1/√2)∣D(p) D ∗ (−p)− D (−p)D ∗ (p)〈 and (1/√2)∣D(p) D ∗ (−p)+ D (−p)D ∗ (p)〈 are eigenstates of CP with eigenvalues + and − (the D∗ is longitudinally polarized). In the heavy quark limit we find that for the spectator diagram, only the eigenstate with eigenvalue CP=+ contributes and, on the contrary, for the exchange diagram only the eigenstate with eigenvalue CP=− contributes. These selection rules follow from the transformation laws of the weak interaction and of the states under the operator CP exp ( i 1 2 πσ 3 (c) where σ 3 (c) is the charm quark spin operator collinear to the momentum. Since the exchange diagram is small relatively to the spectator one, the final state D D ∗ + D D ∗ is approximately a CP eigenstates and has its nice properties concerning CP vilolation tests. We study the information on the angle β of the unitarity triangle that can be obtained by looking at the Cabibbo suppressed mode D + D ∗− +D − D ∗+ in the B d − B d system. If we consider D + D ∗− +D − D ∗+ as a pure CP eigenstate an error of 1% is made in the dilution factor affecting the CP asymmetry. For the sum of all the modes D + D − , D + D ∗− +D − D ∗+ , D ∗+ D ∗− there is dilution factor that differs from 1 by at most a few % and a gain of a factor 5 in rate relatively to the color suppressed mode ΨKs.

CP violation in D decays is negligible in the standard model, and D decay asymmetries could be used in a charm-tau factory to look for or to constrain CP violation beyond the standard model. Asymmetries that depend on D 0 − D 0 mixing are expected to be tiny because of the smallness of both mixing and CP violation. However, interference between standard-model CP-conserving amplitudes and beyond-the-standard-model CP-violating amplitudes relatively enhances CP asymmetries involving final state interaction phases. A charm-tau factory could be sensitive to a new physics scale Λ of O(1 TeV). As an example we consider the mode D 0 → K − π + ( D 0 → K + π − ) . This case is favorable because: (1) it involves a Cabibbo allowed mode, flavor specific, unsuppressed by color factors; (2) the FSI phase difference is known to be large; (3) CP violation coming from the standard model is negligible because penguin diagrams do not contribute (the “background” comes from interference through mixing and doubly Cabibbo suppressed decays). We consider lowest dimension operators contributing to c → su d that could come from: (i) chirality conserving interactions, or (ii) scalar boson couplings. As illustrative examples, we make explicit the left-right symmetric model with two generations, and charged Higgs boson exchange.

The neutron electric dipole moment (Dn) generated by strong CP violation is due to the anomaly plus non-perturbative U (1) effects. It should vanish in quark models, which do not incorporate these two ingredients. Calculations are presented showing how this necessary cancellation does occur in a Lorentz vector potential model, but not in a scalar potential or in a bag model; in the latter cases, it is argued that the non-zero result is a model artefact. In old perturbation theory, the cancellation when present occurs between pair and 1 2 − intermediate state contributions.

We give a full calculation of the leading logarithm QCD corrections to the quark electric dipole moment in the SU(2) L × SU(2) R × U(1) model of CP violation. To estimate the anomalous dimensions one needs to go to two loops, like in the controversial b → sγ transition in the standard model. However, our problem is simpler as it involves only CP violating operators. We have adopted various dimensional regularization schemes (dimensional reduction, anticommuting γ 5 for all dimensions, and 't Hooft-Veltman prescription) and also Pauli-Villars regularization. We obtain the same result for all these regularization procedures.

The decays of the type B d 0 , B d 0 → p p , Λ , Λ c + Λ c + , into a spin 1 2 baryon and its antiparticle proceed in both S-wave (parity conversing) and the P-wave (parity violating), and the final state is not an eigenstate of CP. Generalizing the type of tests of CP violation first proposed by Sanda et al., the CP violating asymmetries are proportional to Γs−Γp. We compute the parity conserving and the parity violating amplitudes within a pole model. The ratio Γs/Γp is of O(1) for pp ,but we find the selection rule Γs = 0 for Λ Λ , and Γp⪡Γs for Λc+ Λ c+ the modes pp and Λ Λ , where the detection efficiency if large, we estimate the Bd0, Bd0 pairs needed to observe the CP asymmetries at the 3σ level to be of the order 1010.

In the Kobayashi-Maskawa model, penguin diagrams can induce CP violating phases in matrix elements of the type n→Λ. This produce a neutron electric dipole moment through subsequent parity violating radiative weak decay Λ→nγ. We can expect ( D n e )≅10 −30 cm , three to four orders of magnitude bigger than the mechanism based on the transition quark electric dipole moment. The reason is essentially that the GIM cancellation comes in the Penguin case from ( α s π ) log m 2 t m 2 c abd not from π −2 (m 2 t −m 2 c ) M 2 W as for the transition quark electric dipole moment.

A recent calculation of semileptonic axial form factors for B → D ∗ ev by Altomari and Wolfenstein is reconsidered. A common assumption for the description of mesons in terms of quarks is shown to be inconsistent with covariance at the lowest order of relativistic corrections. Covariance is restored by the previously overlooked Wigner rotation of the spectator quark spin. The result of Altomari and Wolfenstein for a+ is reproduced, but not that for |. Implications of the CLEO D∗ polarization measurement are discussed.

We study experimental tests for current N = 1 supergravity models in the B 0 − B 0 systems, stemming from flavor-changing coupling between gluinos, quarks and squarks. For light gluinos B d 0 − B d 0 mixing is large, contrarily to the SU(3) c ×SU(2 )×U(1) prediction. Present and future colliders could observe a rate for μ + μ + / μ + μ − as high as 25% for certain mass ranges where m b s GeV and m g GeV , and smaller but observable effects when relaxing these bounds. Besides, for very light m g and m b s GeV , the superpenguin contribution enhances such channels as B d 0 → φ K s , reaching a ratio r= Br ( B d →φ K s Br(B d →ψ K s ) ≥1 in opposition to the SU(3) c ×SU(2)×U(1) value 10 − r −1 due to the ordinary penguin mechanism. The bound on m q 4 m g recently claimed by Goldberg is discussed.

We generalize the London treatment of van der Waals forces to long-range forces induced by instantaneous confining potentials. We give special attention to the main problem of accounting for the intermediate colour-octet states. The result is in contradiction with data on nucleon-nucleon phase shifts for any confining potential V(r) = − α(ΣAλAλA)rα for α > 0.1.

We study the restoration of global symmetries of lattice QCD at finite temperature and chemical potential. The hamiltonian of lattice SU(Nc) QCD in the A0 = 0 gauge has to be supplemented by the Gauss law constraint, that thermal excitations must satisfy. We examine this problem in the strong coupling limit at fixed Nc = 2. The free energy to be minimized must be defined by traces over states restricted to be local color singlets. To compute these traces one can make use of the orthogonality relations of the characters of the gauge group, a simple problem in the case of SU(2). We find the critical curve in the T-μ plane beyond which there is restoration of the global symmetry of the system, the dynamical fermion mass becoming zero. We find, for one flavor, T c = 2m 0 3 (μ=0); μ c =m 0 (T=0) (m 0 = quark dynamical mass at zero temperature ) . Relatively to an unconstrained free energy, the effect of the Gauss law is to increase the critical temperature, as the effective number of thermally excited degrees of freedom has decreased.

The width of ψ(4.414) is surprisingly small for a c c state far above the charm threshold, Γexp ≈ 33 MeV. This fact can be qualitatively understood if one makes the conservative assignment 4 3S1. The nodes of the wave function reflect as zero's of the decay amplitude in the momentum of the decay products, and are responsible for the suppression of the couplings to the ground state charmed mesons, Γ(ψ(4.414)→D D + D D ∗ + D D∗ + D∗ D ∗ + F F + F F ∗ + F F∗ + F∗ F ∗) ≈ 15 MeV. All the modes are suppressed by factors of the order of 103 with respect to the k3 spin counting prediction. The dominant modes are predicted to be D∗ D ∗, F F ∗ + F F∗ and D D . Moreover, we show that the contributions from P-wave charmed mesons are reasonably expected to be suppressed either by phase space or by the nodes if their masses lie within certain range. We emphasize however that the smallness of the photon coupling remains to be understood.

It is shown that the chiral Ward identities and PCAC do not constrain the kaon-to-vacuum amplitude to be quartic in the kaon mass, contrary to a recent claim. The estimate of the K → ππ amplitude by soft-pion techniques needs then the knowledge of both K → π and K → vacuum amplitudes.

By treating the new vectoc meson resonances discovered at DCI as q q excitations, we stress that the experimental result Γ tot ( ω n )⪡ Γ tot ( ϱ n ) and different branching ratios into multipion states present a paradoxical situation. Using quark pair creation model, we try to resolve this through large 1 3 D 1 mixing, implying dominant ϱ n decay via π A 1 channel .

We study the possible interpretation of the exotic 1400 MeV resonance decaying into ηπ recently discovered in the GAMS experiment in π−p→ηπ0n. This state is claimed to have JPCIG = 1−+1−. If confirmed this state could only be interpreted as an hybrid (qqg) or a diquonium (qqqq) state. However, the quark model with constituent gluons, forbids, under rather general assumptions, the decay into ηπ of both hybrids and diquonia. We generalize a selection rule previously derived for diquonia. We then discuss a possible breaking mechanism of these selection rules. Our conclusion is that all interpretations predict an ηπ branching ratio of 1% to a few %. An hybrid with lg = 1 would lead to BR (ηπ)

We compute two-body branching ratios in proton decay in the SU(5) Grand Unification scheme. Using spin-flavor symmetries, we obtain algebraic relations between the matrix elements. The absolute magnitude is fixed from non-leptonic decays of hyperons. Pion modes are very important due to phase space, and ωe + is quite sizeable due to its large matrix element. We find also an important K 0 μ + fraction. Bound state effects are quite crucial since we get a lifetime at the edge of the experimental limits, τ, (p) ≈ 10 31 yr for M X = 6 × 10 14 GeV.

We show that the chiral constraints on the penguin K- π matrix element are satisfied by a cancellation between the well known vacuum insertion estimate of Shifman, Vainshtein and Zakharov and currently omitted matrix elements of bilinear operators. We also show how the usual factorization prescription for K → 2 π does satisfy the chiral constraints.

We propose a non-diagonal generalization of a test, proposed by Wolfenstein, of CP violation in the B 0 d - B 0 d system: e+e− → B01B02 (P wave) → X0 X0 and Y0 are CP eigenstates with the same CP eigenvalue, one one Kobayashi-Maskawa-allowed and the other one KM-forbidden (like ψK0L and π+π−, CP = +1). In the limit (ΔΓ)2, (ΔM)2 ⪡ Γ2 (as is predicted in the standard model for B0d-B0d), the cross section is just proportional to sin2(ϕ1 – ϕ2), where ϕ1, ϕ2 are the phases defined by Sanda et al. for both modes. One can thus in principle isolate a pure non-superweak effect (ϕ1 ≠ ϕ2), like in the ϵ′ parameter of K 0 , K 0 . In the KM model sin2(ϕ1 – ϕ2) ≈ O(1), but the branching ratios of these exclusive decays are expected to be small. Ironically, the KM model predicts the rate of the CP-allowed mode ψK0S, π+ π− to be smaller than the CP-forbidden one ψK0L, π+ π−. In some models of maximal CP violation, the CP-allowed mode is actually strictly forbidden and the CP-forbidden one is allowed.

Hamiltonian lattice SU( c ) QCD with N f massless flavors has a global U(4 N f ) symmetry that reflects in 8 N f massless quarks and breaks down with the appearance of 8 N f 2 Goldstones. Coupling the quarks to an external vector or axial field in a way that is SU ( N c ) gauge invariant and vanishes in the continuum limit (for lattice spacing a ≠0 Lorentz invariance is broken by the lattice and the external field) reduces the symmetry U (4 N f ) to chiral U( N f )×U( N f ). We show in an example that U( N f )×U( N f ) then breaks down to U ( N f ) with N f 2 Goldstone pseudoscalars. The 8 N f 2 Goldstone degeneracy has been lifted by the external field, although the 8 N f massless quarks remain in a subtle way. We suggest possible ways out to the difficulty that loops could in principle make the continuum limit different from QCD.

We propose a model for radiative weak decays of hyperons with baryons exchanges in the s- and u-channels as described by the quark model: the 12+ (56, 0+) for parity conserving, and the first excited 12− (70, 1−) for parity violating amplitudes. Special attention is drawn on the problem of gauge invariance. We get a large ∑+ → pγ asymmetry of the right sign. The parity violating amplitude although SU(3)-suppressed, is of the order δm/ω (δm, SU (3)-breaking parameter; ω, baryon level spacing), which is not small. In the quark model the parity conserving amplitude is also SU(3)-suppressed contrarily to the usual belief.

Using the Bogoliubov-Valatin variational method we write the gap equation (a non-linear integral equation, in general) for a color, fourth-component Lorentz vector interaction between massless quarks. In the case of a potential in r2, it reduces to a non-linear second order differential equation of the sine-Gordon type. We find (besides the usual chiral degeneracy) an infinite number of solutions breaking chiral symmetry, higher in energy as the number of their modes increases. We compute the expectation value of ψ υ, the mass gap, and the shift in energy density between the chiral invariant vacuum and the new broken vacuum.

In the Kobayashi-Maskawa model, the neutron electric dipole moment is a high-order effect in the electroweak interactions. We need a perturbative calculation in two steps: (1) generation of CP -violatingcouplings at the quark level through heavy quark loops, and (2) a perturbative expansion by nearest intermediate states at the bound state level. We examine both aspects for a mechanism proposed by Morel and by Cox et al. where CP violation comes from transition quark electric dipole moments. We retain the lowest lying baryon intermediate states1/2 + (56,0 + )and 1/2 − (70,1 − ). For this mechanism we get at most D n/ e ≈10 −34 cm.

Using a “chromo-harmonic” interquark potential we study the stability of “diquoniums” against the decay into mesons. We find an exact selection rule which implies that “true-diquoniums” are uncoupled from open meson channels for orbital excitation greater than 1. “Mock-diquoniums” only appear for an orbital excitation greater than 8 and are coupled to mesons and to pairs of orbitally excited baryons.

We generalize in a model independent way a selection rule for 1−+ hybrid decay into ηπ and η′π previously derived in potential models. We show, without any further hypothesis than the quenched approximation, that only disconnected graphs contribute to these decays. It follows that these decays are OZI suppressed, with an additional suppression for ηπ proportional to SU (3) breaking (≅sin θ, θ being the ηη′ mixing angle).

In the quark model with current-current interaction, non-leptonic hyperon decays are controlled by the baryon wave function at small distances. An independent estimate of this quantify is provided by a related phenomenon: the baryon electromagnetic hyperfine splittings, given by the Fermi contact interaction. A good estimate is obtained with the standard Cabibbo-suppressed interaction. Important remaining problems for S -waves are emphasized.

Present limits on ϵ'/ϵ in K0 decays point out to a small penguin diagram in agreement with perturbative QCD calculations and unable to explain the ΔI= 1 2 rule. We propose new tests on the role of this contribution by isolating it in some CP conserving amplitudes. Unlike the case of kaon decays, there are exclusive modes in ΔS=1 B decays (like B0d→φK0s, K−π+), not suppressed by Kobayashi-Maskawa mixing angles, where only the penguin contributes. Experimental limits on or the observation of modes of this type compared to decays like B0d→ψK0s, D+F−, that can occur in the Born approximation, can help to elucidate whether the origin of the ΔI= 1 2 rule comes from long-distance non-perturbative effects specific to K decays or from a new phenomenon, common to K and B decays. Moreover, unlike the case of K decays, which involve only pseudo-Goldstone bosons, in B decays we can have a variety of final states that occur through the penguin mechanism and exhibit different chiral structures.

The decay rates of ψdblac; (4.028)→ D D, D D ∗ + D D ∗ , D ∗ , D ∗ D ∗ can be fairly well understood with the assignment this state as a second radial excitation of charmonium. The nodes of the wave function and the different Q -value in each of these decays allow to understand the failure of the simple quark spin counting prediction.

Our quark model treatment of two-body non-leptonic D decays is shown to predict, respectively, enhancement and suppression of the Cabibbo suppressed decays D→KK and ππ with respect to widespread expectation. It also leads to a rather low τ D ≈ 2.5 × 10 −13 s. The discrepancy with the much larger value from semi-leptonic rates, τ D ≈ 10 −12 s, is interpreted through the presence of large non-resonant contributions to the semi-leptonic decays.