Spectra of charmed and bottom baryons with hyperfine interaction

Up to now,the excited charmed and bottom baryon states have still not been well studied experimentally or theoretically.In this paper,we predict the mass of ?*b,the only L=0 baryon state which has not been observed,to be 6069.2 Me V.The spectra of charmed and bottom baryons with the orbital angular momentum L = 1 are studied in two popular constituent quark models,the Goldstone boson exchange(GBE) model and the one gluon exchange(OGE) hyperfine interaction model.Inserting the latest experimental data from the "Review of Particle Physics",we find that in the GBE model,there exist some multiplets(Σc(b),Ξ c(b)and ?c(b)) in which the total spin of the three quarks in their lowest energy states is 3/2,but in the OGE model there is no such phenomenon.This is the most important difference between the GBE and OGE models.These results can be tested in the near future.We suggest more efforts to study the excited charmed and bottom baryons both theoretically and experimentally,not only for the abundance of baryon spectra,but also for determining which hyperfine interaction model best describes nature.     

A relativistic Hartree-Fock model for quark systems

The “relativistic H—F” scheme is applied to baryons and finite multiquark sustems. A two-body confinement potential (r, r² or r³) and the one-gluon-exchange interaction are incorporated. The electric OGE term is treated consistently in all considered systems. With the electric OGE term included, the solutions indicate the little bag. (Os)-closed multiquark states, strange or non-strange, cannot be lower in energy than an aggregate of Δ or Λ.     

Free vibrations of randomly inhomogeneous plates

Consider a large collection of elastic rectangular plates with random inhomogeneities, but otherwise indistinguishable in any overall sense. An expression is obtained for the natural frequency, μ, of such plates, vibrating freely under simply supported boundary conditions, in the form μ = μ⁽⁰⁾ + ?μ⁽¹⁾ + ?²μ⁽²⁾ + … where μ⁽⁰⁾ is the natural frequency of a homogeneous comparison plate, ? is a small real parameter measuring the degree of inhomogeneity, and the coefficients μ⁽¹⁾, μ⁽²⁾, …, are given explicitly. By constructing geometrically a correlation function for a special type of composite plate, μ⁽¹⁾ is computed and hence, to first order in ?, the variance of μ. The paper concludes with a theorem linking the mean and variance of μ to the volume concentration and geometry of the inclusions in the plate.     

One-gluon-exchange effects on semileptonic decay of baryon octet

We study one-gluon-exchange (OGE) effects ong _A /g _V of weak semileptonic decay processes of theSU(3) baryon octet. We especially investigate the systematic behavior of OGE effects on all the possible decay processes and search for better overall agreements between theory and experiment. We adopt the MIT bag model to describe quarks confined in a baryon. We also use a formulation of the perturbative QCD in which gluon field is also confined in the bag. Our calculations respect the boundary conditions which achieve the confinement of each field within the bag. The magnitudes of our corrections tog _A /g _V have a variation of 1 ～30% depending on the decay, processes. They have process-dependence quite different from that of the uncorrected values ofg _A /g _V primarily governed by theSU(6) symmetry. These OGE effects ong _A /g _V reflectSU(6) asymmetric spin-spin correlation between quarks due to the color magnetic interactions. Especially, the OGE corrections tog _A /g _V are very important in the processes, \(\Sigma ^ - \to n + l^ - + \bar v_l ,\Sigma ^ - \to p + l^ - + \bar v_l \) and \(\Xi ^ - \to \Xi ^0 + e^ - + \bar v_e \) . Consequently, we clarify that the OGE effects can sizably improve theoretical values ofg _A /g _V in favor of overall agreements with the present experimental data of semileptonic decays of the baryon octet, at least, in the MIT bag model.     

Lepton-flavor-violating pion decay π+→μ−νμ e + e + and SU(3)C ⊗ SU(3)L ⊗ U(1)N model

Within the minimal SU(3)_C ? SU(3)_L ? U(1)_N model, the lepton-flavor-violating decay π⁺→μ^?ν_μ e ⁺ e ⁺ is calculated without directly invoking lepton mixing. The branching ratio for this rare pion-decay mode is found to be much smaller than the current experimental upper limit. If the anomalous interactions are discarded, this result coincides with the result of the previous calculation.     

QCD estimates for associated charm production by weak neutral currents

We give quantitative estimates for associated charm production in neutrino and antineutrino induced neutral current interactions, based on (a) quantum chromodynamics (QCD) and (b) the quark parton model (QPM) and a phenomenological generalization thereof. We emphasize the need for a precise measurement of the ratio σ(v_μN→v_μe⁺X)/σ(v_μN→μ^?X) and the corresponding ratio for antineutrinos, as these can provide clean tests of certain characteristic features of QCD. Bounds are obtained for single charm production by charm-changing neutral currents.     

Lepton charge and model of weak interactions with μ-e transitions

The gauge model of weak interactions is proposed and μ^±?e^? transitions predicted by the model are discussed. Estimates are given for μ^±→e^? transitions on hadrons like K⁺→π^?μ⁺e⁺ with Γ (K⁺→π^?μ⁺e⁺) ? 10^?11Γ(K⁺ and μ^? capture on nuclei with W(μ^?→e⁺) ? 10^?12W(μ^? → ν). Single μ^± production in e^? beams with a cross section δ ～ 10^?42?10^?41 cm² is predicted.     

Spin-dependent parton distributions in polarized deep inelastic lepton nucleon scattering

We analyze the recently measured first moment Г ^p (Q ²) of the structure functiong ₁ ^p (x,Q ²) obtained in deep inelastic scattering of polarized electrons from polarized protons. It is shown that the recent experimental result Г ^p (〈Q ²〉?10 GeV²)? 0.113 implies a polarized strange quark sea whose total polarization Δs(μ²)??0.22 is comparable to Δμ(μ²)?0.74 and Δd(μ²)??0.50 already at a typically hadronic scale μ=0(1 GeV). Most remarkably, the total polarization due to quark distributions Δμ(μ²)+Δd(μ²)+Δs(μ²) practically vanishes which implies that the spin of the proton is carried by the gluons, ΔG(μ²), and/or the angular momentum of the partons. This surprising conjecture can be experimentally tested with heavy quark production in longitudinally polarized lepton-nucleon scattering. In particular the (real) photon-gluon fusion process γg→Q \(\bar Q\) provides a rather unique measure of ΔG(x,Q ²).     

Operators in a translation invariant two-dimensional bag model

Operator matrix elements are studied in a translation invariant version of the bag model in two-dimensional space time. In particular we calculate the matrix elements of quark fields Q(x), currents J_μ(x), and bilocal currents Q(x)γ_μλ^aQ(0) whose Taylor expansion yields the twist two operators of leptoproduction. The structure functions of this model are related to those of a naive cavity approximation by a particularly simple transformation.     

On the validity of the scaling law for partial-wave amplitudes

It is shown that the scaling law for partial-wave amplitudes Im f^l(s) holds for lγ (√s/4μ) (α(4μ²)?1) log s, if the leading Regge singularity α(t) in the t-channel is bounded by

$\text{Re α(t) ? α(4μ}{}^2\text{+}\text{α(4μ}{}^2\text{)?1}\text{2μ}\text{(}\text{t}\text{?2μ)}$

and is smooth near t = 4μ² in the sense of eq. (4).     

Electromagnetic corrections to neutrino processes in the leading logarithmic approximation,the value of sin θ and the W and Z masses

The parameters of the Weinberg-Salam model can be defined by amplitudes at a momentum scale M = O(M_W, M_Z). We derive the leading logarithmic e.m. correction to the relations giving the neutrino amplitudes at a momentum scale μ ? M in terms of sin²θ(M), α(M), M_W and M_Z. For leptonic processes, the Fermi constant is not corrected, but a running, universal, sin²θ(μ) > sin²θ(M) should be used. The Fermi constant for semileptonic processes is renormalized by a factor $\text{?(μ) > 1}$, for charged currents, and is not renormalized, for neutral current processes. The latter are described by the same sin²θ(μ) as the leptonic ones. We estimate that sin²θ(M) is about 0.013 smaller than the value of sin²θ obtained from semileptonic data with no correction, thereby improving the agreement with grand unified theories. The prediction for W (Z) masses and widths in terms of the low energy parameters are discussed. Using previous calculations at order α, we obtain predictions for the masses which are accurate up to and including terms of order (αlnM²)².     

Estimate of the probability of K+→μ+νμγ decay

About 100 000 K⁺-decays were observed in a magnetic spectrometer with streamer chambers. The estimation for the radiative decay K⁺→μ⁺ν_μγ, R^exp = [W(K⁺→μ⁺ν_μγ)]/[W(K⁺→all)]=(5.8±3.5) x 10^?3, at E_γ ? 9 MeV was obtained and the ratio R = [W(K⁺→π⁺π°)]/[W(K⁺→μ⁺ν_μ)] = 0.328 ± 0.005 was measured.     

Muon-electron universality at high energies and hadronic corrections to e+e− → μ+μ−

It is argued that unitarity and muon-electron universality are sufficient to determine the contribution of hadrons to the imaginary part of the forward amplitude for the process e⁺e^? → μ⁺μ^?. With these assumptions Im T₁^h(e⁺e^? → μ⁺μ^?) = sσ(e⁺e^? → hadrons) to all orders in α. Some consequences of this formula are discussed.     

Anomalous magnetic moment of the muon in the left-right model

The effect of Higgs bosons on the anomalous magnetic moment of the muon is considered within the model that is based on the SU(2)_L×SU(2)_R×U(1)_B–L gauge group and which involves a bidoublet and two triplets of Higgs fields (left-right model). For the Yukawa coupling constants and the masses of Higgs bosons, the regions are found where the model leads to agreement with experimental results obtained at the Brookhaven National Laboratory (BNL) for the anomalous magnetic moment of the muon. In order to explore corollaries from the constraints obtained for the parameters of the Higgs sector, the processes e⁺e^? → μ⁺μ^?, τ⁺τ^? and μ⁺μ^? → μ⁺μ^?, τ⁺τ^? are considered both within the left-right model and within the model involving two Higgs doublets (two-Higgs-doublet model). It is shown that, if the mass of the lightest neutral Higgs boson does indeed lie in the range 3.1–10 GeV, as is inferred from the condition requiring the consistency of the two-Higgs-doublet model with the data of the BNL experiment, this Higgs boson may be observed as a resonance peak at currently operating e⁺e^? colliders (VEPP-4M, CESR, KEKB, PEP-II, and SLC). In order to implement this program, however, it is necessary to reduce considerably the scatter of energy in the e⁺ and e^? beams used, since the decay width of the lightest neutral Higgs boson is extremely small at such mass values. It is demonstrated that, in the case of the left-right model, for which the mass of the lightest neutral Higgs boson is not less than 115 GeV, the resonance peak associated with it may be detected at a muon collider.     

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.     

Study of B s 0 → µ+µ− and B d 0 → µ+µ− decays in flavor-changing Z′ models

Recently, the first evidence for the decay B _s ⁰ → μ ⁺ μ ^? has been announced by the LHCb Collaboration and the measured branching ratio B( _s ⁰ → μ ⁺) = (3.2 _?1.2 ^+1.5 ) × 10^?9 is in good agreement with the standard model (SM) expectation. It has also reported an upper limit for B(B _d ⁰ → μ ⁺ μ ^?) < 9.4 × 10^?10 at 95% confidence level. In this paper, we study the B _s ⁰ → μ ⁺ μ ^? and B _d ⁰ → μ ⁺ μ ^? rare decays in flavor-changing Z′ model. Our estimated branching ratios are enhanced from their SM values and provide signals for new physics.     

Measurement of the nuclear magnetic dipole moment of Au197 and hyperfine structure measurements in the ground states of Au197, Ag107, Ag109 and K39

Using an atomic beam magnetic resonance apparatus the nuclear magnetic dipole momentμ _I of the stable isotope Au¹⁹⁷ was measured directly with the doublet method. The result isμ _I(Au¹⁹⁷)=0.143491 (9)μ _n, uncorrected for atomic diamagnetism. Further hyperfine structure measurements were performed in the ground states of K³⁹, Ag¹⁰⁷, Ag¹⁰⁹ and Au¹⁹⁷ with the following results:Δv(K³⁹)=461.719723 (38) MHzΔv(Ag¹⁰⁷)=1712.512111 (18) MHzΔv(Ag¹⁰⁹)=1976.932075 (17) MHzΔv(Au¹⁹⁷)=6099.320184 (13) MHzg _J(Ag¹⁰⁷)/g _J(K39)=1.0000260 (20)g _J(Au¹⁹⁷)/g _J(K39)=1.0005076 (20).     

InclusiveK *+(890),K *+(1430) and\bar K^{ * - } (890) production inK + p interactions at 32 GeV/c

We present final results on inclusive production ofK ^*+(890),K ^*+(1430) andK ^*?(890) in \(\bar K^ + p\) interactions at 32 GeV/c, based on a statistics of ～27 events/μb. Total cross sections,p _T -andx-dependence of inclusive distributions are compared with experiments at other energies and with the Lund fragmentation model. Spin density matrix elements of theK ^*+(890) are also discussed. The results suggest that “recombination” of both initial state valence quarks \(\bar s\) andu of theK ⁺ intoK ^*+(890), responsible in the Lund model for ～45% of theK ^*+(890) cross section, is strongly suppressed.     

Radiative corrections to νμ + N → μ− + X and their effect on the determination of ϱ2 and sin2θW

We study the O(α) corrections to σ_T(ν_μ + N → μ^? + X). The coefficient of the leading O(αln m_Z) contribution is given by a general theorem as in the case of β decay, while the energy scale accompanying m_Z in the argument of the logarithm as well as mass singularities and non-logarithmic terms are obtained by a detailed quark-parton model calculation. The effect of muon mass singularities, when there is an experimental vut in the low range of the y distribution, is also investigated. Combining these new results with our previous analysis of σ_T(ν_μ + N → ν_μ + X), we calculate theSU(2)_L × U(1) parameter ?_(νμ;h)² and evaluate the effect of the O(α) corrections on the determination of sin²θ_W^exp from deep inelastic ν_μ scattering. Applying these corrections to existing data, we obtain the weigthed average sin²θ_W^exp = 0.216 ± 0.010 ± 0.004. This value when used in conjuction with our previous analysis of the W^± and Z⁰ masses provides the predictions m_W = 83.0_?2.8^+3.0 GeV and m_Z = 93.8_?2.4^+2.5 GeV. For the weak interaction angle defined by modified minimal subtraction we find sin²θ_W(m_W) = 0.215 ± 0.010 ± 0.004, which is in very good agreement with the SU(5) prediction we have recently given.