How to search for doubly charmed baryons and tetraquarks

Possible experimental searches of doubly charmed baryons and tetraquarks at fixed target experiments with high energy hadron beams and a high intensity spectrometer are considered here. The baryons are:Ξ _cc ⁺ (ccd),Ξ _cc ⁺⁺ (ccu), andΩ _cc ⁺ (ccs); and the tetraquark is T (ccūd). Estimates are given of masses, lifetimes, internal structure, production cross sections, decay modes, branching ratios, and yields. Experimental requirements are given for optimizing the signal and minimizing the backgrounds. This paper is designed as an experimental and theoretical review. It may therefore be of assistance in the planning for a future state-of-the-art high statistics charm experiment, in the spirit of the aims of the recent CHARM2000 workshop.     

Structure of some FeII − III hydroxysalt green rusts (carbonate, oxalate, methanoate) from Mössbauer spectroscopy

The abundances of Fe^II and Fe^III environments within green rusts one, GR1s, that intercalate carbonate, oxalate and methanoate (formate) anions are found from Mössbauer spectra for compositions corresponding to [Fe $^{\rm II}_{6}$ Fe $^{\rm III}_{2}$ (OH)₁₆]^2?+??[CO $_{3}^{2-}$ ?5H₂O]^2???, [Fe $^{\rm II}_{4}$ Fe $^{\rm III}_{2}$ (OH)₁₂]^2?+??[CO $_{3}^{2-}$ ?3H₂O]^2???, [Fe $^{\rm II}_{6}$ Fe $^{\rm III}_{2}$ (OH)₁₆]^2?+??[C₂O $_{4}^{2-}$ ?4H₂O]^2??? and [Fe $^{\rm II}_{5}$ Fe $^{\rm III}_{2}$ (OH)₁₄]^2?+??[2HCOO^????3H₂O]^2???. These formulae correspond to orders α, β and γ where cation distances are (2 × a ₀), ( $\surd 3$ × a ₀) or a mixture of both leading to (7 × a ₀), where ratio x = {[Fe^III]/[Fe_total]} = 1/4, 1/3 and 2/7, respectively. Anion distributions within interlayers are also devised and long-range orders determined accordingly.     

The decay of theT=1 isospin triplet inA=12 systems: IV. The energy dependence of the asymmetry coefficients\alpha _{\beta ^ \mp } of the beta-ray angular distribution in aligned12B and12N and the induced pseudotensor interaction

The asymmetry parameters \(\alpha _{\beta ^ \mp } \) of the beta-ray emitted from aligned¹²B and¹²N are evaluated as a function of the energy. The agreement with experimental differential data is excellent for both \(\alpha _{\beta ^ - } \) (W) and \(\alpha _{\beta ^ + } \) (W). This work confirms, using available nuclear model information, that no induced pseudotensor (IPT) interaction is required for a correct theoretical interpretation of the data. An upper limit for the IPT coupling constantf _T is determined from a simultaneous fit of \(\alpha _{\beta ^ - } \) (W) and \(\alpha _{\beta ^ + } \) (W).     

Radiative open charm decay of the Y(3940) , Z(3930) , X(4160) resonances

We determine the radiative decay amplitudes for the decay into D^* and $ \bar{{D}}$ $ \gamma$ , or D ^* _s and $ \bar{{D}}_{s}^{}$ $ \gamma$ of some of the charmonium-like states classified as X , Y , Z resonances, plus some other hidden charm states which are dynamically generated from the interaction of vector mesons with charm. The mass distributions as a function of the $ \bar{{D}}$ $ \gamma$ or $ \bar{{D}}_{s}^{}$ $ \gamma$ invariant mass show a peculiar behavior as a consequence of the D ^* $ \bar{{D}}^{*}_{}$ nature of these states. The experimental search of these magnitudes can shed light on the nature of these states.     

Three-Quark Currents and Baryon Spin

We show that three-quark axial currents as required by broken SU(6) spin-flavor symmetry reduce the quark spin contribution to proton spin from \({{\Sigma}_p = 1}\) (one-quark axial current value) to \({{\Sigma}_p = 0.41(12)}\) consistent with the empirical value \({{\Sigma}_{p, exp} = 0.33(08)}\) . In the case of the \({{\Delta}^+(1232)}\) baryon, we find that three-quark axial currents increase the one-quark axial current value \({{\Sigma}_{{\Delta}^+} = 3}\) to \({{\Sigma}_{{\Delta}^+} = 3.87(22)}\) . We also calculate the quark orbital angular momenta L _u and L _d in the proton and \({{\Delta}^+}\) and interpret our results in terms of the prolate and oblate geometric shapes of these baryons consistent with their intrinsic quadrupole moments.     

Analysis of angular momentum dependence of fission fragment mass-energy distribution within Langevin dynamics

Dependence of fission fragment mass-energy distribution on the angular momentum is studied within Langevin dynamics. The calculations are performed in the framework of the generalized temperature-dependent finite-range liquid drop model. The analysis is done for five compound nuclear systems representing heavy fissioning nuclei, medium fissioning nuclei, and a light fissioning one with the angular momentum varied in a wide range from l = 0 to 70?. The coefficients d〈E _K 〉/dl ² and $d\sigma _{{\rm E}_{\rm K} }^2 /dl^2 $ are extracted. Previous analysis of the dσ _M ² /dl ² coefficient is generalized. Excitation energy dependence of the fission fragment mass-energy distribution is also found. The qualitative comparison of the extracted values with the experimental data reveals good agreement for all the cases. The calculated values of the coefficients dσ _M ² /dl ² and $d\sigma _{{\rm E}_{\rm K} }^2 /dl^2 $ are functions of the angular momentum, in contrast to the experimental estimations.     

Physics beyond the Standard Model through b → s μ ?+? μ ? transition

A comprehensive study of the impact of new-physics operators with different Lorentz structures on decays involving the b ?? s ?? ^?+? ?? ^? transition is performed. The effects of new vector?Caxial vector (VA), scalar?Cpseudoscalar (SP) and tensor (T) interactions on the differential branching ratios, forward?Cbackward asymmetries (A _FB??s), and direct CP asymmetries of ${\bar B}_{\rm s}^0 \to \mu^+ \mu^-$ , ${\bar B}_{\rm d}^0 \to$ $ X_{\rm s} \mu^+ \mu^-$ , ${\bar B}_{\rm s}^0 \to \mu^+ \mu^- \gamma$ , ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ , and ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ are examined. In ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ , we also explore the longitudinal polarization fraction f _L and the angular asymmetries $A_{\rm T}^{(2)}$ and A _LT, the direct CP asymmetries in them, as well as the triple-product CP asymmetries $A_{\rm T}^{\rm (im)}$ and $A^{\rm (im)}_{\rm LT}$ . While the new VA operators can significantly enhance most of the observables beyond the Standard Model predictions, the SP and T operators can do this only for A _FB in ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ .     

The constraints of non-standardWWγ couplings from FCNC processes

It was reported that the contributions of the non-standardWWγ couplings called λ_γ and \(\bar \lambda _\gamma \) to the anomalous magnetic moments and the electric dipole moments of fermions depend on regularization schemes of the loop integral. We find that this dependence does not exist in the contributions of the λ_γ and \(\bar \lambda _\gamma \) couplings to the flavor changing neutral current (FCNC) processes of quarks such asb→sγ. By utilizing the experimental upper bound of the branching ratio of the processB→K ^*γ, we obtain the allowed regions of λ_γ and \(\bar \lambda _\gamma \) that do not depend on regularization schemes of the loop integral. The cut-off independent constraints of the other non-standardWWγ couplings called Δκ_λ and \(\tilde \kappa _\gamma \) are also obtained.     

Characteristics of π−,\bar p,and antinuclei frompp collisions

An investigation of inclusivepp→π^?+? in terms of the covariant Boltzmann factor (BF) including the chemical potential μ indicates a) that the temperatureT increases less rapidly than expected from Stefan's law, b) that a scaling property holds for the fibreball velocity of π^? secondaries, leading to a multiplicity law like ～E _cm ^1/2 at high energy, and c) that μ_π is related to the quark mass: μ_π=2m _q ?m _π the quark massm _q determined by \(T_{\pi ^ - } \) at \(\bar pp\) threshold beingm _q =3T_π?330 MeV. Because ofthreshold effects \(T_{\bar p}< T_{\pi ^ - } \) , whereas \({{\mu _p } \mathord{\left/ {\vphantom {{\mu _p } {\mu _{\pi ^ - } }}} \right. \kern-0em} {\mu _{\pi ^ - } }} \simeq {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2}\) as expected from the quark contents of \(\bar p\) and π. The antinuclei \(\bar d\) and \({{\bar t} \mathord{\left/ {\vphantom {{\bar t} {\overline {He^3 } }}} \right. \kern-0em} {\overline {He^3 } }}\) observed inpp events are formed by coalescence of \(\bar p\) and \(\bar n\) produced in thepp collision. Semi-empirical formulae are proposed to estimate multiplicities of π^?, \(\bar p\) and antinuclei.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Spin,helicity and flavour patterns in exclusive decays of bottom mesons into baryon-antibaryon pairs

I use the constituent quark model to calculate the exclusive decays of bottom mesons into ground state baryon-antibaryon pairs mediated by the weakb→c and b→u transitions. TheW-exchange contributions to these decays are found to be negligible. For theW-decay contributions I find that the simple colour-flavour structure of the 1/2⁺ and 3/2⁺ ground state baryons together with the current-current nonleptonic Hamiltonian leads to many simple and testable predictions. Notable among these is the predicted vanishing of decays involving 3/2⁺ baryons as in \(\overline {B^0 } (B^ - ) \to 3/2^ + \overline {1/2^ + } \) and \(\overline {B^0 } (B^ - ) \to 3/2^ + \overline {3/2^ + } \) . An experimental verification of these selection rules would test the chirality of the basicb→c andb→u transitions. I also derive predictions for the polarization of the final state baryons depending on the assumed mechanism of quark pair creation. These predictions can be checked in the cases where the final state baryons are weakly decaying spin 1/2 hyperons and charmed baryons.     

g-factors of rotational states in 176Hf, 177Hf,and 180Hf

g-factors of rotational states in ¹⁷⁶Hf and ¹⁸⁰Hf were measured with the twelve detector IPAC-apparatus of our laboratory [1]. The natural radioactivity 3.78 · 10¹⁰y ¹⁷⁶Lu and the 5.5 h isomer ^180mHf were used which populate the ground-state rotational bands of ¹⁷⁶Hf and ¹⁸⁰Hf. The integral rotations of γ-γ directional correlations in strong external magnetic fields and in static hyperfine fields of (Lu → Hf)Fe₂ and HfFe₂ were observed. The following results were obtained: The hyperfine field in (Lu → Hf)Fe₂ was calibrated by observing the integral rotation of the 9/2^? first excited state of ¹⁷⁷Hf populated in the decay of 6.7d ¹⁷⁷Lu. The g-factor of this state was redetermined in an external magnetic field as Finally the g-factor of the 2 ₁ ⁺ state of ¹⁷⁶Hf was derived from the measured g(2 ₁ ⁺ ) of ¹⁸⁰Hf by use of the precisely known ratio g(2 ₁ ⁺ , ¹⁷⁶Hf)/g(2₁ ⁺, ¹⁸⁰Hf) [2] as      

The static multipole moments of Δ1236(3/2,3/2) from superconvergence inNγ → Δπ scattering

Saturating superconvergence sum rules inNγ→Δπ scattering byN andΔ, we are able to relate the (isoscalar) dipole magnetic moment \(\tilde \mu _\Delta\) and the quadrupole electric moment \(\tilde Q_\Delta\) of the isobarΔ to the electric charge \(\tilde Z_\Delta\) and the dipole magnetic momentμ _N of the nucleonN. The numerical results are: \(\tilde \mu _\Delta \equiv \mu _{\Delta ^ + } + \mu _{\Delta ^0 } = 3.26\) (in unitse/2M)=2.48 (in unitse/2m), and \(\tilde Q_\Delta \equiv Q_{\Delta ^ + } + Q_{\Delta ^0 } = 0.050\) (in unitse/M ²)=0.029 (in unitse/m ²), whereM(m) is the mass ofΔ(N). Neglecting the pion mass and takingM=m,μ _n /μ _p =?2/3, we get theSU ₆ result μ_Δ+=μ _p .     

2α + t Cluster Structure in 11B

Structures of excited states in ¹¹B are investigated with a method of β – γ constraint antisymmetrized molecular dynamics in combination with the generator coordinate method. Various cluster structures are suggested in excited states. For negative-parity states, we suggest a band with a 2α + t cluster structure. This band starts from the ${3/2^{-}_{3}}$ state and can correspond to the experimental band observed recently. We find that the feature of the ${3/2^{-}_{3}}$ is quite similar to the ${0^{+}_{2}}$ state in ¹²C.     

Z c (4025) as the hadronic molecule with hidden charm

We have studied the loosely bound $D^{*}\bar{D}^{*}$ system. Our results indicate that the recently observed charged charmonium-like structure Z _c (4025) can be an ideal $D^{*}\bar{D}^{*}$ molecular state. We have also investigated its pionic, dipionic, and radiative decays. We stress that both the scalar isovector molecular partner Z _c0 and three isoscalar partners ${\tilde{Z}}_{c0,c1,c2}$ should also exist if Z _c (4025) is a $D^{*}\bar{D}^{*}$ molecular state in the framework of the one-pion-exchange model. Z _c0 can be searched for in the channel e ⁺ e ^?→Y→Z _c0(4025)(ππ)_P-wave where Y can be Y(4260) or any other excited 1^?? charmonium or charmonium-like states such as Y(4360), Y(4660), etc. The isoscalar $D^{*}\bar{D}^{*}$ molecular states ${\tilde{Z}}_{c0,c2}$ with 0⁺(0⁺⁺) and 0⁺(2⁺⁺) can be searched for in the three pion decay channel $e^{+}e^{-}\to Y \to {\tilde{Z}}_{c0,c2} (3\pi)^{I=0}_{\text{P-wave}}$ . The isoscalar molecular state ${\tilde{Z}}_{c1}$ with 0^?(1^+?) can be searched for in the channel ${\tilde{Z}}_{c1}\eta$ . Experimental discovery of these partner states will firmly establish the molecular picture.     

Leptoquark pair production in hadronic interactions

The scalar and vector leptoquark pair production cross sections in hadronic collisions are calculated. In a model independent analysis we consider the most general C and P conserving couplings of gluons to both scalar and vector leptoquarks described by an effective low-energy Lagangian which obeys SU(3)_c invariance. Analytical expressions are derived for the differential and integral scattering cross sections including the case of anomalous vector leptoquark couplings, K _G and Λ_G, to the gluon field. Numerical predictions are given for the kinematic range of the TEVATRON and LHC. The pair production cross sections are also calculated for the resolved photon contributions to at HERA and LEP ? LHC, and for the process at possible future e ^{+ e ?} linear colliders and γγ colliders. Estimates of the search potential for scalar and vector leptoquarks at present and future high energy colliders are given.     

Indecomposable representations with invariant inner product

Consequences of the existence of an invariant (necessarily indefinite) non-degenerate inner product for an indecomposable representation π of a groupG on a space \(\mathfrak{H}\) are studied. If π has an irreducible subrepresentation π₁ on a subspace \(\mathfrak{H}_1 \) , it is shown that there exists an invariant subspace \(\mathfrak{H}_2 \) of \(\mathfrak{H}\) containing \(\mathfrak{H}_1 \) and satisfying the following conditions: (1) the representation π ₁ ^# =π mod \(\mathfrak{H}_2 \) on \(\mathfrak{H}\) mod \(\mathfrak{H}_2 \) is conjugate to the representation (π₁, \(\mathfrak{H}_1 \) ), (2) \(\mathfrak{H}_1 \) is a null space for the inner product, and (3) the induced inner product on \(\mathfrak{H}_2 \) mod \(\mathfrak{H}_1 \) is non-degenerate and invariant for the representation $$\pi _2 = (\pi _2 |_{\mathfrak{H}_2 } )\bmod \mathfrak{H}_1 ,$$ a special example being the Gupta-Bleuler triplet for the one-particle space of the free classical electromagnetic field with \(\mathfrak{H}_1 \) =space of longitudinal photons and \(\mathfrak{H}_2 \) =the space defined by the subsidiary condition.