Another tetraquark structure in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant mass distribution

In this article, we assume that there exists a scalar hidden charm tetraquark state in the π ⁺ χ _c1 invariant mass distribution, and we study its mass using the QCD sum rules. The numerical result M _Z =(4.36±0.18) GeV is consistent with the mass of the Z(4250). The Z(4250) may be a tetraquark state, but other possibilities, such as a hadro-charmonium resonance and a molecular state, are not excluded.     

Admixture of the giant dipole resonance to low lying 1−-states in heavy nuclei

The mass of ¹³ Be has been measured with the reaction ¹³ C(¹⁴ C,¹⁴ O)¹³ Be at E _Lab =337 MeV. A Q-value of Q ₀=–37.02(5) MeV was obtained and the mass excess is M.E.=35.16(5) MeV. If the observed line corresponds to the ground state,¹³ Be is particle unstable with respect to the oneneutron emission by 2.01 MeV. The observed line width of 0.3(2) MeV supports an assignment ofJ =5/2⁺ or 1/2^–, but excludesJ =1/2⁺. An excited state is seen at 3.12(7) MeV; there are indications of a second excited state at 6.5(2) MeV.     

Possible tetraquark states in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant-mass distribution

In this article, we assume that there exist hidden charmed tetraquark states with spin–parity J ^P=1⁻, and we calculate their masses with the QCD sum rules. The numerical result indicates that the masses of the vector hidden charmed tetraquark states are about M _Z =(5.12±0.15) GeV or M _Z =(5.16±0.16) GeV, which are inconsistent with the experimental data on the π ⁺ χ _c1 invariant-mass distribution. The hidden charmed mesons Z ₁, Z ₂ or Z may be scalar hidden charmed tetraquark states, hadro-charmonium resonances or molecular states.     

Λ(1405) as a multiquark state

In the QCD sum rule approach we predict the Λ (1405) mass by choosing the π⁰Σ⁰ multiquark interpolating field. It is found that the mass is about 1.419 GeV from Π₁ (q ²) sum rule which is more reliable than Π_q (q ²) sum rule, where Π_q (q ²) and Π₁ (q ²) are two invariant functions of the correlator Π (q ²). We also present the sum rules for the K ⁺ p and the π⁺Σ⁺ multiquark states, and compare to those for the π⁰Σ⁰ multiquark state. The mass of the Λ (1600) can be also reproduced in our approach. Received: 11 November 1997 / Revised version: 28 April 1998     

Glueballs and the superfluid phase of Two-Color QCD

We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two-color QCD. The simulations are carried out on a 6³×12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. The glueball correlators are evaluated via a multi-step smearing procedure. The amplitude of the glueball correlator peaks in correspondence with the zero temperature chiral transition, μ _c=m _π /2, and the propagators change in a significant way in the superfluid phase, while the Polyakov loop is nearly insensitive to the transition. Standard analysis suggest that lowest mass in the 0⁺⁺ gluonic channel decreases in the superfluid phase, but these observations need to be confirmed on larger and more elongated lattices. These results indicate that a non-zero density induces non-trivial modifications of the gluonic medium.     

<Emphasis Type="Italic">X</Emphasis>(3872) and other possible heavy molecular states

We perform a systematic study of the possible molecular states composed of a pair of heavy mesons such as , , in the framework of the meson exchange model. The exchanged mesons include the pseudoscalar, scalar and vector mesons. Through our investigation, we find the following results. (1) The structure X(3764) is not a molecular state. (2) There exists strong attraction in the range r<1 fm for the system with J=0,1. If future experiments confirm Z ⁺(4051) as a loosely bound molecular state, its quantum number is probably J ^P =0⁺. Its partner state Φ ^**0 may be searched for in the π ⁰ χ _c1 channel. (3) Vector meson exchange provides strong attraction in the channel together with pion exchange. A bound state solution may exist with a reasonable cutoff parameter Λ∼1.4 GeV. X(3872) may be accommodated as a molecular state dynamically although drawing a very definite conclusion needs further investigation. (4) The molecular state may exist.     

Instanton interpolating current for σ-tetraquark

We perform a QCD sum rule analysis for the light scalar meson σ   (f₀(600)$f_0(600)$) with a tetraquark current related to the instanton picture for QCD vacuum. We demonstrate that instanton current, including equal weights of scalar and pseudoscalar diquark–antidiquarks, leads to a strong cancelation between the contributions of high dimension operators in the operator product expansion (OPE). Furthermore, in the case of this current direct instanton contributions do not spoil the sum rules. Our calculation, obtained from the OPE up to dimension 10 operators, gives the mass of σ-meson around 780 MeV.     

Measurements of magnetic moments of Tc isotopes and the hyperfine field of Tc in Fe and Ni

We report measurements of nuclear magnetic resonance on oriented nuclei (NMR-ON) on⁹⁴Tc (I=7⁺,T _1/2=4.9 h),⁹⁵Tc (I =9/2⁺,T _1/2=20 h) and⁹⁶Tc (I =7⁺,T _1/2=4.3 d) in Fe and on⁹⁵Tc and⁹⁶Tc in Ni. In order to elucidate the discrepancies on the hyperfine field of TcFe in the literature, the resonances were measured with high precision as a function of the external magnetic field B_ext up to 2.0 T. In addition, TDPAC measurements were performed on⁹⁹TcFe at T=300 K and 13 K. TheT=0 K hyperfine fields of Tc in Fe and Ni were determined to be –314(3) kG and –51.8(5) kG, respectively. The g-factors of⁹³Tc,⁹⁴Tc,⁹⁵Tc,⁹⁶Tc and⁹⁹Tc(E=181 keV;I =5/2⁺) are redetermined as g(⁹³Tc)=1.405(14), g(⁹⁴Tc)=0.731(7),g(⁹⁵Tc)=1.321(13), g(⁹⁶Tc)=0.727(7), g(⁹⁹Tc)=1.390(17).We wish to thank E. Smolic and G. Seewald for experimental help. This work was funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 06TM353/TP 4, by the Deutsche Forschungsgemeinschaft (DFG) under the contract numbers Ha 1282/3-1,2, and, partly, by the Kernforschungszentrum, Karlsruhe.     

QCD Coulomb gauge approach to exotic hadrons

The Coulomb gauge Hamiltonian model is used to calculate masses for selected J^PC states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs), qˉg hybrid mesons and qˉqˉ tetraquark systems. An odderon Regge trajectory is computed for the J^- glueballs with intercept much smaller than the pomeron, explaining its nonobservation. The lowest 1^-+ hybrid-meson mass is found to be just above 2.2GeV while the lightest tetraquark state mass with these exotic quantum numbers is predicted around 1.4GeV consistent with the observed π(1400).     

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

On lower scalar quark-antiquark nonets

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, k, ηη in the channel with I ^G J ^PC = 0⁺0⁺⁺ are carried out and discussed. In a model-independent approach, confirmation of the σ-meson below 1GeV and definite indications of the QCD nature of other f₀ resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.     

Further study of D+ s decays into π-π+π+

A Dalitz plot analysis of the OZI rule violating decay D⁺ _s into π^-π⁺π⁺ is presented using different partial wave approaches. Scalar and vector waves are described by K-matrices; their production is parameterized in a P-vector approach. Alternatively, Breit–Wigner amplitudes and Flatté parametrization are used. Special emphasis is devoted to scalar mesons. The f₀(980) resonance provides the most significant contribution. Adding f₀(1500) to the scalar wave leads to an acceptable fit while introduction of f₀(1370) and/or f₀(1710) does not lead to significant improvements. A scan of the scalar wave optimizes for M=1452 ± 22 MeV/c ². When f₀(1710) is added, the mass uncertainty increases, and the fit yields M=1470 ± 60 MeV/c ² which is fully compatible with the nominal f₀(1500) mass. The scalar wave seems to exhibit a phase motion of 270° units in the mass range from 1200 to 1650 MeV/c ². PACS 11.80.Et; 13.20.Fc; 14.40.Cs     

Photodissociation dynamics of CF3I investigated by two-color femtosecond laser pulses

We report an experimental study of the multiphoton dissociation dynamics of CF₃I performed on a home-built femtosecond laser pump-probe system, with time-of-flight mass spectrometer. The first repulsive A band and the 5pπ³7sσ υ₂=1 Rydberg state of CF₃I were accessed by one- and two-photon transitions at 267 nm, respectively, with the latter two-photon absorption followed by a further two-photon probe transition at 401 nm to the state of the parent ion. The observed signals from the CF₃ ⁺ and I⁺ fragments show similar multi-component exponential decay patterns but the former is 4 times stronger than the latter. However, the parent CF₃I⁺ signal was observed to evolve in a very different manner, decreasing sharply when probed in the first 289 fs following excitation and subsequently rising again after 860 fs to a constant level below that measured at negative pump-probe delay times when the pump and probe pulses exchange roles. This dip observed in the parent ion profile, is very different from that previously reported at shorter pump wavelengths of 264 nm or 265 nm, and is interpreted as the competition between two different ionization channels. One from the vibrationally excited υ₂=1 of the irradiated Rydberg state and the other from the dissociative vibrational origin of the same electronic state which is populated by internal vibrational relaxation.     

Dilepton production from ρ-mesons in a quark-gluon plasma

Assuming that ρ-mesons exist in a quark-gluon plasma at temperatures close to the QCD phase transition, we calculate the dilepton production rate from q-ˉq annihilation via a ρ-meson state using Vector Meson Dominance. The result is compared to the rates from direct q-ˉq annihilation and from π⁺-π⁻ annihilation. Furthermore we discuss the suppression of low mass dileptons if the quarks assume an effective mass in the quark-gluon plasma. Received: 8 September 1999 / Revised version: 22 October 1999     

Enhanced direct <Emphasis Type="Italic">CP</Emphasis> violation and branching ratios in bottom hadron decays

In the framework of factorization we study direct CP violation in the decays of bottom hadrons containing a strange quark or a charm quark, H _b →f ρ ⁰(ω)→f π ⁺ π ⁻ (H _b is the bottom hadron and f is the product hadron) including the effect of ρ–ω mixing. We find that the CP violating asymmetry can be enhanced greatly via the ρ–ω mixing mechanism when the invariant mass of the π ⁺ π ⁻ pair is in the vicinity of the ω resonance. For the processes associated with b→d transitions, e.g. , , B _c ⁻→D ⁻ π ⁺ π ⁻, B _c ⁻→D ^*− π ⁺ π ⁻, Ξ _b ⁰→Λ π ⁺ π ⁻, and Ω _b ⁻→Ξ ⁻ π ⁺ π ⁻, the maximum CP violating asymmetries can reach about −84%, while for the processes associated with b→s transitions, e.g. , , B _c ⁻→D _s ⁻ π ⁺ π ⁻, B _c ⁻→D _s ^*− π ⁺ π ⁻, Ξ _b ⁻→Ξ ⁻ π ⁺ π ⁻, and Ω _b ⁻→Ω ⁻ π ⁺ π ⁻, the CP violating asymmetries can be enhanced to about 95%. Furthermore, taking ρ–ω mixing into account we calculate the b-hadron decay branching ratios. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.     

Magnetic monopole interactions: Shell structure of meson and baryon states

It is suggested that a low-mass magnetic monopole of Dirac chargeg=(137/2)e may be interacting with ac-quark's magnetic dipole moment to produce Zeeman splitting of meson states. The massM ₀=2397 MeV of the monopole is in contrast to the 10¹⁶-GeV monopoles of grand unification theories (GUT). It is shown that shell structure of energyE _n =M ₀+1/4nM ₀+ exists for meson states. The presence of symmetric meson states leads to the identification of the shell structure. The possible existence of the 2397-MeV magnetic monopole is shown to quantize quark masses in agreement with calculations of quantum chromodynamics (QCD). From the shell structure of meson states, the existence of two new mesons is predicted:(1814±50 MeV) withI ^G(J ^PC =0⁺(0^–+) and _c (3907±100 MeV) withJ ^PC =0^–+. The presence of shell structure for baryon states is shown.     

Some properties of the newly observed X(1835) state at BES

Recently the BES collaboration has announced the observation of a resonant state in the π⁺π^-η’ spectrum in J/ψ→γπ⁺π^-η’ decay. Fitting the data with a 0^-+ state, the mass is determined to be 1833.7 MeV with 7.7σ statistic significance. This state is consistent with the one extracted from previously reported pp̄ threshold enhancement data in J/ψ→γpp̄. We study the properties of this state using QCD anomaly and QCD sum rules, assuming X(1835) to be a pseudoscalar, and we show that it is consistent with the data. We find that this state has a sizeable matrix element , leading to branching ratios of (2.61–7.37)×10^-3 and (2.21–10.61)×10^-2 for J/ψ→γG_p and for G_p→π⁺π^-η^′, respectively. Combining the calculated branching ratio of J/ψ→γG_p and data on threshold enhancement in J/ψ→γpp̄, we determine the coupling for the G_p–p–p̄ interaction. We finally study the branching ratios of the other J/ψ→γ+three mesons decay modes. We find that J/ψ→γG_p→γ(π⁺π^-η,KKπ⁰) can provide useful tests for the mechanism proposed. PACS 11.55.Hx; 12.39.Fe; 12.39.Mk; 13.25.Gv     

Exclusive ωπ<Superscript>0</Superscript> production with muons<Superscript>⋆</Superscript>

Using 160GeV muon scattering data collected with the COMPASS experiment at CERN, the exclusive production of ωπ⁰ via virtual photons was studied. Selective population of a peak around 1250MeV is observed. Possible contributions from spin-parity 1^- are searched for, inspecting decay angular correlations. In particular, the orientation of the ω decay plane may allow a distinction from the 1⁺ b ₁(1235) state. Our observation is compared with indications of a (1250) in annihilation and in γp . Original article based on material presented at HADRON 2007.     

Gluon condensate and the effective gluon mass

Using massive gauge invariant QCD we show explicity how power like corrections to \(\Pi _{\mu v} \left( q \right) = i\int {dx} e^{iq'x} \left\langle {0\left| {j_\mu ^{em} \left( x \right)\bar j_v^{em} \left( 0 \right)} \right|0} \right\rangle \) arise. Using our result for the 1/q ⁴ contribution, a one to one correspondence is made between the gluon condensate and the effective gluon mass. By relating this mass to, \(\langle 0|\frac{{\alpha _s }}{\pi }G_{\mu v}^2 |0\rangle \) a value ofm _gluon=750 MeV is found at ?q ²=10 GeV². In addition, within the context of dimensional regularization, a new technique for evaluating two loop momentum integrals with massive propagators is introduced. This method is a derivative of the Mellin transform technique that was applied to ladder diagrams in the days of Reggeisation.