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Register a new userPossible quantum numbers of the pentaquark Theta^+(1540) in QCD sum rules
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The QCD sum rule technique is employed to investigate pentaquark states with strangeness S = +1 and IJ^P = 0,1/2^pm, 1,1/2^pm, 0,3/2^pm, 1,3/2^pm. Throughout the calculation, emphasis is laid on the establishment of a valid Borel window, which corresponds to a region of the Borel mass, where the operator product expansion converges and the presumed ground state pole dominates the sum rules. Such a Borel window is achieved by constructing the sum rules from the difference of two independent correlators and by calculating the operator product expansion up to dimension 14. Furthermore, we discuss the possibility of the contamination of the sum rules by possible KN scattering states. As a result, we conclude that the 0,3/2^+ state seems to be the most probable candidate for the experimentally observed Theta^+(1540), while we also obtain states with 0,1/2^-, 1,1/2^-, 1,3/2^+ at somewhat higher mass regions.
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The QCD sum rule method is formulated for the strangeness +1 pentaquark baryon with isospin I=0 and spin-parity J^P = 3/2^pm. The spin-3/2 states are considered to be narrower than the spin-1/2 ones, and thus may provide a natural explanation for the experimentally observed narrow width of Theta^+. In order to obtain reliable results in QCD sum rule calculations, we stress the importance of establishing a wide Borel window, where convergence of the operator product expansion and sufficient low-mass strength of the spectral function are guaranteed. To this end, we employ the difference of two independent correlators so that the high-energy continuum contribution is suppressed. The stability of the physical quantities against the Borel mass is confirmed within the Borel window. It is found that the sum rule gives positive evidence for the (I, J^P) = (0, 3/2^+) state with a mass of about 1.4 pm 0.2 GeV, while we cannot extract any evidence for the (0, 3/2^-) state.
We calculate the on-shell $Sigma^0$-$Lambda$ mixing parameter $theta$ with the method of QCD sum rule. Our result is $theta (m^2_{Sigma^0}) =(-)(0.5pm 0.1)$MeV. The electromagnetic interaction is not included.
The data on the reactions K^+Xe --> K^0 gamma X and K^+Xe --> K^+ gamma X, obtained with the bubble chamber DIANA, have been analyzed for possible radiative decays of the Theta^+(1540) baryon: Theta^+ --> K^0 p gamma and Theta^+ --> K^+ n gamma. No signals have been observed, and we derive the upper limits Gamma(Theta^+ --> K^0 p gamma) / Gamma(Theta^+ --> K^0 p) < 0.032 and Gamma(Theta^+ --> K^+ n gamma) / Gamma(Theta^+ --> K^+ n) < 0.041 which, using our previous measurement of Gamma(Theta^+ --> KN) = (0.39+-0.10) MeV, translate to Gamma(Theta^+ --> K^0 p gamma) < 8 keV and Gamma(Theta^+ --> K^+ n gamma) < 11 keV at 90% confidence level. We have also measured the cross sections of K^+ -induced reactions involving emission of a neutral pion: sigma(K^+n --> K^0 p pi^0) = (68+-18) mub and sigma(K^+N --> K^+ N pi^0) = (30+-8) mub for incident K^+ momentum of 640 MeV.
Using the QCD sum rules we test if the charmonium-like structure Y(4260), observed in the $J/psipipi$ invariant mass spectrum, can be described with a $J/psi f_0(980)$ molecular current with $J^{PC}=1^{--}$. We consider the contributions of condensates up to dimension six and we work at leading order in $alpha_s$. We keep terms which are linear in the strange quark mass $m_s$. The mass obtained for such state is $m_{Y}=(4.67pm 0.09)$ GeV, when the vector and scalar mesons are in color singlet configurations. We conclude that the proposed current can better describe the Y(4660) state that could be interpreted as a $Psi(2S) f_0(980)$ molecular state. We also use different $J^{PC}=1^{--}$ currents to study the recently observed $Y_b(10890)$ state. Our findings indicate that the $Y_b(10890)$ can be well described by a scalar-vector tetraquark current.
The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V-A). The sum rules exhibit poor saturation up to current energies below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is used to determine the value of the finite remainder of the (V-A) correlator, and its first derivative, at zero momentum: $bar{Pi}(0) = - 4 bar{L}_{10} = 0.0257 pm 0.0003 ,$ and $bar{Pi}^{prime}(0) = 0.065 pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and $d=8$ vacuum condensates in the Operator Product Expansion are also determined: $<{cal {O}}_{6}> = -(0.004 pm 0.001) {GeV}^6,$ and $<{cal {O}}_{8}> = -(0.001 pm 0.006) {GeV}^8.$
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