Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique in the case of different quark masses

The Bethe-Salpeter equations for quark-antiquark composite systems with different quark masses, such as \(q\bar s(with q = u,d),q\bar Q\), and \(s\bar Q\) (with Q = c, b), are written in terms of spectral integrals. For mesons characterized by the mass M, spin J, and radial quantum number n, the equations are written for the (n, M²) trajectories with fixed J. The mixing between states with different quark spin S and angular momentum L is also discussed.     

Evolution of high-mass diffraction from the light quark valence component of the Pomeron

We analyze the contribution from excitation of the \((q\bar q)(f\bar f), (q\bar q)g_1 \cdots g_n (f\bar f)\) Fock states of a photon to high-mass diffraction in DIS. We show that the large-Q² behavior of this contribution can be described by DLLA evolution from the nonperturbative \(f\bar f\) valence state of the pomeron. Although of higher order in pQCD, the new contribution to high-mass diffraction is comparable to that from the excitation of the \(q\bar qg\) Fock state of the photon.     

Ds+ → π+ π+ π− decay: The $$1^3 P_0 s\bar s$$ component in scalar-isoscalar mesons

We calculate the processes \(D_s^ + \to \pi ^ + s\bar s\) and D _s ⁺ → π⁺resonance, respectively, in the spectator and W-annihilation mechanisms. The data on the reaction D _s ⁺ → π⁺ρ⁰, which is due to the W-annihilation mechanism only, point to a negligibly small contribution of the W annihilation to the production of scalar-isoscalar resonances D _s ⁺ ?π⁺f₀. As to spectator mechanism, we evaluate the \(1^3 P_0 s\bar s\) component in the resonances f₀(980), f₀(1300), and f₀(1500) and broad state f₀(1200–1600) on the basis of data on the decay ratios D _s ⁺ ?π⁺f₀/(D _s ⁺ ?π⁺_θ). The data point to a large \(s\bar s\) component in the \(f_0 (980):40 \lesssim s\bar s \lesssim 70\% \). Nearly 30% of the \(1^3 P_0 s\bar s\) component flows to the mass region 1300–1500 MeV, being shared by f₀(1300), f₀(1500), and broad state f₀(1200–1600): the interference of these states results in a peak near 1400 MeV with the width around 200 MeV. Our calculations show that the yield of the radial-excitation state\(2^3 P_0 s\bar s\)is relatively suppressed, \({{\Gamma (D_s^ + \to \pi ^ + (2^3 P_0 s\bar s))} \mathord{\left/ {\vphantom {{\Gamma (D_s^ + \to \pi ^ + (2^3 P_0 s\bar s))} {\Gamma (D_s^ + \to \pi ^ + (1^3 P_0 s\bar s))}}} \right. \kern-\nulldelimiterspace} {\Gamma (D_s^ + \to \pi ^ + (1^3 P_0 s\bar s))}} \lesssim 0.05\).     

Kaonic production of $ \Lambda$(1405) off deuteron target in chiral dynamics

The K^--induced production of \( \Lambda\)(1405) is investigated in K ^- d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions based on coupled-channels chiral dynamics, in order to discuss the resonance position of the \( \Lambda\)(1405) in the \( \bar{{K}}\) N channel. We find that the K ^- d \( \rightarrow\) \( \Lambda\)(1405)n process favors the production of \( \Lambda\)(1405) initiated by the \( \bar{{K}}\) N channel. The present approach indicates that the \( \Lambda\)(1405) -resonance position is 1420MeV rather than 1405MeV in the \( \pi\) \( \Sigma\) invariant-mass spectra of K ^- d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions. This is consistent with an observed spectrum of the K ^- d \( \rightarrow\) \( \pi^{{+}}_{}\) \( \Sigma^{{-}}_{}\) n with 686-844MeV/c incident K^- by bubble chamber experiments done in the 70s. Our model also reproduces the measured \( \Lambda\)(1405) production cross-section.     

Analysis of th e $$Hb\bar b$$ coupling constant and CP-violation eff ects at th e futur e e+ e− collid er

The \(e^ + e^ - \to b\bar bv\bar v\) process, where υ is an electron, muon, or τ-lepton neutrino, is analyzed in detail for the general form of the coupling constant of a Higgs boson with b quarks, with the (m _b /v)(a+Iγ₅b) parameterization of the \(Hb\bar b\) interaction. This process is shown to be highly sensitive to this coupling constant. Experiments at the future with \(\sqrt s = 500 - GeV\) linear collider will provide limits of 2 and 20% for deviations of the parameters a and b, respectively, from their Standard Model values. Results concerning the \(e^ + e^ - \to b\bar bv\bar v\) process in combination with the independent measurements of the partial width \(\Gamma _{H \to b\bar b}\) can testify to the CP origin of the Higgs sector of the theory.     

Antiproton-nucleus electromagnetic annihilation as a way to access the proton timelike form factors

Contrary to the reaction \( \bar{{p}}\) p \( \rightarrow\) e ⁺ e ^- with a high-momentum incident antiproton on a free target proton at rest, in which the invariant mass M of the e ⁺ e ^- pair is necessarily much larger than the \( \bar{{p}}\) p mass 2m , in the reaction \( \bar{{p}}\) d \( \rightarrow\) e ⁺ e ^- n the value of M can take values near or below the \( \bar{{p}}\) p mass. In the antiproton-deuteron electromagnetic annihilation, this allows to access the proton electromagnetic form factors in the timelike region of q² near the \( \bar{{p}}\) p threshold. We estimate the cross-section \(d\sigma _{\bar pd \to e^ + e^ - n} /d\mathcal{M}\) for an antiproton beam momentum of 1.5GeV/c. We find that near the \( \bar{{p}}\) p threshold this cross-section is about 1pb/MeV. The case of heavy-nuclei target is also discussed. Elements of experimental feasibility are presented for the process \( \bar{{p}}\) d \( \rightarrow\) e ⁺ e ^- n in the context of the \( \overline{{{\rm P}}}\) ANDA project.     

Exotic tetraquark states with the $$qq\bar{Q}\bar{Q}$$ configuration

In this work, we study systematically the mass splittings of the \(qq\bar{Q}\bar{Q}\) (\(q=u\), d, s and \(Q=c\), b) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the \(J^P=0^+\) states and possible stable tetraquarks exist in the \(nn\bar{Q}\bar{Q}\) (\(n=u\), d) and \(ns\bar{Q}\bar{Q}\) systems either with \(J=0\) or with \(J=1\). Possible decay patterns of the tetraquarks are briefly discussed.     

Investigation of the <Emphasis Type="Italic">Hττ</Emphasis> and <Emphasis Type="Italic">Hbb</Emphasis> coupling constants for a scalar (pseudoscalar) Higgs boson at a future linear electron-positron collider

The possibility of setting constraints on the couplings of a scalar (pseudoscalar) Higgs boson to the tau lepton and the b quark in the reactions \(e^ + e^ - \to \nu \bar \nu \tau ^ + \tau ^ - \) and \(e^ + e^ - \to \nu \bar \nu b\bar b\) at a future linear electron-positron collider of total energy \(\sqrt s = 500 GeV\) is studied. The admixture of a new hypothetical pseudoscalar state of the Higgs boson in the H ff vertex is parametrized in the form (m _f /ν)(a+iγ₅b). On the basis of an analysis of differential distributions for the processes under study, it is shown that data from the future linear collider TESLA will make it possible to constrain the parameters a and b as ?0.32≤Δa≤0.24 and ?0.73≤b≤0.73 in the case of the reaction \(e^ + e^ - \to \nu \bar \nu \tau ^ + \tau ^ - \) and as ?0.026≤Δa≤0.027 and ?0.23≤b≤0.23 in the case of the reaction \(e^ + e^ - \to \nu \bar \nu b\bar b\). It is emphasized that the contribution of the fusion subprocess WW → H in the channel involving an electron neutrino is of particular importance, since this contribution enhances the sensitivity of data to the parameters being analyzed.     

Neutron-antineutron oscillations in the trapping box

The problem of n-\(\bar n\) oscillations for ultracold neutrons confined within a trap is reexamined. It is shown that the growth of the \(\bar n\) component with time is to a decent accuracy given by \(P(\bar n) = \varepsilon _{n\bar n}^2 t_L t\), where \(\varepsilon _{n\bar n}\) is the mixing parameter and t _L ～ 1 s is the neutron propagation time between subsequent collisions with the trap walls. Possible corrections to this law and open questions are discussed.     

On the structure of the von Neumann algebras generated by local functions of the free bose field

It is shown that the von Neumann algebra\(R_\mathfrak{B} \)(B) generated by any scalar local functionB(x) of the free fieldA ₀(x) is equal either to\(R_\mathfrak{B} \)(A ₀) or to\(R_\mathfrak{B} \)(:A ₀ ² :). The latter statement holds if the state space space\(\mathfrak{H}_B \) obtained from the vacuum state by repeated application ofB(x) is orthogonal to the one particle subspace. In the proof of these statements, space-time limiting techniques are used.     

Searching for signatures around 1920 MeV of a N<Superscript>*</Superscript> state of three hadron nature

We provide a series of arguments which support the idea that the peak seen in the \( \gamma\) p \( \rightarrow\) K ⁺ \( \Lambda\) reaction around 1920MeV should correspond to the recently predicted state of J ^P = 1/2⁺ as a bound state of K \( \bar{{K}}\) N with a mixture of a ₀(980)N and f ₀(980)N components. At the same time we propose polarization experiments in that reaction as a further test of the prediction, as well as a study of the total cross-section for \( \gamma\) p \( \rightarrow\) K ⁺ K ^- p at energies close to threshold and of dσ/dM _inv for invariant masses close to the two-kaon threshold.     

Die absolute Intensität der durch Elektronenstoß in einer dicken Wolfram-Antikathode erzeugtenL α -Strahlung

The number\(N_{L_\alpha }^{dir} \) (produced) ofL _α -photons produced by electron-bombardment in a thick target of tungsten per incident electron has been measured absolutely with the Ross-filter method and relatively with the crystal-spectrometer method in the energyregion up to the 3.6 times theL _III-ionization energy\(E_{L_{III} } \). The result can be presented in the following empirical form:\(N_{L_\alpha }^{dir} \) (produced)=4π·?·(U ₀?1) ⁿ with ?=0.52·10^?4±5% andn=1.44±0.02\((U_0 = E_0 /E_{L_{III} }< 3.6)\). Out of this the number\(n_{L_{III} } \) ofL _III-ionizations per electron which is slowed down to the energy\(E_{L_{III} } \) within the target, has been evaluated. The computation of\(n_{L_{III} } \) out of the elementary process by usingBethe's non-relativistic formulae for totalL _III-ionization cross sectionQ _L and energy loss-dE/ds is in full agreement with experiment in the region 2<U ₀<3.6, if the constants in\(Q_{L_{III} } \) are chosen as follows:\(B = 4E_{L_{III} } , b_{L_{III} } = 0.25 \cdot 5.89\). By comparison of this result for\(b_{L_{III} } \) with the corresponding value ofb _K in the totalK-ionization cross-sectionQ _K for copper (b _K=0.35·2.26) it is concluded that\(Q_{L_{III} } \) is considerably higher than predicted by theory. The necessary correction factors as e.g. loss ofL _III-ionizations by rediffusion of electrons and portion of indirectly producedL _α -radiation-radiation are determined for tungsten quantitatively.     

Non-extensivity of the chemical potential of polymer melts

Following Flory’s ideality hypothesis, the chemical potential of a test chain of length n immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in n . We argue that an additional contribution \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) ～ +1/\( \rho\) \( \sqrt{{n}}\) arises (\( \rho\) being the monomer density) for all P(N) if n ? 〈N〉 which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory-distributed melts, we obtain \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) \( \approx\) (1 - 2n/〈N〉)/\( \rho\) \( \sqrt{{n}}\) for n ? 〈N〉² , hence, \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) \( \approx\) -1/\( \rho\) \( \sqrt{{n}}\) if n is similar to the typical length of the bath 〈N〉 . Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond fluctuation model. As predicted we find, e.g., the non-exponentiality parameter K _p \( \equiv\) 1 - 〈N ^p〉/p!〈N〉^p to decay as K _p \( \approx\) 1/\( \sqrt{{\langle N \rangle }}\) for all moments p of the distribution.     

Vector tetraquark state candidates: <Emphasis Type="Italic">Y</Emphasis>(4260 / 4220), <Emphasis Type="Italic">Y</Emphasis>(4360 / 4320), <Emphasis Type="Italic">Y</Emphasis>(4390) and <Emphasis Type="Italic">Y</Emphasis>(4660 / 4630)

In this article, we construct the \(C \otimes \gamma _\mu C\) and \(C\gamma _5 \otimes \gamma _5\gamma _\mu C\) type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula \(\mu =\sqrt{M^2_{Y}-(2{\mathbb {M}}_c)^2}\) to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the Y(4260 / 4220), Y(4360 / 4320), Y(4390) and Y(4660 / 4630) as input parameters and fit the pole residues to reproduce the correlation functions at the QCD side. The numerical results support assigning the Y(4660 / 4630) to be the \(C \otimes \gamma _\mu C\) type vector tetraquark state \(c\bar{c}s\bar{s}\), assigning the Y(4360 / 4320) to be \(C\gamma _5 \otimes \gamma _5\gamma _\mu C\) type vector tetraquark state \(c\bar{c}q\bar{q}\), and disfavor assigning the Y(4260 / 4220) and Y(4390) to be the pure vector tetraquark states.     

Is the a0(1450) a c andid ate for the lowest $$q\b ar q1^3 P_0 $$ st ate?

For a ₀(1450), considered as the \(q\bar q1^3 P_0 \) state, “experimental” tensor splitting, c _exp = ?150±40 MeV, appears to be in contradiction with the conventional theory of fine structure. There is no such discrepancy if a ₀(980) belongs to the \(q\bar q1^3 P_J \) multiplet. The hadronic shift of a ₀(980) is shown to be greatly dependent on the value of strong coupling in spin-dependent interaction.     

VEPP-2000 project: Collider,detectors, and physics program

The new VEPP-2000 e⁺e^? collider of maximum energy 2000 MeV, which is under construction at the Budker Institute of Nuclear Physics (Siberian Division, Russian Academy of Sciences, Novosibirsk), is briefly described. Experiments at VEPP-2000 will be performed with two upgraded detectors, CMD-2M and SND. A precise measurement of the total cross section for the process e⁺e^? → hadrons and of the partial cross sections for its exclusive hadronic channels is the main point of the physics program for this machine. These measurements will be aimed at testing QCD and the VMD and CVC models, as well as at refining the hadron contribution to fundamental constants such as the muon anomalous magnetic moment \(a_\mu = \frac{{g - 2}}{2}\) and the fine-structure constant α_em(M _Z ² ). Measurements of the nucleon form factors in the reactions e⁺e^? → p\(\bar p\), n\(\bar n\) at their threshold will also be of great importance.     

Relative yield of charged and neutral heavy meson pairs in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation near threshold

The subject of the charged-to-neutral yield ratio for \(B\bar B\) and \(D\bar D\) pairs near their respective thresholds in e⁺e^? annihilation is revisited. As previously argued for the B mesons, this ratio should exhibit a substantial variation across the ?(4S) resonance due to interference of the resonance scattering phase with the Coulomb interaction between the charged mesons. A simple alternative derivation of the expression describing this effect is presented here, and the analysis is extended to include the D-meson production in the region of the ψ(3770) resonance. The available data on kaon production at the φ(1020) resonance are also discussed in connection with the expected variation of the charged-to-neutral yield ratio.     

$$Q\bar{Q}$$ ($$Q\in \{b,c\}$$Q∈{b,c}) spectroscopy using the Cornell potential

The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schrödinger equation to obtain their mass spectra using only four parameters namely quark mass (\(m_c\), \(m_b\)) and confinement strength (\(A_{c\bar{c}}\), \(A_{b\bar{b}}\)). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited S, P, D and F states. Digamma, digluon and dilepton decays of these mesons are computed using the model parameters and numerical wave functions. The predicted spectroscopy and decay properties for quarkonia are found to be consistent with available data from experiments, lattice QCD and other theoretical approaches. We also compute mass spectra and life time of the \(B_c\) meson without additional parameters. The computed electromagnetic transition widths of heavy quarkonia and \(B_c\) mesons are in tune with available experimental data and other theoretical approaches.     

Leptonic decays of the <Emphasis Type="Italic">W</Emphasis> boson in a strong electromagnetic field

The probability of W-boson decay into a lepton and a neutrino, \(W^ \pm \to \ell ^ \pm \bar \nu _\ell \), in a strong electromagnetic field is calculated. On the basis of the method for deriving exact solutions to relativistic wave equations for charged particles, an exact analytic expression is obtained for the partial decay width \(\Gamma () = \Gamma (W^ + \to \ell ^ + \bar \upsilon _\ell )\) at an arbitrary value of the external-field-strength parameter \( = eM_W^{ - 3} \sqrt { - (F_{\mu \upsilon } q^\upsilon )^2 } \). It is found that, in the region of comparatively weak fields (??1), field-induced corrections to the standard decay width of theW boson in a vacuum are about a few percent. As the external-field-strength parameter is increased, the partial width with respect to W-boson decay through the channel in question, Γ(?), first decreases, the absolute minimum of Γ_min=0.926Γ(0) being reached at ?=0.6116. A further increase in the external-field strength leads to a monotonic growth of the decay width of the W boson. In superstrong fields (??1), the partial width with respect to W boson decay is greater than the corresponding partial width \(\Gamma ^{(0)} (W^ \pm \to \ell ^ \pm \bar \upsilon _\ell )\) in a vacuum by a factor of a few tens.     

New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values \(\{a_{1},a_{2},a_{3},\ldots ,a_{N}\}\) and a function \(g:\textbf {R}\rightarrow \{0,1\}\), we shall determine the following values \(\{g(a_{1}),g(a_{2}),g(a_{3}),\ldots , g(a_{N})\}\) simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of \(N\). Next, we consider it as a number in binary representation; M₁ = (g(a₁),g(a₂),g(a₃),…,g(a _N )). By using \(M\) parallel quantum systems, we have \(M\) numbers in binary representation, simultaneously. The speed of obtaining the \(M\) numbers is shown to outperform the classical case by a factor of \(M\). Finally, we calculate the product; \( M_{1}\times M_{2}\times \cdots \times M_{M}. \) The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.