Analysis of $$D_s D K^*$$ and $$D_s D^{*} K^*$$DsD∗K∗ vertices and branching ratio of $$B^+\rightarrow {K^*}^0 \pi ^+$$B+→K∗0π+

In this paper, the strong form factors and coupling constants of \(D_sDK^*\) and \(D_sD^*K^*\) vertices are investigated within the three-point QCD sum rules method with and without the \(SU_{f}(3)\) symmetry. In this calculation, the contributions of the quark–quark, quark–gluon, and gluon–gluon condensate corrections are considered. As an example of specific application of these coupling constants, the branching ratio of the hadronic decay \(B^+\rightarrow {K^*}^0 \pi ^+\) is analyzed based on the one-particle-exchange which is one of the phenomenological models. In this model, B decays into a \(D_s D^*\) intermediate state, and then these two particles exchange a \(D (D^*)\) producing the final \(K^*\) and \(\pi \) mesons. In order to compute the effect of these interactions, the \(D_s D K^*\) and \(D_s D^* K^*\) form factors are needed.     

(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and SUL(NF) × SUR(NF) symmetry breaking in QCD

It is shown that an (anti-) self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates, $m_f \left\langle {\bar \psi _f \psi _f } \right\rangle $ , is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.     

Rare $$\Lambda _c\rightarrow p \ell ^+\ell ^-$$ decay in the relativistic quark model

The relativistic quark model based on the quasipotential approach with the QCD-motivate potential is employed for the calculation of the form factors of the \(\Lambda _c\rightarrow p\) rare weak transitions. Their momentum dependence is explicitly determined without additional assumptions and extrapolations in the whole kinematical range of the momentum transfer squared \(q^2\). The differential \(\Lambda _c\rightarrow p l^+l^-\) decay branching fractions and angular distributions are calculated on the basis of these form factors. Both the perturbative and effective Wilson coefficients, which include contributions of vector meson resonances, are used. The calculated branching fraction of the \(\Lambda _c\rightarrow p \mu ^+\mu ^-\) rare decay is well consistent with the experimental upper limit very recently set by the LHCb Collaboration.     

Efficient numerical evaluation of Feynman integrals

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with O(10~(-3))accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multiloop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.     

Jet flavor conversions in the quark-gluon plasma

A quark or gluon jet traversing through a quark-gluon plasma can be converted to a gluon or quark jet through scattering with the thermal quarks and gluons in the quark-gluon plasma. Their conversion rates due to two-body elastic and inelastic scattering have recently been evaluated in the lowest order in QCD. Including both energy loss and conversions of quark and gluon jets in the expanding quark-gluon plasma produced in relativistic heavy ion collisions, a net conversion of quark jets to gluon jets has been found. This reduces the difference between the nuclear modification factors for quark and gluon jets in heavy ion collisions and thus enhances the ratios of high transverse momentum protons and antiprotons to pions that are produced from the fragmentation of these jets. To account for the observed similar ratios in central Au + Au and p + p collisions at same energy requires, however, a much larger net quark to gluon jet conversion rate than that given by the lowest-order QCD, indicating the importance of higher-order processes and the strongly coupling properties of the quark-gluon plasma in describing the propagation of jets in the quark-gluon plasma. B.-W. Zhang: On leave from: Institute of Particle Physics, Huazhong Normal University, Wuhan 430079, China Correspondence: C.-M. Ko, Cyclotron Institute and Physics Department, Texas A&M University, College Station, TX 77843-3366, USA     

Calculation of HELAS amplitudes for QCD processes using graphics processing unit (GPU)

We use a graphics processing unit (GPU) for fast calculations of helicity amplitudes of quark and gluon scattering processes in massless QCD. New HEGET (HELAS Evaluation with GPU Enhanced Technology) codes for gluon self-interactions are introduced, and a C++ program to convert the MadGraph generated FORTRAN codes into HEGET codes in CUDA (a C-platform for general purpose computing on GPU) is created. Because of the proliferation of the number of Feynman diagrams and the number of independent color amplitudes, the maximum number of final state jets we can evaluate on a GPU is limited to 4 for pure gluon processes (gg→4g), or 5 for processes with one or more quark lines such as $q\overline{q}\rightarrow 5g$ and qq→qq+3g. Compared with the usual CPU-based programs, we obtain 60–100 times better performance on the GPU, except for 5-jet production processes and the gg→4g processes for which the GPU gain over the CPU is about 20.     

QCD sum rules analysis of the rare B_{c}\rightarrow X\nu\bar{\nu} decays

Taking into account the gluon correction contributions to the correlation function, the form factors relevant to the rare decays are calculated in the framework of the three-point QCD sum rules, where X stands for axial vector particle, AV(D _s1), and vector particles, V(D ^*,D _s ^*). The total decay width as well as the branching ratio of these decays are evaluated using the q ² dependent expressions of the form factors. A comparison of our results with the predictions of the relativistic constituent quark model is presented.     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For thek _⊥ jet finder withy _cut=0.02, we find as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

QCD analysis of forward neutron production in DIS

Observing light-by-light scattering at the large hadron collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the process \({{pp}}\rightarrow {{p}}\gamma \gamma {{p}}\rightarrow {{p}}\gamma \gamma {{p}}\) through graviton exchange in the large extra dimension (LED) model. Typically, when we do the background analysis, we also study the double Pomeron exchange of \(\gamma \gamma \) production. We compare its production in the quark–quark collision mode to the gluon–gluon collision mode and find that contributions from the gluon–gluon collision mode are comparable to the quark–quark one. Our result shows, for extra dimension \(\delta =4\) , with an integrated luminosity \(\mathcal{L} = 200\,\mathrm{fb}^{-1}\) at the 14 TeV LHC, that diphoton production through graviton exchange can probe the LED effects up to the scale \({M}_{S}=5.06 (4.51, 5.11)\,\mathrm{TeV}\) for the forward detector acceptance \(\xi _1 (\xi _2, \xi _3)\) , respectively, where \(0.0015<\xi _1<0.5\) , \(0.1<\xi _2<0.5\) , and \(0.0015<\xi _3<0.15\) .     

The Magnetic Mass of Transverse Gluon, the B-Meson Weak Decay Vertex and the Triality Symmetry of Octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass m _mag becomes approximately equal to T _c at ${T=T_c\sim 1.14\Lambda_{\overline{MS}} \sim 260}$ MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.     

Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M _n (Q ² ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop () perturbative corrections, the contribution of the gluon condensate with corrections and the contribution of the dimension 6 operator G³ are accounted. It is shown that the sum rules for the moments do not work at Q ² = 0, where the perturbation series diverges and the G³ contribution is large. The domain in the (n, Q ² ) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme. Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: ioffe@vitep1.itep.ru RID="b" ID="b" e-mail: zyablyuk@heron.itep.ru     

Feynman formulas for the diffusion of particles with position-dependent mass

In the present paper, Feynman formulas are obtained for Schrödinger semigroups generated by self-adjoint operators which are perturbations of self-adjoint extensions of the second-order Hamiltonian operator ?Δ _g,0/2+V (throughout the paper, the coefficient ?1/2 at Δ _g,0 is omitted to simplify the formulas) which describe the diffusion of a quasiparticle with position-dependent mass varying jump-like on a line. Every extension of this kind is defined by some invertible operator and is characterized by matching conditions at a jump point. The Schrödinger semigroups generated by self-adjoint Laplace operators and defined by the corresponding boundary conditions define solutions of initial-boundary value problems. In turn, the term “Feynman formulas” is applied (in the present case) to an explicit representation of the Schrödinger semigroup \(e^{t\hat H^T } \) in the form of a limit of integrals of finite multiplicity over Cartesian powers of some configuration space. In essence, the Feynman-Kac formula is a “probabilistic interpretation” of the Feynman formulas. Namely, the multiple integrals in the Feynman formulas approximate integrals against some measures on the space of trajectories (functions defined on an interval of the real line and ranging in the configuration space). Thus, the Feynman formulas enable one to evaluate integrals over spaces of trajectories. A crucial role in the proof of the Feynman formulas is played by the Chernoff theorem, which is a generalization of the famous Trotter formula. The result proved in the present paper is a demonstration of a part of the results recently announced by O. G. Smolyanov and H. von Weizäcker (“Feynman Formulas Generated by Self-Adjoint Extensions of the Laplacian,” Dokl. Ross. Akad. Nauk 426 (2), 162–165 (2009) [Doklady Mathematics, 2009 79 (3), 335–338 (2009)]). The formulations of the results in question are inessentially modified here.     

Neutron Star Properties in the Chiral Quark–Meson Coupling Model

We study the properties of neutron stars using the chiral quark–meson coupling model, in which the quark–quark hyperfine interaction due to the exchanges of gluon and pion based on chiral symmetry is considered. We also examine the effects of hyperons and Δ-isobars in a neutron star. Extending the SU(6) spin-flavor symmetry to more general SU(3) flavor symmetry in the vector–meson couplings to baryons, the maximum mass of neutron star can reach the recently observed massive pulsar mass, ${1.97 \pm 0.04 M_{\odot}}$ . In this calculation, Λ and Ξ are generated in a neutron star, while Σ and Δ-isobars do not appear.     

Covariant trace formalism for heavy mesons-wave top-wave transitions

Heavy meson,s- top-wave, weakb→c transitions are studied in the context of the heavy quark effective theory using covariant meson wave functions. We use the trace formalism to evaluate the weak transitions. As expected from heavy quark symmetry, the eight transitions betweens- andp-wave states are described in terms of only two universal form factors which are given in terms of explicit wave function overlap integrals. We present our results in terms of both invariant and helicity amplitudes. Using our helicity amplitude expressions we discuss rate formulae, helicity structure functions and joint angular decay distributions in the decays \(\bar B \to D^{**} ( \to (D,D^* ) + \pi ) + W^ - ( \to l^ - \bar v_l )\) . The heavy quark symmetry predictions for the one pion transitionsD ^**→(D,D ^*)+π are similarly worked out by using trace techniques.     

Infrared Divergences of Three-Loop Vacuum Graghs of Gluon Field at Finite Temperature

The kinds of infrared divergent integrals in three-loop vacuum graghs of gluon field at finite temperature are pointed out and their regularization is discussed. All of the infrared divergences in three-loop vacuum graghs of gluon field are isolated.     

有限温度下胶子场三圈真空图中的红外发散

用热传播子的实时形式对有限温度下胶子场的三圈真空图进行了详细的计算，在维数正规化方案下把真空图中的红外发散全部孤立出来了.