Differential Equations for Definition and Evaluation of Feynman Integrals

It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that presented formalism is convenient for practical calculations of Feynman integrals.Comment: pages, LaTEX, MSU-PHYS-HEP-Lu2/9

Superconductivity by long-range color magnetic interaction in high-density quark matter

We argue that in quark matter at high densities, the color magnetic field remains unscreened and leads to the phenomenon of color superconductivity. Using the renormalization group near the Fermi surface, we find that the long-range nature of the magnetic interaction changes the asymptotic behavior of the gap $\Delta$ at large chemical potential $\mu$ qualitatively. We find $\Delta\sim\mu g^{-5}\exp(-{3\pi^2\over\sqrt{2}}{1\over g})$, where $g$ is the small gauge coupling. We discuss the possibility of breaking rotational symmetry by the formation of a condensate with nonzero angular momentum, as well as interesting parallels to some condensed matter systems with long-range forces.Comment: 14 pages, REVTEX, uses eps

Production of B(c) mesons via fragmentation in the kT-factorization approach

In the framework of the kT-factorization approach we have calculated in the fragmentation model the pT-spectra of B(c) mesons at the energies of the Tevatron and the LHC Colliders and at the large pT domain. We compare the obtained results with the existing experimental data and with the predictions obtained in the collinear parton model.Comment: 10 pages, 2 figure

On charmonia and charmed mesons photoproduction at high energy

We compare the predictions of the collinear parton model and the k_T-factorization approach in J\Psi and D^\star meson photoproduction at HERA energies. It is shown that obtained in the both approaches D^\star meson spectra over p_T and \eta as well as J\Psi meson p_T- and z-spectra are very different. The predictions obtained in the k_T-factorization approach are agree with the experimental data well. We also predict the nontrivial p_T-dependence of the the spin parameter $\alpha(p_T) in the J\Psi photoproduction.Comment: Talk was presented at International Seminar "Heavy quark - 2002", JINR, Dubna, Russia, May-June, 2002. In version 2 we have corrected numerical results for the D^star meson spectr

Final State Interactions in D0→K0K0ˉD^0 \to K^0 \bar{K^0}

It is believed that the production rate of $D^0\to K^0\bar K^0$ is almost solely determined by final state interactions (FSI) and hence provides an ideal place to test FSI models. Here we examine model calculations of the contributions from s-channel resonance $f_J(1710)$ and t-channel exchange to the FSI effects in $D^0\to K^0\bar K^0$. The contribution from s-channel $f_0(1710)$ is sma$For the t-channel FSI evaluation, we employ the one-particle-exchange (OPE) model and Regge model respecti$ The results from two methods are roughly consistent with each other and can reproduce the large rate of $D^0\to K^0\bar K^0$ reasonably well$Comment: Latex, 16 pages, with 2 figure

Deeply virtual electroproduction of photons and mesons on the nucleon : leading order amplitudes and power corrections

We estimate the leading order amplitudes for exclusive photon and meson electroproduction reactions at large Q^2 in the valence region in terms of skewed quark distributions. As experimental investigations can currently only be envisaged at moderate values of Q^2, we estimate power corrections due to the intrinsic transverse momentum of the partons in the meson wavefunction and in the nucleon. To this aim the skewed parton distribution formalism is generalized so as to include the parton intrinsic transverse momentum dependence. Furthermore, for the meson electroproduction reactions, we calculate the soft overlap type contributions and compare with the leading order amplitudes. We give first estimates for these different power corrections in kinematics which are relevant for experiments in the near future.Comment: 59 pages, 21 figure

Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product

Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values of all unit vectors in $V_n$ fills asymptotically (as $n$ tends to infinity) a deterministic convex set $K_{k,t}$ that we describe using a new norm in $\R^k$. Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result result comes together with a law of large numbers for the singular value decomposition of the eigenvectors corresponding to large eigenvalues of a random truncation of a matrix with high eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio

Direct J/psi and psi' hadroproduction via fragmentation in the collinear parton model and k_T-factorization approach

The p_T-spectra for direct J/psi and psi' in hadroproduction at Tevatron energy have been calculated based on NRQCD formalism and fragmentation approximation in the collinear parton model and k_T-factorization approach. We have described the CDF data and obtained a good agreement between the predictions obtained in the parton model and k_T-factorization approach. We performed the calculations using the relevant leading order in alpha_s hard amplitudes and the equal values of the color-octet long-distance matrix elements for the both models.Comment: 10 pages, Latex, 4 eps figures, epsfig.sty, graphics.st

Veneziano like amplitude as a test for AdS/QCD models

The high energy asymptotics of QCD correlation functions is often used as a test for bottom-up holographic models. Since QCD is not strongly coupled in the ultraviolet domain, such a test may look questionable. We propose that the sum over resonance poles emerging in correlators of a bottom-up model should reproduce the structure of a Veneziano like amplitude at zero momentum transfer assuming equivalence of spin and radial states in the latter. This requires a five-dimensional background that suppresses the ultraviolet part in the effective action of a model. We give examples of emerging low-energy holographic models.Comment: 9 pages, accepted by the European Physical Journal C. arXiv admin note: substantial text overlap with arXiv:1102.274

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure