Search

We prove that the Weyl fractional derivative is a useful instrument to express certain properties of the zeta related functions. Specifically, we show that a known reflection property of the Hurwitz zeta function ¿(n, a) of integer first argument can be extended to the more general case of ¿(s, a), with complex s, by replacement of the ordinary derivative of integer order by Weyl fractional derivative of complex order. Besides, ¿(s, a) with (s) > 2 is essentially the Weyl (s-2)-derivative of ¿(2, a). These properties of the Hurwitz zeta function can be immediately transferred to a family of polygamma functions of complex order defined in a natural way. Finally, we discuss the generalization of a recently unveiled reflection property of the Lerch''s transcendent.

With analytical representation for the pp scattering amplitudes introduced and tested at lower energies, a description of high precision is given of the $d\sigma/dt$ data at $\sqrt{s}$= 13 TeV for all values of the momentum transfer, with explicit identification of the real and imaginary parts. In both $t$ and $b$ coordinates the amplitudes have terms identified as of non-perturbative and perturbative nature, with distinction of their influences in forward and large $|t|$ ranges and in central and peripheral regions respectively. In the forward range, the role of the Coulomb-nuclear interference phase is investigated. The energy dependence of the parameters of the amplitudes are reviewed and updated, revealing a possible emergence of a peculiar behavior of elastic and inelastic profiles in b-space for central collisions, which seems to be enhanced quickly at higher energies. Some other models are also briefly discussed in comparison, including the above mentioned behavior in b-space., Comment: 22 pages, 26 figures

Exact analytical forms of solutions for Dispersion Relations for Amplitudes and Dispersion Relations for Slopes are applied in the analysis of pp and $\rm {p \bar p}$ scattering data in the forward range at energies below $\sqrt(s)\approx 30 \GeV$. As inputs for the energy dependence of the imaginary part, use is made of analytic form for the total cross sections and for parameters of the $t$ dependence of the imaginary parts, with exponential and linear factors. A structure for the $t$ dependence of the real amplitude is written, with slopes $B_R$ and a linear factor $\rho-\mu_R t$ that allows compatibility of the data with the predictions from dispersion relations for the derivatives of the real amplitude at the origin. A very precise description is made of all $d\sigma/dt$ data, with regular energy dependence of all quantities. It is shown that a revision of previous calculations of total cross sections, slopes and $\rho$ parameters in the literatures is necessary, and stressed that only determinations based on $d\sigma/dt$ data covering sufficient $t$ range using appropriate forms of amplitudes can be considered as valid.

Based on a study of the properties of the Lerch's transcendent, exact closed forms of dispersion relations for amplitudes and for derivatives of amplitudes in pp and pp scattering are introduced. Exact and complete expressions are written for the real parts and for their derivatives at $t=0$ based on given inputs for the energy dependence of the total cross sections and of the slopes of the imaginary parts. The results are prepared for application in the analysis of forward scattering data of the pp and pp systems at all energies, where exact and precise representations can be written.

Recent measurements of the differential cross sections in the forward region of pp elastic scattering at 7 and 8 TeV show precise form of the $t$ dependence. We propose a detailed analysis of these measurements including the structures of the real and imaginary parts of the scattering amplitude. A good description is achieved, confirming in all experiments the existence of a zero in the real part in the forward region close to the origin, in agreement with the prediction of a theorem by A. Martin, with important role in the observed form of $d\sigma/dt$. Universal value for the position of this zero and regularity in other features of the amplitudes are found, leading to quantitative predictions for the forward elastic scattering at 13 TeV., Comment: 22 pages, 17 figures and 4 tables

A discussion is presented of pp and p p ¯ scattering at high energies which satisfies the requirements of dispersion relations and of a theorem by A. Martin about the zero of the real amplitude. In particular the use of Derivative Dispersion Relations is extended to the control of the slopes of the real and imaginary amplitudes.

A gauge-invariant saddle point expansion for the Yang-Mills vacuum transition amplitude on the basis of the squeezed approximation to the vacuum wave functional is outlined. This framework allows the identification of gauge-invariant infrared degrees of freedom which arise as dominant sets of gauge field orbits and provide the principal input for an essentially analytical treatment of soft amplitudes. The analysis of the soft modes sheds new light on how vacuum fields organize themselves into collective excitations and yields a gauge-invariant representation of instanton and meron effects as well as a new physical interpretation for Faddeev-Niemi knots., Comment: 4 pages

Solutions for the amplitudes that give accurate description of pp and [Formula: see text] scattering at high energies are investigated, with particular attention given to the properties of their zeros and slopes, whose determination is required for the study of the Coulomb interference region. Proper extrapolations of these quantities to the LHC energies are important for the analysis of the forthcoming experiments.

We extend the use of derivative dispersion relations to the study of slopes of the real and imaginary amplitudes in pp and [Formula: see text] elastic scattering. The new relations are tested against the solutions for the amplitudes obtained in the analysis of the high energy data. Extensions beyond the forward direction are investigated.

In a first order theory of dissipative hydrodynamics, we have simulated hydrodynamic evolution of QGP fluid with dissipation due to shear viscosity only. Simulation confirms that compared to an ideal fluid, energy density or temperature of a viscous fluid evolve slowly. Transverse expansion is also more in viscous fluid. We also study the effect of viscosity on particle production. Particle production is enhanced, more at large pT. The elliptic flow on the otherhand decreases and shows a tendency to saturate at large pT.

Elastic vector meson electroproduction is calculated through integrals of the overlap product of photon and vector meson wave functions, multiplied by the amplitude for the scattering of $q \bar{q}$ dipole pairs off the proton. In this nonperturbative QCD calculation, for sizes of the overlap functions that are smaller than the typical ranges of the interaction of the dipoles with the proton, the amplitudes factorize, with overlap strengths (integration extended over the light front coordinates describing the $q \bar{q}$ dipoles) containing all Q² dependence of the observables. This factorization is important in the description of the experimental data for all S-wave vector mesons.

We present a nonperturbative QCD calculation of elastic $J/\psi$ meson production in photon-proton scattering at high energies. Using light cone wave functions of the photon and vector mesons, and the framework of the model of the stochastic QCD vacuum, we calculate the differential and integrated elastic cross sections for $\gamma p \goto J/\psi p $ . With an energy dependence following the two-pomeron model we are able to give a consistent description of the integrated cross sections and the differential cross sections at low $|t|$ in the range from 20 GeV up to the highest HERA energies. We discuss different approaches to introduce saturation and find no specific effects up to energies presently available. We also calculate and compare to experiments the cross section for $\upsilon$ photoproduction., Comment: 24 pages, 10 figures, 4 tables

Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all high energy region, the behavior of observables in the LHC collisions in the range $\sqrt{s}$ = 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV., Comment: 4 pages, 4 figures Contribution to Proceedings of DIFFRACTION 2014

Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energy region, the behavior of observables in the LHC collisions in the range $\sqrt{s}$= 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV., 16 pages, 17 figures

An analysis of p-air cross section data from Extensive Air Shower (EAS) measurements is presented, based on an analytical representation of the pp scattering amplitudes that describes with high precision all available accelerator data at ISR, SPS and LHC energies. The theoretical basis of the representation, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permits reliable extrapolation to high energy cosmic ray and asymptotic energy ranges. Calculations of the p-air production cross section based on Glauber formalism are made using the input values of the pp forward scattering parameters at high energies, with attention given to the independence of the real and imaginary slope parameters. The influence of contributions of diffractive intermediate states, according to Good-Walker formalism, is examined. The comparison with cosmic ray data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behavior of p-air cross sections is investigated in view of the geometric scaling property of the pp amplitudes. The observed energy dependence of the ratio between p-air and pp cross sections in the data is shown to be related to the nature of the pp cross section at high energies, that does not agree with the black disk image., 18 pages, 11 figures

Photo and DIS production of $J/\Psi$ are investigated and compared with calculations based on pQCD in the LLA approximation without and with screening corrections. The calculation includes corrections induced by the real part of the production amplitude, the skewed (off diagonal) gluon structure function and the relativistic Fermi motion within the charmonium system. Our pQCD results are also compared with the predictions obtained from a Regge type two Pomeron model. Our results suggest some preference for our screened model, but the available data does not enable us to exclude any of the three models we have examined. The properties of these models, when extrapolated to both low and very high energies may provide a more effective discrimination between the different parameterizations., Comment: 10 pages, 5 figures in eps files

We examine the latest HERA experimental measurements of the $Q^2$ logarithmic derivative of the proton structure function. We analyze the characteristics of DGLAP with and without screening, as well as a Regge type model, and compare their predictions to all available data on $\slope$ including those for fixed W. Our results show that the present data can be described in pQCD taking into account shadowing corrections. However, such a description cannot be considered a conclusive signal of gluon saturation since the experimental data on $\slope$ do not allow one to discriminate between the various approaches, in spite of their very different construction., 15 pages, & figs in eps files

We investigate the possibility that the process of phi photoproduction may have a significant hard perturbative QCD component. This suggestion is based on a study of the energy dependence of the forward phi photoproduction cross section followed by a calculation where we show that a coherent sum of the pQCD and conventional soft Pomeron contributions provides an excellent reproduction of the experimental data. Our results suggest that the transition from the predominantly soft photoproduction of light rho and omega vector mesons to the predominantly hard photoproduction of heavy J/psi and upsilon is smooth and gradual, similar to the transition observed in deep inelastic scattering studies of the proton structure function in the small x limit. Our predictions for higher HERA energies are presented.

In this work we calculate the form factors of the Λ c and Λ b semileptonic decay using the QCD sum ruels approach. We found that the form factors sum rules are more stable than the respective mass sum rules, and we get a decay rate for Λ c compatible with experiment.

A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to construct the real part, and consist of new mathematical structures of double infinite summations of derivatives. In this new form the derivatives are calculated at the generic value of the energy $E$ and separately at the reference point $E=m$ that is the lower limit of the integration. This new form may be more interesting in certain circumstances and directly shows the origin of the difficulties in convergence that were present in the old truncated forms called standard-DDR. For all cases in which the reductions of the double to single sums were obtained in our previous work, leading to explicit demonstration of convergence, these new expressions are seen to be identical to the previous ones. We present, as a glossary, the most simplified explicit results for the DDR's in the cases of imaginary amplitudes of forms $(E/m)^\lambda[\ln (E/m)]^n$, that cover the cases of practical interest in particle physics phenomenology at high energies. We explicitly study the expressions for the cases with $\lambda$ negative odd integers, that require identification of cancelation of singularities, and provide the corresponding final results., Comment: The final publication is available at http://scitation.aip.org/content/aip/journal/jmp

The two independent correlation functions describing nonperturbative properties of the QCD vacuum are taken into account in the evaluation of the observables of soft high-energy hadron-hadron scattering. The model of the stochastic vacuum provides the framework in which a simple and effective description of the high-energy pp and {bar p}p data can be given, leading to a determination of relevant parameters of nonperturbative QCD and to a good description of the data. The ratio between the non-Abelian and the Abelian parts of the field correlations is studied in terms only of high-energy data and the results are compared to lattice calculations. It is shown that a slow increase of the hadronic radii with the energy accounts for the energy dependence of all observables. {copyright} {ital 1997} {ital The American Physical Society}

The data on $\mathrm{p}\overline{\mathrm{p}}$ elastic scattering at 1.8 and 1.96 TeV are analyzed in terms of real and imaginary amplitudes, in a treatment with high accuracy, covering the whole $t$ range, and satisfying the expectation of dispersion relation for amplitudes and for slopes. A method is introduced for the determination of the total cross section and the other forward scattering parameters and to check compatibility of E-710, CDF, and the recent D0 data. Slopes ${B}_{R}$ and ${B}_{I}$ of the real and imaginary amplitudes, treated as independent quantities, influence the amplitudes in the whole $t$ range and are important for the determination of the total cross section. The amplitudes are fully constructed, and a prediction is made of a marked dip in $d\ensuremath{\sigma}/dt$ in the $|t|$ range $3--5\text{ }\text{ }{\mathrm{GeV}}^{2}$ due to the universal contribution of the process of three-gluon exchange.

A precise analysis of the pp elastic scattering data at 7 TeV in terms of its amplitudes is performed as an extension of previous studies for lower energies. Slopes B R and B I of the real and imaginary amplitudes are independent quantities, and a proper expression for the Coulomb phase is used. The real and imaginary amplitudes are fully disentangled, consistently with forward dispersion relations for amplitudes and for slopes. We present analytic expressions for the amplitudes that cover all t range completely, while values of total cross section σ, ratio ρ, B I , and B R enter consistently to describe forward scattering. It is stressed that the identification of the amplitudes is an essential step for the description of elastic scattering, and pointed out the importance of the experimental investigation of the transition range from non-perturbative to perturbative dynamics, which may confirm the three gluon exchange mechanism observed at lower energies.

Hadronic corrections to the form factors of semileptonic {ital D} and {ital B} decays are evaluated. It is shown that these effects cannot be responsible for the existing discrepancy between theory and experiment in the values of the ratio of longitudinal and transversal polarizations of the {ital {bar K}}{sup 0*} meson in the decay {ital D}{sup +}{r arrow}{ital {bar K}}{sup 0*}{ital e+}{nu}. The effects of the hadronic corrections are shown to be even weaker in the case of the {ital B}{sup +}{r arrow}{ital {bar D}}{sup 0*}{ital e+}{nu} decay.

The equation of motion for the Skyrme model with a pion mass term is studied in the framework of the Painleve analysis, and information is obtained about the singularity structure of its solutions. As in the massless case, singularities exist, consisting of a first‐order pole term superposed to a logarithmic branch point. For the solitonic solutions, the singularities form an infinite sequence of points located on the negative real axis of the squared radial variable, accumulating at the origin. Based on this property and on the asymptotic behavior of the solitonic solutions, an approximate representation is built for the baryonic soliton, which is extremely accurate.

The singularity structure of the solutions of the equations of motion for the Sigma and Skyrme model Lagrangians with the hedgehog ansatz is investigated. In both cases the solutions present superposed a polelike term and a logarithmic branch point. The set of solitonic configurations of the Skyrme model is characterized by the sequence of locations of their singularities on the negative real axis of the dimensionless variable z = (eFπr)2, with an accumulation point at z=0. The first few terms of the Laurent series representing the Skyrme soliton profile are shown to reproduce well the exact values in an interval about the origin. Pade approximants to the residual power series obtained after subtraction of the dominant pole term are modified in order to satisfy the constraints imposed by the asymptotic power series expansion, and approximate representations are built for the Skyrme soliton configuration, which are shown to combine simplicity with accuracy.

All kinds of solution of the Euler–Lagrange equation obtained from the chiral nonlinear sigma model Lagrangian with the hedgehog ansatz for the SU(2) field are investigated. Making use of the scale invariance of the equation of motion, the solutions are classified in families, according to their analytic properties. It will be shown that the energy integral diverges for all possible classes of solution, and that a finite topological charge can be defined for only one class of solution, and has only one possible numerical value (and its negative).

Properties of the Euler–Lagrange differential equation for cos F, where F is the chiral angle of the classical Skyrme soliton in the hedgehog ansatz, are investigated. The power series solution for y=cos F, is obtained that presents the behavior of an almost geometric series, and the existence of single poles located at imaginary values of the radial variable r is shown. Pade approximants are built to the series expansion about the origin, and its terms are modified in order to incorporate the main features of the asymptotic behavior of the field configuration. Thus rational fractions are constructed which provide very good and practical analytical representations of the Skyrme soliton profile function.

The z-zeros of the modified Bessel function of the third kind K_{nu}(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order nu. Approximate expressions for the zeros, applicable in the cases of very small or very large |nu|, are given. The behaviour of the zeros for varying |nu| or arg(nu), obtained numerically, is illustrated by means of some graphics., 14 pages, 3 figures, 1 table. Added a table illustrating the numerical procedure

We study derivative dispersion relations for t not zero, investigating properties of real and imaginary amplitudes in pp and pp elastic scatterings.

We present a nonperturbative QCD calculation of elastic \(J/\psi\) meson production in photon-proton scattering at high energies. Using light cone wave functions of the photon and vector mesons, and the framework of the model of the stochastic QCD vacuum, we calculate the differential and integrated elastic cross sections for \(\gamma p \rightarrow J/\psi p \). With an energy dependence following the two-pomeron model we are able to give a consistent description of the integrated cross sections and the differential cross sections at low |t| in the range from 20 GeV up to the highest HERA energies. We discuss different approaches to introduce rescattering corrections and find no specific effects up to energies presently available. We also calculate and compare to experiments the cross section for \(\Upsilon\) photoproduction.

A nonperturbative calculation of elastic electroproduction of the J/psi meson is presented and compared to the experimental data. Our model describes well the observed dependences of the cross sections on the photon virtuality Q2 and on the energy, and the measured ratio R of longitudinal to transverse cross sections., Five *.eps figures

Applying the recently constructed analytic representation for the pp scattering amplitudes, we present a study of p-air cross sections, with comparison to the data from Extensive Air Shower (EAS) measurements. The amplitudes describe with precision all available accelerator data at ISR, SPS and LHC energies, and its theoretical basis, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permit reliable extrapolation to higher energies and to asymptotic ranges. The comparison with cosmic ray data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behaviour of cross sections is investigated in view of the geometric scaling property of the amplitudes. The amplitudes predict that the proton does not behave as a black disk even at asymptotically high enegies, and we discuss possible non-trivial consequences of this fact for pA collision cross sections at higher energies. dependence. This is a new finding, since the generally accepted idea is that the slope of the differential cross sections varies like simple linear logs, as in Regge phenomenology. This result has a crucial effect for the use of Glauber formalism in the analysis of p-air extended showers at the high energies of our concern, since the value of the slope BI, together with the value of the total cross section, are the basic inputs of the calculation. For the application of the standard Glauber approach, we basically need the amplitudes in forward scattering. In these conditions our amplitudes take simpler exponential forms requiring only two parameters to specify each amplitude. The relevant parameters are then the total cross section σ, the ratio ρ between real and imaginary parts at t = 0, and the slopes BI and BR of each of the two parts. Our full-t analysis (5) provides the energy dependence of these quantities with simple analytical forms that are appropriate for the whole energy range from 50GeV to 100TeV. On the other hand, the log 2 s dependence of the slopes is intimately related to the unitarity condition, as can be seen more clearly in the b-space representation. Another interesting consequences of our representation is that a proton does not behave as a black disk even in asymptotic energy domain. This fact also has important consequences to the estimate of pA collision cross section in the ultra- high energy domain.

We report on some aspects of the activities in Hadron Physics and Relativistic Nuclear Physics in some Latin American countries.

We summarize the contributed papers and the talks in the plenary and parallel sessions in this XXI Brazilian National Meeting on Particles and Fields that are classified as of phenomenology kind. We try to put the activities here developed in the perspective of the existing community of phenomenologists in Brazil 2000.

We review the role of the QCD vacuum structure in the determination of the properties of states and processes occurring in the confinement regime of QCD. The vacuum correlation model of non-perturbative QCD is mentioned as a bridge between the fundamental theory and the description of the experiments. The model of the stochastic vacuum provides the framework in which a simple and effective description of the high-energy pp and p data can be given, leading to a determination of relevant parameters of non-perturbative QCD and to a good description of the data. A slow increase of the hadronic radii with the energy accounts for the energy dependence of all observables.

The dips observed in the differential cross sections of elastic pp and p$\bar{\rm p}$ scattering are studied in terms of the locations of the zeros of the real and imaginary parts of the amplitude and of the sign of real part at large $|t|$. It is confirmed that the differences in shapes of the dips in the pp and p$\bar{\rm p}$ systems are determined by a change of sign of the real tail, which seems to be determined by perturbative QCD contributions.

QCD sum rules for the determination of form factors of $\Lambda_b$ and $\Lambda_c$ semileptonic decays are investigated. With a form for the baryonic current appropriate for the limits of the heavy quark symmetries, the different tensor structures occurring in the two- and three-point functions are separately studied, and in each case general relations are written for the form factors. Particular attention is given to the treatment of the kinematical region ascribed to the continuum. The $t$-dependence of the form factors and the decay rates are numerically evaluated and compared to experimental information., Comment: 45 pages, 14 figures

The eikonal profile function $J(b)$ obtained from the model of the stochastic vacuum is parametrized in a form suitable for comparison with experiment. The amplitude and the extended profile function (including imaginary and real parts) are determined directly from the complete pp and $\overline{p}p$ elastic scattering data at high energies. A full and accurate representation of the data is presented, with a smooth energy dependence of all parameters. The changes needed in the original profile function required for the description of scattering beyond the forward direction are described.

We set up sum rules for heavy lambda decays in a full QCD calculation which in the heavy quark mass limit incorporates the symmetries of heavy quark effective theory. For the semileptonic $\La_c$ decay we obtain a reasonable agreement with experiment. For the $\La_b$ semileptonic decay we find at the zero recoil point a violation of the heavy quark symmetry of about 20%., Comment: Revised version. Title changed. 11 pages (RevTex), 4 PS figures

The functional dependence of the high-energy observables of total cross section and slope parameter on the sizes of the colliding hadrons predicted by the model of the stochastic vacuum and the corresponding relations used in the geometric model of Povh and H\"ufner are confronted with the experimental data. The existence of a universal term in the expression for the slope, due purely to vacuum effects, independent of the energy and of the particular hadronic system, is investigated. Accounting for the two independent correlation functions of the QCD vacuum, we improve the simple and consistent description given by the model of the stochastic vacuum to the high-energy pp and pbar-p data, with a new determination of parameters of non-perturbative QCD. The increase of the hadronic radii with the energy accounts for the energy dependence of the observables., Comment: Latex, using Revtex.style . 2 ps figures. To be published in Physical Review D , July 1997