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Bernd A. Kniehl

Publications and source records attributed to Bernd A. Kniehl.

At least 73 records · Page 4Linked to original sources
arXiv2012

Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions

We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.

hep-th↗
arXiv2012

Bottom-flavored hadrons from top-quark decay at next-to-leading order in the general-mass variable-flavor-number scheme

We study the scaled-energy (x_B) distribution of bottom-flavored hadrons (B) inclusively produced in top-quark decays at next-to-leading order (NLO) in the general-mass variable-flavor-number scheme endowed with realistic, nonperturbative fragmentation functions that are obtained through a global fit to e^+e^- data from CERN LEP1 and SLAC SLC exploiting their universality and scaling violations. Specifically, we study the effects of gluon fragmentation and finite bottom-quark and B-hadron masses. We find the NLO corrections to be significant. Gluon fragmentation leads to an appreciable reduction in the partial decay width at low values of x_B. Hadron masses are responsible for the low-x_B threshold, while the bottom-quark mass is of minor importance. Neglecting the latter, we also study the doubly differential distribution d^2Gamma/[dx_B dcos(theta)] of the partial width of the decay t -> b W^+ -> B l^+ nu_l + X, where theta is the decay angle of the charged lepton in the W-boson rest frame.

hep-ph↗
arXiv2012

J/psi polarization at Tevatron and LHC: Nonrelativistic-QCD factorization at the crossroads

We study the polarization observables of J/psi hadroproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics. We complete the present knowledge of the relativistic corrections by also providing the contribution due to the intermediate ^3P_J^{[8]} color-octet states at this order, which turns out to be quite significant. Exploiting the color-octet long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/psi production, we provide theoretical predictions in the helicity and Collins-Soper frames and compare them with data taken by CDF at Fermilab Tevatron I and II and by ALICE at CERN LHC. The notorious CDF J/psi polarization anomaly familiar from leading-order analyses persists at the quantum level, while the situation looks promising for the LHC, which is bound to bring final clarification.

hep-ph↗
arXiv2012

Renormalization in general theories with inter-generation mixing

We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties.

hep-ph↗
arXiv2012

J/psi production in NRQCD: A global analysis of yield and polarization

We present a rigorous next-to-leading order analysis of J/psi yield and polarization within the factorization theorem of nonrelativistic QCD (NRQCD). To the orders considered, this framework depends on three free parameters, the color-octet long-distance matrix elements. We extract their values in a global fit to inclusive J/psi production data from various hadroproduction, photoproduction, two-photon scattering and electron-positron annihilation experiments. We show that this fit is constrained and stable and describes all data sufficiently well. We then make predictions for J/psi polarization in photo- and hadroproduction and compare them to the currently available data. As for photoproduction, HERA data is not precise enough to draw definite conclusions. But as for hadroproduction, CDF data measured at Tevatron run II is in strong conflict with NRQCD predictions. With early ALICE data being however compatible with NRQCD, the future, more precise polarization measurements at the LHC will thus have the potential to clearly confirm or dismiss LDME universality.

hep-ph↗
arXiv2011

Associated production of Z and neutral Higgs bosons at the CERN Large Hadron Collider

We study the hadroproduction of a CP-even or CP-odd neutral Higgs boson in association with a Z boson in the minimal supersymmetric extension of the standard model (MSSM) We include the contributions from quark-antiquark annihilation at the tree level and those from gluon-gluon fusion, which proceeds via quark and squark loops, and list compact analytic results. We quantitatively analyze the hadronic cross sections at the CERN Large Hadron Collider assuming a favorable supergravity-inspired MSSM scenario.

hep-ph↗
arXiv2011

Probing nonrelativistic QCD factorization in polarized J/psi photoproduction at next-to-leading order

We analyze the polarization observables of J/psi photoproduction at next-to-leading order (NLO) within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD). This is the first NLO study of heavy-quarkonium polarization including the full relativistic corrections due to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]} color-octet (CO) states in the worldwide endeavor to test NRQCD factorization at the quantum level. We present theoretical predictions in the helicity, target, and Collins-Soper frames of DESY HERA, evaluated using the CO long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/psi production, and confront them with recent measurements by the H1 and ZEUS Collaborations. We find the overall agreement to be satisfactory, but the case for NRQCD to be not as strong as for the J/psi yield.

hep-ph↗
arXiv2011

Finding new relationships between hypergeometric functions by evaluating Feynman integrals

Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F_1. From the comparison of this expression with a previously known one, a new relation between the Appell functions F_1 and F_4 is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F_1 function with particular arguments to the hypergeometric function _3F_2 is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F_1 functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F_1 function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F_1 function and the Gaussian hypergeometric function _2F_1 whose argument is the ratio of polynomials of degree six is presented.

math-ph↗
arXiv2011

Counting master integrals: integration by parts vs. differential reduction

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the master integrals of the two-loop sunset diagram that does not follow from the integration-by-parts technique is found.

math-ph↗
arXiv2011

Ultrahigh-energy neutrino-nucleon deep-inelastic scattering and the Froissart bound

We present a simple formula for the total cross section sigma^{nu N} of neutral- and charged-current deep-inelastic scattering of ultrahigh-energy neutrinos on isoscalar nuclear targets, which is proportional to the structure function F_2^{nu N}(M_V^2/s, M_V^2), where M_V is the intermediate-boson mass and s is the square of the center-of-mass energy. The coefficient in the front of F_2^{nu N}(x, Q^2) depends on the asymptotic low-x behavior of F_2^{nu N}. It contains an additional ln(s) term if F_2^{nu N} scales with a power of ln(1/x). Hence, an asymptotic low-x behavior F_2^{nu N} propto ln^2(1/x), which is frequently assumed in the literature, already leads to a violation of the Froissart bound on sigma^{nu N}.

hep-ph↗
arXiv2011

World data of J/psi production consolidate NRQCD factorization at NLO

We calculate the cross sections of inclusive J/psi production in photoproduction and two-photon scattering, involving both direct and resolved photons, and in e^+e^- annihilation at next-to-leading order (NLO) within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the full relativistic corrections due to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]} color-octet (CO) states. Exploiting also our previous results on hadroproduction, we perform a combined fit of the respective CO long-distance matrix elements (LDMEs) to all available high-quality data of inclusive J/psi production, from KEKB, LEP~II, RHIC, HERA, the Tevatron, and the LHC, comprising a total of 194 data points from 26 data sets.

hep-ph↗
arXiv2011

Quark mixing renormalization effects in the determination of |V_{tq}|

We study the numerical effects of several renormalization schemes of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix on the top-quark decay widths. We then employ these results to infer the relative shifts in the CKM parameters |V_{tq}|^2 due to the quark mixing renormalization corrections, assuming that they are determined directly from the top-quark partial decay widths, without imposing unitarity constraints. We also discuss the implications of these effects on the ratio R = Gamma(t -> Wb) / Gamma_t and the determination of |V_{tb}|^2.

hep-ph↗
arXiv2011

Reconciling J/psi production at HERA, RHIC, Tevatron, and LHC with NRQCD factorization at next-to-leading order

We calculate the cross section of inclusive direct J/psi hadroproduction at next-to-leading order (NLO) within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the full relativistic corrections due to the intermediate 1S_0^[8], 3S_1^[8], and 3P_J^[8] color-octet states. We perform a combined fit of the color-octet (CO) long-distance matrix elements to the transverse-momentum (p_T) distributions measured by CDF at the Fermilab Tevatron and H1 at DESY HERA and demonstrate that they also successfully describe the p_T distributions from PHENIX at BNL RHIC and CMS at the CERN LHC as well as the photon-proton c.m. energy and (with worse agreement) the inelasticity distributions from H1. This provides a first rigorous test of NRQCD factorization at NLO. In all experiments, the CO processes are shown to be indispensable.

hep-ph↗
arXiv2010

J/psi production with NRQCD: HERA, Tevatron, RHIC and LHC

We report on our recent calculation of the inclusive direct photo- and hadroproduction of the J/psi meson at next-to-leading order within the factorization formalism of nonrelativistic QCD. We fit the color-octet (CO) long-distance matrix elements , and to the transverse momentum (p_T) distributions measured by CDF at Fermilab Tevatron and by H1 at DESY HERA and show that they also successfully describe the p_T distributions from PHENIX at BNL RHIC and CMS at the CERN LHC as well as the photon-proton c.m. energy and (with worse agreement) the inelasticity distributions from H1. In all experiments, the CO processes are shown to be indispensable.

hep-ph↗
arXiv2010

Direct J/psi photoproduction at next-to-leading-order in nonrelativistic QCD

We calculate the cross section of inclusive direct J/psi photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics, for the first time including the full relativistic corrections due to the intermediate ^1S_0^{[8]}, ^3S_1^{[8]}, and ^3P_J^{[8]} color-octet states. A comparison of our results to recent H1 data suggests that the color octet mechanism is indeed realized in J/psi photoproduction, although the predictivity of our results still suffers from uncertainties in the color-octet long-distance matrix elements.

hep-ph↗
arXiv2010

Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed.

hep-th↗