0000000000066968
AUTHOR
Stefan Groote
Positivity bound on the imaginary part of the right-chiral tensor coupling $g_R$ in polarized top quark decay
We derive a positivity bound on the right-chiral tensor coupling Im $g_R$ in polarized top quark decay by analyzing the angular decay distribution of the three-body polarized top quark decay $t(\uparrow)\to b+\ell^+ +\nu_\ell$ in NLO QCD. We obtain the bound $-0.0420 \le$ Im $g_R \le 0.0420$.
Short chaotic strings and their behaviour in the scaling region
Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary conditions, called chaotic strings. In this short note we show that the fine structure of the self energy of this chaotic string in the scaling region (i.e. for very small coupling) is retained if we reduce the length of the string to three lattice points.
On the rigidity of back-to-back top quark pairs in e^+e^- annihilation
We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in $e^+e^-$ annihilation. Our results are presented in terms of the $E_q$-dependence of the $t\bar tg$ cross section and the dependence on the cosine of the opening angle $\theta_{12}$ between top and antitop for a center of mass energy of $\sqrt{q^2}=500 GeV$. We then go on to determine mean values for the top quark's energy as well as its longitudinal and transverse projections, and for the deviation of $\sin\theta_{12}$ and $\cos\theta_{12}$ from the anticollinearity limits $\sin\theta_{12}=0$ and $\cos\theta_{12}=-1$. For a center of mass energy o…
Analytical results forO(αs)radiative corrections toe+e−→tt¯↑up to a given gluon energy cut
We determine the O({alpha}{sub s}) radiative corrections to polarized top quark pair production in e{sup +}e{sup -} annihilations with a specified gluon energy cut. We write down fully analytical results for the unpolarized and polarized O({alpha}{sub s}) cross sections e{sup +}e{sup -}{yields}tt(G) and e{sup +}e{sup -}{yields}tt{sup {up_arrow}}(G) including their polar orientation dependence relative to the beam direction. In the soft-gluon limit we recover the usual factorizing form known from the soft-gluon approximation. In the limit when the gluon energy cut takes its maximum value we recover the totally inclusive unpolarized and polarized cross sections calculated previously. We provi…
Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities
We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make use of the known closed form $p$-space result to express the moment of a product of three Bessel functions in terms of a sum of Claussen polylogarithms. Using results fo…
"Dynamical" interactions and gauge invariance
Appreciating the classical understanding of the elementary particle the "dynamical" Poincare algebra is developed. It is shown that the "dynamical" Poincare algebra and the equations of motion of particles with arbitrary spin are gauge invariant and that gauge invariance and relativistic invariance stand on equal footings. A "dynamical" non-minimal interaction is constructed explicitly and the Rarita-Schwinger equation is considered in the framework of this "dynamical" interaction.
One-Loop Self Energy and Renormalization of the Speed of Light for some Anisotropic Improved Quark Actions
One-loop corrections to the fermion rest mass M_1, wave function renormalization Z_2 and speed of light renormalization C_0 are presented for lattice actions that combine improved glue with clover or D234 quark actions and keep the temporal and spatial lattice spacings, a_t and a_s, distinct. We explore a range of values for the anisotropy parameter \chi = a_s/a_t and treat both massive and massless fermions.
Calculating loops without loop calculations: Next-to-leading order computation of pentaquark correlators
We compute next-to-leading order (NLO) perturbative QCD corrections to the correlators of interpolating pentaquark currents and their absorptive parts. We employ modular techniques in configuration space which saves us from the onus of having to do loop calculations. The modular technique is explained in some detail. We present explicit NLO results for several interpolating pentaquark currents that have been written down in the literature. Our modular approach is easily adapted to the case of NLO corrections to multiquark correlators with an arbitrary number of quarks/antiquarks.
A new technique for computing the spectral density of sunset-type diagrams: integral transformation in configuration space
We present a new method to investigate a class of diagrams which generalizes the sunset topology to any number of massive internal lines. Our attention is focused on the computation of the spectral density of these diagrams which is related to many-body phase space in $D$ dimensional space-time. The spectral density is determined by the inverse $K$-transform of the product of propagators in configuration space. The inverse $K$-transform reduces to the inverse Laplace transform in any odd number of space-time dimensions for which we present an explicit analytical result.
An interpolation of the vacuum polarization function for the evaluation of hadronic contributions to the muon anomalous magnetic moment
We propose a simple parameterization of the two-point correlator of hadronic electromagnetic currents for the evaluation of the hadronic contributions to the muon anomalous magnetic moment. The parameterization is explicitly done in the Euclidean domain. The model function contains a phenomenological parameter which provides an infrared cutoff to guarantee the smooth behavior of the correlator at the origin in accordance with experimental data in e+ e- annihilation. After fixing a numerical value for this parameter from the leading order hadronic contribution to the muon anomalous magnetic moment the next-to-leading order results related to the vacuum polarization function are accurately re…
Longitudinal contribution to the alignment polarization of quarks produced in e + e - -annihilation: an O (α s ) effect
We calculate the longitudinal contribution to the alignment polarization Pl of quarks produced in e+e− annihilation. In the Standard Model, the longitudinal alignment polarization vanishes at the Born term level and thus receives its first non-zero contribution from the O(αs) tree graph process. We provide analytical and numerical results for the longitudinal alignment polarization of massless and massive quarks, in particular for the recently discovered top quark.
On the evaluation of sunset-type Feynman diagrams
We introduce an efficient configuration space technique which allows one to compute a class of Feynman diagrams which generalize the scalar sunset topology to any number of massive internal lines. General tensor vertex structures and modifications of the propagators due to particle emission with vanishing momenta can be included with only a little change of the basic technique described for the scalar case. We discuss applications to the computation of $n$-body phase space in $D$-dimensional space-time. Substantial simplifications occur for odd space-time dimensions where the final results can be expressed in closed form through rational functions. We present explicit analytical formulas fo…
Group theory aspects of chaotic strings
Chaotic strings are a special type of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. Chaotic strings are generated by the Chebyshev maps T2() and T3(). In this paper we connect the Chebyshev maps via the Galois theory to the cyclic groups Z2 and Z3 and give some ideas how this fundamental connection might lead to the emergence of the familiar Lie group structure of particle physics and, finally, even to the emergence of space-time. The Z3-graded cubic and ternary algebras presented here have been introduced by R. Kerner in 1991 and then developed and elaborated in collaboration with many …
Renormalization group approach to chaotic strings
Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic results for the invariant density of chaotic strings, as well as for the coupling parameter dependence of given observables of the chaotic string such as the vacuum expectation value. A highly nontrivial and selfsimilar parameter dependence is found, produced by perturbative and nonperturbative effects, for which we develop a mathematical description in terms of suitable scaling functions. Our analytic results are in good agreement with numerical simulati…
Top quark mass definition andtt¯production near threshold at the Next Linear Collider
We suggest an infrared-insensitive quark mass, defined by subtracting the soft part of the quark self energy from the pole mass. We demonstrate the deep relation of this definition with the static quark-antiquark potential. At leading order in 1/m this mass coincides with the PS mass which is defined in a completely different manner. Going beyond static limit, the small normalization point introduces recoil corrections which are calculated here as well. Using this mass concept and other concepts for the quark mass we calculate the cross section of e+ e- -> t t-bar near threshold at NNLO accuracy adopting three alternative approaches, namely (1) fixing the pole mass, (2) fixing the PS mass, …
Symmetries and similarities for spin orientation parameters in at SM thresholds
Abstract We consider the spin orientation of the final Z bosons for the processes in the Standard Model. We demonstrate that at the threshold energies of these processes the analytical expressions for the Z boson polarization vectors and alignment tensors coincide ( e + e − → Z H , Z γ ) or are very similar ( e + e − → Z Z ). In addition, we present interesting symmetry properties for the spin orientation parameters.
Mass, zero mass and ... nophysics
In this paper we demonstrate that massless particles cannot be considered as limiting case of massive particles. Instead, the usual symmetry structure based on semisimple groups like $U(1)$, $SU(2)$ and $SU(3)$ has to be replaced by less usual solvable groups like the minimal nonabelian group ${\rm sol}_2$. Starting from the proper orthochronous Lorentz group ${\rm Lor}_{1,3}$ we extend Wigner's little group by an additional generator, obtaining the maximal solvable or Borel subgroup ${\rm Bor}_{1,3}$ which is equivalent to the Kronecker sum of two copies of ${\rm sol}_2$, telling something about the helicity of particle and antiparticle states.
Lorentz invariance and gauge equivariance
Trying to place Lorentz and gauge transformations on the same foundation, it turns out that the first one generates invariance, the second one equivariance, at least for the abelian case. This similarity is not a hypothesis but is supported by and a consequence of the path integral formalism in quantum field theory.
Analytical O(αs) corrections to the beam frame double-spin density matrix elements of e+e−→tt¯
We provide analytical results for the $O({\ensuremath{\alpha}}_{s})$ corrections to the double-spin density matrix elements in the reaction ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}t\overline{t}$. These concern the elements $ll$, $lt$, $ln$, $tt$, $tn$, and $nn$ of the double-spin density matrix elements where $l$, $t$, $n$ stand for longitudinal, transverse and normal orientations with respect to the beam frame spanned by the electron and the top quark momentum.
Transcendental numbers and the topology of three-loop bubbles
We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.
Renormalization aspects of chaotic strings
Chaotic strings are a class of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. In this paper we introduce different types and models for chaotic strings, where 2B-strings with finite length are considered in detail. We demonstrate possibilities to extract renormalized quantities, which are expected to describe essential properties of the string.
Polar angle dependence of the longitudinal polarization of quarks produced in e + e - -annihilation
We calculate one-loop radiative QCD corrections to the three polarized and unpolarized structure functions that determine the beam-quark polar angle dependence of the longitudinal polarization of light and heavy quarks produced in e+e−-annihilations. We present analytical and numerical results for the longitudinal polarization and its polar angle dependence. We discuss in some detail the zero-mass limit of our results and the role of the anomalous spin-flip contributions to the polarization observables in the zero-mass limit. Our discussion includes transverse and longitudinal beam polarization effects.
Complete angular analysis of polarized top quark decay atO(αs)
We calculate the O(alpha_s) radiative corrections to the three spin independent and five spin dependent structure functions that describe the angular decay distribution in the decay of a polarized top quark into a W-boson (followed by the decay W^{+} -> l^{+} + nu_l or by W^{+} -> anti-q + q and a bottom quark. The angular decay distribution is described in cascade fashion, i.e. the decay t(uparrow) -> W^{+} + X_b is analyzed in the top rest system while the subsequent decay W^{+} -> l^{+} + nu_l (or W^{+} -> anti-q + q) is analyzed in the W rest frame. We present our results for the eight O(alpha_s) integrated structure functions in analytical form keeping the mass of the bottom quark fini…
O(αs)corrections to the correlator of finite mass baryon currents
We present analytical next-to-leading order results for the correlator of baryonic currents at the three-loop level with one finite mass quark. We obtain the massless and the HQET limit of the correlator from the general formula as particular cases. We also give explicit expressions for the moments of the spectral density.
Gluon polarization ine+e−→tt¯G
We calculate the linear polarization of gluons radiated off top quarks produced in e{sup +}e{sup {minus}} annihilations. For typical top quark pair production energies at the Next Linear Collider the degree of linear polarization remains close to its soft gluon value of 100{percent} over almost the whole energy spectrum of the gluon. The massive quark results are compared with the corresponding results for the massless quark case. {copyright} {ital 1997} {ital The American Physical Society}
Inclusive decays of B mesons into Ds and at O(αs) including polarization effects
The dominant contribution to the inclusive decays of B mesons into the charm-strangeness mesons Ds and Ds∗ is expected to be given by the partonic process b→c+(Ds−,Ds∗−). We determine the nonperturbative O(1/mb2) and the O(αs) radiative corrections to b→c+(Ds−,Ds∗−) and thereby to the inclusive decays B→Xc+(Ds−,Ds∗−). The new feature of our calculation is that we separately determine the nonperturbative and the O(αs) corrections to the longitudinal (L) and transverse (T) pieces of the spin 1 Ds∗− meson. The longitudinal/transverse composition of the Ds∗− can be probed through its two principal decay modes Ds∗−→Ds−+γand Ds∗−→Ds−+π0 for which we write down the angular decay distributions.
Lepton-mass effects in the decays $H \to ZZ^{\ast} \to \ell^{+} \ell^{-} \tau^{+} \tau^{-}$ and $H \to WW^{\ast} \to \ell \nu \tau \nu_{\tau}$
We consider lepton-mass effects in the cascade decays $H\to Z(\to \ell^{+} \ell^{-})+Z^{\ast}(\to \tau^{+}\tau^{-})$ and $H\to W^{-}(\to \ell^{-}\bar \nu_{\ell})+W^{+\ast}(\to \tau^{+}\nu_{\tau})$. Since the scale of the problem is set by the off-shellness $q^{2}$ of the respective gauge bosons in the limits $(m_{\ell}+m_{\ell'})^{2} \le q^{2} \le (m_{H}-m_{W,Z})^{2}$ and not by $m_{W,Z}^{2}$, lepton-mass effects are non-negligible for the $\tau$ modes in particular close to the threshold of the off-shell decays. Lepton-mass effects show up e.g.\ in the three-fold joint angular decay distribution for the decays. Nonzero lepton masses lead to leptonic helicity-flip contributions which in tur…
New High Order Relations between Physical Observables in Perturbative QCD
We exploit the fact that within massless perturbative QCD the same Green's function determines the hadronic contribution to the $\tau$ decay width and the moments of the $e^+e^-$ cross section. This allows one to obtain relations between physical observables in the two processes up to an unprecedented high order of perturbative QCD. A precision measurement of the $\tau$ decay width allows one then to predict the first few moments of the spectral density in $e^+e^-$ annihilations integrated up to $s\sim m_\tau^2$ with high accuracy. The proposed tests are in reach of present experimental capabilities.
Scaling behaviour of non-hyperbolic coupled map lattices
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value.…
Threshold expansion of Feynman diagrams within a configuration space technique
The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.
Two-loop Anomalous Dimensions of Heavy Baryon Currents in Heavy Quark Effective Theory
We present results on the two-loop anomalous dimensions of the heavy baryon HQET currents $J=(q^TC\Gamma\tau q)\Gamma'Q$ with arbitrary Dirac matrices $\Gamma$ and $\Gamma'$. From our general result we obtain the two-loop anomalous dimensions for currents with quantum numbers of the ground state heavy baryons $\Lambda_Q$, $\Sigma_Q$ and $\Sigma_Q^*$. As a by-product of our calculation and as an additional check we rederive the known two-loop anomalous dimensions of mesonic scalar, pseudoscalar, vector, axial vector and tensor currents $(J=\bar q\Gamma q)$ in massless QCD as well as in HQET.
Leptonicμandτdecays: Mass effects, polarization effects, andO(α)radiative corrections
We calculate the radiative corrections to the unpolarized and the four polarized spectrum and rate functions in the leptonic decay of a polarizedinto a polarized electron. The new feature of our calculation is that we keep the mass of the final state electron finite which is mandatory if one wants to investigate the threshold region of the decay. Analytical results are given for the energy spectrum and the polar angle distribution of the final state electron whose longitudinal and transverse polarization is calculated. We also provide analytical results on the integrated spec- trum functions. We analyze the me → 0 limit of our general results and investigate the quality of the me → 0 approx…
Electroweak and finite width corrections to top quark decays into transverse and longitudinal $ W $-bosons
We calculate the electroweak and finite width corrections to the decay of an unpolarized top quark into a bottom quark and a $ W $-gauge boson where the helicities of the $ W $ are specified as longitudinal, transverse-plus and transverse-minus. Together with the $ O(\alpha_s) $ corrections these corrections may become relevant for the determination of the mass of the top quark through angular decay measurements.
On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arb…
Longitudinal, transverse-plus and transverse-minus W-bosons in unpolarized top quark decays at O(alpha_s)
We consider the O(alpha_s) radiative corrections to the decay of an unpolarized top quark into a bottom quark and a W-gauge boson where the helicities of the W are specified as longitudinal, transverse-plus and transverse-minus. The O(alpha_s) radiative corrections lower the normalized longitudinal rate Gamma_L/Gamma by 1.06% and increase the the normalized transverse-minus rate Gamma_-/Gamma by 2.17%. We find that the normalized transverse-plus rate Gamma_+/Gamma, which vanishes at the Born term level for m_b->0, receives radiative correction contributions at the sub-percent level. We discuss m_b!=0 effects for the Born term and the alpha_s-contributions but find these to be small. Our …
Form-factor-independent test of lepton universality in semileptonic heavy meson and baryon decays
In the semileptonic decays of heavy mesons and baryons the lepton-mass dependence factors out in the quadratic $\cos^2\theta$ coefficient of the differential $\cos\theta$ distribution. We call the corresponding normalized coefficient the convexity parameter. This observation opens the path to a test of lepton universality in semileptonic heavy meson and baryon decays that is independent of form-factor effects. By projecting out the quadratic rate coefficient, dividing out the lepton-mass-dependent factor and restricting the phase space integration to the $\tau$ lepton phase space, one can define optimized partial rates which, in the Standard Model, are the same for all three $(e,\mu,\tau)$ …