61 research outputs found
Non-Abelian Dipole Radiation and the Heavy Quark Expansion
Dipole radiation in QCD is derived to the second order in . A
power-like evolution of the spin-singlet heavy quark operators is obtained to
the same accuracy. In particular, relation between a
short-distance low-scale running heavy quark mass and the \barMS mass is
given. We discuss the properties of the effective QCD coupling \aw(E) which
governs the dipole radiation. This coupling is advantageous for heavy quark
physics.Comment: 12 pages, Late
Two-loop QCD corrections to the heavy quark pair production cross section in e+e- annihilation near the threshold
We present the O(alpha_s) corrections to the cross section for the reaction
e+e- --> gamma^* --> Q \bar Q in the energy region close to the threshold. We
assume that the energy of the reaction is such that both the perturbative
expansion in the strong coupling constant and expansion in the relative
velocity of the heavy quarks can be used. We explicitly obtain terms
O(alpha_s^2/beta^2, alpha_s^2/beta, alpha_s^2) in the relative correction to
the threshold cross section. Using the ideas of asymptotic expansions, we
demonstrate how an expansion of Feynman diagrams in the threshold region is
constructed. From this analysis we obtain a matching relation between the
vector current in full QCD and the quark-antiquark current in NRQCD at leading
order in 1/m and the second order in the strong coupling constant.Comment: 9 pages, revte
Muonium Decay
Modifications of the mu+ lifetime in matter due to muonium (M = mu+ e-)
formation and other medium effects are examined. Muonium and free mu+ decay
spectra are found to differ at O(alpha m_e/m_mu) from Doppler broadening and
O(alpha^2 m_e/m_mu) from the Coulomb bound state potential. However, both types
of corrections are shown to cancel in the total decay rate due to Lorentz and
gauge invariance respectively, leaving a very small time dilation lifetime
difference, (tau_M - tau_mu+)/tau_mu+ = alpha^2 m_e^2/ 2m_mu^2 \simeq 6\times
10^-10, as the dominant bound state effect. It is argued that other medium
effects on the stopped mu+ lifetime are similarly suppressed.Comment: 14 pages, revte
Gauge dependence and matching procedure of a nonrelativistic QED/QCD boundstate formalism
A nonrelativistic boundstate formalism used in contemporary calculations is
investigated. It is known that the effective Hamiltonian of the boundstate
system depends on the choice of gauge. We obtain the transformation charge Q of
the Hamiltonian for an arbitrary infinitesimal change of gauge, by which gauge
independence of the mass spectrum and gauge dependences of the boundstate wave
functions are dictated. We give formal arguments based on the BRST symmetry
supplemented by power countings of Coulomb singularities of diagrams. For
illustration: (1)we calculate Q up to O(1/c), (2)we examine gauge dependences
of diagrams for a decay of a qqbar boundstate up to O(1/c) and show that
cumbersome gauge cancellations can be circumvented by directly calculating Q.
As an application we point out that the present calculations of top quark
momentum distribution in the ttbar threshold region are gauge dependent. We
also show possibilities for incorrect calculations of physical quantities of
boundstates when the on-shell matching procedure is employed. We give a proof
of a justification for the use of the equation of motion to simplify the form
of a local NRQCD Lagrangian. The formalism developed in this work will provide
useful cross checks in computations involving NRQED/NRQCD boundstates.Comment: 30 pages, 15 figures (ver1); Presentations of Introduction and
Conclusion were modified substantially, although none of our findings have
been changed; Side remarks have been added in various parts of the paper.
(ver2); Supplementary remarks and minor corrections (ver3
On the quest for unification - simplicity and antisimplicity
The road towards unification of elementary interactions is thought to start
on the solid ground of a universal local gauge principle. I discuss the
different types of bosonic gauge symmetries in gravitational and
nongravitational (standard model) interactions and their extensions both
fermionic, bosonic and with respect to space-time dimensions. The apparently
paradoxical size and nature of the cosmological constant is sketched, which at
first sight does not readily yield a clue as to the envelopping symmetry
structure of a unified theory. Nevertheless a tentative outlook is given
encouraging to proceed on this road.Comment: 29 pages, 4 figure
Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution
The complete NNLO QCD corrections to the total cross section in the kinematic region close to the top-antitop
threshold are calculated by solving the corresponding Schroedinger equations
exactly in momentum space in a consistent momentum cutoff regularization
scheme. The corrections coming from the same NNLO QCD effects to the top quark
three-momentum distribution are determined. We discuss
the origin of the large NNLO corrections to the peak position and the
normalization of the total cross section observed in previous works and propose
a new top mass definition, the 1S mass M_1S, which stabilizes the peak in the
total cross section. If the influence of beamstrahlung and initial state
radiation on the mass determination is small, a theoretical uncertainty on the
1S top mass measurement of 200 MeV from the total cross section at the linear
collider seems possible. We discuss how well the 1S mass can be related to the
mass. We propose a consistent way to implement the top quark width
at NNLO by including electroweak effects into the NRQCD matching coefficients,
which then can become complex.Comment: 53 pages, latex; minor changes, a number of typos correcte
The Perturbative QCD Potential and the ttbar Threshold
We include the full second-order corrections to the static QCD potential in
the analysis of the ttbar threshold cross section. There is an unexpectedly
large difference between the QCD potential improved by the
renormalization-group equation in momentum space and the potential improved by
the renormalization-group equation in coordinate space. This difference remains
even at a fairly short distance 1/r \simeq 100 GeV and its origin can be
understood within perturbative QCD. We scrutinize the theoretical uncertainties
of the QCD potential in relation to the ttbar threshold cross section. In
particular there exists a theoretical uncertainty which limits our present
theoretical accuracy of the ttbar threshold cross section at the peak to be not
better than 6% within perturbative QCD.Comment: 16 pages, LaTeX. Improved version of hep-ph/9801419 for submission to
a journa
Inclusive Decays of Heavy Quarkonium to Light Particles
We derive the imaginary part of the potential NRQCD Hamiltonian up to order
1/m^4, when the typical momentum transfer between the heavy quarks is of the
order of Lambda_{QCD} or greater, and the binding energy E much smaller than
Lambda_{QCD}. We use this result to calculate the inclusive decay widths into
light hadrons, photons and lepton pairs, up to O(mv^3 x
(Lambda_{QCD}^2/m^2,E/m)) and O(mv^5) times a short-distance coefficient, for
S- and P-wave heavy quarkonium states, respectively. We achieve a large
reduction in the number of unknown non-perturbative parameters and, therefore,
we obtain new model-independent QCD predictions. All the NRQCD matrix elements
relevant to that order are expressed in terms of the wave functions at the
origin and six universal non-perturbative parameters. The wave-function
dependence factorizes and drops out in the ratio of hadronic and
electromagnetic decay widths. The universal non-perturbative parameters are
expressed in terms of gluonic field-strength correlators, which may be fixed by
experimental data or, alternatively, by lattice simulations. Our expressions
are expected to hold for most of the charmonium and bottomonium states below
threshold. The calculations and methodology are explained in detail so that the
evaluation of higher order NRQCD matrix elements in this framework should be
straightforward. An example is provided.Comment: 61 pages, 9 figures. Minor change
Top quark mass definition and top quark pair production near threshold at the NLC
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, and (3) fixing the new mass which we call the PS-bar mass. We demonstrate
that perturbative predictions for the cross section become much more stable if
we use the PS or the PS-bar mass for the calculations. A careful analysis
suggests that the top quark mass can be extracted from a threshold scan at NLC
with an accuracy of about 100-200 MeV.Comment: published version, 21 pages in LaTeX including 11 PostScript figure
Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation
We use various methods of Borel integration to calculate the binding ground
energies and masses of b-bbar and t-tbar quarkonia. The methods take into
account the leading infrared renormalon structure of the hard+soft part of the
binding energies E(s), and of the corresponding quark pole masses m_q, where
the contributions of these singularities in M(s) = 2 m_q + E(s) cancel.
Beforehand, we carry out the separation of the binding energy into its
hard+soft and ultrasoft parts. The resummation formalisms are applied to
expansions of m_q and E(s) in terms of quantities which do not involve
renormalon ambiguity, such as MSbar quark mass, and alpha_s. The
renormalization scales are different in calculations of m_q, E(s) and E(us).
The MSbar mass of b quark is extracted, and the binding energies of t-tbar and
the peak (resonance) energies for (t+tbar) production are obtained.Comment: 23 pages, 8 double figures, revtex4; the version to appear in
Phys.Rev.D; extended discussion between Eqs.(25) and (26); the paragraph
between Eqs.(32) and (33) is new and explains the numerical dependence of the
residue parameter on the factorization scale; several new references were
added; acknowledgments were modified; the numerical results are unchange
- …