1,060 research outputs found
Fixing the conformal window in QCD
A physical characterization of Landau singularities is emphasized, which
should trace the lower boundary N_f^* of the conformal window in QCD and
supersymmetric QCD. A natural way to disentangle ``perturbative'' from
``non-perturbative'' contributions to amplitudes below N_f^* is suggested.
Assuming an infrared fixed point persists in the perturbative part of the QCD
coupling even below N_f^* leads to the condition \gamma(N_f^*)=1, where \gamma
is the critical exponent. Using the Banks-Zaks expansion, one gets 4<N_f^*<6.
This result is incompatible with the existence of an analogue of Seiberg
duality in QCD. The presence of a negative ultraviolet fixed point is required
both in QCD and in supersymmetric QCD to preserve causality within the
conformal window. Evidence for the existence of such a fixed point in QCD is
provided.Comment: 10 pages, 1 figure, extended version of a talk given at the
QCDNET2000 meeting, Paris, September 11-14 2000; main new material added is
evidence for negative ultraviolet fixed point in QC
Conformal expansions and renormalons
The large-order behaviour of QCD is dominated by renormalons. On the other
hand renormalons do not occur in conformal theories, such as the one describing
the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since
the fixed-point has a perturbative realization, all-order perturbative
relations exist between the conformal coefficients, which are renormalon-free,
and the standard perturbative coefficients, which contain renormalons.
Therefore, an explicit cancellation of renormalons should occur in these
relations. The absence of renormalons in the conformal limit can thus be seen
as a constraint on the structure of the QCD perturbative expansion. We show
that the conformal constraint is non-trivial: a generic model for the
large-order behaviour violates it. We also analyse a specific example, based on
a renormalon-type integral over the two-loop running-coupling, where the
required cancellation does occur.Comment: 10 pages, to appear in Phys. Lett.
RS-invariant all-orders renormalon resummations for some QCD observables
We propose a renormalon-inspired resummation of QCD perturbation theory based
on approximating the renormalization scheme (RS) invariant effective charge
beta-function coefficients by the portion containing the highest power of
=--, for SU() QCD with quark flavours.
This can be accomplished using exact large- all-orders results. The
resulting resummation is RS-invariant and the exact next-to-leading order (NLO)
and next-to-NLO (NNLO) coefficients in any RS are included. This improves on a
previously employed naive resummation of the leading- piece of the
perturbative coefficients which is RS-dependent, making its comparison with
fixed-order perturbative results ambiguous. The RS-invariant resummation is
used to assess the reliability of fixed-order perturbation theory for the
-ratio, the analogous -lepton decay ratio , and
Deep Inelastic Scattering (DIS) sum rules, by comparing it with the exact NNLO
results in the effective charge RS. For the -ratio and , where
large-order perturbative behaviour is dominated by a leading ultra-violet
renormalon singularity, the comparison indicates fixed-order perturbation
theory to be very reliable. For DIS sum rules, which have a leading infra-red
renormalon singularity, the performance is rather poor. In this way we estimate
that at LEP/SLD energies ideal data on the -ratio could determine
to three-significant figures, and for the we
estimate a theoretical uncertainty
corresponding to . This encouragingly small
uncertainty is much less than has recently been deduced from comparison with
the ambiguous naive resummation.Comment: 25 pages, uses LaTeX, 12 Postscript figures, epsfig.sty 'elsart.sty'
and 'elsart12.sty' are available via anonymous-ftp at
ftp://ftp.tex.ac.uk/tex-archive/macros/latex/contrib/supported/elsevie
The 4-loop quark mass anomalous dimension and the invariant quark mass
We present the analytical calculation of the four-loop quark mass anomalous
dimension in Quantum Chromodynamics within the minimal subtraction scheme. On
the basis of this result we find that the so-called invariant quark mass is a
very good reference mass for the accurate evolution of the running MS-bar quark
mass in phenomenological applications. We also obtain for the first time a
complete 4-th order perturbative QCD expression for a physical quantity, the
total Higgs boson decay rate into hadrons, and analyze the infrared fixed point
for this case.Comment: 11 pages, Late
Infrared Renormalons and Finite Volume
We analyze the perturbative expansion of a condensate in the O(N) non-linear
sigma model for large N on a two dimensional finite lattice. On an infinite
volume this expansion is affected by an infrared renormalon. We extrapolate
this analysis to the case of the gluon condensate of Yang-Mills theory and
argue that infrared renormalons can be detected by performing perturbative
studies even on relatively small lattices.Comment: LaTeX file, 6 figures in postscrip
Infrared renormalons and analyticity structure in pQCD
Relation between the infrared renormalons, the Borel resummation
prescriptions, and the analyticity structure of Green functions in perturbative
QCD (pQCD) is investigated. A specific recently suggested Borel resummation
prescription resulted in the Principal Value and an additional power-suppressed
correction that is consistent with the Operator Product Expansion. Arguments
requiring the finiteness of the result for any power coefficient of the leading
infrared renormalon, and the consistency in the case of the absence of that
renormalon, require that this prescription be modified. The apparently most
natural modification leads to the result represented by the Principal Value.
The analytic structure of the amplitude in the complex coupling plane, obtained
in this way, is consistent with that obtained in the literature by other
methods.Comment: 6 pages, revtex4, 1 eps-figure; improved version - the paragraph
containing Eqs.(18) and (19) is new, as well as the next paragraph; the Title
modified; some references added; version to appear in Phys. Rev.
QCD Corrections to t anti-b H^- Associated Production in e^+ e^- Annihilation
We calculate the QCD corrections to the cross section of e^+ e^- -> t anti-b
H^- and its charge-conjugate counterpart within the minimal supersymmetric
extension of the Standard Model. This process is particularly important if m_t
b H^+ and e^+ e^- -> H^+ H^- are
not allowed kinematically. Large logarithmic corrections that arise in the
on-mass-shell scheme of quark mass renormalization, especially from the t
anti-b H^- Yukawa coupling for large values of tan(beta), are resummed by
adopting the modified minimal-subtraction scheme, so that the convergence
behavior of the perturbative expansion is improved. The inclusion of the QCD
corrections leads to a significant reduction of the theoretical uncertainties
due to scheme and scale dependences.Comment: 21 pages (Latex), 8 figures (Postscript); detailed discussion of
scheme and scale dependences adde
Renormalon Singularities of the QCD Vacuum Polarization Function to Leading Order in
We explicitly determine the residues and orders of all the ultra-violet (UV)
and infra-red (IR) renormalon poles in the Borel plane for the QCD vacuum
polarization function (Adler D-function), to leading order in an expansion in
the number of quark flavours, . The singularity structure is precisely
as anticipated on general grounds. In particular, the leading IR renormalon is
absent, in agreement with operator product expansion ideas. There is a curious
and unexplained symmetry between the third and higher UV and IR renormalon
residues. We are able to sum up separately UV and IR contributions to obtain
closed form results involving -functions. We argue that the leading UV
renormalon should have a more complicated structure than conventionally
assumed. The disappearance of IR renormalons in flavour-saturated SU() QCD
is shown to occur for or 9.Comment: 22 pages of LaTeX, revisions to this paper are mainly typographica
Relating Physical Observables in QCD without Scale-Scheme Ambiguity
We discuss the St\"uckelberg-Peterman extended renormalization group
equations in perturbative QCD, which express the invariance of physical
observables under renormalization-scale and scheme-parameter transformations.
We introduce a universal coupling function that covers all possible choices of
scale and scheme. Any perturbative series in QCD is shown to be equivalent to a
particular point in this function. This function can be computed from a set of
first-order differential equations involving the extended beta functions. We
propose the use of these evolution equations instead of perturbative series for
numerical evaluation of physical observables. This formalism is free of
scale-scheme ambiguity and allows a reliable error analysis of higher-order
corrections. It also provides a precise definition for as the pole in the associated 't Hooft scheme. A concrete application to
is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages,
DOE/ER/40322-17
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
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