186 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
Next-to-next-to-leading soft-gluon corrections for the top quark cross section and transverse momentum distribution
I present results for top quark production in hadronic collisions at LHC and
Tevatron energies. The soft-gluon corrections to the differential cross section
are resummed at next-to-next-to-leading-logarithm (NNLL) accuracy via the
two-loop soft anomalous dimension matrices. Approximate
next-to-next-to-leading-order (NNLO) differential and total cross sections are
calculated. Detailed theoretical predictions are shown for the t tbar cross
section and the top quark p_T distribution at the Tevatron and the LHC.Comment: 23 pages, 14 figures; additional results and figure
On the renormalization of multiparton webs
We consider the recently developed diagrammatic approach to soft-gluon
exponentiation in multiparton scattering amplitudes, where the exponent is
written as a sum of webs - closed sets of diagrams whose colour and kinematic
parts are entangled via mixing matrices. A complementary approach to
exponentiation is based on the multiplicative renormalizability of intersecting
Wilson lines, and their subsequent finite anomalous dimension. Relating this
framework to that of webs, we derive renormalization constraints expressing all
multiple poles of any given web in terms of lower-order webs. We examine these
constraints explicitly up to four loops, and find that they are realised
through the action of the web mixing matrices in conjunction with the fact that
multiple pole terms in each diagram reduce to sums of products of lower-loop
integrals. Relevant singularities of multi-eikonal amplitudes up to three loops
are calculated in dimensional regularization using an exponential infrared
regulator. Finally, we formulate a new conjecture for web mixing matrices,
involving a weighted sum over column entries. Our results form an important
step in understanding non-Abelian exponentiation in multiparton amplitudes, and
pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure
Probing QCD dynamics in two-photon interactions at high energies
In this paper the two-photon interactions at high energies are investigated
considering different approaches for the QCD dynamics. In particular, we
calculate the total cross section in different theoretical
approches and present a comparison among the predictions of the BFKL dynamics
at leading and next-to-leading order with those from saturation physics. We
analyze the possibility that the future linear colliders could discriminate
between these different approaches.Comment: 14 pages, 2 figures. Version to be published in Journal of Physics G:
Nuclear and Particle Physic
Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
We show that the Pade Approximant (PA) approach for resummation of
perturbative series in QCD provides a systematic method for approximating the
flow of momentum in Feynman diagrams. In the large- limit, diagonal
PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-setting method to
higher orders in a renormalization scale- and scheme-invariant manner, using
multiple scales that represent Neubert's concept of the distribution of
momentum flow through a virtual gluon. If the distribution is non-negative, the
PA's have only real roots, and approximate the distribution function by a sum
of delta-functions, whose locations and weights are identical to the optimal
choice provided by the Gaussian quadrature method for numerical integration. We
show how the first few coefficients in a perturbative series can set rigorous
bounds on the all-order momentum distribution function, if it is positive. We
illustrate the method with the vacuum polarization function and the Bjorken sum
rule computed in the large- limit.Comment: 28 pages, LaTeX, including 6 figures requires epsfig.st
An infrared approach to Reggeization
We present a new approach to Reggeization of gauge amplitudes based on the
universal properties of their infrared singularities. Using the "dipole
formula", a compact ansatz for all infrared singularities of massless
amplitudes, we study Reggeization of singular contributions to high-energy
amplitudes for arbitrary color representations, and any logarithmic accuracy.
We derive leading-logarithmic Reggeization for general cross-channel color
exchanges, and we show that Reggeization breaks down for the imaginary part of
the amplitude at next-to-leading logarithms and for the real part at
next-to-next-to-leading logarithms. Our formalism applies to multiparticle
amplitudes in multi-Regge kinematics, and constrains possible corrections to
the dipole formula starting at three loops.Comment: 4 page
Why Pad\'e Approximants reduce the Renormalization-Scale dependence in QFT?
We prove that in the limit where the beta function is dominated by the 1-loop
contribution (``large beta_0 limit'') diagonal Pad\'e Approximants (PA's) of
perturbative series become exactly renormalization scale (RS) independent. This
symmetry suggest that diagonal PA's are resumming correctly contributions from
higher order diagrams that are responsible for the renormalization of the
coupling-constant. Non-diagonal PA's are not exactly invariant, but generally
reduce the RS dependence as compared to partial-sums. In physical cases,
higher-order corrections in the beta function break the symmetry softly,
introducing a small scale and scheme dependence. We also compare the Pad\'e
resummation with the BLM method. We find that in the large-N_f limit using the
BLM scale is identical to resumming the series by a non-diagonal PA.Comment: 25 pages, LateX. Replaced so that the figures would fit into the page
siz
On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
A closed formula is obtained for the infrared singularities of dimensionally
regularized, massless gauge-theory scattering amplitudes with an arbitrary
number of legs and loops. It follows from an all-order conjecture for the
anomalous-dimension matrix of n-jet operators in soft-collinear effective
theory. We show that the form of this anomalous dimension is severely
constrained by soft-collinear factorization, non-abelian exponentiation, and
the behavior of amplitudes in collinear limits. Using a diagrammatic analysis,
we demonstrate that these constraints imply that to three-loop order the
anomalous dimension involves only two-parton correlations, with the possible
exception of a single color structure multiplying a function of conformal cross
ratios depending on the momenta of four external partons, which would have to
vanish in all two-particle collinear limits. We argue that such a function does
not appear at three-loop order, and that the same is true in higher orders. Our
formula predicts Casimir scaling of the cusp anomalous dimension to all orders
in perturbation theory, and we explicitly check that the constraints exclude
the appearance of higher Casimir invariants at four loops. Using known results
for the quark and gluon form factors, we derive the three-loop coefficients of
the 1/epsilon^n pole terms (with n=1,...,6) for an arbitrary n-parton
scattering amplitude in massless QCD. This generalizes Catani's two-loop
formula proposed in 1998.Comment: 46 pages, 9 figures; v2: improved treatment of collinear limits,
references added; v3: improved discussion of non-abelian exponentiation,
references updated; v4: typo in eq. (17) fixed, references updated; v5:
additional term in (17
From Webs to Polylogarithms
We compute a class of diagrams contributing to the multi-leg soft anomalous
dimension through three loops, by renormalizing a product of semi-infinite
non-lightlike Wilson lines in dimensional regularization. Using non-Abelian
exponentiation we directly compute contributions to the exponent in terms of
webs. We develop a general strategy to compute webs with multiple gluon
exchanges between Wilson lines in configuration space, and explore their
analytic structure in terms of , the exponential of the Minkowski
cusp angle formed between the lines and . We show that beyond the
obvious inversion symmetry , at the level of the
symbol the result also admits a crossing symmetry , relating spacelike and timelike kinematics, and hence argue that
in this class of webs the symbol alphabet is restricted to and
. We carry out the calculation up to three gluons connecting
four Wilson lines, finding that the contributions to the soft anomalous
dimension are remarkably simple: they involve pure functions of uniform weight,
which are written as a sum of products of polylogarithms, each depending on a
single cusp angle. We conjecture that this type of factorization extends to all
multiple-gluon-exchange contributions to the anomalous dimension.Comment: 64 pages, 8 figure
A novel series solution to the renormalization group equation in QCD
Recently, the QCD renormalization group (RG) equation at higher orders in
MS-like renormalization schemes has been solved for the running coupling as a
series expansion in powers of the exact 2-loop order coupling. In this work, we
prove that the power series converges to all orders in perturbation theory.
Solving the RG equation at higher orders, we determine the running coupling as
an implicit function of the 2-loop order running coupling. Then we analyze the
singularity structure of the higher order coupling in the complex 2-loop
coupling plane. This enables us to calculate the radii of convergence of the
series solutions at the 3- and 4-loop orders as a function of the number of
quark flavours . In parallel, we discuss in some detail the
singularity structure of the coupling at the 3- and 4-loops in
the complex momentum squared plane for . The
correspondence between the singularity structure of the running coupling in the
complex momentum squared plane and the convergence radius of the series
solution is established. For sufficiently large values, we find
that the series converges for all values of the momentum squared variable
. For lower values of , in the scheme,
we determine the minimal value of the momentum squared above
which the series converges. We study properties of the non-power series
corresponding to the presented power series solution in the QCD Analytic
Perturbation Theory approach of Shirkov and Solovtsov. The Euclidean and
Minkowskian versions of the non-power series are found to be uniformly
convergent over whole ranges of the corresponding momentum squared variables.Comment: 29 pages,LateX file, uses IOP LateX class file, 2 figures, 13 Tables.
Formulas (4)-(7) and Table 1 were relegated to Appendix 1, some notations
changed, 2 footnotes added. Clarifying discussion added at the end of Sect.
3, more references and acknowledgments added. Accepted for publication in
Few-Body System
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