29 research outputs found
The decay b -> s g at NLL in the Standard Model
I present the Standard Model calculation of the decay rate for b -> s g (g
denotes a gluon) at next-to-leading logarithms (NLL). In order to get a
meaningful physical result, the decay b -> s g g and certain contributions of b
-> s \bar{f} f (where f are the light quark flavours u, d and s) have to be
included as well. Numerically we get BR^(NLL) = (5.0 +/- 1.0) * 10^{-3} which
is more than a factor 2 larger than the leading logarithmic result BR^(LL) =
(2.2 +/- 0.8) * 10^{-3}. Further, I consider the impact of this contribution on
the charmless hadronic branching ratio BRc, which could be used to extract the
CKM-ratio |V_(ub)/V_(cb)| with more accuracy. Finally, I have a short look at
BRc in scenarios where the Wilson coefficient C_8 is enhanced by new physics.Comment: 7 pages including 5 postscript figures; uses epsfi
Belokurov-Usyukina loop reduction in non-integer dimension
Belokurov-Usyukina loop reduction method has been proposed in 1983 to reduce
a number of rungs in triangle ladder-like diagram by one. The disadvantage of
the method is that it works in d=4 dimensions only and it cannot be used for
calculation of amplitudes in field theory in which we are required to put all
the incoming and outgoing momenta on shell. We generalize the
Belokurov-Usyukina loop reduction technique to non-integer d=4-2e dimensions.
In this paper we show how a two-loop triangle diagram with particular values of
indices of scalar propagators in the position space can be reduced to a
combination of three one-loop scalar diagrams. It is known that any one-loop
massless momentum integral can be presented in terms of Appell's function F_4.
This means that particular diagram considered in the present paper can be
represented in terms of Appell's function F_4 too. Such a generalization of
Belokurov-Usyukina loop reduction technique allows us to calculate that diagram
by this method exactly without decomposition in terms of the parameter e.Comment: 6 pages, 3 figure
Two loop QCD vertices at the symmetric point
We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at
the symmetric subtraction point at two loops in the MSbar scheme. In addition
we renormalize each of the three vertices in their respective momentum
subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the
wave functions, coupling constant and gauge parameter renormalization constants
of each of the schemes relative to MSbar are determined analytically. These are
then used to derive the three loop anomalous dimensions of the gluon, quark,
Faddeev-Popov ghost and gauge parameter as well as the beta-function in an
arbitrary linear covariant gauge for each MOM scheme. There is good agreement
of the latter with earlier Landau gauge numerical estimates of Chetyrkin and
Seidensticker.Comment: 36 latex pages, anc directory contains txt file with anomalous
dimensions, beta-functions, coupling constant mappings, conversion functions
and amplitudes in analytic for
Banks-Zaks fixed point analysis in momentum subtraction schemes
We analyse the critical exponents relating to the quark mass anomalous
dimension and beta-function at the Banks-Zaks fixed point in Quantum
Chromodynamics (QCD) in a variety of representations for the quark in the
momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific
range of values of the number of quark flavours, estimates of the exponents
appear to be scheme independent. Using the recent five loop modified minimal
subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the
fixed point location we estimate the associated exponent as 0.263-0.268 for the
SU(3) colour group and 12 flavours when the quarks are in the fundamental
representation.Comment: 33 latex pages, 25 tables, anc directory contains txt file with
electronic version of renormalization group function
Virtual O(\a_s) corrections to the inclusive decay
We present in detail the calculation of the O(\a_s) virtual corrections to
the matrix element for b \to s \g. Besides the one-loop virtual corrections
of the electromagnetic and color dipole operators and , we include
the important two-loop contribution of the four-Fermi operator . By
applying the Mellin-Barnes representation to certain internal propagators, the
result of the two-loop diagrams is obtained analytically as an expansion in
. These results are then combined with existing O(\a_s)
Bremsstrahlung corrections in order to obtain the inclusive rate for B \to X_s
\g. The new contributions drastically reduce the large renormalization scale
dependence of the leading logarithmic result. Thus a very precise Standard
Model prediction for this inclusive process will become possible once also the
corrections to the Wilson coefficients are available.Comment: 29 pages, uses epsfig.sty, 12 postscript figures include
From correlation functions to scattering amplitudes
We study the correlators of half-BPS protected operators in N=4
super-Yang-Mills theory, in the limit where the positions of the adjacent
operators become light-like separated. We compute the loop corrections by means
of Lagrangian insertions. The divergences resulting from the light-cone limit
are regularized by changing the dimension of the integration measure over the
insertion points. Switching from coordinates to dual momenta, we show that the
logarithm of the correlator is identical with twice the logarithm of the
matching MHV gluon scattering amplitude. We present a number of examples of
this new relation, at one and two loops.Comment: typos corrected, references adde
From Correlators to Wilson Loops in Chern-Simons Matter Theories
We study n-point correlation functions for chiral primary operators in three
dimensional supersymmetric Chern-Simons matter theories. Our analysis is
carried on in N=2 superspace and covers N=2,3 supersymmetric CFT's, the N=6
ABJM and the N=8 BLG models. In the limit where the positions of adjacent
operators become light-like, we find that the one-loop n-point correlator
divided by its tree level expression coincides with a light-like n-polygon
Wilson loop. Remarkably, the result can be simply expressed as a linear
combination of five dimensional two-mass easy boxes. We manage to evaluate the
integrals analytically and find a vanishing result, in agreement with previous
findings for Wilson loops.Comment: 32 pages, 6 figures, JHEP
General massive one-loop off-shell three-point functions
In this work we compute the most general massive one-loop off-shell
three-point vertex in D-dimensions, where the masses, external momenta, and
exponents of propagators are arbitrary. This follows our previous paper in
which we have calculated several new hypergeometric series representations for
massless and massive (with equal masses) scalar one-loop three-point functions,
in the negative dimensional approach.Comment: 16 pages, 2 figures, 4 table
On form factors in N=4 sym
In this paper we study the form factors for the half-BPS operators
and the stress tensor supermultiplet
current up to the second order of perturbation theory and for the
Konishi operator at first order of perturbation theory in
SYM theory at weak coupling. For all the objects we observe the
exponentiation of the IR divergences with two anomalous dimensions: the cusp
anomalous dimension and the collinear anomalous dimension. For the IR finite
parts we obtain a similar situation as for the gluon scattering amplitudes,
namely, apart from the case of and the finite part has
some remainder function which we calculate up to the second order. It involves
the generalized Goncharov polylogarithms of several variables. All the answers
are expressed through the integrals related to the dual conformal invariant
ones which might be a signal of integrable structure standing behind the form
factors.Comment: 35 pages, 7 figures, LATEX2
Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop
We calculate three-point functions of two protected operators and one
twist-two operator with arbitrary even spin j in N=4 SYM theory to one-loop
order. In order to carry out the calculations we project the indices of the
spin j operator to the light-cone and evaluate the correlator in a soft-limit
where the momentum coming in at the spin j operator becomes zero. This limit
largely simplifies the perturbative calculation, since all three-point diagrams
effectively reduce to two-point diagrams and the dependence on the one-loop
mixing matrix drops out completely. The results of our direct calculation are
in agreement with the structure constants obtained by F.A. Dolan and H. Osborn
from the operator product expansion of four-point functions of half-BPS
operators.Comment: references update