A
bstract
The renormalization constant
Z
J
of the flavor-singlet axial-vector current with a non-anticommuting
γ
5
in dimensional regularization is determined to order
α
s
3
in QCD with massless ...quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation
∂
μ
J
5
μ
R
=
α
s
4
π
n
f
T
F
F
F
˜
R
between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the equality between the
MS
¯
renormalization constant
Z
F
F
˜
associated with the operator
F
F
˜
R
and that of
α
s
is verified explicitly to hold true at 4-loop order. This equality automatically ensures a relation between the respective anomalous dimensions,
γ
J
=
α
s
4
π
n
f
T
F
γ
FJ
, at order
α
s
4
given the validity of the axial-anomaly equation which was used to determine the non-
MS
¯
piece of
Z
J
for the particular
γ
5
prescription in use.
In computing the two-loop QCD corrections to a class of Feynman
diagrams for the process
q\overline{q} \rightarrow ZH
q
q
¯
→
Z
H
in Higgs effective field theory, we discover a striking phenomenon. ...We
find the need for an additional local composite operator in the
renormalised Lagrangian while employing a non-anticommuting
\gamma_5
γ
5
in dimensional regularisation. The computation using anticommuting
\gamma_5
γ
5
,
however, does not require any such amendment.
A
bstract
We compute all helicity amplitudes for four particle scattering in massless QCD with
n
f
fermion flavours to next-to-next-to-leading order (NNLO) in perturbation theory. In particular, we ...consider all possible configurations of external quarks and gluons. We evaluate the amplitudes in terms of a Laurent series in the dimensional regulator to the order required for future next-to-next-to-next-to-leading order (N
3
LO) calculations. The coefficients of the Laurent series are given in terms of harmonic polylogarithms that can readily be evaluated numerically. We present our findings in the conventional dimensional regularisation and in the t’Hooft-Veltman schemes.
A
bstract
We study a set of two-loop non-planar master integrals needed for the NNLO QCD corrections to diphoton and dijet production at hadron colliders. The top-sector topology contains an internal ...massive fermion loop and is known to contain elliptic curves. Leveraging the method of differential equations, we provide a comprehensive discussion for deriving an
ϵ
-factorized differential equation related to the most intricate sector within the Feynman integral family. Despite the dependence on multiple scales and the presence of two elliptic sectors, we demonstrate how to leverage the properties of their maximal cuts and the factorization of the Picard-Fuchs operator to deal with the complexity of the analytic computation. In particular, we construct a transformation matrix that brings the differential equations into a format enabling the convenient expression of analytic results in terms of Chen’s iterated integrals.
A
bstract
Through this article, we present the two-loop massless QCD corrections to the production of di-Higgs and di-pseudo-Higgs boson through quark annihilation in the large top quark mass limit. ...Within dimensional regularisation, we employ the non-anticommuting
γ
5
and treat it under the Larin prescription. We discover the absence of any additional renormalisation, so-called contact renormalisation, that could arise from the short distance behaviour of two local operators. This finding is in corroboration with the operator product expansion. By examining the results, we discover the lack of similarity in the highest transcendentality weight terms between these finite remainders and that of a pair of half-BPS primary operators in maximally supersymmetric Yang-Mills theory. We need these newly computed finite remainders to calculate observables involving di-Higgs or di-pseudo- Higgs at the next-to-next-to-leading order. We implement the results to a numerical code for further phenomenological studies.
A
bstract
We discuss the constraints on quark and gluon energy-momentum tensors in QCD that follow from the requirement of Renormalisation-Group invariance of the traces of these operators. Our study ...covers the most general form of the latter traces, while the energy-momentum tensors themselves are only subjected to very mild constraints. We derive Renormalisation-Group equations for the two finite independent functions of the strong coupling constant and renormalisation scale of minimal subtraction which completely define the energy-momentum tensors. We demonstrate that previously proposed definitions of the renormalized quark and gluon energy-momentum tensors are special cases of our results assuming no explicit dependence on the renormalisation scale. Finally, we present
MS
¯
-renormalised quark and gluon energy-momentum tensors at four-loop order.
A
bstract
We present the analytic evaluation of the second-order corrections to the massive form factors, due to two-loop vertex diagrams with a vacuum polarization insertion, with exact dependence ...on the external and internal fermion masses, and on the squared momentum transfer. We consider vector, axial-vector, scalar and pseudoscalar interactions between the external fermion and the external field. After renormalization, the finite expressions of the form factors are expressed in terms of polylogarithms up to weight three.
A
bstract
The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated ...analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no similarity with similar amplitudes in QCD.
We consider the production of a pseudo-scalar particle
at the LHC, and present accurate theoretical predictions for its inclusive cross section in gluon fusion. The prediction is based on combining ...fixed-order perturbation theory and all-order threshold resummation. At fixed order we include the exact next-to-next-to-leading order (NNLO) plus an approximate next-to-next-to-next-to-leading order (NFormula: see textLOFormula: see text) which is based on the recent computation at this order for the scalar case. We then add threshold resummation at next-to-next-to-next-to leading logarithmic accuracy (NFormula: see textLLFormula: see text). Various forms of threshold resummation are considered, differing by the treatment of subleading terms, allowing a robust estimate of the theoretical uncertainties due to missing higher orders. With particular attention to pseudo-scalar masses of 200 and 750 GeV, we also observe that perturbative convergence is much improved when resummation is included. Additionally, results obtained with threshold resummation in direct QCD are compared with analogous results as computed in soft-collinear effective theory, which turn out to be in good agreement. We provide precise predictions for pseudo-scalar inclusive cross section at 13 TeV LHC for a wide range of masses. The results are available through updated versions of the public codes ggHiggs and TROLL.
Full text
Available for:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
High energy behaviour of form factors Ahmed, Taushif; Henn, Johannes M.; Steinhauser, Matthias
The journal of high energy physics,
06/2017, Volume:
2017, Issue:
6
Journal Article
Peer reviewed
Open access
A
bstract
We solve renormalization group equations that govern infrared divergences of massless and massive form factors. By comparing to recent results for planar massive three-loop and massless ...four-loop form factors in QCD, we give predictions for the high-energy limit of massive form factors at the four- and for the massless form factor at five-loop order. Furthermore, we discuss the relation which connects infrared divergences regularized dimensionally and via a small quark mass and extend results present in the literature to higher order.
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