Collinear functions for QCD resummations Catani, Stefano; Dhani, Prasanna K.
The journal of high energy physics,
03/2023, Volume:
2023, Issue:
3
Journal Article
Peer reviewed
Open access
A
bstract
The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to ...define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Different collinear functions are obtained by integrating the splitting kernels over different phase-space regions that depend on the hard-scattering observables of interest. The collinear functions depend on an auxiliary vector
n
μ
that can be either light-like (
n
2
= 0) or time-like (
n
2
>
0). In the case of transverse-momentum dependent (TMD) collinear functions, we show that the use of a time-like auxiliary vector avoids the rapidity divergences, which are instead present if
n
2
= 0. The perturbative computation of the collinear functions lead to infrared (IR) divergences that can be properly factorized with respect to IR finite functions that embody the logarithmically-enhanced collinear contributions to hard-scattering cross sections. We evaluate various collinear functions and their
n
μ
dependence at
O
(
α
S
). We compute the azimuthal-correlation component of the TMD collinear functions at
O
α
S
2
, and we present the results of the
O
α
S
2
contribution of linearly-polarized gluons to transverse-momentum resummation formulae. Beyond
O
α
S
2
the collinear functions of initial-state colliding partons are process dependent, as a consequence of the violation of strict collinear factorization of QCD squared amplitudes.
A
bstract
We compute the two-loop massless QCD corrections to the four-point amplitude
g
+
g
→
H
+
H
resulting from effective operator insertions that describe the interaction of a Higgs boson with ...gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.
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 present here the first result on the three-loop gluon jet function in perturbative QCD. Using the three-loop coefficient functions J. A. M. Vermaseren, A. Vogt, and S. Moch, Nucl. Phys. B724, 3 ...(2005)., G. Soar, S. Moch, J. A. M. Vermaseren, and A. Vogt, Nucl. Phys. B832, 152 (2010). for deep-inelastic scattering via the exchange of a virtual photon that couples to quarks or a scalar that couples to gluons and employing the KG equation, renormalization group invariance and factorization theorem, we obtain both the quark and the gluon jet functions up to the three-loop level. The former agrees with the recent result R. Brüser, Z. L. Liu, and M. Stahlhofen, Phys. Rev. Lett. 121, 072003 (2018).. These jet functions being universal ingredients in the SCET framework, will play an important role in the phenomenological studies at the Large Hadron Collider, such as resummation of jet observables and also in N-jettiness subtraction method.
Full text
Available for:
CMK, CTK, FMFMET, IJS, NUK, PNG, UM
A
bstract
We present virtual contributions up to two loop level in perturbative Quantum Chromodynamic (QCD) to the decay of pseudo-scalar Higgs boson (
A
) to three gluons (
g
) and also to quark (
q
...), anti-quark (
q
¯
) and a gluon. With appropriate crossing, they are well suited for predicting the differential distribution of
A
in association with a jet in hadron colliders up to next-to-next-to-leading order (NNLO) in strong coupling constant and also for the subsequent decay of
A
to hadrons. We use effective field theory approach to integrate out the top quarks in the heavy top limit. The resulting theory involves two pseudo-scalar composite operators describing the interaction of
A
with gluons as well as with quark and anti-quark. We perform our computation in dimensional regularisation and use minimal subtraction (
M
S
¯
) scheme to renormalise strong coupling constant as well as the composite operators. The ultraviolet (UV) finite amplitudes contain infrared (IR) divergences that are found to be in agreement with the predictions by Catani. For both the amplitudes namely
A
→
ggg
and
A
→
q
q
¯
g
, the leading transcendental terms at one and two loops are found to be identical to those in a three point form factor (FF) of the half-BPS operator in
N
=
4
Supersymmetric Yang Mills (SYM) theory when the QCD color factors are adjusted in a specific way. We present our results in terms of harmonic polylogs well suited for further numerical study.
A
bstract
We analyze in detail the most singular behaviour of processes involving triple-collinear splittings with massive particles in the quasi-collinear limit, and present compact expressions for ...the splitting amplitudes and the corresponding splitting kernels at the squared-amplitude level. Our expressions fully agree with well-known triple-collinear splittings in the massless limit, which are used as a guide to achieve the final expressions. These results are important to quantify dominant mass effects in many observables, and constitute an essential ingredient of current high-precision computational frameworks for collider phenomenology.
We present a formalism that resums threshold-enhanced logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We achieve ...this by exploiting the factorization properties and K+G equations satisfied by the soft and virtual parts of the cross section. We compute for the first time compact and most general expressions in two-dimensional Mellin space for the resummed coefficients. Using various state-of-the-art multiloop and multileg results, we demonstrate the numerical impact of our resummed results up to next-to-next-to-leading order for the rapidity distribution of the Higgs boson at the LHC. We find that inclusion of these threshold logs through resummation improves the reliability of perturbative predictions.
Full text
Available for:
CMK, CTK, FMFMET, IJS, NUK, PNG, UM
We consider the production of pairs of lepton through the Drell-Yan process at the LHC and present the most accurate prediction on their rapidity distribution. While the fixed order prediction is ...already known to next-to-next-to-leading order in perturbative QCD, the resummed contribution coming from threshold region of phase space up to next-to-next-to-leading logarithmic (NNLL) accuracy has been computed in this article. The formalism developed in 1–3 has been used to resum large threshold logarithms in the two dimensional Mellin space to all orders in perturbation theory. We have done a detailed numerical comparison against other approaches that resum certain threshold logarithms in Mellin-Fourier space. Our predictions at NNLL level are close to theirs even though at leading logarithmic and next-to-leading logarithmic level we differ. We have also investigated the impact of these threshold logarithms on the stability of perturbation theory against factorization and renormalization scales. While the dependence on these scales does not get better with resummed results, the convergence of the perturbative series shows a better trend compared to the fixed order predictions. This is evident from the reduction in the K-factor for the resummed case compared to fixed order. We also present the uncertainties on the predictions resulting from parton distribution functions.
Full text
Available for:
CMK, CTK, FMFMET, IJS, NUK, PNG, UM
A
bstract
We present the first results on the two-loop massless QCD corrections to the four-point amplitude
b
+
b
¯
→
H
+
H
in the five flavor scheme, treating bottom quarks as massless. This ...amplitude is sensitive to the trilinear Higgs boson coupling. Our two-loop result for this amplitude constitutes of purely virtual contributions to the next-to-next-to-leading order QCD predictions for the production of a pair of Higgs bosons at the Large Hadron Collider. Using these two loop amplitudes and exploiting the universality of the soft contributions in perturbative QCD, we obtain the NNLO QCD effects in the soft plus virtual approximation. We find that the inclusion of higher order terms reduce the uncertainties resulting from the unphysical renormalisation and factorisation scales.
A
bstract
We present three point form factors (FF) in
N
=
4
Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the ‘t Hooft coupling using Feynman ...diagrammatic approach. We have chosen on shell final states consisting of
gϕϕ
and
ϕλλ
, where
ϕ, λ, g
are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani’s IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for
gϕϕ
agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.
PDF
