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Register a new userThe NNLO soft function for the pair invariant mass distribution of boosted top quarks
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At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order (NNLO) corrections to the soft function appearing in this factorization formula, thus providing the final piece needed to evaluate at NNLO the differential cross section in the virtual plus soft approximation in the large invariant-mass limit. Technically, this amounts to evaluating the vacuum expectation value of a soft Wilson loop operator built out of light-like Wilson lines for each of the four partons participating in the hard scattering process, with a certain constraint on the total energy of the soft radiation. Our result turns out to be surprisingly simple, because in the sum of all graphs the three and four parton contributions multiply color structures whose coefficients are governed by the non-abelian exponentiation theorem.
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We obtain a soft plus virtual approximation to the NNLO QCD contributions to the top-pair invariant mass distribution at hadron colliders. It is valid up to corrections of order m_t^2/M^2, with M the pair invariant mass. This is currently the most complete QCD calculation for a differential cross section in top-quark pair production, and is useful for describing the high invariant mass region characteristic of boosted top quarks. We use our results to construct an improved NNLO approximation for the pair invariant mass distribution and compare it with previous, less complete approximations based on logarithmic terms from NNLL soft-gluon resummation alone. We find that the new NNLO approximation produces moderate enhancements of the differential cross section compared to previous ones, the effect being slightly more important at low values of invariant mass than at high ones. On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime.
We review a Soft Collinear Effective Theory approach to the study of factorization and resummation of QCD effects in top-quark pair production. In particular, we consider differential cross sections such as the top-quark pair invariant mass distribution and the top-quark transverse momentum and rapidity distributions. Furthermore, we focus our attention on the large invariant mass and large transverse momentum kinematic regions, characteristic of boosted top quarks. We discuss the factorization of the differential cross section in the double soft gluon emission and small top-quark mass limit, both in Pair Invariant Mass (PIM) and One Particle Inclusive (1PI) kinematics. The factorization formulas can be employed in order to implement the simultaneous resummation of soft emission and small mass effects up to next-to-next-to-leading logarithmic accuracy. The results are also used to construct improved next-to-next-to-leading order approximations for the differential cross sections.
We study jet substructures of a boosted polarized top quark, which undergoes the semileptonic decay $tto bell u$, in the perturbative QCD framework. The jet mass distribution (energy profile) is factorized into the convolution of a hard top-quark decay kernel with the bottom-quark jet function (jet energy function). Computing the hard kernel to leading order in QCD and inputting the latter functions from the resummation formalism, we observe that the jet mass distribution is not sensitive to the helicity of the top quark, but the energy profile is: energy is accumulated faster within a left-handed top jet than within a right-handed one, a feature related to the $V-A$ structure of weak interaction. It is pointed out that the energy profile is a simple and useful jet observable for helicity discrimination of a boosted top quark, which helps identification of physics beyond the Standard Model at the Large Hadron Collider. The extension of our analysis to other jet substructures, including those associated with a hadronically decaying polarized top quark, is proposed.
We analyse the semileptonic decay of a polarised top-quark with a large velocity based on the perturbative QCD factorisation framework. Thanks to the factorisation and the spin decomposition, the production part and the decay part can be factorised and the spin dependence is introduced in the decay part. The decay part is converted to the top-jet function which describes the distribution of jet observables and the spin is translated to the helicity of the boosted top. Using this top-jet function, the energy profile of b-jet is investigated and it is turned out that the sub-jet energy for the helicity-minus top is accumulated faster than that for the helicity-plus top. This behaviour for the boosted top can be understood with the negative spin-analysing-power of b-quark in the polarised-top decay.
We investigate the invariant-mass distribution of top-quark pairs near the $2m_t$ threshold, which has strong impact on the determination of the top-quark mass $m_t$. We show that higher-order non-relativistic corrections lead to large contributions which are not included in the state-of-the-art theoretical predictions. We derive a factorization formula to resum such corrections to all orders in the strong-coupling, and calculate necessary ingredients to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numeric results. We find that the resummation effect significantly enhances the differential cross section in the threshold region, and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of $m_t$ will lead to a value closer to the result of direct measurement.
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