The $q_{\mathrm{T}}$ and $Δϕ_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
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| Formato: | Preprint |
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2024
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| author | Ju, Wan-Li Schoenherr, Marek |
| author_facet | Ju, Wan-Li Schoenherr, Marek |
| contents | In this paper, we present the resummation-improved differential transverse momentum and azimuthal decorrelation cross sections, $dσ_{t\bar{t}}/dq_{\mathrm{T}}$ and $dσ_{t\bar{t}}/dΔϕ_{t\bar{t}}$, in top-antitop pair production at the LHC. Our calculation is based on the observation that both cross sections are dominated by topologies where the top-quark pair is well separated, expressed in their relative velocity $β_{t\bar{t}}\sim\mathcal{O}(1)$, at colliding energies of $\sqrt{s}=13\,\text{TeV}$ or higher. Therefore, the asymptotic behaviour in the limits $q_{\mathrm{T}}\to0$ and $Δϕ_{t\bar{t}}\to0$ can mostly be captured by the soft and collinear resummation in the HQET$+$SCET framework. Nevertheless, starting at NNLL, Coulomb singularities emerge in the threshold regime, $β_{t\bar{t}}\to0$, in both the hard sector and its evolution kernels, leading to unphysical results upon integration over the entire $β_{t\bar{t}}$ range. To this end, two prescriptions, dubbed the D- and R-prescription, are introduced to regularise these Coulomb singularities. They embody two fundamentally different methods to truncate the threshold enhanced terms, rendering their contribution finite. In the absence of a combined threshold and small-transverse-momentum resummation, we present a quantitative assessment of the ambiguity introduced by the choice of prescription, itself a test of the sensitivity of our calculation to such threshold enhancements, for both the $dσ_{t\bar{t}}/dq_{\mathrm{T}}$ and $dσ_{t\bar{t}}/dΔϕ_{t\bar{t}}$ spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $q_{\mathrm{T}}$ and $Δϕ_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities Ju, Wan-Li Schoenherr, Marek High Energy Physics - Phenomenology In this paper, we present the resummation-improved differential transverse momentum and azimuthal decorrelation cross sections, $dσ_{t\bar{t}}/dq_{\mathrm{T}}$ and $dσ_{t\bar{t}}/dΔϕ_{t\bar{t}}$, in top-antitop pair production at the LHC. Our calculation is based on the observation that both cross sections are dominated by topologies where the top-quark pair is well separated, expressed in their relative velocity $β_{t\bar{t}}\sim\mathcal{O}(1)$, at colliding energies of $\sqrt{s}=13\,\text{TeV}$ or higher. Therefore, the asymptotic behaviour in the limits $q_{\mathrm{T}}\to0$ and $Δϕ_{t\bar{t}}\to0$ can mostly be captured by the soft and collinear resummation in the HQET$+$SCET framework. Nevertheless, starting at NNLL, Coulomb singularities emerge in the threshold regime, $β_{t\bar{t}}\to0$, in both the hard sector and its evolution kernels, leading to unphysical results upon integration over the entire $β_{t\bar{t}}$ range. To this end, two prescriptions, dubbed the D- and R-prescription, are introduced to regularise these Coulomb singularities. They embody two fundamentally different methods to truncate the threshold enhanced terms, rendering their contribution finite. In the absence of a combined threshold and small-transverse-momentum resummation, we present a quantitative assessment of the ambiguity introduced by the choice of prescription, itself a test of the sensitivity of our calculation to such threshold enhancements, for both the $dσ_{t\bar{t}}/dq_{\mathrm{T}}$ and $dσ_{t\bar{t}}/dΔϕ_{t\bar{t}}$ spectra. |
| title | The $q_{\mathrm{T}}$ and $Δϕ_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.03501 |