arXiv subjects

Darren J. Scott

Publications and source records attributed to Darren J. Scott.

14 recordsLinked to original sources

arXiv2025

Jet veto resummation for STXS $H+$1-jet bins at aNNLL$'$+NNLO

Measurements of Higgs boson processes by the ATLAS and CMS experiments at the LHC use Simplified Template Cross Sections (STXS) as a common framework for the combination of measurements in different decay channels and their further interpretation, e.g. to measure Higgs couplings. The different Higgs production processes are measured in predefined kinematic regions -- the STXS bins -- requiring precise theory predictions for each individual bin. In gluon-fusion Higgs production a main division is into 0-jet, 1-jet, and $\geq 2$-jet bins, which are further subdivided in bins of the Higgs transverse momentum $p_T^H$. Requiring a fixed number of jets induces logarithms $\ln p_T^{\mathrm{cut}}/Q$ in the cross section where $p_T^{\mathrm{cut}}$ is the jet-$p_T$ threshold and $Q\sim p_T^H\sim m_H$ the hard-interaction scale. These jet-veto logarithms can be resummed to all orders in perturbation theory to achieve the highest possible perturbative precision. We provide state-of-the art predictions for the $p_T^H$ spectrum in exclusive $H+$1-jet production and the corresponding $H+$1-jet STXS bins in the kinematic regime $p_T^{\mathrm{cut}} \ll p_T^H\sim m_H$. We carry out the resummation at NNLL$'$ accuracy, using theory nuisance parameters to account for the few unknown ingredients at this order, and match to full NNLO. We revisit the jet-veto factorization for this process and find that it requires refactorizing the total soft function into a global and soft-collinear contribution in order to fully account for logarithms of the signal jet radius. The leading nonglobal logarithms are also included, though they are numerically small for the region of phenomenological interest.

hep-ph↗

arXiv2023

Electroweak input schemes and universal corrections in SMEFT

The choice of an electroweak (EW) input scheme is an important component of perturbative calculations in Standard Model Effective Field Theory (SMEFT). In this paper we perform a systematic study of three different EW input schemes in SMEFT, in particular those using the parameter sets $\{M_W, \, M_Z, \, G_F\}$, $\{M_W, \, M_Z, \, α\}$, or $\{α, \, M_Z, \, G_F\}$. We discuss general features and calculate decay rates of $Z$ and $W$ bosons to leptons and Higgs decays to bottom quarks in these three schemes up to next-to-leading order (NLO) in dimension-six SMEFT. We explore the sensitivity to Wilson coefficients and perturbative convergence in the different schemes, and show that while the latter point is more involved than in the Standard Model, the dominant scheme-dependent NLO corrections are universal and can be taken into account by a simple set of substitutions on the leading-order results. Residual NLO corrections are then of similar size between the different input schemes, and performing calculations in multiple schemes can give a useful handle on theory uncertainties in SMEFT predictions and fits to data.

hep-ph↗

arXiv2022

NNLO event generation for $\boldsymbol{pp \to Zh \to \ell^+\ell^- b \bar b}$ production in the SM effective field theory

We consider associated $Zh$ production with $Z \to \ell^+ \ell^-$ and $h \to b \bar b$ decays in hadronic collisions. In the framework of the Standard Model effective field theory (SMEFT) we calculate the QCD corrections to this process and achieve next-to-next-to-leading order plus parton shower (NNLO$+$PS) accuracy using the MiNNLO$_{\rm PS}$ method. This precision is obtained for a subset of six SMEFT operators, including the corrections from effective Yukawa- and chromomagnetic dipole-type interactions. Missing higher-order QCD effects associated with the considered dimension-six operators are estimated to have a relative numerical impact of less than a percent on the total rate once existing experimental limits on the relevant Wilson coefficients are taken into account. We provide a dedicated Monte Carlo (MC) code that evaluates the NNLO SMEFT corrections on-the-fly in the event generation. This MC generator is used to study the numerical impact of NNLO$+$PS corrections on the kinematic distributions in $pp \to Zh \to \ell^+ \ell^- b \bar b$ production employing simple SMEFT benchmark scenarios. We identify the invariant mass $m_{b \bar b}$ of the two $b$-tagged jets as well as the three-invariant jet mass $m_{b \bar b j}$ as particularly interesting observables to study SMEFT effects. These distributions receive contributions that change both their normalisation and shape with the latter modifications depending on the exact jet definition. To our knowledge SMEFT effects of this type have so far not been discussed in the literature. The presented MC generator can also serve as a starting point to obtain NNLO$+$PS accuracy for a suitable enlarged set of effective operators in the future.

hep-ph↗

arXiv2020

The leading jet transverse momentum in inclusive jet production and with a loose jet veto

We study the transverse momentum of the leading jet in the limit where the jet radius is small, $R\ll 1$. We introduce the leading-jet function to calculate this cross section for an inclusive jet sample, and the subleading-jet function when a loose veto on additional jets is imposed, i.e. $p_{T,J} \gtrsim p_T^{\rm veto}$. These jet functions are calculated at next-to-leading order in QCD and the resummation of jet radius logarithms is explored. We present phenomenological results for Higgs + 1 jet production, for both the jet and Higgs transverse momentum distribution. We find that, while the $R \ll 1$ limit of the cross section provides a good description of the full NLO result, even for values as large as $R=0.8$, simply retaining the leading logarithm at this order does not. Indeed, the NLO contribution to the hard function and, to a lesser extent, non-logarithmic corrections to the jet function are sizable and must be included to obtain the correct cross section. In the inclusive cross section we find that the $α_s^2 \ln^2R$ corrections are several precent, while in exclusive cross sections at large $p_{T,J}$ and small $R$ they can reach 20%. However, it is not clear how important the resummation of these logarithms is, given the presence of other large corrections at NNLO.

hep-ph↗

arXiv2020

Top-quark pair production at complete-NLO accuracy with NNLO+NNLL$'$ corrections in QCD

We describe predictions for top-quark pair differential distributions at hadron colliders, which combine state-of-the-art NNLO QCD calculations and NLO electroweak corrections together with double resummation at NNLL$'$ accuracy of threshold logarithms and small-mass logarithms. This is the first time that such a combination has appeared in the literature. Numerical results are presented for the invariant-mass distribution, the transverse-momentum distribution as well as rapidity distributions.

hep-ph↗

arXiv2019

NLO corrections to $h\to b\bar b$ decay in SMEFT

We calculate the full set of next-to-leading order (NLO) corrections to $h\to b\bar{b}$ decay in the dimension-6 Standard Model Effective Field Theory (SMEFT). Our calculation forms the basis for precision studies of this decay mode in effective field theory, providing analytic and numerical results for contributions of the 45 dimension-6 operators appearing at NLO. On the technical side, we discuss several complications in NLO SMEFT computations which have not yet been addressed in the literature. These include subtleties in Higgs-$Z$ mixing, electric charge renormalization, and especially the treatment of tadpoles in SMEFT. In particular, we highlight the role of decoupling relations in eliminating potentially large tadpole corrections to the decay rate in hybrid renormalization schemes which employ the $\overline{\hbox{MS}}$~scheme for some Standard Model parameters (such as the $b$-quark mass and electric charge) and the on-shell scheme for others.

hep-ph↗

arXiv2018

Resummation for rapidity distributions in top-quark pair production

We extend our framework for the simultaneous resummation of soft and small-mass logarithms to rapidity distributions in top quark pair production. We give numerical results for the rapidity distribution of the top quark or the anti-top quark, as well as the rapidity distribution of the $t\bar{t}$ pair, finding that resummation effects stabilize the dependence of the differential cross sections on the choice of factorization scale. We compare our results with recent measurements at the Large Hadron Collider and find good agreement. Our results may be useful in the extraction of the gluon parton distribution function from $t\bar{t}$ production.

hep-ph↗

arXiv2018

Resummation for (boosted) top-quark pair production at NNLO+NNLL' in QCD

We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL' accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL' accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the M_{tt} and top-quark p_T distributions in the boosted regime where fixed order calculations may become strongly dependent on the choice of dynamic scales. With the help of numeric and analytic arguments we confirm that the choice for the factorization and renormalization scales advocated recently by some of the authors is indeed optimal. We further derive a set of optimized kinematics-dependent scales for the matching functions which appear in the resummed calculations. Our NNLO+NNLL' prediction for the top-pair invariant mass is significantly less sensitive to the choice of factorization scale than the fixed order prediction, even at NNLO. Notably, the resummed and fixed order calculations are in nearly perfect agreement with each other in the full M_{tt} range when the optimal dynamic scale is used. For the top-quark p_T distribution the resummation performed here has less of an impact and instead we find that upgrading the matching with fixed-order from NLO+NNLL' to NNLO+NNLL' to be an important effect, a point to be kept in mind when using NLO-based Monte Carlo event generators to calculate this distribution.

hep-ph↗

arXiv2017

Neutrino Jets from High-Mass $W_R$ Gauge Bosons in TeV-Scale Left-Right Symmetric Models

We re-examine the discovery potential at hadron colliders of high-mass right-handed (RH) gauge bosons $W_R$ - an inherent ingredient of Left-Right Symmetric Models (LRSM). We focus on the regime where the $W_R$ is very heavy compared to the heavy Majorana neutrino $N$, and investigate an alternative signature for $W_R \rightarrow N$ decays. The produced neutrinos are highly boosted in this mass regime. Subsequently, their decays via off-shell $W_R$ bosons to jets, i.e., $N \rightarrow \ell^\pm j j$ are highly collimated, forming a single neutrino jet $(j_N)$. The final-state collider signature is then $\ell^\pm j_N$, instead of the widely studied $\ell^\pm\ell^\pm jj$. Present search strategies are not sensitive to this hierarchical mass regime due to the breakdown of the collider signature definition. We take into account QCD corrections beyond next-to-leading order (NLO) that are important for high-mass Drell-Yan processes at the 13 TeV Large Hadron Collider (LHC). For the first time, we evaluate $W_R$ production at NLO with threshold resummation at next-to-next-to-leading logarithm (NNLL) matched to the threshold-improved parton distributions. With these improvements, we find that a ${W_R}$ of mass $M_{W_R} = 3~(4)~[5]$ TeV and mass ratio of $(m_N/M_{W_R})<0.1$ can be discovered with a $5-6 σ$ statistical significance at 13 TeV after ${10~(100)~[2000]~\text{fb}^{-1}}$ of data. Extending the analysis to the hypothetical 100 TeV Very Large Hadron Collider (VLHC), $5σ$ can be obtained for $W_R$ masses up to $M_{W_R}=15~(30)$ with approximately $100~\text{fb}^{-1}~(10~\text{ab}^{-1})$.

hep-ph↗

arXiv2016

One-loop corrections to $h\to b\bar b$ and $h\to τ\bar τ$ decays in the Standard Model Dimension-6 EFT: four-fermion operators and the large-$m_t$ limit

We calculate a set of one-loop corrections to $h\to b\bar b$ and $h\to τ\bar τ$ decays in the dimension-6 Standard Model effective field theory (SMEFT). In particular, working in the limit of vanishing gauge couplings, we calculate directly in the broken phase of the theory all large logarithmic corrections and in addition the finite corrections in the large-$m_t$ limit. Moreover, we give exact results for one-loop contributions from four-fermion operators. We obtain these corrections within an extension of the widely used on-shell renormalisation scheme appropriate for SMEFT calculations, and show explicitly how UV divergent bare amplitudes from a total of 21 different SMEFT operators are rendered finite within this scheme. As a by-product of the calculation, we also compute to one-loop order the logarithmically enhanced and finite large-$m_t$ corrections to muon decay in the limit of vanishing gauge couplings, which is necessary to implement the $G_F$ input parameter scheme within the SMEFT.

hep-ph↗

arXiv2016

QCD radiative corrections for $h\to b\bar b$ in the Standard Model Dimension-6 EFT

We calculate the $\mathcal{O}(α_s)$ QCD corrections to the inclusive $h\to b\bar b$ decay rate in the dimension-6 Standard Model Effective Field Theory (SMEFT). The QCD corrections multiplying the dimension-6 Wilson coefficients which alter the $hb\bar b$-vertex at tree-level are proportional to the Standard Model (SM) ones, so next-to-leading order results can be obtained through a simple rescaling of the tree-level decay rate. On the other hand, contributions from the operators $Q_{bG}$ and $Q_{HG}$, which alter the $gb\bar b$-vertex and introduce a $hgg$-vertex respectively, enter at $\mathcal{O}(α_s)$ and induce sizeable corrections which are unrelated to the SM ones and cannot be anticipated through a renormalisation-group analysis. We present compact analytic results for these contributions, which we recommend to be included in future phenomenological studies.

hep-ph↗

arXiv2016

Resummed differential cross sections for top-quark pairs at the LHC

We present state of the art resummation predictions for differential cross sections in top-quark pair production at the LHC. They are derived from a formalism which allows the simultaneous resummation of both soft and small-mass logarithms, which endanger the convergence of fixed-order perturbative series in the boosted regime, where the partonic center-of-mass energy is much larger than the mass to the top quark. We combine such a double resummation at NNLL$'$ accuracy with standard soft-gluon resummation at NNLL accuracy and with NLO calculations, so that our results are applicable throughout the whole phase space. We find that the resummation effects on the differential distributions are significant, bringing theoretical predictions into better agreement with experimental data compared to fixed-order calculations. Moreover, such effects are not well described by the NNLO approximation of the resummation formula, especially in the high-energy tails of the distributions, highlighting the importance of all-orders resummation in dedicated studies of boosted top production.

hep-ph↗

arXiv2015

QCD resummations for boosted top production

We present new results for QCD corrections to the top-pair invariant mass and top-quark $p_T$ distributions in boosted top-quark pair production at hadron colliders. They are derived from a formalism which allows the joint resummation of soft and small-mass logarithms at NNLL$'$ order, thus taking into account all potentially large corrections in the boosted regime, where the partonic center-of-mass energy is parameterically much larger than the mass of the top quark. We match these results with those from standard soft-gluon resummation away from the small-mass limit to NNLL order and also with NLO fixed-order calculations, so that our results are valid in the maximum possible range of phase space. The resummation effects on the $p_T$ and top-pair invariant mass distributions are significant, bringing theory predictions into better agreement with experimental data compared to pure NLO calculations.

hep-ph↗

arXiv2013

Webs and Posets

The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together give rise to colour factors corresponding to connected graphs. The colour and kinematic degrees of freedom of individual diagrams in a web are entangled by mixing matrices of purely combinatorial origin. In this paper we relate the combinatorial study of these matrices to properties of partially ordered sets (posets), and hence obtain explicit solutions for certain families of web-mixing matrix, at arbitrary order in perturbation theory. We also provide a general expression for the rank of a general class of mixing matrices, which governs the number of independent colour factors arising from such webs. Finally, we use the poset language to examine a previously conjectured sum rule for the columns of web-mixing matrices which governs the cancellation of the leading subdivergences between diagrams in the web. Our results, when combined with parallel developments in the evaluation of kinematic integrals, offer new insights into the all-order structure of infrared singularities in non-Abelian gauge theories.

hep-th↗