Precision Global Determination of the B → X s γ Decay Rate
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Engineering topics
Tackmann, Frank J.
Publications and source records attributed to Tackmann, Frank J..
Drell-Yan q T resummation of fiducial power corrections at N 3 LL
We consider Drell-Yan production pp → V*X → LX at small q T << Q, where q T and Q are the total transverse momentum and invariant mass of the leptonic final state L. Experimental measurements require fiducial cuts on L, which in general introduce enhanced, linear power corrections in q T /Q. We show that they can be unambiguously predicted from factorization, and resummed to the same order as the leading-power contribution. For the fiducial q T spectrum, they constitute the complete linear power corrections. We thus obtain predictions for the fiducial q T spectrum to N 3 LL and next-to-leading-power in q T /Q. Matching to full NNLO ($α$$^{2}_{s}$), we find that the linear power corrections are indeed the dominant ones, and once included by factorization, the remaining fixed-order corrections become almost negligible below q T ≲ 40 GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial Φ* spectrum at N 3 LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of q T and Φ*. We also consider the $p$$^{ℓ}_{T}$ spectrum. We show that it develops leptonic power corrections in q T /(Q – 2$p$$^{ℓ}_{T}$), which diverge near the Jacobian peak $p$$^{ℓ}_{T}$ ~ Q/2 and must be kept to all powers to obtain a meaningful result there. Doing so, we obtain for the first time an analytically resummed result for the $p$$^{ℓ}_{T}$ spectrum around the Jacobian peak at N 3 LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. We show that in practice this is equivalent to often-used recoil prescriptions, for which our results now provide rigorous, formal justification. Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, which for Z/γ* → ℓℓ or W → ℓν directly map onto the commonly used angular coefficients, but also holds for arbitrary leptonic final states. In particular, for suitably defined Born-projected leptons it still yields a LO-like angular decomposition even when including QED final-state radiation. Finally, we also discuss the application to q T subtractions. Including the unambiguously predicted fiducial power corrections significantly improves their performance, and in particular makes them applicable near kinematic edges where they otherwise break down due to large leptonic power corrections.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A toolbox for $$q_{T}$$ and 0-jettiness subtractions at $$\hbox {N}^3\hbox {LO}$$
We derive the leading-power singular terms at three loops for both $q_T$ and 0-jettiness, $T_0$, for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for $q_T$ and $T_0$ subtractions at N 3 LO, which are an important ingredient for matching N 3 LO calculations with parton showers. We obtain the full three-loop structure of the relevant beam and soft functions, which are necessary ingredients for the resummation of $q_T$ and $T_0$ at N 3 LL' and N 4 LL order, and which constitute important building blocks in other contexts as well. The nonlogarithmic boundary coefficients of the beam functions, which contribute to the integrated subtraction terms, are not yet fully known at three loops. By exploiting consistency relations between different factorization limits, we derive results for the $q_T$ and $T_0$ beam function coefficients at N 3 LO in the z→1 threshold limit, and we also estimate the size of the unknown terms beyond threshold.
Physics↗
Impact of isolation and fiducial cuts on qT and N-jettiness subtractions
Kinematic selection cuts and isolation requirements are a necessity in experimental measurements for identifying prompt leptons and photons that originate from the hard-interaction process of interest. We analyze how such cuts affect the application of the q T and N-jettiness subtraction methods for fixed-order calculations. We consider both fixed-cone and smooth-cone isolation methods. We find that kinematic selection and isolation cuts both induce parametrically enhanced power corrections with considerably slower convergence compared to the standard power corrections that are already present in inclusive cross sections without additional cuts. Using analytic arguments at next-to-leading order we derive their general scaling behavior as a function of the subtraction cutoff. We also study their numerical impact for the case of gluon-fusion Higgs production in the H → γγdecay mode and for pp → γγ direct diphoton production. We find that the relative enhancement of the additional cut-induced power corrections tends to be more severe forq T , where it can reach an order of magnitude or more, depending on the choice of parameters and subtraction cutoffs. We discuss how all such cuts can be incorporated without causing additional power corrections by implementing the subtractions differentially rather than through a global slicing method. We also highlight the close relation of this formulation of the subtractions to the projection-to-Born method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Subleading power rapidity divergences and power corrections for q T
A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum (q T ) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-x logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding MS¯-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the q T spectrum for color-singlet production, for which we compute the complete $q$ $^{2}_{T}$/Q 2 suppressed power corrections at O(α s ), including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Power corrections for N-jettiness subtractions at $ \mathcal{O}\left({\alpha}_s\right) $
We continue the study of power corrections for N -jettiness subtractions by analytically computing the complete next-to-leading power corrections at O(α s ) for colorsinglet production. This includes all nonlogarithmic terms and all partonic channels for Drell-Yan and gluon-fusion Higgs production. These terms are important to further improve the numerical performance of the subtractions, and to better understand the structure of power corrections beyond their leading logarithms, in particular their universality. We emphasize the importance of computing the power corrections differential in both the invariant mass, Q, and rapidity, Y, of the color-singlet system, which is necessary to account for the rapidity dependence in the subtractions. This also clarifies apparent disagreements in the literature. Performing a detailed numerical study, we find excellent agreement of our analytic results with a previous numerical extraction.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
N -jettiness subtractions for g g → H at subleading power
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Soft functions for generic jet algorithms and observables at hadron colliders
Here, we introduce a method to compute one-loop soft functions for exclusive N - jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the N -jettiness hemisphere decomposition of ref. [1] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti- k T , XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in pp → L + 1 jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius R . We find that the small- R results, including corrections up to O(R 2 ), accurately capture the full behavior over a large range of R .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Subleading power corrections for N -jettiness subtractions
Here, the N -jettiness observable T N provides a way of describing the leading singular behavior of the N -jet cross section in the τ = T N = Q → 0 limit, where Q is a hard interaction scale. We consider subleading power corrections in the τ << 1 expansion, and employ soft-collinear effective theory to obtain analytic results for the dominant α s τlnτ and α 2 s τln 3 τ subleading terms for thrust in e + e – collisions and 0-jettiness for q¯q-initiated Drell-Yan–like processes at hadron colliders. These results can be used to significantly improve the numerical accuracy and stability of the N -jettiness subtraction technique for performing fixed order calculations at next-to-leading order and next-to-next-to-leading order. They reduce the size of missing power corrections in the subtractions by an order of magnitude. We also point out that the precise definition of N -jettiness has an important impact on the size of the power corrections and thus the numerical accuracy of the subtractions. The sometimes employed definition of N -jettiness in the hadronic center-ofmass frame suffers from power corrections that grow exponentially with rapidity, causing the power expansion to deteriorate away from central rapidity. This degradation does not occur for the original N -jettiness definition, which explicitly accounts for the boost of the Born process relative to the frame of the hadronic collision, and has a well-behaved power expansion throughout the entire phase space. Integrated over rapidity, using this N -jettiness definition in the subtractions yields another order of magnitude improvement compared to employing the hadronic-frame definition.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Factorization for jet radius logarithms in jet mass spectra at the LHC
To predict the jet mass spectrum at a hadron collider it is crucial to account for the resummation of logarithms between the transverse momentum of the jet and its invariant mass m J . For small jet areas there are additional large logarithms of the jet radius R, which affect the convergence of the perturbative series. We present an analytic framework for exclusive jet production at the LHC which gives a complete description of the jet mass spectrum including realistic jet algorithms and jet vetoes. It factorizes the scales associated with m J , R, and the jet veto, enabling in addition the systematic resummation of jet radius logarithms in the jet mass spectrum beyond leading logarithmic order. We discuss the factorization formulae for the peak and tail region of the jet mass spectrum and for small and large R, and the relations between the different regimes and how to combine them. Regions of experimental interest are classified which do not involve large nonglobal logarithms. We also present universal results for nonperturbative effects and discuss various jet vetoes.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Underlying-event sensitive observables in Drell–Yan production using GENEVA
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Exploiting jet binning to identify the initial state of high-mass resonances
If a new high-mass resonance is discovered at the Large Hadron Collider, model-independent techniques to identify the production mechanism will be crucial to understand its nature and effective couplings to Standard Model particles. In this paper, we present a powerful and model-independent method to infer the initial state in the production of any high-mass color-singlet system by using a tight veto on accompanying hadronic jets to divide the data into two mutually exclusive event samples (jet bins). For a resonance of several hundred GeV, the jet binning cut needed to discriminate quark and gluon initial states is in the experimentally accessible range of several tens of GeV. It also yields comparable cross sections for both bins, making this method viable already with the small event samples available shortly after a discovery. Theoretically, the method is made feasible by utilizing an effective field theory setup to compute the jet cut dependence precisely and model independently and to systematically control all sources of theoretical uncertainties in the jet binning, as well as their correlations. Finally, we use a 750 GeV scalar resonance as an example to demonstrate the viability of our method.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Employing helicity amplitudes for resummation
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. In this study, we construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in 4- and d-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for pp → H + 0, 1, 2 jets, pp → W/Z/γ + 0, 1, 2 jets, and pp → 2, 3 jets. Finally, these operator bases are completely crossing symmetric, so the results can easily be applied to processes with e + e - and e - p collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
XCone: N-jettiness as an exclusive cone jet algorithm
We introduce a new jet algorithm called XCone, for eXclusive Cone, which is based on minimizing the event shape N -jettiness. Because N -jettiness partitions every event into N jet regions and a beam region, XCone is an exclusive jet algorithm that always returns a fixed number of jets. We use a new “conical geometric” measure for which well-separated jets are bounded by circles of radius R in the rapidity-azimuth plane, while overlapping jet regions automatically form nearest-neighbor “clover jets”. This avoids the split/merge criteria needed in inclusive cone algorithms. A key feature of XCone is that it smoothly transitions between the resolved regime where the N signal jets of interest are well separated and the boosted regime where they overlap. The returned value of N -jettiness also provides a quality criterion of how N -jet-like the event looks. We also discuss the N -jettiness factorization theorems that occur for various jet measures, which can be used to compute the associated exclusive N -jet cross sections. In a companion paper [1], the physics potential of XCone is demonstrated using the examples of dijet resonances, Higgs decays to bottom quarks, and all-hadronic top pairs.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Dissecting Soft Radiation with Factorization
An essential part of high-energy hadronic collisions is the soft hadronic activity that underlies the primary hard interaction. It includes soft radiation from the primary hard partons, secondary multiple parton interactions (MPI), and factorization-violating effects. The invariant mass spectrum of the leading jet in $Z+\mathrm{jet}$ and $H+\mathrm{jet}$ events is directly sensitive to these effects, and we use here a QCD factorization theorem to predict its dependence on the jet radius $R$, jet ${p}_{T}$, jet rapidity, and partonic process for both the perturbative and nonperturbative components of primary soft radiation. We prove that the nonperturbative contributions involve only odd powers of $R$, and the linear $R$ term is universal for quark and gluon jets. The hadronization model in Pythia8 agrees well with these properties. The perturbative soft initial state radiation (ISR) has a contribution that depends on the jet area in the same way as the underlying event, but this degeneracy is broken by dependence on the jet ${p}_{T}$. The size of this soft ISR contribution is proportional to the color state of the initial partons, yielding the same positive contribution for $gg{\rightarrow}Hg$ and $gq{\rightarrow}Zq$, but a negative interference contribution for $q\overline{q}{\rightarrow}Zg$. Hence, measuring these dependencies allows one to separate hadronization, soft ISR, and MPI contributions in the data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗