Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where |t| ≪ s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude’s rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. We also discuss criteria for factorization violation.

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An effective field theory for forward scattering and factorization violation

The transverse momentum distribution of massive neutral vector bosons can be measured to high accuracy at hadron colliders The transverse momentum is caused by a partonic recoil, and is determined by QCD dynamics We compute the single and double-differential transverse momentum distributions for fully inclusive Z/γ
 ∗ production including leptonic decay to next-to-next-to-leading order (NNLO) in perturbative QCD We also compute the same distributions normalised to the cross sections for inclusive Z/γ
 ∗ production, ie integrated over the transverse momentum of the lepton pair We compare our predictions for the fiducial cross sections to the 8 TeV data set from the ATLAS and CMS collaborations, which both observed a tension between data and NLO theory predictions, using the experimental cuts and binning We find that the inclusion of the NNLO QCD effects does not fully resolve the tension with the data for the unnormalised p
 distribution However, we observe that normalising the NNLO Z-boson transverse momentum distribution by the NNLO Drell-Yan cross section substantially improves the agreement between experimental data and theory, and opens the way for precision QCD studies of this observable

/pdf/the-nnlo-qcd-corrections-to-z-boson-production-at-large-eholi438eh.pdf

The NNLO QCD corrections to Z boson production at large transverse momentum

Model-independent constraints on $\Delta F=2$ operators and the scale of new physics

In recent years, experiments revealed intriguing hints for new physics (NP) in semi-leptonic B decays. Both in charged current processes, involving b → cτν transitions, and in the neutral currents b → sl +l −, a preference for NP compared to the standard model (SM) of more that 3σ and 5σ was found, respectively. In addition, there is the long-standing tension between the theory prediction and the measurement of the anomalous magnetic moment (AMM) of the muon (aμ) of more than 3σ. Since all these observables are related to the violation of lepton flavor universality (LFU), a common NP explanation seems not only plausible but is even desirable. In this context, leptoquarks (LQs) are especially promising since they give tree-level effects in semi-leptonic B decays, but only loop-suppressed effects in other flavor observables that agree well with their SM predictions. Furthermore, LQs can lead to a mt/mμ enhanced effect in aμ, allowing for an explanation even with (multi) TeV particles. However, a single scalar LQ representation cannot provide a common solution to all three anomalies. In this article we therefore consider a model in which we combine two scalar LQs: the SU(2)L singlet and the SU(2)L triplet. Within this model we compute all relevant 1-loop effects and perform a comprehensive phenomenological analysis, pointing out various interesting correlations among the observables. Furthermore, we identify benchmark points which are in fact able to explain all three anomalies (b → cτν, b → sl +l − and aμ), without violating bounds from other observables, and study their predictions for future measurements.

/pdf/flavor-phenomenology-of-the-leptoquark-singlet-triplet-model-22cwle4xzb.pdf

Flavor phenomenology of the leptoquark singlet-triplet model

Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading-power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the radiative jet function, responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.

/pdf/a-factorization-approach-to-next-to-leading-power-threshold-4f3c8knq10.pdf

A factorization approach to next-to-leading-power threshold logarithms

https://pure.uva.nl/ws/files/9800687/The_method_of_regions.pdf

The method of regions and next-to-soft corrections in Drell–Yan production

We study the phenomenology of simplified ${Z}^{\ensuremath{'}}$ models with a global $U(2{)}^{3}$ flavor symmetry in the quark sector, broken solely by the Standard Model Yukawa couplings. This flavor symmetry, known as less-minimal flavor violation, protects $\mathrm{\ensuremath{\Delta}}F=2$ processes from dangerously large new physics (NP) effects and at the same time provides a free complex phase in $b\ensuremath{\rightarrow}s$ transitions, allowing for an explanation of the hints for additional direct $CP$ violation in kaon decays (${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$) and in hadronic $B$-decays ($B\ensuremath{\rightarrow}K\ensuremath{\pi}$ puzzle). Furthermore, including the couplings of the ${Z}^{\ensuremath{'}}$ boson to the leptons, it is possible to address the intriguing hints for NP (above the $5\ensuremath{\sigma}$ level) in $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ transitions. Taking into account all flavor observables in a global fit, we find that our model can (for the first time) provide a common explanation for ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$, the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ puzzle and $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ data. Sizeable $CP$ violation in $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ observables, in particular ${A}_{8}$, is predicted, which can be tested in the near future, and an explanation of the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ and ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ puzzles leads to effects in dijet tails at the LHC that are not far below the current limits. If we require that also $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ anomalies are explained, cancellations in dimuon tails (possibly by a second ${Z}^{\ensuremath{'}}$) are needed to satisfy LHC data.

Z′ models with less-minimal flavor violation

High-energy QCD amplitudes at two loops and beyond

Using an iterative solution of rapidity evolution equations, we compute partonic $2\to 2$ gauge theory amplitudes at four loops in full colour up to the Next-to-Next-to-Leading Logarithms (NNLL) in the Regge limit. By contrasting the resulting amplitude with the exponentiation properties of soft singularities we determine the four-loop correction to the soft anomalous dimension at this logarithmic accuracy, which universally holds in any gauge theory. We find that the latter features quartic Casimir contributions beyond those appearing in the cusp anomalous dimension. Finally, in the case of ${\cal N}=4$ super Yang-Mills, we also determine the finite hard function at four loops through NNLL in full colour.

Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour

There are strong similarities between charge-parity ($CP$) violating observables in hadronic $B$ decays (in particular $\mathrm{\ensuremath{\Delta}}{A}_{CP}^{\ensuremath{-}}$ in $B\ensuremath{\rightarrow}K\ensuremath{\pi}$) and direct $CP$ violation in kaon decays (${\ensuremath{\epsilon}}^{\ensuremath{'}}$): All these observables are very sensitive to new physics (NP) which is at the same time $CP$ and isospin violating (i.e., NP with complex couplings which are different for up quarks and down quarks). Intriguingly, both the measurements of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ and $\mathrm{\ensuremath{\Delta}}{A}_{CP}^{\ensuremath{-}}$ show deviations from their Standard Model predictions, calling for a common explanation (the latter is known as the $B\ensuremath{\rightarrow}K\ensuremath{\pi}$ puzzle). For addressing this point, we parametrize NP using a gauge invariant effective field theory approach combined with a global $U(2{)}^{3}$ flavor symmetry in the quark sector (also known as less-minimal flavor violation). We first determine the operators which can provide a common explanation of ${\ensuremath{\epsilon}}^{\ensuremath{'}}$ and $\mathrm{\ensuremath{\Delta}}{A}_{CP}^{\ensuremath{-}}$ and then perform a global fit of their Wilson coefficients to the data from hadronic $B$ decays. Here we also include e.g., the recently measured $CP$ asymmetry in ${B}_{s}\ensuremath{\rightarrow}KK$ as well as the purely isospin violating decay ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\rho}}^{0}$, finding a consistent NP pattern providing a very good fit to data. Furthermore, we can at the same time explain ${\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon}$ for natural values of the free parameters within our $U(2{)}^{3}$ flavor approach, and this symmetry gives interesting predictions for hadronic decays involving $b\ensuremath{\rightarrow}d$ transitions.

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Leonardo Vernazza

Papers

The method of regions and next-to-soft corrections in Drell–Yan production

Z′ models with less-minimal flavor violation

High-energy QCD amplitudes at two loops and beyond

Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour

Correlating ε′/ε with hadronic B decays via U(2)3 flavor symmetry