Within the Standard Model, the branching fraction of the rare decay $$ {B}_s\to {K}^0{\overline{K}}^0 $$ is related to other decay rates and CP asymmetries through the approximate SU(3) flavor symmetry of the strong interactions and the heavy-quark limit. Three such relations were shown to be violated at a level of about 3$\textit{σ}$ each. By means of a systematic search for new-physics explanations of these puzzles, we find that possible solutions are highly fine-tuned and either excluded by other data or rather implausible. The tight correlation between $$ {B}_s\to K\overline{K} $$ and $\textit{B}$ → $\textit{πK}$ decays, which is maintained even in the presence of flavor-specific new-physics operators, plays a central role in our analysis.

United States

Yuval Grossman

Germany

Matthias Neubert

Israel

Yosef Nir

Yogev Shpilman

Yehonatan Viernik

$$ {B}_s\to {K}^0{\overline{K}}^0 $$ beyond the Standard Model

<p>We analyze the low-energy dynamics of gap-between-jets cross sections at hadron colliders, for which phase factors in the hard amplitudes spoil collinear cancellations and lead to double (“super-leading”) logarithmic behavior. Based on a method-of-regions analysis, we identify three-loop contributions from perturbative active-active Glauber-gluon exchanges with the right structure to render the cross section consistent with PDF factorization below the gap veto scale. The Glauber contributions we identify are unambiguously defined without regulators beyond dimensional regularization.</p>

Switzerland

Thomas Becher

Patrick Hager

Sebastian Jaskiewicz

Dominik Schwienbacher

Factorization Restoration through Glauber Gluons

Jet observables at hadron colliders feature “super-leading” logarithms, double-logarithmic corrections resulting from a breakdown of color coherence due to complex phases in hard-scattering amplitudes. While these effects only arise in high orders of perturbation theory and are suppressed in the large- limit, they formally constitute leading logarithmic corrections to the cross sections. We present the first analysis of the corresponding contributions to a hadronic cross section, including all partonic channels and interference effects. Interestingly, some interference terms in partonic $$ q\overline{q} $$ → $$ q\overline{q} $$ scattering are only linearly suppressed in 1 . Our results for the → 2 jets gap-between-jets cross section demonstrate the numerical importance of super-leading logarithms for small values of the veto scale , showing that these contributions should be accounted for in precision studies of such observables.

Giuliano Martinelli

Michel Stillger

Super-leading logarithms in

A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

Philipp Böer

Xiaofeng Xu

Renormalization-group improved resummation of super-leading logarithms

The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of Glauber phases. Building on the formalism of [1], it is shown that the leading terms in this series for large N  c  can be resummed in closed form in renormalization-group improved perturbation theory. This remarkable observation suggests that large-N  c  methods might also be helpful to study other aspects of non-global logarithms at hadron colliders, and to combine our analytic results with amplitude-level parton showers.

Resummation of Glauber phases in non-global LHC observables for large N  c

The weak decays K  ±  → π  ±  a offer a powerful probe of axion-like particles (ALPs). In this work, we provide a comprehensive analysis of these processes within chiral perturbation theory, extending existing calculations by including complete next-to-leading order (NLO) contributions and isospin-breaking corrections at first order in (m  d  – m  u ). We show that the consistent incorporation of ALPs in the QCD and weak chiral Lagrangians requires a non-trivial extension of the corresponding operator bases, which we describe in detail. Furthermore, we show that in the presence of an ALP the so-called “weak mass term”, which is unobservable in the Standard Model, is non-redundant already at leading order. We find that NLO corrections associated with flavor-violating ALP couplings modify the leading-order result by a few percent, with negligible uncertainties. NLO corrections proportional to flavor-conserving ALP couplings lead to potentially larger corrections, which, however, are accompanied by sizable uncertainties mainly due to the currently limited knowledge of various low-energy constants. We study how these corrections impact bounds on the ALP couplings, first model independently, and then specializing to the case of an ALP with flavor-universal couplings in the UV. Our findings confirm that the decays K  ±  → π  ±  a provide the strongest particle-physics constraints for m  a  ≲ 300 MeV. In addition, we point out that these bounds have interesting implications for the ALP couplings to nucleons, which were so far only constrained by astrophysical measurements and non-accelerator experiments.

Claudia Cornella

Anne Galda

Daniel Wyler

K ± → π ±a at next-to-leading order in chiral perturbation theory and updated bounds on ALP couplings

Axions and axion-like particles emerge in many models for physics beyond the Standard Model. Thus, they have gained increasing research interest in both experimental and theoretical physics apart from their original proposition as a solution to the strong CP-problem. Among other aspects it has recently been shown that ALPs can potentially provide a solution to the long-lasting discrepancy between theory and experiment of the anomalous magnetic moment of the muon. Provided that the ALP has flavor-violating couplings to leptons, they can also mediate flavor-violating decays like  $$\mu \rightarrow e\gamma $$  <math> <mrow> <mi>μ</mi> <mo>→</mo> <mi>e</mi> <mi>γ</mi> </mrow> </math>  . Both processes are mediated through related form factors that we compute to two-loop order. We further show numerical implications of our calculations and how they might affect constraints on ALP couplings derived from experiments.

Marvin Schnubel

Two-loop contributions of axion-like particles to electromagnetic and chromomagnetic form factors

The resummation of the “Glauber series” in non-global LHC observables is extended to processes with gluons in the initial state. This series simultaneously incorporates large double-logarithmic corrections, the so-called “super-leading logarithms”, together with higher-order exchanges of pairs of Glauber gluons associated with the large numerical factor (iπ)2. On a technical level, the main part of this work is devoted to the systematic reduction of the appearing color traces and construction of basis structures, which consist of thirteen elements for gg and eleven elements for qg scattering. Numerical estimates for wide-angle gap-between-jet cross sections at the parton level show that, in particular for gg scattering at relatively small vetoes Q 0, the contribution involving four Glauber exchanges gives a sizeable correction and should not be neglected.

Glauber phases in non-global LHC observables: resummation for gluon-initiated processes

We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy   <math> <msqrt> <mover> <mi>s</mi> <mo>̂</mo> </mover> </msqrt> </math>  $$ \sqrt{\hat{s}} $$ , and low-energy matrix elements, which are sensitive to the low scale Q 0 ≪   <math> <msqrt> <mover> <mi>s</mi> <mo>̂</mo> </mover> </msqrt> </math>  $$ \sqrt{\hat{s}} $$  characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary 2 → M jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called “super-leading logarithms” discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for pp → 2 jets processes, but suppressed in H/Z and H/Z + jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.

China

Ding Shao

Factorization of non-global LHC observables and resummation of super-leading logarithms

The low-energy effective field theory (LEFT) provides the appropriate framework to describe particle interactions below the scale of electroweak symmetry breaking, μ  w  ~ v. By matching the Standard Model onto the LEFT, non-zero Wilson coefficients of higher-dimensional operators are generated, suppressed by the corresponding power of 1/v. An axion or axion-like particle (ALP) with mass m  a  ≪ μ  w  that interacts with the Standard Model via classically shift-invariant dimension-five operators would also contribute to the LEFT Wilson coefficients, since it can appear as a virtual particle in divergent Green’s functions and thus has an impact on the renormalization of the LEFT operators. We present the full set of one-loop ALP-induced source terms modifying the renormalization-group evolution equations of the LEFT Wilson coefficients up to dimension-six order. Our framework allows for model-independent ALP searches at low energies from current bounds on LEFT Wilson coefficients. As a concrete application, we present an improved prediction for ALP effects on the anomalous magnetic moment of the muon.