Decomposition of d = 9 short-range 0νββ decay operators at one-loop level

We perform a systematical study of the dimension-9 short-range 0νββ decay operators at one-loop level. There are only six genuine topologies which generate eight diagrams, and the recipe to identify the possible one-loop realizations of the 0νββ decay operators is sketched. Certain hypercharge assignments are excluded by the absence of tree-level diagrams in a genuine one-loop model. The mediators of each decomposition can generate Majorana neutrino masses which are discussed up to two-loop level. We present an example of 0νββ decay model in which the neutrino masses are generated at two-loop level, and the short-range contribution can be comparable with the mass mechanism in some region of parameter space.

Two-loop application of the Breitenlohner-Maison/’t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

We apply the BMHV scheme for non-anticommuting γ5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

Extracting Einstein from the loop-level double-copy

The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity.

Infrared Effects

It is shown that the presence of zero mass particles makes the elements of the S-matrix divergent. We explain the physical origin of such divergences. We argue that they are due to the long range of the interactions which violate the assumptions we made when we derived the asymptotic conditions for scattering. We study these divergences in the particular case of QED at tree, as well as one-loop level and present the Bloch–Nordsieck solution. We show that the cancellation of infrared divergences among virtual exchanged and real emitted soft photons is true to all orders in the perturbation expansion and we obtain the Sudakov double logarithm formula for Coulomb scattering.

On differential operators and unifying relations for 1-loop Feynman integrands

We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

Probing the dark axion portal with muon anomalous magnetic moment

We propose a new scenario of using the dark axion portal at one-loop level to explain the recently observed muon anomalous magnetic moment by the Fermilab Muon g-2 experiment. Both axion/axion-like particle (ALP) and dark photon are involved in the same vertex with photon. Although ALP or dark photon alone cannot explain muon $$g-2$$ g - 2 , since the former provides only negative contribution while the latter has very much constrained parameter space, dark axion portal can save the situation and significantly extend the allowed parameter space. The observed muon anomalous magnetic moment provides a robust probe of the dark axion portal scenario.

Gluon fragmentation into 3$$ {P}_J^{\left[1,8\right]} $$ quark pair and test of NRQCD factorization at two-loop level

The next-to-leading order (NLO) ($$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in 3$$ {P}_J^{\left[1,8\right]} $$ P J 1 8 states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) perturbative NRQCD matrix elements ⟨$$ {\mathcal{O}}^3{P}_J^{\left[1,8\right]} $$ O 3 P J 1 8 (3$$ {S}_1^{\left[8\right]} $$ S 1 8 )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

Lotty – The loop-tree duality automation

Elaborating on the novel formulation of the loop-tree duality, we introduce the Mathematica package Lotty that automates the latter at multi-loop level. By studying the features of Lotty and recalling former studies, we discuss that the representation of any multi-loop amplitude can be brought in a form, at integrand level, that only displays physical information, which we refer to as the causal representation of multi-loop Feynman integrands. In order to elucidate the role of Lotty in this automation, we recall results obtained for the calculation of the dual representation of integrands up-to four loops. Likewise, within Lotty framework, we provide support to the all-loop causal representation recently conjectured by the same author. The numerical stability of the integrands generated by Lotty is studied in two-loop planar and non-planar topologies, where a numerical integration is performed and compared with known results.

Three-loop vertex integrals at symmetric point

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the ε-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.