The effects of quark-sector Lorentz violation on deep inelastic electron-proton scattering are studied. We show that existing data can be used to establish first constraints on numerous coefficients for Lorentz violation in the quark sector at an estimated sensitivity of parts in a million.Comment: 8 pages, version published in Physics Letters

We address the subject of chiral anomalies in two and four dimensional theories. Ambiguities associated with the γ 5 algebra within divergent integrals are identified, even though the physical dimension is not altered in the process of regularization. We present a minimal prescription that leads to unique results and apply it to a series of examples. For the particular case of abelian theories with effective chiral vertices, we show: 1-Its implication on the way to display the anomalies democratically in the Ward identities. 2-The possibility to fix an arbitrary surface term in such a way that a momentum routing independent result emerges. This leads to a reinterpretation of the role of momentum routing in the process of choosing the Ward identity to be satisfied in an anomalous process. 3-Momentum Routing Invariance (MRI) is a necessary and sufficient condition to assure vectorial gauge invariance of effective chiral Abelian gauge theories. We also briefly discuss the case of complete chiral theories, using the Chiral Schwinger Model as an example. *

We address the study of gauge invariance in the Standard Model Extension which encompasses all Lorentz-violating terms originated by spontaneous symmetry breaking at the Planck scale. In particular, we fully evaluate Ward identities involving two and three point functions and derive the conditions which assure gauge invariance of the electromagnetic sector of the Standard Model Extension at one-loop. We show that momentum routing invariance is sufficient to fix arbitrary and regularization dependent parameters intrinsic to perturbation theory in the diagrams involved. A scheme which judiciously collects finite but undetermined quantum corrections is employed, a particularly subtle issue in the presence of γ5 matrices.

A framework is presented for the factorization of high-energy hadronic processes in the presence of Lorentz and CPT violation. The comprehensive effective field theory describing Lorentz and CPT violation, the Standard-Model Extension, is used to demonstrate factorization of the hadronic tensor at leading order in electroweak interactions for deep inelastic scattering and for the Drell-Yan process. Effects controlled by both minimal and nonminimal coefficients for Lorentz violation are explored, and the equivalent parton-model description is derived. The methodology is illustrated by determining cross sections and studying estimated attainable sensitivities to Lorentz violation using real data collected at the Hadronen-Elektronen Ring Anlage and the Large Hadron Collider and simulated data for the future US-based electron-ion collider.√ 2 (γ 0 + γ 3 ), γ i ⊥ = γ 1 , γ 2 . The ellipses

It is generally assumed that in order to preserve Bose symmetry in the left-(or right-chiral) current it is necessary to equally distribute the chiral anomaly between the vectorial and the axial Ward identities, requiring the use of counterterms to restore consistency. In this work, we show how to calculate the quantum breaking of the left-and right-chiral currents in a way that allows to preserve Bose symmetry independently of the chiral anomaly, using the Implicit Regularization method.

a b s t r a c tIn this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

The induction of a Lorentz-and CPT-violating Chern-Simons-like term in a fermionic theory embedded in linearized quantum gravity is reassessed. We explicitly show that gauge symmetry on underlying Feynman diagrams does not fix the arbitrariness inherent to such induced term at one loop order. We present the calculation in a nonperturbative expansion in the Lorentz-violating parameter bµ and within a framework which, besides operating in the physical dimension, judiciously parametrizes regularization dependent arbitrary parameters usually fixed by symmetries.

We compute the two-loop $$\beta $$ β -function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.