Algebraic Structure of Lepton and Quark Flavor Invariants and CP Violation

Lepton and quark flavor invariants are studied, both in the Standard Model with a dimension five Majorana neutrino mass operator, and in the seesaw model. The ring of invariants in the lepton sector is highly non-trivial, with non-linear relations among the basic invariants. The invariants are classified for the Standard Model with two and three generations, and for the seesaw model with two generations, and the Hilbert series is computed. The seesaw model with three generations proved computationally too difficult for a complete solution. We give an invariant definition of the CP-violating angle theta in the electroweak sector

Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching

The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $\Delta B= \pm \Delta L = \pm 1$, $\Delta L=\pm 2$, and $\Delta L=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order $1/\Lambda^2$ is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.Comment: 44 pages, 22 tables; version published in JHE

On Gauge Invariance and Minimal Coupling

The principle of minimal coupling has been used in the study of Higgs boson interactions to argue that certain higher dimensional operators in the low-energy effective theory generalization of the Standard Model are suppressed by loop factors, and thus smaller than others. It also has been extensively used to analyze beyond-the-standard-model theories. We show that in field theory, and even in quantum mechanics, the concept of minimal coupling is ill-defined and inapplicable as a general principle, and give many pedagogical examples which illustrate this fact. We also clarify some related misconceptions about the dynamics of strongly coupled gauge theories. Many arguments in the literature on Higgs boson interactions that use minimal coupling, particularly in pseudo-Goldstone Higgs theories, are inherently flawed.Comment: 25 pp, 2 figures v2: refs added, JHEP version, conclusions unchange

Analysis of General Power Counting Rules in Effective Field Theory

We derive the general counting rules for a quantum effective field theory (EFT) in $\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of cross sections is controlled by the $\Lambda$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ($\chi$PT). The relation between $\Lambda$ and $f$ is generalized to $\mathsf{d}$ dimensions. We show that the naive dimensional analysis $4\pi$ counting is related to $\hbar$ counting. The EFT counting rules are applied to $\chi$PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.Comment: V2: more details and examples added; version published in journal. 17 pages, 4 figures, 2 table

Non-Perturbative Effects in μ→eγ\mu \to e \gamma

We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q \sigma^{\mu \nu} q)(\bar \ell \sigma_{\mu \nu} \ell)$ to the purely leptonic process $\mu \to e \gamma$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $\mu \to e$ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $\Lambda_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions.Comment: 21 pages, 1 figure; version published in JHE

A Lattice Test of 1/N_c Baryon Mass Relations

1/N_c baryon mass relations are compared with lattice simulations of baryon masses using different values of the light-quark masses, and hence different values of SU(3) flavor-symmetry breaking. The lattice data clearly display both the 1/N_c and SU(3) flavor-symmetry breaking hierarchies. The validity of 1/N_c baryon mass relations derived without assuming approximate SU(3) flavor-symmetry also can be tested by lattice data at very large values of the strange quark mass. The 1/N_c expansion constrains the form of discretization effects; these are suppressed by powers of 1/N_c by taking suitable combinations of masses. This 1/N_c scaling is explicitly demonstrated in the present work.Comment: 13 pages, 20 figures; v2 version to be published in PR

Renormalization Group Scaling of Higgs Operators and \Gamma(h -> \gamma \gamma)

We compute the renormalization of dimension six Higgs-gauge boson operators that can modify \Gamma(h -> \gamma \gamma) at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consistent with renormalization group evolution. We study the implications of our results for Higgs phenomenology and for new physics models which attempt to explain a deviation in \Gamma(h -> \gamma \gamma). We derive a new relation between the S parameter and the \Gamma(h -> \gamma \gamma) and \Gamma(h ->Z \gamma) decay rates.Comment: 20 pp. 2 fi

Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC

Previous work on electroweak radiative corrections to high energy scattering using soft-collinear effective theory (SCET) has been extended to include external transverse and longitudinal gauge bosons and Higgs bosons. This allows one to compute radiative corrections to all parton-level hard scattering amplitudes in the standard model to NLL order, including QCD and electroweak radiative corrections, mass effects, and Higgs exchange corrections, if the high-scale matching, which is suppressed by two orders in the log counting, and contains no large logs, is known. The factorization structure of the effective theory places strong constraints on the form of gauge theory amplitudes at high energy for massless and massive gauge theories, which are discussed in detail in the paper. The radiative corrections can be written as the sum of process-independent one-particle collinear functions, and a universal soft function. We give plots for the radiative corrections to q qbar -> W_T W_T, Z_T Z_T, W_L W_L, and Z_L H, and gg -> W_T W_T to illustrate our results. The purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at 2 TeV for transverse W pair production, and increasing rapidly with energy. The estimated theoretical uncertainty to the partonic (hard) cross-section in most cases is below one percent, smaller than uncertainties in the parton distribution functions (PDFs). We discuss the relation between SCET and other factorization methods, and derive the Magnea-Sterman equations for the Sudakov form factor using SCET, for massless and massive gauge theories, and for light and heavy external particles.Comment: 44 pages, 30 figures. Refs added, typos fixed. ZL ZL plots removed because of a possible subtlet