We study a non-universal flavor scenario at the level of the Standard Model Effective Field Theory, according to which the matrix of Wilson coefficients $\textit{c}$ of an up-type electroweak quark dipole operator is aligned with the up-type Yukawa coupling. Such an alignment usually follows from the assumption of Minimal Flavor Violation (MFV), away from which we step by allowing the entries of $\textit{c}$ to be sizable along the first quark generations. A particular example, which we refer to as “inverse hierarchy MFV”, features Wilson coefficients inversely proportional to quark masses, and arises from BSM models respecting MFV and containing heavy fields that replicate the mass hierarchy of SM quarks. We then analyze the phenomenology driven by $\textit{c}$ at colliders and at lower-energy flavor experiments. We show that precision measurements of the process $\textit{pp}$ → $\textit{Wh}$ → $\textit{γγℓν}$ at FCC-$\textit{hh}$ could set an upper bound on |$\textit{c}$ | ≲ $$ \mathcal{O} $$ (10 )(Λ$\textit{/}$TeV) , with Λ the cutoff of the effective field theory. This bound is an order of magnitude stronger than the existing LHC bounds. Moreover, we estimate that $\textit{Wh}$ → $$ b\overline{b}\ell \nu $$ at HL-LHC could also give competitive bounds. In the low-energy regime, we consider bounds arising from rare kaon decays, which turn out to be loose, | $$ {c}_{uW}^{11} $$ | $\textit{<}$ $$ \mathcal{O} $$ (1)(Λ$\textit{/}$TeV) . We finally demonstrate that our flavor and operator assumptions can be derived from a weakly-coupled UV model, which we choose to simultaneously illustrate the UV origin of inverse hierarchy MFV.

United States

Germany

France

Quentin Bonnefoy

Jonathan Kley

Di Liu

United Kingdom

Alejo Rossia

China

Chang-Yuan Yao

Aligned yet large dipoles: a SMEFT study

The quantum chromodynamics (QCD) axion may solve the strong <math><mi>C</mi><mi>P</mi></math> problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>PQ</mi></mrow></msub></math> Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals.

Joshua N. Benabou

Netherlands

Malte Buschmann

Soubhik Kumar

Benjamin R. Safdi

Cosmological dynamics of string theory axion strings

We extend the covariant color-kinematics duality introduced by Cheung and Mangan to effective field theories. We focus in particular on relations between the effective field theories of gluons only and of gluons coupled to bi-adjoint scalars. Maps are established between their respective equations of motion and between their tree-level scattering amplitudes. An additional rule for the replacement of flavor structures by kinematic factors realizes the map between higher-derivative amplitudes. As an example of new relations, the pure-gluon amplitudes of mass dimension up to eight, featuring insertions of the F 3 and F 4 operators which satisfy the traditional color-kinematics duality, can be generated at all multiplicities from just renormalizable amplitudes of gluons and bi-adjoint scalars. We also obtain closed-form expressions for the kinematic numerators of the dimension-six gluon effective field theory, which are valid in D space-time dimensions. Finally, we find strong evidence that this extended covariant color-kinematics duality relates the (DF)2+YM(+ϕ 3) theories which, at low energies, generate infinite towers of operators satisfying the traditional color-kinematics duality, beyond aforementioned F 3 and F 4 ones.

CERN

Belgium

Gauthier Durieux

Jasper Nepveu

Higher-derivative relations between scalars and gluons

We study thermal production of dark matter (DM) in a realization of the minimal models of Bonnefoy et al. [Phys. Rev. Lett. 131, 221802 (2023)], where parity is used to solve the strong <math><mi>C</mi><mi>P</mi></math> problem by transforming the entire Standard Model (SM) into a mirror copy. Although the mirror electron <math><msup><mi>e</mi><mo>′</mo></msup></math> is a good DM candidate, its viability is mired by the presence of the mirror up quark <math><msup><mi>u</mi><mo>′</mo></msup></math>, whose abundance is intimately related to the <math><msup><mi>e</mi><mo>′</mo></msup></math> abundance and must be suppressed. This can be achieved through a sequential freeze-in mechanism, where mirror photons are first produced from SM gluons, and then the mirror photons produce <math><msup><mi>e</mi><mo>′</mo></msup></math>. After computing the details of this double freeze-in, we discuss the allowed parameter space of the model, which lies at the threshold of experimental observations. We find that this origin of <math><msup><mi>e</mi><mo>′</mo></msup></math> DM requires a low reheating temperature after inflation and is consistent with the baryon asymmetry arising from leptogenesis, providing mirror neutrinos have a significant degeneracy. Finally, we show that this <math><msup><mi>e</mi><mo>′</mo></msup></math> DM is not compatible with Higgs parity, the simplest scheme with exact parity, unless SM parameters deviate significantly from their central values or the minimal model is extended.

Lawrence Hall

Claudio Andrea Manzari

Amara McCune

Christiane Scherb

Dark matter in a mirror solution to the strong <math><mi>C</mi><mi>P</mi></math> problem

We propose theories of a complete mirror world with parity (<math><mi>P</mi></math>) solving the strong <math><mi>C</mi><mi>P</mi></math> problem. <math><mrow><mi>P</mi></mrow></math> exchanges the entire standard model with its mirror copy. We derive bounds on the two new mass scales that arise: <math><msup><mi>v</mi><mo>′</mo></msup></math> where parity and mirror electroweak symmetry are spontaneously broken, and <math><msub><mi>v</mi><mn>3</mn></msub></math> where the color groups break to the diagonal strong interactions. The strong <math><mi>C</mi><mi>P</mi></math> problem is solved even if <math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>≪</mo><msup><mrow><mi>v</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math>, when heavy colored states at the scale <math><msub><mi>v</mi><mn>3</mn></msub></math> may be accessible at LHC and future colliders. Furthermore, we argue that the breaking of <math><mi>P</mi></math> introduces negligible contributions to <math><msub><mover><mi>θ</mi><mo>¯</mo></mover><mi>QCD</mi></msub></math>, starting at three-loop order. The symmetry breaking at <math><msub><mi>v</mi><mn>3</mn></msub></math> can be made dynamical, without introducing an additional hierarchy problem.

Colorful Mirror Solution to the Strong <math><mi>C</mi><mi>P</mi></math> Problem

The idea that the gravity-induced breaking of global symmetries is encoded in Planck-suppressed operators is not scale invariant: heavy particles which have nothing to do with the UV completion of gravity can mediate the breaking and produce low-energy operators (partly) suppressed by their own mass scales. Such contributions from heavy fields are typically subdominant with respect to the least Planck-suppressed operators, unless the latter are forbidden, as is usual in solutions to the axion quality problem based on four-dimensional gauge symmetries. Therefore, with a focus on axion physics, I investigate such situations and present toy examples where a nonminimal sector of heavy fields coupling to the axion generates operators whose coefficients are orders of magnitude larger than the naive Planck-suppressed estimates, despite gravity being the only source of breaking. I also stress that the key features of these toy models, namely several families of heavy fields with family-dependent gauge charges, are already present in some nonminimal QCD axion models, using the axiflavon/flaxion and the lighter-than-usual KSVZ axion as examples. This suggests that gauge-symmetry-based solutions to the axion quality problem, or of any quality problem really, need to describe complete UV scenarios or make precise UV assumptions.

Heavy fields and the axion quality problem

In the electroweak sector of the Standard Model, CP violation arises through a very particular interplay between the three quark generations, as described by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism and the single Jarlskog invariant J 4. Once generalized to the Standard Model Effective Field Theory (SMEFT), this peculiar pattern gets modified by higher-dimensional operators, whose associated Wilson coefficients are usually split into CP-even and odd parts. However, CP violation at dimension four, i.e., at the lowest order in the EFT expansion, blurs this distinction: any Wilson coefficient can interfere with J 4 and mediate CP violation. In this paper, we study such interferences at first order in the SMEFT expansion, 𝒪(1/Λ2), and we capture their associated parameter space via a set of 1551 linear CP-odd flavor invariants. This construction describes both new, genuinely CP-violating quantities as well as the interference between J 4 and CP-conserving ones. We call this latter possibility opportunistic CP violation. Relying on an appropriate extension of the matrix rank to Taylor expansions, which we dub Taylor rank, we define a procedure to organize the invariants in terms of their magnitude, so as to retain only the relevant ones at a given precision. We explore how this characterization changes when different assumptions are made on the flavor structure of the SMEFT coefficients. Interestingly, some of the CP-odd invariants turn out to be less suppressed than J 4, even when they capture opportunistic CPV, demonstrating that CP-violation in the SM, at dimension 4, is accidentally small.

Emanuele Gendy

Christophe Grojean

Joshua Ruderman

Opportunistic CP violation

It is generally believed that global symmetries, in particular, axion shift symmetries, can only be approximate. This motivates one to quantify the breaking of the shift invariance that characterizes the flavorful effective couplings of an axionlike particle to standard model fermions. We identify a minimal set of Jarlskog-like flavor invariants that vanish if and only if the axion is shift symmetric. Therefore, they represent order parameters for the breaking of the axion shift symmetry. We illustrate properties of the invariants by matching to a UV model, studying the <math><mi>C</mi><mi>P</mi></math> transformation of the invariants, calculating their renormalization group evolution, and investigating similar conditions in the low-energy effective field theory below the electroweak scale. Finally, we discuss the order parameter associated to the nonperturbative shift-breaking induced by the axion-gluons coupling, which is also flavorful.

Shift-Invariant Orders of an Axionlike Particle

It is well-known that gravitino propagation in standard supergravities is free of any causality problems. However, two issues related to gravitino propagation were recently uncovered in specific supergravities with nonlinear supersymmetry. One of them concerns potential acausality/superluminality, whereas the second one arises from the vanishing of the sound speed at specific points during inflation. The former is famously related to positivity constraints on specific EFT operators, derived from dispersion relations on the energy-growing part of scattering amplitudes, and indeed we show that subluminality constraints for the gravitino are related via the equivalence theorem to positivity bounds in low-energy goldstino actions. However, the former are stronger, in the sense that they apply to functions of the scalar fields not only in the ground state, but for any field values such as those scanned by time-dependent solutions, unlike bounds derived from 2 → 2 scattering amplitudes in the vacuum. We also argue that nontrivial causality constraints arise only in the case where nonlinear supersymmetry in the matter sector is encoded into superfield constraints which do not seem to arise from microscopic two-derivative lagrangians, in particular for the orthogonal constraint used to build minimal models of inflation in supergravity. This allows us to propose simple alternatives which maintain the minimality of the spectra and are causal in all points of the theory parameter space. We also discuss minimal supergravity models of inflation along these lines.

Gabriele Casagrande

Emilian Dudas

Causality constraints on nonlinear supersymmetry

As SMEFT is a framework of growing importance to analyze high-energy data, understanding its parameter space is crucial. The latter is commonly split into CP-even and CP-odd parts, but this classification is obscured by the fact that CP violation is actually a collective effect that is best captured by considering flavor-invariant combinations of Lagrangian parameters. First we show that fermion rephasing invariance imposes that several coefficients associated to dimension-six operators can never interfere with operators of dimension ≤ 4 and thus cannot appear in any physical observable at   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ 1/Λ2. For those that can, instead, we establish a one-to-one correspondence with CP-odd flavor invariants, all linear with respect to SMEFT coefficients. We explicitly present complete lists of such linear CP-odd invariants, and carefully examine their relationship to CP breaking throughout the parameter space of coefficients of dimension ≤ 4. Requiring that these invariants all vanish, together with the Jarlskog invariant, the strong-CP phase, and the 6 CP-violating dimension-6 bosonic operators, provides 699(+1 + 1 + 6) conditions for CP conservation to hold in any observable at leading order,   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1/Λ2).