We investigate several phenomenological implications of the Weak Gravity Conjecture (WGC). We find that the WGC implies that the SM neutrinos must be electrically neutral, that the electric charge in the SM must be quantized, and that the photon must be massless. In addition, we use the WGC to set lower bounds on the electric charge of milli-charged particles (mCP), the gauge coupling of several <math altimg='si1.svg'><mi>U</mi><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></math> extensions of the SM, their kinetic mixing parameter with the SM <math altimg='si2.svg'><mi>U</mi><msub><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo stretchy='false'>)</mo></mrow><mrow><mtext>EM</mtext></mrow></msub></math>, and the axion couplings to photons and fermions. We also set an upper bound on the lifetime of the proton.

India

Fayez Abu-Ajamieh

United States

Nobuchika Okada

Sudhir K. Vempati

Implications of the weak gravity conjecture on charge, kinetic mixing, the photon mass, and more

We propose a generalized formulation of the Scalar Weak Gravity Conjecture (SWGC) based on the analogy with the derivation of the Gauge Weak Gravity Conjecture (GWGC). We discuss some phenomenological implications of this Generalized SWGC, including the scale of New Physics (NP) when applied to the SM Higgs sector, and the bounds on the axion's couplings to fermions and to the photon when it is applied to the axion. The Generalized SWGC constraints rule out most of the parameter space of axion-nucleon couplings, leaving only a tiny region.

The generalized scalar weak gravity conjecture and its implications

We use the weak gravity conjecture (WGC) to investigate the impact of charge dequantization arising from non-local QED on the scale of non-locality of neutrinos. We find this scale to be $$\lesssim 49$$ TeV as implied by direct bounds and $$\lesssim 15$$ TeV as implied by cosmological bounds, which could be probed in future colliders. We also investigate the electric force and potential in non-local QED and use them to reformulate the weak gravity conjecture (WGC) in non-local QED.

Sudhir Vempati

Aspects of non-local QED and the weak gravity conjecture

We study some phenomenological aspects of Lee-Wick (LW) QED. In particular, we show that LW QED implies charge dequantization and a flavor-dependent LW scale. We study the implications of the Weak Gravity Conjecture (WGC) in LW QED and calculate the modified electric force and potential and use the former to reformulate the WGC in LW QED. We also calculate the photon self-energy and the Uehling potential in LW QED. We show that bounds on milli-charged particles from matter neutrality experiments set stringent limits on the LW scale of fermions and of the photon.

China

Pratik Chattopadhyay

Marco Frasca

Phenomenological aspects of Lee-Wick QED

Di-Higgs couplings to fermions of the form <math><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mover><mrow><mi>f</mi></mrow><mo>‾</mo></mover><mi>f</mi></math> are absent in the Standard Model, however, they are present in several physics Beyond Standard Model (BSM) extensions, including those with vector-like fermions. In Effective Field Theories (EFTs), such as the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT), these couplings appear at dimension 6 and can in general, be flavour-violating (FV). In the present work, we employ a bottom-up approach to investigate the FV in the lepton and quarks sectors through the di-Higgs effective couplings. We assume that all FV arises from this type of couplings and assume that the Yukawa couplings <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> are given by their SM values, i.e. <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>δ</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>/</mo><mi>v</mi></math>. In the lepton sector, we set upper limits on the Wilson coefficients <math><msub><mrow><mi>C</mi></mrow><mrow><mi>l</mi><msup><mrow><mi>l</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math> from <math><mi>l</mi><mo>→</mo><mn>3</mn><msup><mrow><mi>l</mi></mrow><mrow><mo>′</mo></mrow></msup></math> decays, <math><mi>l</mi><mo>→</mo><mi>l</mi><mi>γ</mi></math> decays, muonium oscillations, the <math><msub><mrow><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>μ</mi></mrow></msub></math> anomaly, LEP searches, muon conversion in nuclei, FV Higgs decays, and Z decays. We also make projections on some of these coefficients from Belle II, the Mu2e experiment and the LHC's High Luminosity (HL) run. In the quark sector, we set upper limits on the Wilson coefficients <math><msub><mrow><mi>C</mi></mrow><mrow><mi>q</mi><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math> from meson oscillations and from B-physics searches. A key takeaway from this study is that current and future experiments should set out to measure the effective di-Higgs couplings <math><msub><mrow><mi>C</mi></mrow><mrow><mi>f</mi><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math>, whether these couplings are FV or flavour-conserving. We also present a matching between our formalism and the SMEFT operators and show the bounds in both bases.

Italy

Flavor violating di-Higgs couplings

We investigate anomalies in the class of nonlocal field theories that have been proposed as an ultraviolet completion of four-dimensional quantum field theory with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by the string field theory and ghost-free nonlocal approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired nonlocal extension of QED. We show that the vector anomaly vanishes as required by gauge invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in the scale of nonlocality. We also calculate the nonlocal vector and axial currents explicitly and present an illustrative example by applying our results to the decay of <math><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><mi>γ</mi><mi>γ</mi></math>.

United Kingdom

Poland

Anish Ghoshal

Anomalies in string-inspired nonlocal extensions of QED

We provide the corrected calculation of the (g − 2) μ  in non-local QED previously done in the literature. In specific, we show the proper technique for calculating loops in non-local QED and use it to find the form factors F 1(q 2) and F 2(q 2) in non-local QED. We also utilize this technique to calculate some novel results in non-local QED, including calculating the correction to the photon self-energy, the modification to the classical Coulomb potential, the modification to the energy levels of the hydrogen atom, and the contribution to the Lamb shift. We also discuss charge dequantization through non-locality, and show that the experimental bounds on the electric charge on Dirac neutrinos, translate into strong flavor-dependent bounds on the scale on non-locality that range between 105 −1010 TeV. We also discuss the inconsistencies of unrenormalized non-local Quantum Field Theories (QFTs) and the need for renormalizing them, even when they are free from UV divergences.

Corrected calculation for the non-local solution to the g − 2 anomaly and novel results in non-local QED

We propose a renormalization scheme for non-local Quantum Field Theories (QFTs) with infinite derivatives inspired by string theory. Our Non-locality Renormalization Scheme (NRS) is inspired by Dimensional Regularization (DR) in local QFTs and is shown to significantly improve the UV behavior of non-local QFTs. We illustrate the scheme using simple examples from the  $$\phi ^{3}$$  <math> <msup> <mi>ϕ</mi> <mn>3</mn> </msup> </math>   and  $$\phi ^{4}$$  <math> <msup> <mi>ϕ</mi> <mn>4</mn> </msup> </math>   theories, then we evaluate the viability of NRS-enhanced non-local QFTs to solve the hierarchy problem using a simplified toy model. We find that non-locality protects the mass of a light scalar from receiving large corrections from any UV sector to which it couples, as long as the non-locality scale  $$\Lambda $$  <math> <mi>Λ</mi> </math>   is sufficiently smaller than the scale of the UV sector. We also find that NRS eliminates any large threshold corrections from the IR sector.

A proposed renormalization scheme for non-local QFTs and application to the hierarchy problem

Measuring the Higgs couplings accurately at colliders is one of the best routes for finding physics Beyond the Standard Model (BSM). If the measured couplings deviate from the SM predictions, then this would give rise to energy-growing processes that violate tree-level unitarity at some energy scale, indicating new physics. In this paper, we extend previous work on unitarity bounds from the Higgs potential and the Higgs couplings to vector bosons, the top quark, γγ and γZ; to the Higgs coupling to gg. We show that the scale of new physics could be as low as ∼10 TeV, which although beyond the reach of the LHC, is well within the reach of the future 100-TeV collider, and can also be probed indirectly in the High Luminosity LHC (HL-LHC).

The scale of new physics from the Higgs couplings to

Measuring the Higgs couplings accurately at colliders is one of the best routes for finding physics Beyond the Standard Model (BSM). If the measured couplings deviate from the SM predictions, then this would give rise to energy-growing processes that violate tree-level unitarity at some energy scale, indicating new physics. In this paper, we extend previous work on unitarity bounds from the Higgs potential and the Higgs couplings to vector bosons and the top quark; to the Higgs couplings to γγ and γZ. We find that while the HL-LHC might be able to find new physics in the γZ sector, the scale of new physics in both sectors is mostly beyond its reach. However, accurate measurements of the leading couplings of the two sectors in the HL-LHC can place stringent limits on both the scale of new physics and on other Higgs couplings that are difficult to measure. In addition, the scale of new physics is mostly within the reach of the 100 TeV collider.