MIT Center for Theoretical Physics – a Leinweber Institute

The Standard Model prediction for the rare $K_L\toμ^+μ^-$ decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the $u$, $d$ and $s$ quarks, provided terms falling as the inverse square of the omitted charm quark mass, $1/m_c^2$ are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancelation, this three-flavor theory contains additional low-energy constants that depend on $m_c$. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with $u$ and $d$ quark masses that are heavier than physical.

Diffraction is characterized by forward scattering and a large rapidity gap. Ordinary hard scattering also produces gapped events and presents a significant background to identification of diffractively produced events. We present a fully differential factorization of gapped hard $ep$ scattering. We find that the unpolarized azimuthally-dependent structure functions $F_{3,4}^{\rm gap}$ and the longitudinal $F_L^{\rm gap}$ vanish at leading power for hard scattering. Azimuthal dependence is thus a pure diffractive signature. This is borne out in Monte Carlo simulations.

We use effective field theory techniques to factorize elastic, single, and double diffractive forward $pp$ scattering in the Regge limit $|t|\ll s$, where $t$ is the squared momentum transfer. These processes involve a large rapidity gap and comprise about half the total $pp$ cross section. We explain why the diffractive PDFs appearing in $ep$ diffraction do not appear as universal hadronic functions for $pp$ diffraction. For $|t|\sim Λ_{\rm QCD}^2$, we show that the hadronic functions in $ep$ and $pp$ diffraction differ, and hence are non-universal. In general, we prove that rapidity anomalous dimensions are universal between diffractive $ep$ and $pp$ processes, and that color-singlet (Pomeron) evolution equations can be determined at the amplitude level.

The measurement of the sum of neutrino masses is among the primary promises of precision cosmology, achievable by combining complementary early- and late-Universe probes. However, these datasets currently exhibit mild-to-strong disagreements within $Λ$CDM and its simplest extensions, giving rise to multiple tensions, including the Hubble tension, the preference for “negative” neutrino mass, and indications of evolving dark energy. It has recently been shown that these tensions can be alleviated by adopting a higher value of the optical depth to reionization parameter, $τ$, when large-scale cosmic microwave background (CMB) polarization data are ignored. We extend this proposal and show that an especially high prior on $τ= 0.11 \pm 0.006$ simultaneously addresses all three of these tensions, significantly reducing the need for new physics beyond $Λ$CDM. We determine the “concordance” value of $τ$ by requiring physical neutrino mass and consistency of the Hubble constant, $H_0$, inferred from the CMB and that preferred by the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) and full-shape measurements. Within this high-$τ$ Universe, we obtain the first $2σ$ detection of a positive neutrino mass, $Σm_ν = 0.10^{+0.04}_{-0.05}$~eV at 68% C.L., while restoring cosmological concordance between datasets within $Λ$CDM. In particular, low-redshift distance predictions are consistent with DESI BAO observations and the inferred dark-energy equation-of-state parameters are consistent with a cosmological constant, both with and without supernovae data. The concordance power of our $τ$ prior further motivates new measurements of $τ$, e.g., through large angular scale CMB polarization observations with the \textit{LiteBIRD}, CLASS, or proposed PICO experiments. (Abridged)