We study quantum electrodynamics (QED) corrections to operator matrix elements involving heavy composite particles (e.g., heavy-mesons, nuclei, and atoms). We define a new notion of reducible and irreducible graphs which is useful for systems with many discrete excited states. The equivalence of the Lehman-Symanzik-Zimmerman (LSZ) reduction formula and old fashioned perturbation theory is explicitly demonstrated. The self-energy and vertex corrections are defined (to all orders), and the one-loop corrections are reduced to operator matrix elements which may be evaluated by hadronic, nuclear, or atomic theorists. The gauge dependence of the various pieces are studied in detail at one loop, and cancellation of spurious contributions are demonstrated in a class of covariant gauges; Coulomb gauge is also discussed. The formalism is applied to superallowed beta decay where the one-loop structure is connected to existing literature based on current algebra techniques. We further identify the well known <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msup><mi>Z</mi><mn>2</mn></msup><msup><mi>α</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> isospin breaking correction from the intranuclear Coulomb field as arising from two-loop diagrams. We comment on future applications of our results to the radiative corrections necessary in extractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo stretchy="false">|</mo></math>, in particular for corrections that required beyond one-loop order.

United States

Ryan Plestid

Mark B. Wise

Vertex corrections and wavefunction renormalization for atoms, nuclei, and other heavy composite particles

We study axionlike particles (ALPs) in beam dump experiments, focusing on the Search for Hidden Particles (SHiP, at CERN) experiment and the Beam Dump eXperiment (BDX, at JLab). Many existing projections for sensitivity to ALPs in beam dump experiments have focused on production from either the primary proton/electron beam, or—in the case of SHiP—the secondary (high-energy) photons produced by neutral meson decays (e.g., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></math>). In this work, we study the subsequent production of axions from the full electromagnetic shower in the target, finding order-of-magnitude enhancements in the visible decay yields across a wide range of axion masses. We update SHiP’s sensitivity curve and provide new projections for BDX. Both experiments will be able to reach currently unexplored regions of ALP parameter space.

Samuel Patrone

Canada

Nikita Blinov

CERN

Long-lived axionlike particles from electromagnetic cascades

Details of the two-loop analysis of long-distance QED radiative corrections to neutron beta decay are presented. Explicit expressions are given for hard, jet, and soft functions appearing in the factorization formula that describes the limit of small electron mass and large electron energy. Numerical enhancements from the infrared region are resummed using renormalization group methods. Power corrections, cancellation of singularities in the small-mass expansion, renormalization scheme dependence, and bound-state effects are also discussed. These results provide the most precise determination of long-distance radiative corrections to neutron beta decay and impact the determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo stretchy="false">|</mo></math> from the measured neutron lifetime and thus set a target for uncertainty reductions in the experimental and short-distance inputs.

Zehua Cao

Richard J. Hill

Peter Vander Griend

Factorization and resummation of QED radiative corrections for neutron beta decay

We consider ultralight scalar dark matter that couples to right-handed neutrinos. Due to the high density of neutrinos in the early universe, the background neutrino density dominates the dynamics of the scalar field, and qualitatively alters the field’s cosmological evolution. This effect has not been included in previous literature, and changes the interpretation of cosmological data and its interplay with laboratory experiments. To illustrate these points a simplified model of a 1 + 1 setup with a single scalar field is analyzed.

Sophia Tevosyan

The cosmology of ultralight scalar dark matter coupled to right-handed neutrinos

The traditional Fermi function ansatz for nuclear beta decay describes enhanced perturbative effects in the limit of large nuclear charge <italic>Z</italic> and/or small electron velocity <italic>&#946;</italic>. We define and compute the quantum field theory object that replaces this ansatz for neutron beta decay, where neither of these limits hold. We present a new factorization formula that applies in the limit of small electron mass, analyze the components of this formula through two loop order, and resum perturbative corrections that are enhanced by large logarithms. We apply our results to the neutron lifetime, supplying the first two-loop input to the long-distance corrections. Our result can be summarized as <display><formula id='fm0010'><math altimg='si1.svg'><msub><mrow><mi>&#964;</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>&#215;</mo><mo stretchy='false'>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>d</mi></mrow></msub><msup><mrow><mo stretchy='false'>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='true' maxsize='2.4ex' minsize='2.4ex'>[</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>3</mn><msup><mrow><mi>&#955;</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='true' maxsize='2.4ex' minsize='2.4ex'>]</mo><mo stretchy='true' maxsize='2.4ex' minsize='2.4ex'>[</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><msub><mrow><mi mathvariant='normal'>&#916;</mi></mrow><mrow><mi>R</mi></mrow></msub><mo stretchy='true' maxsize='2.4ex' minsize='2.4ex'>]</mo><mo linebreak='badbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mn>5263.284</mn><mo stretchy='false'>(</mo><mn>17</mn><mo stretchy='false'>)</mo><mspace width='0.2em' /><mi mathvariant='normal'>s</mi></mrow><mrow><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>27.04</mn><mo stretchy='false'>(</mo><mn>7</mn><mo stretchy='false'>)</mo><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>3</mn></mrow></msup></mrow></mfrac><mspace width='0.25em' /><mo>,</mo></math></formula></display> with <math altimg='si2.svg'><mo stretchy='false'>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo stretchy='false'>|</mo></math> the up-down quark mixing parameter, <math altimg='si3.svg'><msub><mrow><mi>&#964;</mi></mrow><mrow><mi>n</mi></mrow></msub></math> the neutron's lifetime, <italic>&#955;</italic> the ratio of axial to vector charge, and <math altimg='si4.svg'><msub><mrow><mi mathvariant='normal'>&#916;</mi></mrow><mrow><mi>R</mi></mrow></msub></math> the short-distance matching correction. We find a shift in the long-distance radiative corrections compared to previous work, and discuss implications for extractions of <math altimg='si2.svg'><mo stretchy='false'>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>d</mi></mrow></msub><mo stretchy='false'>|</mo></math> and tests of the Standard Model.

The Fermi function and the neutron's lifetime

We study the modifications to decay amplitudes in heavy to heavy semileptonic decays with multiple hadrons in the final state due to intermediate heavy hadrons being off-shell or having a finite width. Combining Heavy Hadron Chiral Perturbation Theory (HH$\textit{χ}$PT) with a BCFW on-shell factorization formula, we show that these effects induce $$ \mathcal{O} $$ (1/$\textit{M}$) corrections to the standard results computed in the narrow-width approximation and therefore are important in extracting form factors from data. A combination of perturbative unitarity, analyticity, and reparameterization invariance fully determine these corrections in terms of known Isgur-Wise functions without the need to introduce new form factors. In doing so, we develop a novel technique to compute the boundary term at complex infinity in the BCFW formula for theories with derivatively coupled scalars. While we have used the $$ \overline{B} $$ → $\textit{Dπℓν}$ decay as an example, these techniques can generally be applied to effective field theories with (multiple) distinct reference vectors.

Michele Papucci

Off-shell vertices in heavy particle effective theories and B $\textit{→}$ D$\textit{πℓν}$

We propose to search for millicharged particles produced in high-intensity electron beam dumps using small ultralow-threshold sensors. As a concrete example, we consider a Skipper-CCD placed behind the beam dump in Hall A at Jefferson Lab. We compute the millicharged particle flux, including both electromagnetic cascade and meson productions emanating from an aluminum target. We find that the sensitivity of a modest 2 × 14 array of Skipper-CCDs can exceed the sensitivity of all existing searches for millicharged particle masses below 1.5 GeV, and is either competitive or world leading when compared to other proposed experiments. Our results demonstrate that small-scale ultralow threshold silicon devices can enhance the reach of accelerator-based experiments, while fitting comfortably within existing experimental halls.

Rouven Essig

Peiran Li

Zhen Liu

Megan McDuffie

Hailin Xu

Probing millicharged particles at an electron beam dump with ultralow-threshold sensors

We simulate dark-vector, $\textit{V}$, production from electromagnetic cascades at the recently approved SHiP experiment. The cascades (initiated by photons from $\textit{π}$ → $\textit{γγ}$) can lead to 3–4 orders of magnitude increase of the event rate relative to using primary production alone. We provide new SHiP sensitivity projections for dark photons and electrophilic gauge bosons, which are significantly improved compared to previous literature. The main gain in sensitivity occurs for long-lived dark vectors with masses below ~ 50 − 300 MeV. The dominant production mode in this parameter space is low-energy annihilation $\textit{e}$ $\textit{e}$ → $\textit{V}$ ($\textit{γ}$). This motivates a detailed study of backgrounds and efficiencies in the SHiP experiment for sub-GeV signals.

Tao Zhou

Kevin Kelly

Patrick Fox

Long-lived vectors from electromagnetic cascades at SHiP

In this work we consider sub-leading $\textit{O}$($\textit{Z}$ $\textit{α}$ ) corrections to coherent elastic neutrino nucleus scattering (CEvNS). These corrections are not negligible by power counting since nuclei with large coherent cross sections have sizeable nuclear charges e.g. $\textit{Zα}$ ∼ 0.4. We find that the corrections are much smaller than naive power counting in $\textit{Zα}$ would suggest and that Coulomb corrections do not substantially alter predictions for CEvNS in the Standard Model. We comment on similarities to older literature on mesonic and muonic atoms.

Coulomb corrections for coherent neutrino nucleus scattering

Charged leptons produced by high-energy and ultrahigh-energy neutrinos have a substantial probability of emitting prompt internal bremsstrahlung <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo>+</mo><mi>N</mi><mo stretchy="false">→</mo><mo>ℓ</mo><mo>+</mo><mi>X</mi><mo>+</mo><mi>γ</mi></mrow></math>. This can have important consequences for neutrino detection. We discuss observable consequences at high- and ultrahigh-energy neutrino telescopes and the Large Hadron Collider’s (LHC’s) Forward Physics Facility. Logarithmic enhancements can be substantial (e.g., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>20</mn><mo>%</mo></math>) when either the charged lepton’s energy or the rest of the cascade is measured. We comment on final state radiation’s impacts on measuring the inelasticity distribution, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ν</mi><mo>/</mo><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> flux ratio, throughgoing muons, and double-bang signatures for high-energy neutrino observation. Furthermore, for ultrahigh-energy neutrino observation, we find that final state radiation increases the overall detectable energy by as much as 20%, affects flavor measurements, and decreases the energy of both Earth-emergent tau leptons and regenerated tau neutrinos. Many of these have significant impacts on measuring neutrino fluxes and spectra. Finally, for the LHC’s Forward Physics Facility, we find that final state radiation will impact future extractions of strange quark parton distribution functions. Final state radiation should be included in future analyses at neutrino telescopes and the Forward Physics Facility.