The gluon emission from an energetic heavy quark is suppressed in the forward direction below the angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Θ</mi><mo>≲</mo><msub><mi>m</mi><mi>Q</mi></msub><mo>/</mo><mi>E</mi></math> for a quark of mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>Q</mi></msub></math> and energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math> according to perturbative quantum chromodynamics (QCD) (“dead cone”). Another consequence is the suppression of energetic particles in the jet, which has been observed already for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-quark jets. The suppression of the forward particles can be explained by an application of the modified leading logarithmic approximation of perturbative QCD. In this paper, we investigate whether this type of analysis can be carried out also for top-quark jets with a much higher heavy-quark mass allowing for QCD tests in this new kinematic regime. The new aspect of this analysis is the finite lifetime of the top quark. We consider for simplicity the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo stretchy="false">→</mo><mi>b</mi><mo>ℓ</mo><mi>ν</mi></math>, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math> quark radiates gluons as well and partially obscures the dead cone. Guided by the decay amplitude in leading order in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></math>, we propose a method to separate the radiation by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mrow><mi>t</mi><mi>b</mi></mrow><mo stretchy="true">^</mo></mover></math> dipole in the decay process, which is superimposed on the primary radiation from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mrow><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></mrow><mo stretchy="true">^</mo></mover></math> dipole involving the top-quark dead-cone effect. The momentum distributions of partons or hadrons are determined for finite decay angles of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-quark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Θ</mi><mi>b</mi></msub></math> and extrapolated in the forward direction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Θ</mi><mi>b</mi></msub><mo>=</mo><mn>0</mn></math> where the radiation from the decay process is expected to vanish. This method is successfully tested at the parton level, and the results obtained for hadrons are compatible with the modified leading logarithmic approximation relation with an accuracy of around 15%. Our calculations are carried out with the pythia 8.3 Monte Carlo event generator.

Germany

Stefan Kluth

Wolfgang Ochs

France

Redamy Perez-Ramos

How to identify the dead cone in the top-quark jet

We investigate the atmospheric production and subsequent detection of sub-GeV dark mesons within the framework of a confining dark sector coupled to the Standard Model (SM) via a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></msub></math> vector portal. High-energy cosmic-ray interactions in the atmosphere produce dark quarks through proton bremsstrahlung, rare decays of Standard Model mesons, and Drell-Yan processes, which subsequently hadronize into dark mesons. We adopt a modified quark combination model to describe the nonperturbative dark hadronization process, allowing for a detailed event-level characterization of the dark meson flux. We simulate the flux and the interactions of these relativistic dark mesons in the Jiangmen Underground Neutrino Observatory (JUNO) using the genie generator, considering both elastic scattering off nuclei and deep inelastic scattering channels. Adopting a large-energy-singles-inspired conservative signal definition with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>15</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>&lt;</mo><msub><mi>E</mi><mrow><mi>vis</mi></mrow></msub><mo>&lt;</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and vetoing events containing final-state neutrons, we derive projected 90% C.L. sensitivities to the coupling strength between the dark gauge boson and the SM sector for a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>kton</mi><mo>·</mo><mi>year</mi></math> exposure. For the representative benchmark masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msup><mi>Z</mi><mo>′</mo></msup></msub><mo>=</mo><mn>0.001</mn></math>, 0.01, and 0.1 GeV, the projected JUNO reach corresponds to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>g</mi><mrow><mi>SM</mi></mrow><mn>90</mn></msubsup><mo>=</mo><mn>6.48</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.75</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2.37</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, respectively. This reach is found to be only mildly sensitive to order-one variations of the hadronization parameter, as illustrated by the choices <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mi>β</mi></msub><mo>=</mo><mn>1</mn><mo>/</mo><mn>3</mn></math>, 1, and 3.

China

Zirong Chen

Dan Chi

Jinmian Li

Junle Pei

Search for cosmic-ray-produced dark mesons via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></msub></math> portal at JUNO

We study neutrino-induced charged-current coherent pion production (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mrow><mi>CC</mi><mo>−</mo><mi>Coh</mi></mrow><mi>π</mi></mrow></math>) as a tool for constraining the neutrino flux at the Deep Underground Neutrino Experiment (DUNE). The neutrino energy and flavor in the process can be directly reconstructed from the outgoing particles, making it especially useful to specifically constrain the muon neutrino component of the total flux. The cross section of this process can be obtained using the Adler relation with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math>-Ar elastic scattering cross section taken either from external data or, as we explore, from a simultaneous measurement in the DUNE near detector. We develop a procedure that leverages <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>μ</mi></msub><mrow><mi>CC</mi><mo>−</mo><mi>Coh</mi></mrow><mi>π</mi></math> events to fit for the neutrino flux while simultaneously accounting for relevant effects in the cross section. We project that this method has the statistical power to constrain the uncertainty on the normalization of the flux at its peak to a few percent. This study demonstrates the potential utility of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>μ</mi></msub><mrow><mi>CC</mi><mo>−</mo><mi>Coh</mi></mrow><mi>π</mi></math> flux constraint, though further work will be needed to determine the range of validity and precision of the Adler relation upon which it relies, as well as to measure the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math>-Ar elastic scattering cross section to the requisite precision. We discuss the experimental and phenomenological developments necessary to unlock the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ν</mi><mi>μ</mi></msub><mrow><mi>CC</mi><mo>−</mo><mi>Coh</mi></mrow><mi>π</mi></math> process as a “standard candle” for neutrino experiments.

United States

Mun Jung Jung

Vishvas Pandey

Gray Putnam

David W. Schmitz

Neutrino-induced charged-current coherent pion production for constraining the muon neutrino flux at DUNE

We use supersymmetric chiral dynamics perturbed by anomaly-mediated supersymmetry breaking to obtain a high-quality, composite axion that solves the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi><mi>P</mi></mrow></math> problem. The strong dynamics arises from a supersymmetric SU(10) chiral gauge theory with massless matter chiral superfields. This leads to a stable, nonsupersymmetric vacuum, calculated exactly, where a spontaneously broken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> global symmetry, identified with the Peccei-Quinn (PQ) symmetry, gives rise to a composite QCD axion. The chiral gauge theory also admits a discrete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>4</mn></msub></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mrow><mn>8</mn><mo>,</mo><mn>16</mn></mrow></msub></math>) gauge symmetry that forbids PQ-violating operators up to dimension eight. An extension to an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>14</mn><mo stretchy="false">)</mo><mo>×</mo><msub><mi mathvariant="double-struck">Z</mi><mn>12</mn></msub></math> chiral gauge theory incorporates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> grand unification where the unification scale is identified with the PQ-breaking scale and PQ-violating operators are forbidden up to dimension 20. The supersymmetry breaking scale, near 100 TeV, ameliorates the Higgs hierarchy problem, while colored Nambu–Goldstone bosons may be detected at future colliders via decays to gluons or form heavy isotopes.

Tony Gherghetta

Japan

Hitoshi Murayama

Bea Noether

Pablo Quílez

High-quality axion from exact SUSY chiral dynamics

We present an analysis of the radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> in a dispersive framework, where the two-pion subsystem undergoes strong final-state interactions that cover the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> regions. We employ a coupled-channel Muskhelishvili-Omnès framework that allows for a consistent treatment of two scalar resonances and crossed-channel singularities induced by the Born and vector-meson exchanges. We explicitly verify the equivalence between the modified and standard Muskhelishvili-Omnès representations for vector-meson pole contributions when the isoscalar Omnès matrix is chosen asymptotically bounded, and we adopt the standard representation in decay kinematics. This yields, for the first time, a parameter-free dispersive prediction for the kaon Born rescattering, which provides a dominant contribution. To obtain a good fit to the KLOE and SND data, we employ a once-subtracted coupled-channel dispersion relation with heavier left-hand cut contributions and two unknown subtraction constants. The results demonstrate the consistency among the data for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> scattering, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi></math> fusion, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> radiative decay, thereby validating the underlying dispersive formalism and the input used for the hadronic Omnès matrix and left-hand cuts.

Bai-Long Hoid

Igor Danilkin

Marc Vanderhaeghen

Dispersive analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ϕ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> process

We perform canonical quantization of general relativity, as an effective quantum field theory below the Planck scale, within the Becchi-Rouet-Stora-Tyutin (BRST)-invariant framework. We show that the promotion of constraints to dynamical equations of motion for auxiliary fields leads to the healthy Hamiltonian flow. In particular, we show that the classical properties of Einstein’s gravity, such as vanishing Hamiltonian modulo boundary contribution, are realized merely as an expectation value in appropriate physical states. Most importantly, the physicality is shown not to entail trivial time evolution for correlation functions. In the present approach, we quantize the theory once and for all around the Minkowski vacuum and treat other would-be classical backgrounds as BRST-invariant coherent states. This is especially important for cosmological spacetimes as it uncovers features that are not visible in ordinary semiclassical treatment. The Poincaré invariance of the vacuum, essential for our quantization, provides strong motivation for spontaneously broken supersymmetry.

Lasha Berezhiani

Gia Dvali

Australia

Otari Sakhelashvili

Consistent canonical quantization of gravity: Recovery of classical GR from BRST-invariant coherent states

Electromagnetic probes of neutrinos can provide insights into physics beyond the Standard Model. Among the possible electromagnetic interactions of neutrinos is neutrino polarizability, a dimension-7 effective operator that couples two neutrinos to two photons. In this manuscript, we study a realization of the neutrino polarizability operator in which one of the active neutrinos is replaced by a sterile neutrino. We derive new constraints on this active-sterile neutrino polarizability from its contribution to neutrino-nucleus scattering with a single photon in the final state at neutrino experiments. We show that a realization of this operator via a light mediator can explain the MiniBooNE low-energy excess while remaining consistent with other experimental constraints. Finally, we comment on additional model realizations of this higher-dimensional operator.

Julia Gehrlein

Anil Thapa

Adrian Thompson

Enhanced active-sterile neutrino polarizability at the intensity frontier

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi><mo>≤</mo><msub><mi>j</mi><mi>max</mi></msub></math>. We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>j</mi><mi>max</mi></msub></math> for both pure and mixed Gaussian initial density matrices. For the simplest truncation, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>j</mi><mi>max</mi></msub><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

Anjali A. Agrawal

Evan Budd

Alexander F. Kemper

Vladimir V. Skokov

Andrey Tarasov

Shaswat Tiwari

JIMWLK on a quantum computer

Using data samples with a total integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>22.1</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> at center-of-mass energies between 4.008 and 4.951 GeV collected with the BESIII detector, the cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> process are measured. The obtained cross sections are found to be approximately one-half of those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math>, consistent with the isospin symmetry expectation. A coherent fit to the dressed cross sections is performed, with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo></math> parameters fixed at the values measured in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math>. The significances of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4390</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4660</mn><mo stretchy="false">)</mo></math> are both larger than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>, and their masses and widths are consistent with the previous measurement in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> process.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J.C. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Y.T. Feng

M. Fritsch

Cross section measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.008</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to 4.951 GeV

We perform dimensional reduction of the dimension-6 standard model effective field theory (SMEFT) to order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>g</mi><mn>4</mn></msup></math> in coupling constants <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>. This analysis includes one-loop contributions to kinetic terms and quartic couplings, as well as two-loop contributions, where operators such as four-fermion interactions first appear, to squared mass terms. Using lattice data, we provide evidence that, in contrast with previous statements in the literature, the SMEFT may undergo a first-order phase transition even for null <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>ϕ</mi><msup><mo stretchy="false">|</mo><mn>6</mn></msup></math> at zero temperature—where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> is the Higgs doublet—opening the door to entirely unexplored directions in model building. In such case, however, our analysis implies that the phase transition is not sufficiently strong, narrowing down the new physics that allows for electroweak baryogenesis.