<p>We compute the Gross-Llewellyn Smith sum rule, i.e., the lowest odd moment of the parity-violating structure function, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>3</mn></msub></math>, of the nucleon from a lattice QCD calculation of the Compton amplitude. Our calculations are performed on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>48</mn><mn>3</mn></msup><mo>×</mo><mn>96</mn></math> lattices at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> symmetric point for two lattice spacings. We extract the moments for several values of the current momenta in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.5</mn><mo>≲</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>≲</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, covering both the nonperturbative and perturbative regimes. We compare our moments to the Gross-Llewellyn Smith sum rule and discuss the implications for higher-twist effects, a determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> from a hadronic quantity complementing the phenomenological and other lattice approaches, and electroweak box contributions crucial for Cabibbo–Kobayashi–Maskawa matrix unitarity studies.</p>

Australia

K.U. Can

J.A. Crawford

United Kingdom

R. Horsley

P.E.L. Rakow

T.G. Schar

Germany

G. Schierholz

H. Stüben

R.D. Young

J.M. Zanotti

Gross-Llewellyn Smith sum rule from lattice QCD

If dark matter carries a baryon number of two, neutron-antineutron oscillations could require its presence to manifest themselves. If it is in addition very light, in the micro-eV range or up to a few orders of magnitude below, these oscillations could even exhibit a Rabi resonance. Though the magnetic tuning required to convert a macroscopic number of neutrons into antineutrons is not realistic, sizeable enhancements remain possible. Building on this observation, axionic realizations for this scenario are systematically analyzed. For true QCD axion models, we find that the Goldstone boson nature of the axion imposes the presence of axionless $$ n-\overline{n} $$ mixing effects, either in vacuum or in decays, which are sufficiently constrained experimentally to leave no room for axion-induced oscillations. Thus, a generic scalar or axion-like dark matter background would have to exist to induce resonant $$ n-\overline{n} $$ oscillations. Yet, if Nature has taken that path to relate dark matter and baryon number violation, the experimental signature would be striking and certainly worth pursuing.

France

Théo Brugeat

Christopher Smith

Dark-matter induced neutron-antineutron oscillations

In the non-relativistic limit, two types of dark matter axion interactions with fermions are thought to dominate: one is induced by the spatial gradient of the axion field and called the axion wind, and the other by the time-derivative of the axion field, generating axioelectric effects. By generalizing Schiff theorem, it is demonstrated that this latter operator is actually strongly screened. For a neutral fermion, it can be entirely rotated away and is unobservable. For charged fermions, the only effect that can peek through the screening is an axion-induced electric dipole moment (EDM). These EDMs are not related to the axion coupling to gluons, represent a prediction of the Dirac theory analogous to the  $$g=2$$  <math> <mrow> <mi>g</mi> <mo>=</mo> <mn>2</mn> </mrow> </math>   magnetic moments, are not further screened by the original Schiff theorem, and are ultimately responsible for inducing the usual axioelectric ionization. The two main phenomenological consequences are then that first the axion-induced nucleon EDM could be significantly larger than expected from the axion gluonic coupling, and second, that the electron EDM could also become available, and could actually be highly sensitive to relic axions.

On the fermionic couplings of axionic dark matter

The Effective Field Theory (EFT) Lagrangian for a generic axion-like particle (ALP) has many free parameters, and leaves quite some freedom for the expected phenomenology. In this work, we set up more constrained EFTs by enforcing true axion-like properties for the ALP. Indeed, though the Peccei-Quinn symmetry of the QCD axion is anomalous, it is so in specific ways, and this shows up as consistency conditions between the gauge boson and fermion couplings. We propose to enforce such conditions, as inspired from the DFSZ and KSVZ scenarios, on the generic ALP EFTs. These truly axion-like ALP EFTs are then particularly well-suited as benchmark scenarios, to be used in the search for ALPs both at colliders and at low-energy experiments.

Fernando Arias-Aragón

CERN

Jérémie Quevillon

Axion-like ALPs

In this paper, axion models supplemented by leptoquarks and diquarks are systematically analyzed. Turning on some couplings to and among these latter states permits us to unify the Peccei-Quinn symmetry with baryon (<math><mi>B</mi></math>) and lepton (<math><mi>L</mi></math>) numbers, such that the axion becomes associated to the spontaneous breaking of the three <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> symmetries. All possible four- and six-fermion patterns of <math><mi>B</mi></math> and <math><mi>L</mi></math> violation are discussed, including those inducing proton decay, with <math><mi>Δ</mi><mi>B</mi><mo>=</mo><mn>1</mn></math> and <math><mi>Δ</mi><mi>L</mi><mo>=</mo><mo>±</mo><mn>1</mn><mo>,</mo><mo>±</mo><mn>3</mn></math>, neutron-antineutron oscillations with <math><mi>Δ</mi><mi>B</mi><mo>=</mo><mn>2</mn></math>, and Majorana neutrino masses with <math><mi>Δ</mi><mi>L</mi><mo>=</mo><mn>2</mn></math>. Scenarios in which one or two axion fields necessarily appear in any <math><mi>B</mi></math> and/or <math><mi>L</mi></math> violating operators are also constructed. Nucleon decays would then necessarily involve an axion in the final state, while neutron-antineutron oscillations would only happen in an axionic background. This could have implications for the neutron lifetime puzzle, and more generally, opens the door to new phenomenological and cosmological applications.

Leptoquarks, axions and the unification of <math><mi>B</mi></math>, <math><mi>L</mi></math>, and Peccei-Quinn symmetries

In this paper, we discuss the construction of Effective Field Theories (EFTs) in which a chiral fermion, charged under both gauge and global symmetries, is integrated out. Inspired by typical axion models, these symmetries can be spontaneously broken, and the global ones might also be anomalous. In this context, particular emphasis is laid on the derivative couplings of the Goldstone bosons to the fermions, as these lead to severe divergences and ambiguities when building the EFT. We show how to precisely solve these difficulties within the path integral formalism, by adapting the anomalous Ward identities to the EFT context. Our results are very generic, and when applied to axion models, they reproduce the non-intuitive couplings between the massive SM gauge fields and the axion. Altogether, this provides an efficient formalism, paving the way for a systematic and consistent methodology to build entire EFTs involving anomalous symmetries, as required for axion or ALP searches.

Pham Vuong

Axion effective action

In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>4</mn></mrow></msubsup><mo>)</mo></math>-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent fixed-order pQCD contribution for GLS sum rule, e.g. <math><msup><mrow><mi>S</mi></mrow><mrow><mi>GLS</mi></mrow></msup><mo>(</mo><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>3</mn><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>PMC</mi></mrow></msub><mo>=</mo><msubsup><mrow><mn>2.559</mn></mrow><mrow><mo>−</mo><mn>0.024</mn></mrow><mrow><mo>+</mo><mn>0.023</mn></mrow></msubsup></math>, where the error is squared average of those from <math><mi>Δ</mi><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>Z</mi></mrow></msub><mo>)</mo></math>, the predicted <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>5</mn></mrow></msubsup><mo>)</mo></math>-order terms predicted by using the Padé approximation approach. After applying the PMC, a more convergent pQCD series has been obtained, and the contributions from the unknown higher-order terms are highly suppressed. In combination with the nonperturbative high-twist contribution, our final prediction of GLS sum rule agrees well with the experimental data given by the CCFR collaboration.

China

Xu-Dong Huang

Xing-Gang Wu

Qing Yu

Xu-Chang Zheng

Jun Zeng

The Gross-Llewellyn Smith sum rule up to -order QCD corrections

The low-energy effective theory (<math><mo>∼</mo><mi>TeV</mi></math>) of the little Higgs model with <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>6</mn><mo>)</mo><mo>/</mo><mi>S</mi><mi>p</mi><mo>(</mo><mn>6</mn><mo>)</mo></math>, as proposed by Low, Skiba, and Smith (LSS), exhibits a two-Higgs-doublet model (2HDM) structure. The symmetry dictates interesting Yukawa patterns, translating to nontrivial fermion couplings with both of the Higgs doublets. The couplings of the scalars with the fermions can induce flavor-changing neutral currents (FCNC), which get constraints from flavor physics observables such as <math><mrow><mi>BR</mi><mo>(</mo><mi>B</mi><mo>→</mo><msub><mi>X</mi><mi>s</mi></msub><mi>γ</mi><mo>)</mo></mrow></math>, <math><msub><mi>B</mi><mi>s</mi></msub><mo>−</mo><msub><mover><mi>B</mi><mo>¯</mo></mover><mi>s</mi></msub></math> mixing, etc. The precision measurement of the <math><mi>Z</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> vertex, the top and Higgs masses along with other Higgs coupling measurements at the Large Hadron Collider (LHC) also enforce severe restrictions on the LSS model. Direct LHC search results of beyond-the-Standard-Model (BSM) particles also impose bounds on the masses. We probe the LSS model in view of the above constraints through a random scan in the multidimensional parameter space. We observe, contrary to the general 2HDM scenario, that the emergent 2HDM from the LSS model is less constrained from the flavor data and the <math><mi>Z</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> measurement but is severely constrained from the electroweak (EW) searches at the LHC. From the flavor data and <math><mi>Z</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math>, we find that the charged Higgs mass is relaxed, with <math><mi>tan</mi><mi>β</mi></math> being restricted to 0.5–5, whereas the charged Higgs mass is pushed to larger than 1 TeV along with <math><mi>tan</mi><mi>β</mi></math> being further restricted to <math><mo>&lt;</mo><mn>3</mn></math> when the LHC bounds are incorporated.

India

Nilanjana Kumar

Soumya Sadhukhan

Emergent 2HDM in the Low-Skiba-Smith little Higgs model: Musings from flavor and electroweak physics

Because the Peccei-Quinn (PQ) symmetry has to be anomalous to solve the strong <math><mi>C</mi><mi>P</mi></math> puzzle, some colored and chiral fermions have to transform nontrivially under this symmetry. But when the Standard Model (SM) fermions are charged, as in the PQ or Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) models, this symmetry ends up entangled with the SM global symmetries, baryon (<math><mi>B</mi></math>) and lepton (<math><mi>L</mi></math>) numbers. This raises several questions addressed in this paper. First, the compatibility of axion models with some explicit <math><mi>B</mi></math>- and/or <math><mi>L</mi></math>-violating effects is analyzed, including those arising from seesaw mechanisms, electroweak instanton interactions, or explicit <math><mi>B</mi></math>- and <math><mi>L</mi></math>-violating effective operators. Second, how many of these effects can be simultaneously present is quantified, along with the consequences for the axion mass and vacuum alignment if too many of them are introduced. Finally, large classes of <math><mi>B</mi></math>- and/or <math><mi>L</mi></math>-violating interactions without impact on axion phenomenology are identified, like, for example, the various implementations of the type-I and -II seesaw mechanisms in the DFSZ context.

Baryon and lepton number intricacies in axion models

The axion couplings to SM gauge bosons are derived in various models, and shown to always arise entirely from non-anomalous fermion loops. They are thus independent of the anomaly structure of the model. This fact is without consequence for vector gauge interactions like QCD and QED, but has a major impact for chiral gauge theories. For example, in the DFSZ axion model, the couplings of axions to electroweak gauge bosons do not follow the pattern expected from chiral anomalies, as we prove by an explicit calculation. The reason for this mismatch is traced back to triangle Feynman diagrams sensitive to the anomalous breaking of the vector Ward identity, and is ultimately related to the conservation of baryon and lepton numbers. Though our analyses are entirely done for true axion models, this observation could have important consequences for axion-like particle searches.