Our recent works <cross-refs refid='br0010 br0020' id='crs0020'>[1,2]</cross-refs> revisit the proof of chiral symmetry breaking in the confining regime of four-dimensional QCD-like theories, i.e. <math altimg='si1.svg'><mi>S</mi><mi>U</mi><mo stretchy='false'>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy='false'>)</mo></math> gauge theories with <math altimg='si2.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></math> flavors of vectorlike quarks in the fundamental representation. The analysis relies on the structure of &#8216;t Hooft anomaly matching and persistent mass conditions for theories with same <math altimg='si3.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and different <math altimg='si2.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></math>. In this paper, we work out concrete examples with <math altimg='si4.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>3</mn></math> and <math altimg='si5.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>5</mn></math> to support and elucidate the results of <cross-refs refid='br0010 br0020' id='crs0030'>[1,2]</cross-refs>. Within the same examples, we also test some claims made in earlier works.

Italy

Luca Ciambriello

Roberto Contino

Ling-Xiao Xu

On the proof of chiral symmetry breaking through anomaly matching in QCD-like theories: An exemplification

We demonstrate that chiral symmetry breaking occurs in the confining regime of QCD-like theories with <math altimg='si1.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> colors and <math altimg='si2.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></math> flavors. Our proof is based on a novel strategy, called &#8216;downlifting&#8217;, by which solutions of the 't Hooft anomaly matching and persistent mass conditions for a theory with <math altimg='si3.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></math> flavors are constructed from those of a theory with <math altimg='si2.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></math> flavors, while <math altimg='si1.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> is fixed. By induction, chiral symmetry breaking is proven for any <math altimg='si22.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>&#8805;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></math> in the confining regime, where <math altimg='si5.svg'><msub><mrow><mi>p</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></math> is the smallest prime factor of <math altimg='si1.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math>. The proof can be extended to <math altimg='si6.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></math> under the additional assumption on the absence of phase transitions when quark masses are sent to infinity. Our results do not rely on assumptions on the spectrum of massless bound states other than the fact that they are color-singlet hadrons.

Andrea Luzio

France

Marcello Romano

A novel strategy to prove chiral symmetry breaking in QCD-like theories

We critically reconsider the argument based on ’t Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional quantum chromodynamics-like theories with <math><msub><mi>N</mi><mi>c</mi></msub><mo>&gt;</mo><mn>2</mn></math> colors and <math><msub><mi>N</mi><mi>f</mi></msub></math> flavors. The main line of reasoning relies on a property of the solutions of the anomaly matching and persistent mass equations called <math><msub><mi>N</mi><mi>f</mi></msub></math>-independence. In previous works, the validity of <math><msub><mi>N</mi><mi>f</mi></msub></math>-independence was assumed based on qualitative arguments, but it was never proven rigorously. We provide a detailed proof and clarify under which (dynamical) conditions it holds. Our results are valid for a generic spectrum of massless composite fermions including baryons and exotics.

Proof of chiral symmetry breaking from anomaly matching in QCD-like theories

We discuss heavy particles that can be used to pin down the faithful Standard Model (SM) gauge group and their patterns in the SM effective field theory (SMEFT). These heavy particles are not invariant under a specific ℤ 6 subgroup of SU(3) c  × SU(2) L  × U(1) Y , which however acts trivially on all the SM particles, hence the faithful SM gauge group remains undetermined. Different realizations of the faithful SM gauge group correspond to different spectra of heavy particles, and they also correspond to distinct sets of line operators with one-form global symmetry acting on them. We show that the heavy particles not invariant under the ℤ 6 group cannot appear in tree-level ultraviolet completions of SMEFT, this enforces us to consider one-loop UV completions of SMEFT to identify the ℤ 6 non-invariant heavy particles. We demonstrate with examples that correlations between Wilson coefficients provide an efficient way to examine models with ℤ 6 non-invariant heavy particles. Finally, we prove that all the scalars that can trigger electroweak symmetry breaking must be invariant under the ℤ 6 group, hence they cannot be used to probe the faithful SM gauge group.

Belgium

Hao-Lin Li

Understanding the SM gauge group from SMEFT

We propose an alternative scenario for the axion misalignment mechanism based on the nontrivial interplay between the axion and a light dilaton in the early universe. Dark matter abundance is still sourced by the initial misalignment of the axion field, whose motion along the potential kicks the dilaton field away from its minimum, and dilaton starts to oscillate later with a delayed onset time for oscillation and a relatively large misalignment value due to the kick; eventually the dilaton dominates over the axion in their energy densities, and the dilaton is identified as dark matter. The kick effect due to axion motion is the most significant if the initial field value of dilaton is near its minimum; therefore, we call this scenario the axion “free-kick” misalignment mechanism, where the axion plays the role similar to a football player. Dark matter abundance can be obtained with a lower axion decay constant compared to the conventional misalignment mechanism.

Seokhoon Yun

Axion free-kick misalignment mechanism

As one of the key properties of the Higgs boson, the Higgs total width is sensitive to the global profile of the Higgs boson couplings, and thus new physics would modify the Higgs width. We investigate the total width in various new physics models, including various scalar extensions, composite Higgs models, and the fraternal twin Higgs model. Typically, the Higgs width is smaller than the standard model value due to mixture with other scalars if the Higgs is elementary, or curved Higgs field space for the composite Higgs. On the other hand, except for the possible invisible decay mode, the enhanced Yukawa coupling in the two Higgs doublet model or the exotic fermion embeddings in the composite Higgs could enhance the Higgs width greatly. The precision measurement of the Higgs total width at the high-luminosity LHC can be used to discriminate certain new physics models.

China

Qing-Hong Cao

Jiang-Hao Yu

What can we learn from the total width of the Higgs boson?  

We use the spectral lag catalog of 46 short GRBs aggregated by Xiao et al. (Astrophys J Lett 924:L29, 2022), to carry out an independent search for Lorentz invariance violation (LIV). For this purpose, we use a power-law model as a function of energy for the intrinsic astrophysical induced spectral lags. The expansion history of the universe needed for constraining LIV was obtained in a non-parametric method using cosmic chronometers. We use Bayesian model comparison to determine if the aforementioned spectral lags show evidence for LIV as compared to only astrophysically induced lags. We do not find any evidence for LIV, and obtain 95% CL lower limits on the corresponding energy scale to be  $$4 \times 10^{15}$$  <math> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> </mrow> </math>   GeV and  $$6.8 \times 10^{9}$$  <math> <mrow> <mn>6.8</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> </mrow> </math>   GeV for the linear and quadratic LIV models respectively. Our results obtained by using the flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for characterizing the cosmic expansion history are consistent with those obtained using chronometers.

India

Shantanu Desai

Rajdeep Agrawal

Germany

Haveesh Singirikonda

Search for Lorentz invariance violation using Bayesian model comparison applied to Xiao et al. GRB spectral lag catalog

We present a model that solves the strong CP problem via an axion parametrically heavier than the standard one. Within this picture the Standard Model quarks are embedded into a larger non-abelian Grand Color group that at high scales splits into ordinary QCD and an additional confining dynamics under which exotic chiral fermions are charged. Crucially, the vacuum expectation value of the axion is automatically relaxed to zero because the only renormalizable source of explicit CP violation, beyond those encoded in the topological angles, is contained in the Standard Model Yukawa couplings, and is therefore very suppressed. The Grand Color axion potential is controlled by the scale of the new confining group and is much larger than the QCD contribution, such that its dynamics is less exposed to the so-called “axion quality problem”. Potentially observable corrections to the effective topological angle can also arise, in our model as well as in a large class of heavy axion scenarios, from non-renormalizable Peccei-Quinn-conserving interactions, which introduce a new “heavy axion quality problem”. Our model has a very minimal field content, it relies entirely on gauge invariance and does not require the introduction of additional symmetries beyond the usual one postulated by Peccei and Quinn. The phenomenology is very rich and can be tested at colliders as well as via cosmological observations. A particularly interesting portion of parameter space predicts a visible Grand Color axion of mass above the GeV and decay constant larger than a few TeV.

Alessandro Valenti

Luca Vecchi

Grand Color axion

Recent works argue that the pattern of chiral symmetry breaking in QCD-like theories can be derived from supersymmetric (SUSY) QCD with perturbation of anomaly-mediated SUSY breaking (AMSB). Nevertheless, despite the fact that AMSB needs to be a small (but still exact) perturbation, two other major problems remain unsolved: first, in order to derive the chiral symmetry breaking pattern, one needs to minimize the potential along a certain specific direction, identifying this direction fully as an outcome is nontrivial given the moduli space of degenerate vacua in the SUSY limit; second, when SUSY is broken, non-holomorphic states might emerge and be relevant for determining the vacuum structure. In this work, we try to resolve these problems and discuss their physical implica- tions. For this purpose, we focus on SUSY QCD with N  f  ≤ N  c  + 1 and perturb the theories using AMSB. Without minimizing the potential along a certain specific direction in the moduli space, we successfully derive the expected chiral symmetry breaking pattern when N  f  &lt; N  c . However, when N  f  = N  c  and N  f  = N  c  + 1, we show that tree-level AMSB would induce runaway directions, along which baryon number is spontaneously broken, and the vacua with broken baryon number can be deeper while the field values are not far from the origin. This implies that phase transitions and/or non-holomorphic physics are necessary. In order to derive the expected chiral symmetry breaking pattern of non-SUSY QCD starting from the SUSY limit and AMSB, baryon number conservation is needed as an input rather than obtained as an output. Moreover, we perform explicit consistency checks on “ultraviolet insensitivity” for different N  f  by adding the holomorphic mass term for the last flavor, we find that the “jump” of AMSB potential indeed matches the contribution from the holomorphic mass term. We also show in general that, when tree-level AMSB is not vanishing, the origin of the moduli space in s-confining theories does not persist as a minimum.

On the derivation of chiral symmetry breaking in QCD-like theories and S-confining theories

We propose a soft-breaking mechanism for dark matter (DM) shift symmetry in a class of composite dark matter models, where both DM and the Higgs boson arise as pseudo Nambu-Goldstone bosons from novel strong dynamics. Our mechanism is utilized to suppress the nonderivative portal coupling between the Higgs boson and DM particle, which can evade the stringent bound of current DM direct detection experiments. Otherwise, this nonderivative portal coupling would naturally be at the same order of the Higgs quartic, rendering this class of models under severe crisis. For realizing the soft-breaking mechanism, we introduce vectorlike top partners dubbed “softons” to restore the shift symmetry of DM in the top Yukawa sector, which, however, is only broken by the softon masses. The portal coupling automatically vanishes as the shift-symmetry-breaking softon masses approach zero. Specifically, we present a proof-of-concept model of soft breaking based on the coset <math><mi>O</mi><mo>(</mo><mn>6</mn><mo>)</mo><mo>/</mo><mi>O</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> and the simplest fermion embedding, and study its DM phenomenology, where we show a large amount of novel parameter space is opened up by using the soft-breaking mechanism.