We investigate the collider signatures of a maximally flavor-violating $ U(1)_{L_\mu-L_\tau} $ model, where a new gauge boson $ Z^\prime $ and scalar triplets induce lepton flavor-changing interactions in the $\textit{μ}$-$\textit{τ}$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $ m_{Z^\prime} $ and the effective parameters $ \tilde{g}/m_{Z^\prime} $ , whereas it remains largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $ m_{Z^\prime} $ , and beam polarization can significantly suppress the Standard Model backgrounds while enhancing new physics contributions. We find that, in the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results show that multi-lepton final states are powerful probes of the $ U(1)_{L\mu - L_\tau} $ framework and can offer valuable guidance for future searches at muon and electron-positron colliders.

China

Jianing Qin

Fei Huang

Honglei Li

Zhi-Long Han

Jin Sun

Collider probes of four-lepton final states in maximally flavor-violating ${U(1)_{L_\mu-L_\tau}} $ model * Supported by National Natural Science Foundation of China (12505112, 11805081), Shandong Province Natural Science Foundation (ZR2024QA138, ZR2022MA056) and State Key Laboratory of Dark Matter Physics, University of Jinan Disciplinary Cross-Convergence Construction Project 2024 (XKJC- 202404) and Jin Sun is supported by IBS under the project code, (IBS-R018-D1)

We explore strongly correlated materials with tilted Dirac cone by introducing a method to realize this spectral feature within a holographic setup. Following the work by Moradpouri et al, we construct an asymptotically AdS spacetime by uplifting the vielbein of Volovik et al. to tilt the flat spacetime light cone. We then couple the resulting metric to holographic fermions and compute their spectral functions, confirming the presence of a tilted Dirac cone in momentum space. We also calculate the topological number using the holographic Green’s function and find that the Chern number is independent of the tilting parameter. Additionally, we show that the optical conductivity exhibits a Drude peak even at zero chemical potential, revealing nontrivial strong-coupling effects absent in field-theoretic models.

South Korea

Jeong-Won Seo

Taewon Yuk

Sang-Jin Sin

Tilted Dirac cones and their topology in holographic materials

We extend a top-down holographic model of a Weyl semimetal to finite charge density and compute the fermionic spectral function by introducing two probe fermions of opposite chirality. The model is controlled by the boundary fermion mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>M</mi></mrow></math> and the chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>. In the zero density, small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> limit, we recover four energy bands, two Weyl points, and linear dispersion in their vicinity, the hallmarks of a Weyl semimetal. As <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> increases, the bands between the Weyl points become progressively compressed and the spectral weight associated with those bands is smeared out. At finite charge density, we map the Fermi surface in momentum space and identify a Lifshitz transition: two distinct Fermi pockets, each enclosing a different Weyl point, merge into a single large Fermi surface that encloses both. This transition can be induced by either control parameter. Varying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi></math> alters the band structure and thus the band shape, which drives the Lifshitz transition, whereas changing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> shifts the bands relative to the Fermi level without qualitatively changing the band structure, producing the Lifshitz transition by moving the band positions.

Cheng-Yuan Lu

Xian-Hui Ge

Lifshitz transition in a holographic finite density flavor brane Weyl semimetal

We propose a method to constrain the scaling dimension of the operators of the strongly interacting systems (SIS) using the holographic setup. We demonstrate our method using the holographic superconductor theory. The idea is to consider the inside as well as the outside of the AdS black hole in which the gap equations has higher order singularities. Then the equivalence principle requests the solution be smoothly connected at the horizon, which request the vanishing of log divergent term as well as an indefinite conditionally convergent terms that can lead to any real number according to Riemann. As a result, one gets quantized values of the scaling dimension of the condensing operator. This is a pleasant surprise because so far one gets the constraints on the scaling dimension only by a hard analysis with bootstrap ansatz.

Yoon-Seok Choun

Ki-Seok Kim

Scaling dimension of operators from the black hole interior

We study the longitudinal beam single spin asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>L</mi><mi>U</mi></mrow><mrow><mi>sin</mi><msub><mi>ϕ</mi><mi>R</mi></msub></mrow></msubsup></math> of dihadron production in the semi-inclusive deep inelastic scattering process with a polarized electron beam scattering off an unpolarized proton target. The asymmetry arises from the convolutions of the twist-3 parton distribution function (PDF) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> and the twist-2 dihadron fragmentation function (DiFF) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>∢</mo></mrow></msubsup></mrow></math> as well as the twist-2 PDF <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> and the twist-3 DiFF <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>G</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow><mrow><mo>∢</mo></mrow></msup></mrow></math>. Using the spectator model calculations for the twist-3 PDF <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> and the DiFFs <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>∢</mo></mrow></msubsup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>G</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow><mrow><mo>∢</mo></mrow></msup></mrow></math>, we estimate the beam single spin asymmetry (BSA) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mrow><mi>L</mi><mi>U</mi></mrow><mrow><mi>sin</mi><msub><mi>ϕ</mi><mi>R</mi></msub></mrow></msubsup></math> at the kinematical configuration of CLAS and CLAS12. We find good agreement with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>h</mi></msub></math>-dependencies data, though <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math>-dependencies show discrepancies. We include the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math> and provide predictions for COMPASS, EIC, and EicC. The negligible contribution from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⊗</mo><msup><mrow><mover accent="true"><mrow><mi>G</mi></mrow><mrow><mo stretchy="false">˜</mo></mrow></mover></mrow><mrow><mo>∢</mo></mrow></msup></mrow></math> supports the Wandzura-Wilczek approximation, while our results highlight the importance of QCD evolution in twist-3 PDF analyses.

Yanli Li

Keyang She

Hui Li

Xiaoyu Wang

De-Min Li

Zhun Lu

Beam single spin asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mi>L</mi><mi>U</mi></mrow><mrow><mi>sin</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></msubsup></mrow></math> of the dihadron production in SIDIS process

In the field of particle physics, the phenomenon of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) process has always been a significant focus. This paper focuses on the single longitudinal spin asymmetry $$A_{UL }^{\sin (3\phi _{h}-\phi _{R})}$$ in the dihadron production during this process and combines the transverse-momentum-dependent dihadron fragmentation function (DiFF) $$H_1^{\perp }$$ to deeply analyze its underlying mechanism. Here, the involved DiFF $$H_1^{\perp }$$ is the analogue of the Collins function for single-hadron production and it describes the fragmentation of a transversely polarized quark at leading twist. Recent studies have shown that the azimuthal asymmetry signal observed by the COMPASS collaboration in the dihadron SIDIS is weak. To reveal the reason for this small signal and to study the asymmetry, we calculate the unknown T-odd DiFF $$H_1^{\perp }$$ using the spectator model. The spectator model, widely used in SIDIS, describes the internal structure of hadrons and the hadronization mechanism. This model has successfully explained dihadron production in unpolarized and single-polarized processes. During the research process, while maintaining the transverse momentum dependence of the hadron pair, we employ the transverse momentum dependent(TMD) factorization framework, using this method and the model, we first simulate the asymmetry in the COMPASS energy region and compare it with experimental data. Furthermore, we predict the same asymmetry at the HERMES, expecting to provide valuable theoretical references for relevant experimental studies.

Lei Tan

Gang Li

Mao Song

Xuan Luo

Single spin asymmetry $$ A _ { U L } ^ { \sin ( 3 \phi _ { h } - \phi _{ R } ) }$$ in dihadron production in SIDIS

We investigate the fermionic properties of a dyonic Gubser-Rocha model in the context of gauge/gravity duality. This model incorporates both a magnetic field and momentum relaxation. We have derived this model’s scaling exponent, revealing the influence of the magnetic field and momentum relaxation on low-energy physics. As the magnetic field strength and momentum relaxation increase, the spectral function of the dual field changes significantly. Specifically, we observe variations in the scaling exponent, Fermi momentum, and dispersion relations as the magnetic field increases, highlighting the system’s transition from a Fermi liquid to a non-Fermi liquid, and eventually to an insulating state. Our analysis of the magneto-scattering rate reveals that it is nearly zero in the Fermi liquid region, increases significantly in the non-Fermi liquid region, and ultimately arrives at a maximum value in the insulating state.

Holographic fermions in the dyonic Gubser-Rocha black hole

We first study a non-relativistic field theory model for the Kondo lattice by introducing the Kondo condensation, whose main effect is the hybridization of the flat band of the localized electron with dispersive one of the itinerant electron. The problem here is that the resulting Kondo condensation arises only in strong coupling where the validity of the mean field theory is questionable. Therefore, we build a holographic mean field theory of the Kondo lattice with strong coupling by identifying the effect of the lattice with the fermion’s spectral shape due to the coupling with the order parameter representing the symmetry breaking. For the flat band spectrum we use the mixed quantization, and for the dispersive spectrum we intoduce the second fermion in standard quantization. The coupling of the two fermions with the scalar order representing the Kondo condensation provides the hybrization of the two spectrum, reproducing the main feature of the Kondo lattice together with the fuzzy character of the spectrum of the strongly coupled system.

Young-Kwon Han

Debabrata Ghorai

Holographic mean field theory and Kondo lattice

One of the most wanted features of holography in its condensed matter physics application is to encode the structure of lattice, which is the most direct data of the material. In this paper, we propose a method to encode the lattice structure by embedding the tight binding data into the Dirac equation in the anti–de Sitter bulk. We explicitly worked out the idea for the graphene and Haldane models, and the result shows that some degrees of freedom escape the free-electron on-shell curve, and Green’s function loses the pole structure completely. It implies that the electronic structure is not described by the band structure only, which is consistent with what many angle-resolved photoemission spectroscopy data tell us, and it also implies that the system is in non-Fermi liquid even for the graphene, which is consistent with recent experiments for the clean graphene.

Encoding the lattice in the holography

The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without introducing any order parameter. We then classify the Mott gap, depending on the shape of the gap in the density of states and whether the Fermi surface is touching the valence bond or not, into three classes: i) Symmetric gap, ii) Asymmetric gap with isolated Fermi sea. iii) Asymmetric gap with Fermi sea touching the valence band. Finally, we identify possible non-minimal gauge interactions that produce a flatband without symmetry breaking.