Within the framework of nonrelativistic quantum chromodynamics (NRQCD) factorization, we compute the ( mathcal{O}left({v}^4right) ) relativistic corrections to the fragmentation of a heavy quark into the color-singlet ( {}^1{S}_0^{left[1right]} ) and ( {}^3{S}_1^{left[1right]} ) quarkonium states. Using the Collins-Soper definition of the fragmentation function, we reproduce the known ( mathcal{O}left({v}^2right) ) results. We find that the ( mathcal{O}left({v}^4right) ) correction gives a positive contribution relative to the leading order result over a wide range of the light-cone momentum fraction z, while its magnitude remains much smaller than that of the ( mathcal{O}left({v}^2right) ) correction. This behavior indicates a good convergence of the NRQCD relativistic expansion in this process. We further extend the calculation to the fragmentation functions in the unequal-mass case at ( mathcal{O}left({v}^4right) ) and obtain the corresponding analytical expressions.
{"title":"Order-v4 corrections to heavy quark fragmentation to S-wave heavy quarkonium","authors":"Sai Cui, Yi-Jie Li, Guang-Zhi Xu, Kui-Yong Liu","doi":"10.1007/JHEP03(2026)138","DOIUrl":"10.1007/JHEP03(2026)138","url":null,"abstract":"<p>Within the framework of nonrelativistic quantum chromodynamics (NRQCD) factorization, we compute the <span>( mathcal{O}left({v}^4right) )</span> relativistic corrections to the fragmentation of a heavy quark into the color-singlet <span>( {}^1{S}_0^{left[1right]} )</span> and <span>( {}^3{S}_1^{left[1right]} )</span> quarkonium states. Using the Collins-Soper definition of the fragmentation function, we reproduce the known <span>( mathcal{O}left({v}^2right) )</span> results. We find that the <span>( mathcal{O}left({v}^4right) )</span> correction gives a positive contribution relative to the leading order result over a wide range of the light-cone momentum fraction <i>z</i>, while its magnitude remains much smaller than that of the <span>( mathcal{O}left({v}^2right) )</span> correction. This behavior indicates a good convergence of the NRQCD relativistic expansion in this process. We further extend the calculation to the fragmentation functions in the unequal-mass case at <span>( mathcal{O}left({v}^4right) )</span> and obtain the corresponding analytical expressions.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)138.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a theory of SU(9) dark grand unification, where dark matter consists of asymmetric dark baryons from the Sp(4)D dark QCD sector. By unifying the dark color gauge group with the Standard Model gauge group, the asymmetry generation in both sectors originates from a common process that preserves a U(1)D−(B−L) symmetry, resulting in comparable number densities. Furthermore, thanks to dark grand unification, the Sp(4)D dark QCD sector shares a similar matter content with the QCD sector, leading to comparable running of the gauge couplings from the scale as high as 1015 GeV. This predicts a dark color confinement scale and thus dark baryon masses around the GeV scale, comparable to visible baryon masses. Together with the similar number densities, the model provides an explanation for the observed similarity between the energy densities of dark matter and baryons, ρD ≈ 5 ρB. The model also features some novel phenomenology, including a GeV-scale flavored dark QCD sector with diquark dark baryons and light dark mesons. The interaction between the dark sector and the visible sector occurs via a new Z′ boson with a mass of ( mathcal{O}(10) ) TeV, which could be searched for at future hadron colliders. We also briefly discuss an SU(8) dark grand unified theory featuring an SU(3)D dark QCD sector.
{"title":"Comparable dark matter and baryon energy densities from dark grand unification","authors":"Yi Chung","doi":"10.1007/JHEP03(2026)135","DOIUrl":"10.1007/JHEP03(2026)135","url":null,"abstract":"<p>We investigate a theory of SU(9) dark grand unification, where dark matter consists of asymmetric dark baryons from the Sp(4)<sub><i>D</i></sub> dark QCD sector. By unifying the dark color gauge group with the Standard Model gauge group, the asymmetry generation in both sectors originates from a common process that preserves a U(1)<sub><i>D−</i>(<i>B−L</i>)</sub> symmetry, resulting in comparable number densities. Furthermore, thanks to dark grand unification, the Sp(4)<sub><i>D</i></sub> dark QCD sector shares a similar matter content with the QCD sector, leading to comparable running of the gauge couplings from the scale as high as 10<sup>15</sup> GeV. This predicts a dark color confinement scale and thus dark baryon masses around the GeV scale, comparable to visible baryon masses. Together with the similar number densities, the model provides an explanation for the observed similarity between the energy densities of dark matter and baryons, <i>ρ</i><sub><i>D</i></sub> ≈ 5 <i>ρ</i><sub><i>B</i></sub>. The model also features some novel phenomenology, including a GeV-scale flavored dark QCD sector with diquark dark baryons and light dark mesons. The interaction between the dark sector and the visible sector occurs via a new <i>Z′</i> boson with a mass of <span>( mathcal{O}(10) )</span> TeV, which could be searched for at future hadron colliders. We also briefly discuss an SU(8) dark grand unified theory featuring an SU(3)<sub><i>D</i></sub> dark QCD sector.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)135.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as ( {textrm{e}}^{S_0} ), where S0 is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of ( mathcal{N}=2 ) and (small) ( mathcal{N}=4 ) JT supergravity, and then explore the new cases of spectra from ( mathcal{N}=3 ) and large ( mathcal{N}=4 ) JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.
{"title":"Extended JT supergravity and random matrix models: The power of the string equation","authors":"Clifford V. Johnson, Maciej Kolanowski","doi":"10.1007/JHEP03(2026)126","DOIUrl":"10.1007/JHEP03(2026)126","url":null,"abstract":"<p>A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as <span>( {textrm{e}}^{S_0} )</span>, where <i>S</i><sub>0</sub> is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of <span>( mathcal{N}=2 )</span> and (small) <span>( mathcal{N}=4 )</span> JT supergravity, and then explore the new cases of spectra from <span>( mathcal{N}=3 )</span> and large <span>( mathcal{N}=4 )</span> JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)126.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrea Autieri, Stefano Camarda, Leandro Cieri, Giancarlo Ferrera, German F. R. Sborlini
We consider the transverse momentum (qT) distribution of neutral charged bosons at hadron colliders. We perform the resummation of the logarithmically-enhanced effects due to simultaneous QCD and QED initial-state radiation, up to mixed next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of such mixed QCD⊗QED resummed contributions on top of pure QCD corrections, finding percent-level effects.
{"title":"Transverse-momentum resummation at mixed QCD⊗QED NNLL accuracy for Z boson production at hadron colliders","authors":"Andrea Autieri, Stefano Camarda, Leandro Cieri, Giancarlo Ferrera, German F. R. Sborlini","doi":"10.1007/JHEP03(2026)113","DOIUrl":"10.1007/JHEP03(2026)113","url":null,"abstract":"<p>We consider the transverse momentum (<i>q</i><sub><i>T</i></sub>) distribution of neutral charged bosons at hadron colliders. We perform the resummation of the logarithmically-enhanced effects due to simultaneous QCD and QED initial-state radiation, up to mixed next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of such mixed QCD⊗QED resummed contributions on top of pure QCD corrections, finding percent-level effects.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)113.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The axion is a well-motivated and generic extension of the Standard Model. If produced in the early universe, axions may still be relativistic today, forming a Cosmic Axion Background (CaB) potentially detectable in direct detection experiments. Although CaB is expected to be broadband, which makes it challenging to be detected, a high-quality-factor microwave cavity acts as a narrowband filter with response peaked at its resonant frequency. We propose a new strategy using multi-cavity arrays to distinguish signal from background noise by exploiting spatial correlations of the axion-induced electric field which are set by the cavity quality factor. We compute the two-point correlation function for electric fields in spatially separated cavities sourced by an isotropic CaB. Analyzing various cavity geometries, we find that stacked, wide-base cavity arrays offer coherent enhancement of the axion signal. We apply our formalism to prospective upgrades of the ADMX experiment, including configurations with four and eighteen coupled cavities. Although these arrays do not achieve a coherent enhancement, optimizing the geometry could potentially yield an ( mathcal{O}(1) ) improvement in the sensitivity to the CaB.
{"title":"Cosmic Axion Background detection using resonant cavity arrays","authors":"Soobeom Chung, Jeff A. Dror","doi":"10.1007/JHEP03(2026)123","DOIUrl":"10.1007/JHEP03(2026)123","url":null,"abstract":"<p>The axion is a well-motivated and generic extension of the Standard Model. If produced in the early universe, axions may still be relativistic today, forming a Cosmic Axion Background (C<i>a</i>B) potentially detectable in direct detection experiments. Although C<i>a</i>B is expected to be broadband, which makes it challenging to be detected, a high-quality-factor microwave cavity acts as a narrowband filter with response peaked at its resonant frequency. We propose a new strategy using multi-cavity arrays to distinguish signal from background noise by exploiting spatial correlations of the axion-induced electric field which are set by the cavity quality factor. We compute the two-point correlation function for electric fields in spatially separated cavities sourced by an isotropic C<i>a</i>B. Analyzing various cavity geometries, we find that stacked, wide-base cavity arrays offer coherent enhancement of the axion signal. We apply our formalism to prospective upgrades of the ADMX experiment, including configurations with four and eighteen coupled cavities. Although these arrays do not achieve a coherent enhancement, optimizing the geometry could potentially yield an <span>( mathcal{O}(1) )</span> improvement in the sensitivity to the C<i>a</i>B.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)123.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yong jun Ahn, Matteo Baggioli, Hyun-Sik Jeong, Masataka Matsumoto
Holographic D-brane constructions, governed by the Dirac-Born-Infeld (DBI) action, play a central role in the AdS/CFT correspondence, particularly in applications to quantum chromodynamics and condensed matter systems. In this work, we demonstrate how to equip these bottom-up holographic models with dynamical boundary gauge fields, thereby introducing electromagnetic interactions into their dual field theory descriptions. As a direct application of this formalism, we compute the dispersion relations of the lowest quasinormal modes around both equilibrium and nonequilibrium steady states, and show that their behavior matches the predictions from hydrodynamics with dynamical U(1) symmetry.
{"title":"Holographic D-brane constructions with dynamical gauge fields","authors":"Yong jun Ahn, Matteo Baggioli, Hyun-Sik Jeong, Masataka Matsumoto","doi":"10.1007/JHEP03(2026)118","DOIUrl":"10.1007/JHEP03(2026)118","url":null,"abstract":"<p>Holographic D-brane constructions, governed by the Dirac-Born-Infeld (DBI) action, play a central role in the AdS/CFT correspondence, particularly in applications to quantum chromodynamics and condensed matter systems. In this work, we demonstrate how to equip these bottom-up holographic models with dynamical boundary gauge fields, thereby introducing electromagnetic interactions into their dual field theory descriptions. As a direct application of this formalism, we compute the dispersion relations of the lowest quasinormal modes around both equilibrium and nonequilibrium steady states, and show that their behavior matches the predictions from hydrodynamics with dynamical U(1) symmetry.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)118.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The particle model building of cosmological collider physics often involves boost-breaking bilinear mixing between a heavy particle and the nearly massless inflaton mode. In cosmological correlators, such a mixing is obtained by taking a folded limit of a generic tree graph, which is a special case of degenerate kinematics. In this work, we continue our exploration of massive inflationary amplitudes with a focus on degenerate kinematics. With a suitable change of variables, we derive new differential equations and full analytical solutions for generic tree graphs, making it trivial to take the folded limit and partial-energy limit at a vertex. Our result shows that folded tree graphs generally involve functions of smaller transcendental weights than their nondegenerate counterparts. In particular, the inflaton bispectrum with triple massive exchanges can be expressed in terms of a trivariate Kampé de Fériet function and simpler hypergeometric functions.
{"title":"Massive inflationary amplitudes: new representations and degenerate limits","authors":"Zhong-Zhi Xianyu, Jiaju Zang","doi":"10.1007/JHEP03(2026)122","DOIUrl":"10.1007/JHEP03(2026)122","url":null,"abstract":"<p>The particle model building of cosmological collider physics often involves boost-breaking bilinear mixing between a heavy particle and the nearly massless inflaton mode. In cosmological correlators, such a mixing is obtained by taking a folded limit of a generic tree graph, which is a special case of degenerate kinematics. In this work, we continue our exploration of massive inflationary amplitudes with a focus on degenerate kinematics. With a suitable change of variables, we derive new differential equations and full analytical solutions for generic tree graphs, making it trivial to take the folded limit and partial-energy limit at a vertex. Our result shows that folded tree graphs generally involve functions of smaller transcendental weights than their nondegenerate counterparts. In particular, the inflaton bispectrum with triple massive exchanges can be expressed in terms of a trivariate Kampé de Fériet function and simpler hypergeometric functions.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)122.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we initiate the study of lepton flavor violating (LFV) dark matter (DM) interactions, expanding our focus beyond the flavor-conserving DM interactions typically considered in conventional direct and indirect detections. We work in an effective field theory (EFT) framework, focusing on the leading-order local operators of the form, ( {overline{ell}}_jGamma {ell}_i{textrm{DM}}^2 ), where (ij) = (eμ, eτ, μτ) and the DM includes the three well-known scenarios: a scalar, a fermion, and a vector. We derive the invariant-mass distribution for the three-body decay ℓi → ℓj + DM + DM and demonstrate that it can be used to distinguish between different operator structures and to determine the DM mass. By utilizing current experimental bounds on the charged muon LFV decay involving neutrinos and the ratio of tau leptonic decay widths, we establish stringent limits on the effective scale associated with each operator. Additionally, for the eμ flavor combination, we investigate the muon four-body radiative decay (μ → e + DM + DM + γ) to complement our probe of such interactions. Finally, we examine muonium invisible decays based on the derived bounds on the effective operators and find that the branching ratios can be significantly enhanced compared to the predictions of the standard model. In particular, any future observation of the para-muonium invisible decay serves as a compelling signature for these flavored DM interactions.
{"title":"Charged lepton flavor violating decays with a pair of light dark matter and muonium invisible decay","authors":"Sahabub Jahedi, Yi Liao, Xiao-Dong Ma","doi":"10.1007/JHEP03(2026)114","DOIUrl":"10.1007/JHEP03(2026)114","url":null,"abstract":"<p>In this paper, we initiate the study of lepton flavor violating (LFV) dark matter (DM) interactions, expanding our focus beyond the flavor-conserving DM interactions typically considered in conventional direct and indirect detections. We work in an effective field theory (EFT) framework, focusing on the leading-order local operators of the form, <span>( {overline{ell}}_jGamma {ell}_i{textrm{DM}}^2 )</span>, where (<i>ij</i>) = (<i>eμ, eτ, μτ</i>) and the DM includes the three well-known scenarios: a scalar, a fermion, and a vector. We derive the invariant-mass distribution for the three-body decay <i>ℓ</i><sub><i>i</i></sub> → <i>ℓ</i><sub><i>j</i></sub> + DM + DM and demonstrate that it can be used to distinguish between different operator structures and to determine the DM mass. By utilizing current experimental bounds on the charged muon LFV decay involving neutrinos and the ratio of tau leptonic decay widths, we establish stringent limits on the effective scale associated with each operator. Additionally, for the <i>eμ</i> flavor combination, we investigate the muon four-body radiative decay (<i>μ</i> → <i>e</i> + DM + DM + <i>γ</i>) to complement our probe of such interactions. Finally, we examine muonium invisible decays based on the derived bounds on the effective operators and find that the branching ratios can be significantly enhanced compared to the predictions of the standard model. In particular, any future observation of the para-muonium invisible decay serves as a compelling signature for these flavored DM interactions.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)114.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrzej Pokraka, Marcus Spradlin, Anastasia Volovich, He-Chen Weng
The full 245-letter symbol alphabet for all planar massless two-loop six-point Feynman integrals was recently determined in arXiv:2412.19884 and arXiv:2501.01847. In a parallel mathematical development, it was shown in arXiv:2408.14956 that there is an embedding of the cluster algebra associated to the partial flag variety ( {mathcal{Fl}}_{2,n-2;n} ), which describes the kinematics of n massless particles, into that of the Grassmannian Gr(n–2, 2n–4). In this paper we connect these developments by showing that most of the rational symbol letters can be expressed in terms of flag cluster variables, and that all of the algebraic symbol letters arise from infinite mutation sequences.
{"title":"Symbol alphabets in QCD and flag cluster algebras","authors":"Andrzej Pokraka, Marcus Spradlin, Anastasia Volovich, He-Chen Weng","doi":"10.1007/JHEP03(2026)120","DOIUrl":"10.1007/JHEP03(2026)120","url":null,"abstract":"<p>The full 245-letter symbol alphabet for all planar massless two-loop six-point Feynman integrals was recently determined in arXiv:2412.19884 and arXiv:2501.01847. In a parallel mathematical development, it was shown in arXiv:2408.14956 that there is an embedding of the cluster algebra associated to the partial flag variety <span>( {mathcal{Fl}}_{2,n-2;n} )</span>, which describes the kinematics of <i>n</i> massless particles, into that of the Grassmannian Gr(<i>n</i>–2, 2<i>n</i>–4). In this paper we connect these developments by showing that most of the rational symbol letters can be expressed in terms of flag cluster variables, and that all of the algebraic symbol letters arise from infinite mutation sequences.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)120.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bhubanjyoti Bhattacharya, Suneth Jayawardana, Nausheen R. Shah
The Standard Model (SM) of particle physics fails to explain the observed hierarchy in fermion masses or the origin of fermion-flavor structure. We construct a model to explain these observations in the quark sector. We introduce a spectrum of new particles consisting of six of each — massive singlet vector-like quarks (VLQs), singlet scalars, and SU(2)-doublet scalars. SM quark masses are generated when the neutral components of the SU(2)-doublet scalars acquire non-zero vacuum expectation values (VEVs). We impose global symmetries to ensure that Yukawa couplings stay roughly flavor diagonal and democratic (of the same order), as well as to suppress tree-level flavor-changing neutral currents. Quark-mass hierarchy then follows from a hierarchy in scalar VEVs. The singlet scalars also acquire weak-scale VEVs. Together with the VLQs, they act as messengers between different generations of quarks in the SM. These messenger particles are responsible for generating the elements of the Cabibbo-Kobayashi-Masakawa (CKM) matrix which depend on the ratios of the singlet VEVs and VLQ masses. Constructed this way, the CKM matrix is found to be independent of the SM fermion masses. Using the measured values of the CKM matrix elements and assuming order-one couplings, we derive constraints on the masses of the VLQs and discuss prospects for probing our model in the near future.
{"title":"The deconstruction of flavor in the privately democratic Higgs sector","authors":"Bhubanjyoti Bhattacharya, Suneth Jayawardana, Nausheen R. Shah","doi":"10.1007/JHEP03(2026)116","DOIUrl":"10.1007/JHEP03(2026)116","url":null,"abstract":"<p>The Standard Model (SM) of particle physics fails to explain the observed hierarchy in fermion masses or the origin of fermion-flavor structure. We construct a model to explain these observations in the quark sector. We introduce a spectrum of new particles consisting of six of each — massive singlet vector-like quarks (VLQs), singlet scalars, and SU(2)-doublet scalars. SM quark masses are generated when the neutral components of the SU(2)-doublet scalars acquire non-zero vacuum expectation values (VEVs). We impose global symmetries to ensure that Yukawa couplings stay roughly flavor diagonal and democratic (of the same order), as well as to suppress tree-level flavor-changing neutral currents. Quark-mass hierarchy then follows from a hierarchy in scalar VEVs. The singlet scalars also acquire weak-scale VEVs. Together with the VLQs, they act as messengers between different generations of quarks in the SM. These messenger particles are responsible for generating the elements of the Cabibbo-Kobayashi-Masakawa (CKM) matrix which depend on the ratios of the singlet VEVs and VLQ masses. Constructed this way, the CKM matrix is found to be <i>independent</i> of the SM fermion masses. Using the measured values of the CKM matrix elements and assuming order-one couplings, we derive constraints on the masses of the VLQs and discuss prospects for probing our model in the near future.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2026 3","pages":""},"PeriodicalIF":5.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP03(2026)116.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}