Quark Mass Research Articles

The Third Family Quark Mass Hierarchy and FCNC in the Universal Seesaw Model

Abstract We present the study of the quark sector of the universal seesaw model with $\mathrm{SU(2)_L \times SU(2)_R \times U(1)_{Y^{\prime }}}$ gauge symmetry in the massless case of the two lightest quark families. This model aims to explain the mass hierarchy of the third family quark by introducing a vector-like quark (VLQ) partner for each quark. In this model, we introduce $\mathrm{SU(2)_L}$ and $\mathrm{SU(2)_R}$ Higgs doublets. We derive explicitly the Lagrangian for the quark sector, Higgs sector, and kinetic terms of the gauge fields, starting from the Lagrangian, which is invariant under $\mathrm{SU(2)_L \times SU(2)_R \times U(1)_{Y^{\prime }}}$ gauge symmetry. At each stage of the symmetry breaking, we present the Lagrangian with the remaining gauge symmetry. Additionally, we investigate the flavor-changing neutral currents (FCNCs) of the Higgs (h) and Z-bosons in the interaction with the top, heavy top, bottom, and heavy bottom quarks.

An event generator for Lepton-Hadron deep inelastic scattering at NLO+PS with POWHEG including mass effects

We present a generator for lepton nucleon collisions in the DIS regime, focusing in particular on processes with a massive lepton and/or a massive quark in the final state. We have built a full code matching NLO QCD corrections to parton shower Monte Carlo programs in the POWHEG-BOX framework. Our code can be used to compute NLO+PS accurate fully differential predictions for neutral current and charged current processes, including processes with an incoming tau neutrino, and/or including charm quarks in the final state. We also made comparisons with available data and predictions for the new neutrino experiments at CERN.

Open charm tetraquarks in broken SU(3)F symmetry

Prompted by a recent lattice QCD calculation, we review the SU(3) light quark flavor structure of charmed tetraquarks with spin 0 diquarks. Fermi statistics forces the three light quarks to be in the representation 3¯⊗3¯=3⊕6¯. This agrees with the weak repulsion in the 15 of the 3⊗8 in D¯K scattering studied on the lattice. We analyze the 3⊕6¯ multiplet broken by the strange quark mass and determine the five independent masses from the known masses of diquarks. The mass of Ds0*(2317) is predicted within 50 MeV accuracy. The recently observed D¯s−−(2900) and D¯s0(2900), likely part of a I=1 multiplet, with flavor composition c¯q¯q′s, and X0(2900), an isosinglet with flavor composition c¯s¯ud, fit naturally in a 3⊕6¯ structure as the first radial excitations. We discuss also the decay modes of Ds0*(2317), of the radial excitations and of the predicted particles. Published by the American Physical Society 2024

Study of the isoscalar scalar bcu¯d¯ tetraquark Tbc with lattice QCD

We present a lattice QCD study of the elastic S-wave DB¯ scattering in search of tetraquark candidates with explicitly exotic flavor content bcu¯d¯ in the isospin I=0 and JP=0+ channel. We use four lattice QCD ensembles with dynamical u/d, s, and c quark fields generated by the MILC collaboration. A nonrelativistic QCD Hamiltonian, including improvement coefficients up to O(αsv4), is utilized for the bottom quarks. For the rest of the valence quarks we employ a relativistic overlap action. Five different valence quark masses are utilized to study the light quark mass dependence of the DB¯ scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic DB¯ scattering amplitudes are extracted employing Lüscher’s prescription. The light quark mass dependence of the continuum extrapolated amplitudes suggests an attractive interaction between the B¯ and D mesons. At the physical pseudoscalar meson mass (Mps=Mπ) the DB¯ scattering amplitude has a subthreshold pole corresponding to a binding energy of −39(−6+4)(−18+8) MeV with respect to the DB¯ threshold. The critical Mps at which the DB¯ scattering length diverges and the system becomes unbound corresponds to Mps*=2.94(15)(5) GeV. This result can hold significant experimental relevance in the search for a bound scalar Tbc tetraquark, which could well be the next “doubly heavy” bound tetraquark to be discovered with only weak decay modes. Published by the American Physical Society 2024

SU(2)L deconstruction and flavour (non)-universality

We study two-site deconstructions of the SU(2)L gauge group factor of the SM. Models based on this approach can explain the hierarchies of the quark masses and CKM mixing between third and light families if these fields are localised on different sites by the presence of hierarchical new physics scales. The model leads to an accidental global U(2)q × U(3)u × U(3)d flavour symmetry which prevents dangerously large effects in flavour observables, making a TeV extension of the SM possible. Given the structure of the PMNS matrix in the neutrino sector, we explore different possibilities for the arrangement of the leptons on the two sites, and consider different models with U(2)ℓ or U(3)ℓ flavour symmetries. The phenomenology of the models is mostly governed by a massive vector triplet of SU(2)L. We study the interesting interplay between LHC searches and precision observables. In particular, one of the models can give a sizeable lepton flavour universal effect in the Wilson coefficient C9 while naturally suppressing contributions to C10, as suggested by current b → sℓ+ℓ− data, predicting simultaneously a mild positive shift in the W boson mass.

Semiclassics for the QCD vacuum structure through T2-compactification with the baryon-’t Hooft flux

We study QCD vacuum structure with the topological θ angle using a recently proposed semiclassical approach on ℝ2 × T2 with the ’t Hooft and baryon magnetic fluxes. Under the assumption of adiabatic continuity in this setup, the confining vacuum can be described by the dilute gas of center vortices. With this semiclassical approach, we derive the 2d effective description at small T2 and successfully explain the reasonable theta dependence of the QCD vacuum: in the one-flavor QCD at θ = π, the CP symmetry is spontaneously broken for quark mass above a critical value and restored for a subcritical mass, while the CP symmetry is always spontaneously broken in the multi-flavor QCD at θ = π. From our semiclassical description, we discuss implications to the 4d chiral Lagrangian and propose how the η′ meson should be incorporated in consistent with known global structures: the periodicity of the η′ should be extended from the naive one 2π to 2πN. Additionally, we revisit the phase diagram of Nf = 1 + 1 and Nf = 1 + 1 + 1 QCD on the up and down quark mass plane, confirming and refining the existence of the CP-broken Dashen phase.

Effect of charm quark on chiral phase transition in Nf=2+1+1 holographic QCD

We investigate the effect of the charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark-flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark-flavor symmetry breaking which is associated with the violation of the U(1) axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, and then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark-mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm-quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark-flavor system. The critical exponents related to the chiral phase transition are also addressed. Published by the American Physical Society 2024

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

B meson mixing at NNLO: technical aspects

We provide details to several technical aspects which are important for the calculation of next-to-next-to-leading order corrections to the mixing of neutral B mesons. This includes the computation of the master integrals for finite charm and bottom quark masses, projectors for products of up to 22 γ matrices and tensor integrals with up to rank 11.

Flavor mixing and solution structures in Dyson–Schwinger equations for a two-flavor system

We solved the Dyson–Schwinger (DS) equations for a two-flavor system with symmetry to study its flavor mixing effects. Initially, we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions. Using the point interaction model, the DS equations can be solved analytically, and we found that these solutions can be classified into three groups, each forming an ellipse. These solutions exhibit SO(2) symmetry, while the original SU(2) symmetry at the Lagrangian level is dynamically broken to SO(2), corresponding to the emergence of flavor mixing effects. However, this flavor mixing effect does not manifest in the final physical state. By utilizing the system’s SO(2) symmetry, we can diagonalize the propagators of the DS equations, eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split. These mass eigenstates have identical quantum numbers but different masses. If we can correspond these to quark particles of different generations, we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum. Finally, we provide the corresponding numerical results using a more realistic interaction model.

Ratios of the light quark masses: Cubic curve versus ellipse

The bounds on the light quark masses are obtained by fitting the squares of pseudoscalar meson masses mπ2 and mK2 to second order in 1/Nc expansion. The result is an algebraic cubic curve whose coefficients are the known Weinberg values for the quark mass ratios mu/md and ms/md. Additional restrictions arise when using the ratio ms/mud=27.23(10) quoted by FLAG for lattice simulations with four quark flavors. This provides a tight constraint on the ratio mu/md=0.455(8). Published by the American Physical Society 2024

Schwarzschild deformed supergravity background: Possible geometry origin of fermion generations and mass hierarchy

The problem of fermion masses hierarchy in the Standard Model is considered on a toy model of a 10-dimensional space-time with a IIA supergravity type background. The Dirac equation written on this background, after compactification of extra four- and one-dimensional subspaces, gives the spectrum of Fermi fields which profiles in five dimensions and corresponding Higgs generated masses in four dimensions depend on the eigenvalues of Dirac operator on the named compact subspaces. Schwarzschild Euclidean deformation of the supergravity throat with the “apple-shaped” conical singularity permits to leave only three nondivergent angular modes interpreted as three generations of the down-type quarks. The resulting expressions for the quark masses are a geometry version of the Froggatt-Nielsen mechanism. Published by the American Physical Society 2024

Chiral phase transition in soft-wall AdS/QCD with scalar-dilaton coupling

The chiral phase boundary of nuclear matter is expected to have a critical point where the rapid crossover of lattice methods at zero chemical potential becomes a first-order phase transition. Phenomenological models based on the AdS/CFT correspondence, known as AdS/QCD, have succeeded in capturing many features of nuclear matter, with recent progress in producing the expected critical point. We study a model that produces a critical point in the chiral phase diagram by introducing a coupling between the scalar chiral field and the dilaton. We examine the effect of the scalar-dilaton coupling on the critical point. We also study the zero-temperature chiral dynamics, which must allow for spontaneous chiral symmetry breaking in the limit of zero quark mass. We find that when the scalar-dilaton coupling is large enough to ensure correct zero-temperature chiral dynamics, a critical point is present only if the quark mass is greater than 12.8 MeV. Published by the American Physical Society 2024

Enhanced four-body decays of charged Higgs bosons into off-shell pseudoscalar Higgs and W±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^\\pm $$\\end{document} boson pairs in a lepton-specific 2-Higgs doublet model

We study the time-honoured decay H±→AW±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^\\pm \\rightarrow A W^\\pm $$\\end{document} but for the first time, we do so for the case of both A and W±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^\\pm $$\\end{document} being off-shell, therefore computing a 1→4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\rightarrow 4$$\\end{document} body decay. We show that the corresponding decay rate not only extends the reach of H±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^\\pm $$\\end{document} searches to small masses of the latter but also that the results of our implementation differ significantly from the yield of the 1→3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\rightarrow 3$$\\end{document} body decay over the phase space region in which the latter is normally used. We show the phenomenological relevance of this implementation in the case of the so-called lepton-specific 2-Higgs Doublet Model (2HDM) over the mass region wherein the aforementioned 1→4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\rightarrow 4$$\\end{document} body decay can dominate just beyond the top (anti)quark mass. This mass region is accessible in the lepton-specific 2HDM as the Yukawa couplings are such that limits from b→sγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b \\rightarrow s \\gamma $$\\end{document} and τ→μντνμ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au \\rightarrow \\mu \ u _{\ au } \\bar{\ u _\\mu }$$\\end{document} observables on MH±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{H^\\pm }$$\\end{document} are rather mild. However, we emphasize that similar effects may occur in other 2HDM types, as the W±H∓A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^\\pm H^\\mp A$$\\end{document} vertex is 2HDM type independent.

Observations on spontaneous chiral symmetry breaking and the mass gap of QCD in finite volume

We present a lattice quantum chromodynamics (QCD) simulation with 2 + 1 + 1 flavor full QCD ensembles using near-physical quark masses and different spatial sizes L, at a ∼ 0.055 fm. The results show that the scalar and pesudoscalar 2-point correlator with a valence pion mass of approximately 230 MeV become degenerated at L ≤ 1.0 fm, and such an observation suggests that the spontaneous chiral symmetry breaking disappears effectively at this point. At the same time, the mass gap between the nucleon and pion masses remains larger than ΛQCD in the entire L ∈ [0.2, 0.7] fm range.

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ∈ [0.25, 0.75] at the largest pion momentum Pz ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

Machine learning mapping of lattice correlated data

We discuss a machine learning (ML) regression model to reduce the computational cost of disconnected diagrams in lattice QCD calculations. This method creates a mapping between the results of fermionic loops computed at different quark masses and flow times. The ML mapping, trained with just a small fraction of the complete data set, makes use of translational invariance and provides consistent result with comparable uncertainties over the calculation done over the whole ensemble, resulting in a significant computational gain.

Nontriviality of dynamical Chern-Simons gravity and the standard model

Given the growing interest in gravitational-wave and cosmological parity-violating effects in dynamical Chern-Simons (dCS) gravity, it is crucial to investigate whether the scalar-gravitational Pontryagin term in dCS gravity persists when formulated in the context of the U(1)B−L anomaly in the standard model (SM). In particular, it has been argued that dCS gravity can be reduced to Einstein gravity after “rotating away” the gravitational-Pontryagin coupling into the phase of the Weinberg operator—analogous to the rotation of the axion zero mode into the quark mass matrix. We find that dCS gravity is nontrivial if the scalar field ϕ has significant spacetime dependence from dynamics. We provide a comprehensive consideration of the dCS classical and quantum symmetries relevant for embedding a dCS sector in the SM. We find that, because of the baryon/lepton number chiral gravitational anomaly, the scalar-Pontryagin term cannot be absorbed by a field redefinition. Assuming a minimal extension of the SM, we also find that a coupling of the dCS scalar with right-handed neutrinos induces both the scalar-Pontryagin coupling and an axionlike phase in the dimension-five Weinberg operator. We comment on the issue of gauging the U(1)B−L, the observational effects with these two operators present for upcoming experiments, and the origin of dCS gravity in string theory. Published by the American Physical Society 2024

Chiral-vacuum excited replicae in QCD modeling

We present a detailed study of the Bardeen-Cooper-Schrieffer (BCS) gap equation “replicae” or excited vacuum states, orthogonal to the ground-state one, in the chiral-quark sector of the Hamiltonian Coulomb-gauge model of chromodynamics. Analyzing the number of negative eigenmodes of the energy density’s Hessian we believe that we have identified all of the (negative energy-density) vacua of this nonlinear system, namely the ground BCS state and one (or two) replicae for slightly massive (or massless) quarks, given the interaction strength typical of the strong interactions. The meson spectrum over each of the replicae looks similar, so the differences are not significant enough given model uncertainties, but matrix elements are more sensitive and allow to distinguish them. We propose to look for such excited vacua in lattice gauge theory by trying to identify excitations with scalar quantum numbers which have energies proportional to the lattice volume (unlike conventional mesons for which the mass stabilizes to a constant upon taking the infinite volume limit). Published by the American Physical Society 2024

Form factor for Dalitz decays from J/ψ to light pseudoscalars* *Supported by the National Natural Science Foundation of China (11935017, 12293060, 12293065, 12293061, 12293062, 12293063, 12075253, 12192264, 12175063, 12205311, 12070131001 (CRC 110 by DFG and NNSFC)), the National Key Research and Development Program of China (2020YFA0406400), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302). The Chroma software

We calculate the form factor for the Dalitz decay with being the SU( ) flavor singlet pseudoscalar meson. The difference among the partial widths at different can be attributed in part to the and quark mass dependences induced by the anomaly dominance. in both is well described by the single pole model . Combined with the known experimental results of the Dalitz decays , the pseudoscalar mass dependence of the pole parameter is approximated by with and . These results provide inputs for future theoretical and experimental studies on the Dalitz decays .