Quark Mass Spectrum Research Articles

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.

Do the small numbers in the quark mixing arise from new physics?

We put forward the conjecture that the small numbers in the V_text {CKM} matrix, are generated by physics beyond the Standard Model. We identify as small numbers V_{ub} and the strength of CP violation, measured by |text {Im}Q|, where Q stands for a rephasing invariant quartet of V_text {CKM}. We illustrate how the conjecture can be realised in the context of an extension of the Standard Model where an up-type vector-like quark is introduced leading to a realistic spectrum of quark masses and an effective V_text {CKM} in agreement with experiment.

Grand Unified Origin of Gauge Interactions and Families Replication in the Standard Model

The tremendous phenomenological success of the Standard Model (SM) suggests that its flavor structure and gauge interactions may not be arbitrary but should have a fundamental first-principle explanation. In this work, we explore how the basic distinctive properties of the SM dynamically emerge from a unified New Physics framework tying together both flavor physics and Grand Unified Theory (GUT) concepts. This framework is suggested by a novel anomaly-free supersymmetric chiral E6×SU(2)F×U(1)F GUT containing the SM. Among the most appealing emergent properties of this theory is the Higgs-matter unification with a highly-constrained massless chiral sector featuring two universal Yukawa couplings close to the GUT scale. At the electroweak scale, the minimal SM-like effective field theory limit of this GUT represents a specific flavored three-Higgs doublet model consistent with the observed large hierarchies in the quark mass spectra and mixing already at tree level.

REvolver: Automated running and matching of couplings and masses in QCD

In this article we present REvolver, a C++ library for renormalization group evolution and automatic flavor matching of the QCD coupling and quark masses, as well as precise conversion between various quark mass renormalization schemes. The library systematically accounts for the renormalization group evolution of low-scale short-distance masses which depend linearly on the renormalization scale and sums logarithmic terms of high and low scales that are missed by the common logarithmic renormalization scale evolution. The library can also be accessed through Mathematica and Python interfaces and provides renormalization group evolution for complex renormalization scales as well. Program summaryProgram Title:REvolverCPC Library link to program files:https://doi.org/10.17632/m6cjfmzsxb.1Developer's repository link:https://gitlab.com/REvolver-hep/REvolverCode Ocean capsule:https://codeocean.com/capsule/6150064Licensing provisions: GPLv3 or laterProgramming language:C++, Python, Wolfram LanguageNature of problem: The strong coupling and the quark masses are fundamental parameters of QCD that are scheme and renormalization-scale dependent. The choice of scheme depends on the active number of flavors and the range of scales, and is dictated by the requirements to minimize the size of corrections and to sum large logarithmic corrections to all orders. For the strong coupling and the quark masses at high scales, the MS‾ scheme with logarithmic scale dependence is used. For quark masses at low scales, short-distance mass schemes with linear scale-dependence are used. The REvolver library provides conversions for the strong coupling and the most common quark mass schemes, with renormalization scale evolution implemented such that all types of large logarithmic terms are summed to all orders, accounting for flavor threshold effects and state-or-the-art correction terms. The pole mass, which is not a short-distance mass and contains a sizable renormalon ambiguity, is treated as a derived quantity.Solution method: Renormalization group equations are solved for complex-valued scales to machine precision based on fast-converging iterative algorithms and analytic all-order expressions. Matching relations for the strong coupling at flavor thresholds are computed in a way that gives equal results for upward and downward evolution. Core objects allow to define an arbitrary number of physical scenarios for strong coupling values and quark mass spectra, where options for precision and matching scales can be set freely, and values for quark masses in all common schemes including the pole mass can be extracted. All REvolver routines are implemented entirely in C++ and can be accessed through Mathematica and Python interfaces.

Sequentially loop-generated quark and lepton mass hierarchies in an extended Inert Higgs Doublet model

Extended scalar and fermion sectors offer new opportunities for generating the observed strong hierarchies in the fermion mass and mixing patterns of the Standard Model (SM). In this work, we elaborate on the prospects of a particular extension of the Inert Higgs doublet model where the SM hierarchies are generated sequentially by radiative virtual corrections in a fully renormalisable way, i.e. without adding any non-renormalisable Yukawa terms or soft-breaking operators to the scalar potential. Our model has a potential to explain the recently observed RK and RK∗ anomalies, thanks to the non universal U1X assignments of the fermionic fields that yield non universal Z′ couplings to fermions. We explicitly demonstrate the power of this model for generating the realistic quark, lepton and neutrino mass spectra. In particular, we show that due to the presence of both continuous and discrete family symmetries in the considered framework, the top quark acquires a tree-level mass, lighter quarks and leptons get their masses at one- and two-loop order, while neutrino masses are generated at three-loop level. The minimal field content, particle spectra and scalar potential of this model are discussed in detail.

GUT inspired SO(5)×U(1)×SU(3) gauge-Higgs unification

$SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification model inspired by $SO(11)$ gauge-Higgs grand unification is constructed in the Randall-Sundrum warped space. The 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Fermion multiplets are introduced in the bulk in the spinor, vector and singlet representations of $SO(5)$ such that they are implemented in the spinor and vector representations of $SO(11)$. The mass spectrum of quarks and leptons in three generations is reproduced except for the down quark mass. The small neutrino masses are explained by the gauge-Higgs seesaw mechanism which takes the same form as in the inverse seesaw mechanism in grand unified theories in four dimensions.

Quark mass matrices, textures and CKM precision measurements

In the light of several recent analyses pointing toward texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized “[Formula: see text]-diagonal” basis within the Standard Model framework using the unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured [Formula: see text] values of the three physical parameters namely [Formula: see text], [Formula: see text] and [Formula: see text] naturally lead to the vanishing of (11) element in the down type quark mass matrix and that the single measurable CP violating phase [Formula: see text] in the CKM matrix is sufficient enough in [Formula: see text] to explain the observed mixing pattern in a suitable basis. The leading order as well as exact analytic phenomenological solutions are addressed for the modest pattern of quark mass matrices derived from CKM matrix and precision measurements of mixing parameters.

The breaking of flavor democracy in the quark sector**Supported by National Natural Science Foundation of China (11375207) and National Basic Research Program of China (2013CB834300)

The democracy of quark flavors is a well-motivated flavor symmetry, but it must be properly broken in order to explain the observed quark mass spectrum and flavor mixing pattern. We reconstruct the texture of flavor democracy breaking and evaluate its strength in a novel way, by assuming a parallelism between the Q=+2/3 and Q=−1/3 quark sectors and using a nontrivial parametrization of the flavor mixing matrix. Some phenomenological implications of such democratic quark mass matrices, including their variations in the hierarchy basis and their evolution from the electroweak scale to a super-high energy scale, are also discussed.

The discrete charm of flavour and CP violation

We point out that in the Standard Model (SM) there is no explanation why |V23|2 + |V13|2 is of order 10−3. A framework is described for explaining this small mixing, involving the introduction of vector-like quarks. A symmetry is introduced so that at a first stage VCKM = 1I and only the third generation of quarks acquires a mass. It is shown that when interactions of vector like quarks are taken into account a realistic quark mass spectrum is generated together with a correct VCKM matrix.

General scan in flavor parameter space in models with vector quark doublets and an enhancement in the B → Xsγ process**Supported by Natural Science Foundation of China (11375001) and Talents Foundation of Education Department of Beijing

In models with vector-like quark doublets, the mass matrices of up and down type quarks are related. Precise diagonalization of the mass matrices has become an obstacle in numerical studies. In this work we first propose a diagonalization method. As its application, in the Standard Model with one vector-like quark doublet we present the quark mass spectrum and Feynman rules for the calculation of B → Xsγ. We find that i) under the constraints of the CKM matrix measurements, the mass parameters in the bilinear term are constrained to a small value by the small deviation from unitarity; ii) compared with the fourth generation extension of the Standard Model, there is an enhancement to the B → Xsγ process in the contribution of vector-like quarks, resulting in a non-decoupling effect in such models.

A revisit of the quark mass spectra and flavor mixing based on the S3 flavor symmetry

In this paper, we propose a simple model based on the S3 flavor symmetry, in which a perturbation ansatz is suggested that the flavor symmetry is explicitly broken down via S3 [Formula: see text]Z2 [Formula: see text] in the up-quark sector and via S3 [Formula: see text]Z3 [Formula: see text] in the down-quark sector. Our model is successful in obtaining the strong hierarchy of mass matrices of both up-type quarks and down-type quarks, but unsuccessful in obtaining the realistic mixing between the third generation and the first two, as in other models based on S3 flavor symmetry proposed in the literature. Through detailed analysis, we find the reason for the unsuccesses in our model which is related to the reducibility of the three-dimensional representation of the S3 group. We conclude that any perturbations in mass matrices preserving the partial symmetry of S3 cannot help getting realistic mixing between the third generation and first two without fine-tuning.

Exact one-loop evolution invariants in the standard model

Guided by considerations of flavour symmetry, we construct a set of exact Standard Model (SM) renormalisation group evolution invariants which link quark masses and mixing parameters. We examine their phenomenological implications and infer a simple combination of Yukawa coupling matrices which plays a unique role in the SM, suggesting a possible new insight into the observed spectrum of quark masses. Our evolution invariants are readily generalised to the leptons in the case of Dirac neutrinos, but do not appear to be relevant for either quarks or leptons in the MSSM.

Erratum: SpontaneousCPviolation inE6supersymmetric grand unified theory with SU(2) flavor and anomalous U(1) symmetries [Phys. Rev. D80, 115011 (2009)

We construct a model of spontaneous CP violation in E6 supersymmetric grand unified theory. In the model, we employ an SU(2)F flavor symmetry and an anomalous U(1)A symmetry. The SU(2)F flavor symmetry is introduced to provide the origin of hierarchical structures of Yukawa coupling and to ensure the universality of sfermion soft masses. The anomalous U(1)A symmetry is introduced to realize the doublet-triplet mass splitting, to provide the origin of hierarchical structures of Yukawa couplings, and to solve the mu problem. In the model, CP is spontaneously broken by the SU(2)F breaking in order to provide a Kobayashi-Maskawa phase and to evade the supersymmetric CP problem. However, a naive construction of the model generally leads to unwanted outcome, Arg[mu b*]=O(1), when CP violating effects in the flavor sector are taken into account. We cure this difficulty by imposing a discrete symmetry and find that this prescription can play additional roles. It ensures that realistic up-quark mass and Cabibbo angle are simultaneously realized without cancellation between O(1) coefficients. Also, severe constraints from the chromo-electric dipole moment of the quark can be satisfied without destabilizing the weak scale. The discrete symmetry reduces the number of free parameters, but the model is capable of reproducing quark and lepton mass spectra, mixing angles, and a Jarlskog invariant. We obtain characteristic predictions Vub sim O(lambda^4) (lambda=0.22) and |Vcb Yb| = |Yc| at the grand unified theory scale.

SpontaneousCPviolation inE6supersymmetric grand unified theory with SU(2) flavor and anomalous U(1) symmetries

We construct a model of spontaneous $CP$ violation in ${\mathrm{E}}_{6}$ supersymmetric grand unified theory. In the model, we employ an $\mathrm{SU}(2{)}_{\mathrm{F}}$ flavor symmetry and an anomalous $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry. The $\mathrm{SU}(2{)}_{\mathrm{F}}$ flavor symmetry is introduced to provide the origin of hierarchical structures of Yukawa coupling and to ensure the universality of sfermion soft masses. The anomalous $\mathrm{U}(1{)}_{\mathrm{A}}$ symmetry is introduced to realize the doublet-triplet mass splitting, to provide the origin of hierarchical structures of Yukawa couplings, and to solve the $\ensuremath{\mu}$ problem. In the model, $CP$ is spontaneously broken by the $\mathrm{SU}(2{)}_{\mathrm{F}}$ breaking in order to provide a Kobayashi-Maskawa phase and to evade the supersymmetric $CP$ problem. However, a naive construction of the model generally leads to an unwanted outcome, $\mathrm{arg}[\ensuremath{\mu}{b}^{*}]=\mathcal{O}(1)$, when $CP$ violating effects in the flavor sector are taken into account. We cure this difficulty by imposing a discrete symmetry and find that this prescription can play additional roles. It ensures that the realistic up-quark mass and Cabibbo angle are simultaneously realized without cancellation between $\mathcal{O}(1)$ coefficients. Also, severe constraints from the chromo-electric dipole moment of the quark can be satisfied without destabilizing the weak scale. The discrete symmetry reduces the number of free parameters, but the model is capable of reproducing quark and lepton mass spectra, mixing angles, and a Jarlskog invariant. We obtain characteristic predictions ${V}_{ub}\ensuremath{\sim}\mathcal{O}({\ensuremath{\lambda}}^{4})$ ($\ensuremath{\lambda}=0.22$) and $|{V}_{cb}{Y}_{b}|=|{Y}_{c}|$ at the grand unified theory scale.

Dynamics behind the quark mass hierarchy

We introduce a new class of models describing the quark mass hierarchy. In this class, the dynamics primarily responsible for electroweak symmetry breaking (EWSB) leads to the mass spectrum of quarks with no (or weak) isospin violation. Moreover, the values of these masses are of the order of the observed masses of the down-type quarks. Then, strong (although subcritical) horizontal diagonal interactions for the t quark plus horizontal flavor-changing neutral interactions between different families lead (with no fine-tuning) to a realistic quark mass spectrum. In this scenario, many composite Higgs bosons occur. A concrete model with the dynamical EWSB with the fourth family is described in detail.

Flavor changing neutral current constraints from Kaluza-Klein gluons and quark mass matrices in the Randall-Sundrum I framework

We continue our previous study on what are the allowed forms of quark mass matrices in the Randall-Sundrum framework that can reproduce the experimentally observed quark mass spectrum and the pattern of Cabibbo-Kobayashi-Maskawa mixing. We study the constraints the $\ensuremath{\Delta}F=2$ processes in the neutral meson sector placed on the admissible forms found there, and we found only the asymmetrical type of quark mass matrices arising from anarchical Yukawa structures remain viable at the few TeV scale reachable at the LHC. We study also the decay of the first Kaluza-Klein (KK) excitation of the gluon. We give the decay branching ratios of the first KK gluon into quark pairs, and we point out that measurements of the decay width and just one of the quark spins in the dominant $\overline{t}t$ decays can be used to extract the effective coupling of the first KK gluon to top quarks for both chiralities. This provides a further probe into the flavor structure of the Randall-Sundrum framework.

Lattice results on QCD at high temperature and non-zero baryon number density

Studies of QCD thermodynamics on the lattice now can be performed with an almost realistic quark mass spectrum and on quite large lattices. This will soon allow a controlled extrapolation to the continuum limit. We present recent results on the QCD equation of state, discuss deconfining and chiral symmetry restoring aspects of the QCD transition at vanishing chemical potential and show results on baryon number, electric charge and strangeness fluctuations. We briefly discuss the generic structure of Taylor expansion coefficients in the vicinity of the chiral phase transition and comment on the determination of the anticipated chiral critical point within the framework of Taylor expansions of the QCD partition function.

U(3)-flavor nonet scalar as an origin of the flavor mass spectra

According to an idea that the quark and lepton mass spectra originate in a VEV structure of a U(3)-flavor nonet scalar Φ, the mass spectra of the down-quarks and charged leptons are investigated. The U(3) flavor symmetry is spontaneously and completely broken by non-zero and non-degenerated VEVs of Φ, without passing any subgroup of U(3). The ratios (me+mμ+mτ)/(me+mμ+mτ)2 and memμmτ/(me+mμ+mτ)3 are investigated based on a toy model.

Radiative fermion mass hierarchy in a nonsupersymmetric unified theory

In nonsupersymmetric grand unified models a ``radiative fermion mass hierarchy'' can be achieved in which the spectrum of quark and lepton masses is determined entirely by physics at the unification scale, with many relations following from the unified gauge symmetry, and with the masses of the lightest family arising from loops. A simple, realistic, and predictive model of this kind is presented. A ``doubly lopsided'' structure, known to lead to bilarge neutrino mixing, plays a crucial role in the radiative hierarchy.

Phenomenology of theSU(3)c⊗SU(3)L⊗U(1)Xmodel with exotic charged leptons

A phenomenological analysis of the three-family model based on the local gauge group $SU(3{)}_{c}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{X}$ with exotic charged leptons, is carried out. Instead of using the minimal scalar sector able to break the symmetry in a proper way, we introduce an alternative set of four Higgs scalar triplets, which combined with an anomaly-free discrete symmetry, produce quark and charged lepton mass spectrum without hierarchies in the Yukawa coupling constants. We also embed the structure into a simple gauge group and show some conditions to achieve a low energy gauge coupling unification, avoiding possible conflict with proton decay bounds. By using experimental results from the CERN-LEP, SLAC linear collider, and atomic parity violation data, we update constraints on several parameters of the model.