arXiv subjects

H. M. Chan

Publications and source records attributed to H. M. Chan.

At least 19 recordsLinked to original sources

arXiv2021

Unified FSM treatment of CP physics extended to hidden sector giving (i) $δ_{CP}$ for leptons as prediction, (ii) new hints on the material content of the universe

A unified treatment of CP physics for quarks and leptons in the framed standard model (FSM) is extended to include the predicted hidden sector giving as consequences: (i) that an earlier part-estimate of the Jarlskog invariant $J'$ for leptons is turned into a prediction for its actual value, i.e., $J' \sim -0.012$ ($δ'_{CP} \sim 1.11 π$), which is of the right order of magnitude, of the right sign, and in the range of values favoured by present experiment, (ii) some novel twists to the effects of CP-violation on the material content of the universe.

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arXiv2018

The $Z$ boson in the Framed Standard Model

The framed standard model (FSM), constructed initially for explaining the existence of three fermion generations and the hierarchical mass and mixing patterns of quarks and leptons, suggests also a "hidden sector" of particles including some dark matter candidates. It predicts in addition a new vector boson $G$, with mass of order TeV, which mixes with the $γ$ and $Z$ of the standard model yielding deviations from the standard mixing scheme, all calculable in terms of a single unknown parameter $m_G$. Given that standard mixing has been tested already to great accuracy by experiment, this could lead to contradictions, but it is shown here that for the three crucial and testable cases so far studied (i) $m_Z - m_W$, (ii) $Γ(Z \rightarrow \ell^ + \ell^-)$, (iii) $Γ(Z \rightarrow$ hadrons), the deviations are all within the present stringent experimental bounds provided $m_G > 1$ TeV, but should soon be detectable if experimental accuracy improves. This comes about because of some subtle cancellations, which might have a deeper reason that is not yet understood. By virtue of mixing, $G$ can be produced at the LHC and appear as a $\ell^+ \ell^-$ anomaly. If found, it will be of interest not only for its own sake but serve also as a window on to the "hidden sector" into which it will mostly decay, with dark matter candidates as most likely products.

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arXiv2018

A Closer Study of the Framed Standard Model Yielding Testable New Physics plus a Hidden Sector with Dark Matter Candidates

This closer study of the FSM: [I] retains the earlier results in offering explanation for the existence of three fermion generations, as well as the hierarchical mass and mixing patterns of leptons and quarks; [II] predicts a vector boson $G$ with mass of order TeV which mixes with $γ$ and $Z$ of the standard model. The subsequent deviations from the standard mixing scheme are calculable in terms of the $G$ mass. While these deviations for (i) $m_Z - m_W$, (ii) $Γ(Z \rightarrow \ell^+ \ell^-)$, and (iii) $Γ(Z \rightarrow {\rm hadrons})$ are all within present experimental errors so long as $m_G > 1$ TeV, they should soon be detectable if the $G$ mass is not too much bigger; [III] suggests that in parallel to the standard sector familiar to us, there is another where the roles of flavour and colour are interchanged. Though quite as copiously populated and as vibrant in self-interactions as our own, it communicates but little with the standard sector except via mixing through a couple of known portals, one of which is the $γ-Z-G$ complex noted in [II] above, and the other is a scalar complex which includes the standard model Higgs. As a result, the new sector appears hidden to us as we appear hidden to them, and so its lowest members with masses of order 10 MeV, being electrically neutral and seemingly stable, but abundant, may make eligible candidates as constituents of dark matter. A more detailed summary of these results together with some remarks on the model's special theoretical features can be found in the last section of the text.

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arXiv2012

On the Corner Elements of the CKM and PMNS Matrices

Recent experiments show that the top-right corner element ($U_{e3}$) of the PMNS, like that ($V_{ub}$) of the CKM, matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element ($U_{τ1}$), again as in the CKM case ($V_{ub} < V_{td}$). An attempt in explaining these facts would seem an excellent test for any model of the mixing phenomenon. Here, it is shown that if to the assumption of a universal rank-one mass matrix, long favoured by phenomenologists, one adds that this matrix rotates with scale, then it follows that (A) by inputting the mass ratios $m_c/m_t, m_s/m_b, m_μ/m_τ$, and $m_2/m_3$, (i) the corner elements are small but nonzero, (ii) $V_{ub} < V_{td}$, $U_{e 3} < U_{τ1}$, (iii) estimates result for the ratios $V_{ub}/V_{td}$ and $U_{e 3}/U_{τ1}$, and (B) by inputting further the experimental values of $V_{us}, V_{tb}$ and $U_{e2},U_{μ3}$, (iv) estimates result for the values of the corner elements themselves. All the inequalities and estimates obtained are consistent with present data to within expectation for the approximations made.

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arXiv2012

A Comprehensive Mechanism Reproducing the Mass and Mixing Parameters of Quarks and Leptons

It is shown that if, from the starting point of a universal rank-one mass matrix long favoured by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only 6 real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles $θ_{12}, θ_{13}, θ_{23}$ in $ν$-oscillation, and the masses $m_c, m_μ, m_e$) agree well with experiment, mostly to within experimental errors; 4 others ($m_s, m_u, m_d, m_{ν_2}$), the experimental values for which can only be inferred, agree reasonably well; while 2 others ($m_{ν_1}, δ_{CP}$ for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass $m_{ν_R}$ and (ii) the strong CP angle $θ$ inherent in QCD. One notes in particular that the output value for $\sin^2 2 θ_{13}$ from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit 2 new testable constraints: (i) that $θ_{23}$ must depart from its "maximal" value: $\sin^2 2 θ_{23} \sim 0.935 \pm 0.021$, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only $|\sin δ_{CP}| \leq 0.31$ if not vanishing altogether.

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arXiv2011

Developing the Framed Standard Model

The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and 3 fermion generations as part of the framed gauge theory structure, is here developed further to show that it gives both quarks and leptons hierarchical masses and mixing matrices akin to what is experimentally observed. Among its many distinguishing features which lead to the above results are (i) the vacuum is degenerate under a global $su(3)$ symmetry which plays the role of fermion generations, (ii) the fermion mass matrix is "universal", rank-one and rotates (changes its orientation in generation space) with changing scale $μ$, (iii) the metric in generation space is scale-dependent too, and in general non-flat, (iv) the theta-angle term in the QCD action of topological origin gets transformed into the CP-violating phase of the CKM matrix for quarks, thus offering at the same time a solution to the strong CP problem.

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arXiv2011

Exploring Framed Gauge Theory as Basis for Physical Models

It is shown that by introducing as dynamical variables in the formulation of gauge theories the frame vectors (or vielbeins) in internal symmetry space, in addition to the standard gauge boson and matter fermion fields, one obtains: (i) for the $su(2) \times u(1)$ symmetry, the standard electroweak theory with the Higgs field thrown in as part of the framed gauge theoretical structure, (ii) for the $su(3) \times su(2) \times u(1)$ symmetry, a "framed standard model" with, apart from the Higgs field as before, a global $su(3)$ symmetry to play the role of fermion generations, plus some other properties which are shown elsewhere to give to both quarks and leptons hierarchical mass and mixing patterns similar to those experimentally observed. Besides, the "framing" of the standard model as such has brought the particle theory closer in structure to the theory of gravity where vierbeins have long figured as dynamical variables. Although most of the results have already been reported before, time and hindsight have allowed their presentation in this review to be made more transparent and succint.

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arXiv2011

Mass Hierarchy, Mixing, CP-Violation and Higgs Decay---or Why Rotation is Good for Us

The idea of a rank-one rotating mass matrix (R2M2) is reviewed detailing how it leads to ready explanations both for the fermion mass hierarchy and for the distinctive mixing patterns between up and down fermion states, which can be and have been tested against experiment and shown to be fully consistent with existing data. Further, R2M2 is seen to offer, as by-products: (i) a new solution of the strong CP problem in QCD by linking the theta-angle there to the Kobayashi-Maskawa CP-violating phase in the CKM matrix, and (ii) some novel predictions of possible anomalies in Higgs decay observable in principle at the LHC. A special effort is made to answer some questions raised.

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arXiv2010

A Solution of the Strong CP Problem Transforming the theta-angle to the KM CP-violating Phase

It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta-angle term in the QCD action of topological origin can be eliminated by chiral transformations, while giving still nonzero masses to all quarks. Instead, the effects of such transformations get transmitted by the rotation to the CKM matrix as the KM phase giving, for $θ$ of order unity, a Jarlskog invariant typically of order $10^{-5}$ as experimentally observed. Strong and weak CP violations appear then as just two facets of the same phenomenon.

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arXiv2009

Possible Anomalies in Higgs Decay: Charm Suppression and Flavour-Violation

It is suggested that the Higgs boson may have a branching ratio into the $c \bar{c}$ mode suppressed by several orders of magnitude compared with conventional predictions and in addition some small but detectable flavour-violating modes such as $b \bar{s}$ and $τ\barμ$. The suggestion is based on a scheme proposed and tested earlier for explaining the mixing pattern and mass hierarchy of fermions in terms of a rotating mass matrix. If confirmed, the effects would cast new light on the geometric origin of fermion generations and of the Higgs field itself.

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arXiv2007

A Model Behind the Standard Model

In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$ plus the 3 assumptions: (A) scalar fields as vielbeins in internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour \cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical significance to scalar fields, (II) a theoretical criterion on what scalar fields are to be introduced, (III) a partial explanation of why $su(2)$ appears broken while $su(3)$ confines, (IV) baryon-lepton number (B - L) conservation, (V) the standard electroweak structure, (VI) a 3-valued generation index for leptons and quarks, and (VII) a dynamical system with all the essential features of an earlier phenomenological model \cite{genmixdsm} which gave a good description of the known mass and mixing patterns of quarks and leptons including neutrino oscillations. There are other implications the consistency of which with experiment, however, has not yet been systematically explored. A possible outcome is a whole new branch of particle spectroscopy from $su(2)$ confinement, potentially as rich in details as that of hadrons from colour confinement, which will be accessible to experiment at high energy.

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arXiv2007

New Angle on the Strong CP and Chiral Symmetry Problems from a Rotating Mass Matrix

It is shown that when the mass matrix changes in orientation (rotates) in generation space for changing energy scale, then the masses of the lower generations are not given just by its eigenvalues. In particular, these masses need not be zero even when the eigenvalues are zero. In that case, the strong CP problem can be avoided by removing the unwanted $θ$ term by a chiral transformation in no contradiction with the nonvanishing quark masses experimentally observed. Similarly, a rotating mass matrix may shed new light on the problem of chiral symmetry breaking. That the fermion mass matrix may so rotate with scale has been suggested before as a possible explanation for up-down fermion mixing and fermion mass hierarchy, giving results in good agreement with experiment.

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arXiv2006

Higgs Fields as Vielbeins of Internal Symmetry Space

An earlier suggestion that scalar fields in gauge theory may be introduced as frame vectors or vielbeins in internal symmetry space, and so endowed with geometric significance, is here sharpened and refined. Applied to a $u(1) \times su(2)$ theory this gives exactly the Higgs structure of the standard electroweak theory. Applied to an $su(3)$ theory, it gives a structure having much in common with a phenomenological model previously constructed to explain fermion mixing and mass hierarchy. The difference in physical outcome for the two theories is here traced to the difference in structure between the two symmetry groups.

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arXiv2003

Fermion Generations and Mixing from Dualized Standard Model

We review a possible solution to the fermion generation puzzle based on a nonabelian generalization of electric--magnetic duality derived some years ago. This nonabelian duality implies the existence of another SU(3) symmetry dual to colour, which is necessarily broken when colour is confined and so can play the role of the ``horizontal'' symmetry for fermion generations. When thus identified, dual colour then predicts 3 and only 3 fermion generations, besides suggesting a special Higgs mechanism for breaking the generation symmetry. A phenomenological model with a Higgs potential and a Yukawa coupling constructed on these premises is shown to explain immediately all the salient qualitative features of the fermion mass hierarchy and mixing pattern, excepting for the moment CP-violation. Calculations already carried out to 1-loop order is shown to give with only 3 adjustable parameters the following quantities all to within present experimental error: all 9 CKM matrix elements $|V_{rs}|$ for quarks, the neutrino oscillation angles or the MNS lepton mixing matrix elements $|U_{μ3}|, |U_{e 3}|$, and the mass ratios $m_c/m_t, m_s/m_b, m_μ/m_τ$. The special feature of this model crucial for deriving the above results is a fermion mass matrix which changes its orientation (rotates) in generation space with changing energy scale, a feature which is shown to have direct empirical support.

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arXiv2001

Lepton Transmutation in the Dualized Standard Model

The successful explanation of fermion mixing and of the fermion mass hierarchy by the Dualized Standard Model (DSM) scheme is based on the premises of a fermion mass matrix rotating in generation space with changing scales at a certain speed, which could in principle lead to sizeable flavour-violation observable in high sensitivity experiments such as BaBar. However, a full perturbative calculation to 1-loop order reported here shows that this kinematical, flavour-violating effect of a rotating mass matrix is off-set in the DSM by parallel effects from rotating wave functions and vertices giving in the end only very small flavour-violations which are unlikely to be detectable by present experiments. The result means that at least for the present the DSM scheme has survived yet another threat to its validity, which is indeed its most stringent and dangerous to-date. It also provides some clarification of certain concepts connected with the rotating mass matrix which had previously been found puzzling.

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arXiv2000

A Solution of the Generation Puzzle from Yang-Mills Duality

A solution to the generation puzzle based on a nonabelian generalization of electric-magnetic duality is briefly reviewed. It predicts 3 and only 3 generations of fermions and explains the hierarchical mass spectrum as well as the main features in both the quark and lepton mixing matrices. A calculation to leading perturbative order already gives reasonable values to about half of the Standard Model parameters.

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arXiv2000

Fermion transmutation - a renormalization effect in gauge theory

A new category of phenomena is predicted in which fermions of different flavours can transmute into one another, for example $e \to μ$ or $e \to τ$, as a consequence of the `rotating' mass matrix due to renormalization. As examples, calculations will be presented for various such processes. Some of these could be accessible to experiments in the near future.

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arXiv1999

Flavour-Changing Neutral Currents in the Dualized Standard Model

The Dualized Standard Model which gives explanations for both fermion generations and Higgs fields has already been used to calculate fermion mass and mixing parameters with success. In this paper, we extend its application to low energy FCNC effects deriving bounds for various processes in terms of one single mass scale. Using then experimental information from K_L - K_S mass difference and air showers beyond the GZK cut-off, these bounds are converted into rough, order-of-magnitude predictions. In particular, the estimates for the decay K_L \to e^\pm μ^\mp and for the mass difference between the neutral D-mesons seem accessible to experiment in the near future.

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