0000000000009227
AUTHOR
José Bordes
Circumstantial Evidence for Rotating Mass Matrix from Fermion Mass and Mixing Data
It is shown that existing data on the mixing between up and down fermion states and on the hierarchical mass ratios between fermion generations, as far as can be so analysed at present, are all consistent with the two phenomena being both consequences of a mass matrix rotating in generation space with changing energy scale. As a result, the rotating mass matrix can be traced over some 14 orders of magnitude in energy from the mass scale of the $t$-quark at 175 GeV to below that of the atmospheric neutrino at 0.05 eV.
A solution to 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 theta 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.
Kinematical Lepton Transmutation in $e^+ e^-$ Collision and Vector Boson Decay
The change in orientation in generation space (rotation) of the fermion mass matrix with changing scales can lead to flavour-violations through just the kinematics of a non-diagonal mass matrix. Such effects for the reactions: $e^+ e^- \longrightarrow e^\pm \mu^\mp, e^\pm \tau^\mp, \mu^\pm \tau^\mp$, and for the decays of vector bosons into the same channels, are calculated following a method suggested earlier which gives the differential cross section for each reaction and the branching ratio for each decay mode in terms of an overall normalization depending only on the speed at which the mass matrix rotates. A rotation speed estimated earlier, under certain assumptions from the fermion mi…
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 $\gamma$ 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) $\Gamma(Z \rightarrow \ell^+ \ell^-)$, and (iii) $\Gamma(Z \rightarrow {\rm hadrons})$ 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; […
Factorization in closed string field theory
Abstract The so long made assumption, that a general closed-string vertex operator V should be built as a product of left- and right-moving vertex operators, rests on the fact that the closed-string Fock spce is constructed as a tensor product of left- and right-moving open-string Fock spaces. In this letter we will relax this assumption by proving that factorization of closed-string vertices is a general rule.
New expressions for string loop amplitudes leading to an ultrasimple conception of string dynamics
New expressions are derived for string loop amplitudes as overlap integrals of string wave functionals. They are shown to take the form of exchange terms coming from the Bose-Einstein symmetrization between string segments. One is thus led to the ultrasimple conception that string theory is basically free, and that ``string interactions'' are merely due to the fact that strings are composite objects with Bose-Einstein segments as constituents.
Suggestions for identifying the primary of post GZK air showers
A procedure is suggested for systematically narrowing the choice of possible primaries for (UHECR) air showers with energies beyond the Greisen-Zatsepin-Kuz'min cut-off of $4 \times 10^{19} eV$.
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 (c) over 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 (s) over bar and tau(mu) over bar. 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.
A dynamical mechanism for quark mixing and neutrino oscillations
We show that assuming fermion generations to be given by a gauge symmetry plus a certain Higgs mechanism for its breaking, the known empirical features of quark and lepton mixing can be largely explained, including in particular the fact that the mixing (CKM) matrix element $U_{\mu3}$ responsible for the muon anomaly in atmospheric neutrinos is near maximal and much larger than their quark counterparts $V_{cb}$ and $ V_{ts}$, while the corner elements for both quarks ($V_{ub}, V_{td}$) and leptons ($U_{e3}$) are all very small. The mechanism also gives automatically a hierarchical fermion mass spectrum which is intimately related to the mixing pattern.
CKM matrix and fermion masses in the dualized standard model
A Dualized Standard Model recently proposed affords a natural explanation for the existence of Higgs fields and of exactly 3 generations of fermions, while giving at the same time the observed fermion mass hierarchy together with a tree-level CKM matrix equal to the identity matrix. It further suggests a method for generating from loop corrections the lower generation masses and nondiagonal CKM matrix elements. In this paper, the proposed calculation is carried out to 1-loop. It is found first that with the method suggested one can account readily for the masses of the second generation fermions as a `leakage' from the highest generation. Then, with the Yukawa couplings fixed by fitting the…
Accommodating three low-scale anomalies (g-2, Lamb shift, and Atomki) in the framed standard model
The framed Standard Model (FSM) predicts a [Formula: see text] boson with mass around 20 MeV in the “hidden sector,” which mixes at tree level with the standard Higgs [Formula: see text] and hence acquires small couplings to quarks and leptons which can be calculated in the FSM apart from the mixing parameter [Formula: see text]. The exchange of this mixed state [Formula: see text] will contribute to [Formula: see text] and to the Lamb shift. By adjusting [Formula: see text] alone, it is found that the FSM can satisfy all present experimental bounds on the [Formula: see text] and Lamb shift anomalies for [Formula: see text] and [Formula: see text], and for the latter for both hydrogen and …
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 exp…
Charm-quark mass from weighted finite energy QCD sum rules
The running charm-quark mass in the scheme is determined from weighted finite energy QCD sum rules involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of s, the squared energy. The optimal kernels are found to be a simple pinched kernel and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s plane, and the latter allows us to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theo…
Updates to the Dualized Standard Model on Fermion Masses and Mixings
The Dualized Standard Model has scored a number of successes in explaining the fermion mass hierarchy and mixing pattern. This note contains updates to those results including (a) an improved treatment of neutrino oscillation free from previous assumptions on neutrino masses, and hence admitting now the preferred LMA solution to solar neutrinos, (b) an understanding of the limitation of the 1-loop calculation so far performed, thus explaining the two previous discrepancies with data, and (c) an analytic derivation and confirmation of the numerical results previously obtained.
Witten's Cubic Vertex in the Comma Theory (I)
In is shown explicitly that the Witten's interaction 3-vertex is a solution to the comma overlap equations; hence establishing the equivalence between the conventional and the "comma" formulation of interacting string theory at the level of vertices.
Implications of a Rotating Mass Matrix
The fermion mass matrix, in addition to having eigenvalues (masses) which run, also changes its orientation (rotates) with changing energy scales. This means that its eigenstates at one scale will no longer be eigenstates at another scale, leading to effects where fermions of different flavours can ``transmute'' into one another. In this paper, the implications of a rotating mass matrix are analysed and possible transmuation effects are investigated both in the Standard Model (SM) and in the so-called Dualized Standard Model (DSM) that we advocate, arriving at the conclusion that some transmutational decays such as $\psi \longrightarrow \mu \tau$, $\Upsilon \longrightarrow \mu \tau$ or $\pi…
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 $\mu$, (iii) the metric in generation space is scale-dependent too, and in …
Neutrinoless double beta decay in the dualized standard model
The Dualized Standard Model offers a {\it raison d'\^etre} for 3 fermion generations and an explanation for their distinctive mass and mixing patterns, reproducing to a reasonable accuracy the empirical mixing matrix and mass spectrum for both quarks and leptons in terms of just a few parameters. With its parameters thus fixed, the result is a highly predictive framework. In particular, it is shown that it gives explicit parameter-free predictions for neutrinoless double beta decays. For $^{76}Ge$, it predicts a half-life of $10^{28}-10^{30}$ years, which satisfies the present experimental lower bound of $1.8 \times 10^{25}$ years.
Photo-transmutation of leptons
By photo-transmutation of leptons we mean photon-lepton reactions of the following type: $\gamma l_\alpha \longrightarrow \gamma l_\beta$ with $l_\alpha \neq l_\beta$, occurring as a consequence of the lepton mass matrix changing its orientation (rotating) under changing scales. In this paper, we first discuss these reactions in general terms, then proceed to the calculation of their cross sections in two specific schemes, one within the framework of the conventional Standard Model, the other being the so-called Dualized Standard Model we ourselves advocate. Although the cross section obtained is generally small the calculation reveals certain special circumstances where these reactions may…
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.
Bose-Fermi equivalence and interacting string field theory
Abstract We show that the bosonic and the fermionic realization of the ghost vertex in the Half-String (HS) Operator approach to Witten's String Field Theory (WSFT) are equivalent. In the process we discover that higher vertices (i.e., N > 3) can be eliminated in WSFT using only the overlap conditions defining the interaction vertex and ghost number counting.
Operator approach to the Gluing Theorem in String Field Theory
An algebraic proof of the Gluing Theorem at tree level of perturbation theory in String Field Theory is given. Some applications of the theorem to closed string non-polynomial action are briefly discussed
On the corner elements of the CKM and PMNS matrices
Recent experiments show that the top-right corner element (U-e3) of the PMNS matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element (U-tau 1). 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(mu)/m(tau), and m(2)/m(3), i) the corner elements are small but nonzero, ii) V-ub < V-td, U-e3 < U-tau 1, iii) estimates result for the ratios V-ub/V-td and U-e3/U-tau 1, and B) by inputting further the experimental values of V-us, V-tb and U-e2, U-mu 3,…
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 $\gamma$ 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 s…
B meson decay constants f B c $$ {f}_{B_c} $$ , f B s $$ {f}_{B_s} $$ and f B from QCD sum rules
Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant f B c $$ {f}_{B_c} $$ , and revisit f B and f B s $$ {f}_{B_s} $$ . Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are f B c $$ {f}_{B_c} $$ = 528 ± 19 MeV, f B = 186 ± 14 MeV, and f B s $$ {f}_{B_s} $$ = 222 ± 12 MeV.
Flavor 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 \mu^\mp and for the mass difference between the neutral D-mesons seem accessible to experiment in the near future.
Features of quark and lepton mixing from differential geometry of curves on surfaces
It is noted that the CKM matrix elements for both quarks and leptons as conceived in the Dualized Standard Model (DSM) can be interpreted as direction cosines obtained by moving the Darboux trihedron (a 3-frame) along a trajectory on a sphere traced out through changing energy scales by a 3-vector factorized from the mass matrix. From the `Darboux' analogues of the well-known Serret--Frenet formulae for space curves, it is seen that the corner elements ($V_{ub}, V_{td}$ for quarks, and $U_{e3}, U_{\tau 1}$ for leptons) are associated with the (geodesic) torsion, while the other off-diagonal elements ($V_{us}, V_{cd}$ and $V_{cb}, V_{ts}$ for quarks, and $U_{e2}, U_{\mu 1}$ and $U_{\mu 3}, U…
Possible test for the suggestion that air showers with E > 1020eV are due to strongly interacting neutrinos
The suggestion is made that air showers with energies beyond the Greisen-Zatsepin-Kuz'min spectral cut-off may have primary vertices some 6 km lower in height than those of proton initiated showers with energies below the GZK cut-off. This estimate is based on the assumption that post-GZK showers are due to neutrinos having acquired strong interactions from generation-changing dual gluon exchange as recently proposed.
QCD sum rule determination of the charm-quark mass
QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the $\bar{MS}$ scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form $p(s) = 1 - (s_0/s)^2$, where $s_0$ is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range $s \simeq 20 - 25 GeV^2$. This feature leads to a substantial reduction in the sensitivity of the results to changes in $s_0$, as well as to a much reduced impact of the experimental u…
Fermion mixing and mass hierarchy as consequences of mass matrix rotation
It is shown that a fermion mass matrix changing in orientation (rotating) with changing scales can give a simple yet near-quantitative explanation for quark mixing, neutrino oscillations and the fermion mass hierarchy.
Chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes-Renner relation
The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order P…
Relationship between the comma theory and Witten’s string field theory
The comma representation of interacting string field theory is further elucidated. The proof that Witten's vertex solves the comma overlap equations is established. In this representation, the associativity of the star algebra is seen to hold. The relationship of the symmetry K in the standard formulation of Witten's string field theory to that in the comma theory is discussed.
DandDSdecay constants from QCD duality at three loops
Using special linear combinations of finite energy sum rules which minimize the contribution of the unknown continuum spectral function, we compute the decay constants of the pseudoscalar mesons B and Bs. In the computation, we employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running bottom quark mass. The sum rules show remarkable stability over a wide range of the upper limit of the finite energy integration. We obtain the following results for the pseudoscalar decay constants: fB = 178±14 MeV and fBs = 200±14 MeV. The results are somewhat lower than recent predictions based on Borel transform, lattice computations or HQET. Our sum …
N-string vertices in string field theory.
We give the general form of the vertex corresponding to the interaction of an arbitrary number of strings. The technique employed relies on the ``comma" representation of String Field Theory where string fields and interactions are represented as matrices and operations between them such as multiplication and trace. The general formulation presented here shows that the interaction vertex of N strings, for any arbitrary N, is given as a function of particular combinations of matrices corresponding to the change of representation between the full string and the half string degrees of freedom.
A first test of the framed standard model against experiment
The framed standard model (FSM) is obtained from the standard model by incorporating, as field variables, the frame vectors (vielbeins) in internal symmetry space. It gives the standard Higgs boson and 3 generations of quarks and leptons as immediate consequences. It gives moreover a fermion mass matrix of the form: $m = m_T \alpha \alpha^\dagger$, where $\alpha$ is a vector in generation space independent of the fermion species and rotating with changing scale, which has already been shown to lead, generically, to up-down mixing, neutrino oscillations and mass hierarchy. In this paper, pushing the FSM further, one first derives to 1-loop order the RGE for the rotation of $\alpha$, and then…
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 (i.e. rotates) in generation space for a changing energy scale, 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 theta term by a chiral transformation not in contradiction with the nonvanishing quark masses experimentally observed. Similarly, a rotating mass matrix may shed new light on the problem of chhiral symmetry breaking. That the fermion mass matrix may so rotate with the scale has been suggested before as a possible explanation for up-down fer…
The three-vertex in the closed half-string field theory and the general gluing and resmoothing theorem
In this letter we prove that the half-string three-vertex in closed string field theory satisfies the general gluing and resmoothing theorem. We also demonstrate how one calculates amplitudes in the half-string approach to closed string field theory, by working out explicitly a few simple three-amplitudes.
B and B-s decay constants from QCD duality at three loops
Using special linear combinations of finite energy sum rules which minimize the contribution of the unknown continuum spectral function, we compute the decay constants of the pseudoscalar mesons B and B_s. In the computation, we employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running bottom quark mass. The sum rules show remarkable stability over a wide range of the upper limit of the finite energy integration. We obtain the following results for the pseudoscalar decay constants: f_B=178 \pm 14 MeV and f_{B_s}=200 \pm 14 MeV. The results are somewhat lower than recent predictions based on Borel transform, lattice computations or HQET…
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 favored 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 six 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 theta(12), theta(13), theta(23) in nu-oscillation, and the masses m(c), m(mu), m(e)) agree well with experiment, mostly to within experimental errors; four others (m(s), m(u), m(d), m(nu 2)), the expe…
Chiral condensates from tau decay: a critical reappraisal
The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion, with the results: {O}_{6}=-(0.00226 \pm 0.00055) GeV^6, and O_8=-(0.0053 \pm 0.0033) GeV^8 from pinched FESR, and compatible values from the minimizing polynomial FESR. Som…
Generation patterns, modified $\gamma-Z$ mixing, and hidden sector with dark matter candidates as framed standard model results
A descriptive summary is given of the results to-date from the framed standard model (FSM) which: Assigns geometric meaning to the Higgs field and to fermion generations, hence offering an explanation for the observed mass and mixing patterns of quarks and leptons, reproducing near-quantitatively 17 of SM parameters with only 7. Predicts a new vector boson [Formula: see text] which mixes with [Formula: see text] and [Formula: see text], leading to deviations from the SM mixing scheme. For [Formula: see text] TeV, these deviations are within present experimental errors but should soon be detectable at LHC when experimental accuracy is further improved. Suggests the existence of a hidden sec…
B and B(S) decay constants from moments of finite energy sum rules in QCD
We use an appropriate combination of moments of finite energy sum rules in QCD in order to compute the B_q-meson decays constants f_B and f_{B_s}.We perform the calculation using a two-loop computation of the imaginary part of the pseudoscalar two point function in terms of the running bottom quark mass. The results are stable with the so called QCD duality threshold and they are in agreement with the estimates obtained from Borel transform QCD sum rules and lattice computations.
Neutrino Oscillations in the Dualized Standard Model
A method developed from the Dualized Standard Model for calculating the quark CKM matrix and masses is applied to the parallel problem in neutrino oscillations. Taking the parameters determined from quarks and the masses of two neutrinos: $m_3^2 \sim 10^{-2} - 10^{-3} eV^2$ suggested by atmospheric neutrino data, and $m_2^2 \sim 10^{-10} eV^2$ suggested by the long wave-length oscillation (LWO) solution of the solar neutrino problem, one obtains from a parameter-free calculation all the mixing angles in reasonable agreement with existing experiment. However, the scheme is found not to accommodate comfortably the mass values $m_2^2 \sim 10^{-5} eV^2$ suggested by the MSW solution for solar n…
Coherent muon-electron conversion in the dualized standard model
Muon-electron conversion in nuclei is considered in the framework of the Dualized Standard Model. The ratio $B_{\mu-e}$ of the conversion rate to the total muon capture rate is derived, and computed for several nuclei in a parameter-free calculation using parameters previously determined in different physical contexts. The values obtained all lie within the present experimental bounds, but some are so close as to seem readily accessible to experiments already being planned. Similar considerations are applied also to muon-electron conversion in muonium but give rates many orders of magnitude below the present experiment limit.