arXiv subjects

J. Bordes

Publications and source records attributed to J. Bordes.

At least 19 recordsLinked to original sources

arXiv2020

Photon quantum entanglement in the MeV regime and its application in PET imaging

Positron Emission Tomography (PET) is a widely-used imaging modality for medical research and clinical diagnosis. Here we demonstrate, through detailed experiments and simulations, an exploration of the benefits of exploiting the quantum entanglement of linear polarisation between the two positron annihilation photons utilised in PET. A new simulation, which includes the predicted influence of quantum entanglement on the interaction of MeV-scale photons with matter, is validated by comparison with experimental data from a cadmium zinc telluride (CZT) PET demonstrator apparatus. In addition, a modified setup enabled the first experimental constraint on entanglement loss for photons in the MeV regime. Quantum-entangled PET offers new methodologies to address key challenges in next generation imaging. As an indication of the potential benefits, we present a simple method to quantify and remove in-patient scatter and random backgrounds using only the quantum entanglement information in the PET events.

physics.med-ph↗

arXiv2015

Finite Energy Sum Rules with Legendre Polynomial Kernels

In this note we report about a method to deal with finite energy sum rules. With a reasonable knowledge of the main resonances of the spectrum, the method guarantees that we can find a nice duality matching between the low energy hadronic data and asymptotic QCD at high energies.

hep-ph↗

arXiv2014

$B$ Meson Decay Constants $f_{B_c}$, $f_{B_s}$ 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 $f_{B_c}$, and revisit $f_B$ and $f_{B_s}$. 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 $f_{B_c} = 528 \pm 19$ MeV, $f_B = 186 \pm 14$ MeV, and $f_{B_s} = 222 \pm 12$ MeV.

hep-ph↗

arXiv2012

Corrections to the ${\bf SU(3)\times SU(3)}$ Gell-Mann-Oakes-Renner relation and chiral couplings $L^r_8$ and $H^r_2$

Next to leading order corrections to the $SU(3) \times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $ψ_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $δ_K = (55 \pm 5)%$. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral $SU(2) \times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) \times SU(2)$, $δ_π$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3) \times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at the scale of the $ρ$-meson mass.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv2012

Bottom-quark mass from finite energy QCD sum rules

Finite energy QCD sum rules involving both inverse and positive moment integration kernels are employed to determine the bottom quark mass. The result obtained in the $\bar{\text {MS}}$ scheme at a reference scale of $10\, {GeV}$ is $\bar{m}_b(10\,\text{GeV})= 3623(9)\,\text{MeV}$. This value translates into a scale invariant mass $\bar{m}_b(\bar{m}_b) = 4171 (9)\, {MeV}$. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv2011

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 uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the $\bar{MS}$ scheme at a scale of 3 GeV is $\bar{m}_c (3 GeV) = 987 \pm 9 MeV$, where the error includes all sources of uncertainties added in quadrature.

hep-ph↗

arXiv2010

Charm-quark mass from weighted finite energy QCD sum rules

The running charm-quark mass in the $\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) 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 {\it 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 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 theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three different methods, fixed order perturbation theory (FOPT), contour improved perturbation theory (CIPT), and a fixed renormalization scale $μ$ (FMUPT). The final result is $\bar{m}_c (3\, {GeV}) = 1008\,\pm\, 26\, {MeV}$, in a wide region of stability against changes in the integration radius $s_0$ in the complex s-plane.

hep-ph↗

arXiv2010

Chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner relation

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ 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 Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, $δ_π$, the value $δ_π= (6.2, \pm 1.6)%$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $<0|\bar{u} u|0> \simeq <0|\bar{d} d|0> \equiv <0|\bar{q} q|0>|_{2\,\mathrm{GeV}} = (- 267 \pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 (ν_χ= M_ρ) = - (5.1 \pm 1.8)\times 10^{-3}$, or $H^r_2 (ν_χ= M_η) = - (5.7 \pm 2.0)\times 10^{-3}$.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv2005

D and D_{S} decay constants from QCD duality at three loops

We compute the decay constants of the pseudoscalar mesons D and D_{s} using a linear combination of finite energy sum rules which minimize the contribution of the unknown continuum spectral function. We employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running charm quark mass. The theoretical uncertainties arising from the QCD asymptotic expansion are quite relevant in this case due to the relative small scale of the charm mass. We obtain the following results: f_{D}=177 \pm 21 MeV and f_{D_{s}}=205 \pm 22 MeV. These results, within the error bars, are in good agreement with estimates obtained using Borel transform QCD sum rules, but somewhat smaller than results of recent lattice computations.

hep-ph↗

arXiv2005

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. Our sum rule approach of exploiting QCD quark hadron duality differs significantly from the usual ones, and we believe that the errors due to theoretical uncertainties are smaller.

hep-ph↗

arXiv2004

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.

hep-ph↗

arXiv2003

Bottom quark mass and QCD duality

The mass of the bottom quark is analyzed in the context of QCD finite energy sum rules. In contrast to the conventional approach, we use a large momentum expansion of the QCD correlator including terms to order α_{s}^{2}(m_{b}^{2}/q^{2})^{6} with the upsilon resonances from e^{+}e^{-} annihilation data as main input. A stable result m_{b}(m_{b})=4.19\pm 0.05 GeV} for the bottom quark mass is obtained. This result agrees with the independent calculations based on the inverse moment analysis.

hep-ph↗