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<jats:title>Abstract</jats:title> <jats:p>The Jiangmen Underground Neutrino Observatory (JUNO) features a 20 kt multi-purpose underground liquid scintillator sphere as its main detector. Some of JUNO's features make it an excellent location for <jats:inline-formula> <jats:tex-math><?CDATA $ ^8 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M2.jpg" xlink:type="simple" /> </jats:inline-formula>B solar neutrino measurements, such as its low-energy threshold, high energy resolution compared with water Cherenkov detectors, and much larger target mass compared with previous liquid scintillator detectors. In this paper, we present a comprehensive assessment of JUNO's potential for detecting <jats:inline-formula> <jats:tex-math><?CDATA $ ^8 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M3.jpg" xlink:type="simple" /> </jats:inline-formula>B solar neutrinos via the neutrino-electron elastic scattering process. A reduced 2 MeV threshold for the recoil electron energy is found to be achievable, assuming that the intrinsic radioactive background <jats:inline-formula> <jats:tex-math><?CDATA $ ^{238} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M4.jpg" xlink:type="simple" /> </jats:inline-formula>U and <jats:inline-formula> <jats:tex-math><?CDATA $ ^{232} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M5.jpg" xlink:type="simple" /> </jats:inline-formula>Th in the liquid scintillator can be controlled to 10 <jats:inline-formula> <jats:tex-math><?CDATA $ ^{-17} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M6.jpg" xlink:type="simple" /> </jats:inline-formula> g/g. With ten years of data acquisition, approximately 60,000 signal and 30,000 background events are expected. This large sample will enable an examination of the distortion of the recoil electron spectrum that is dominated by the neutrino flavor transformation in the dense solar matter, which will shed new light on the inconsistency between the measured electron spectra and the predictions of the standard three-flavor neutrino oscillation framework. If <jats:inline-formula> <jats:tex-math><?CDATA $ \Delta m^{2}_{21} = 4.8\times10^{-5}\; (7.5\times10^{-5}) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M7.jpg" xlink:type="simple" /> </jats:inline-formula> eV <jats:inline-formula> <jats:tex-math><?CDATA $ ^{2} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M8.jpg" xlink:type="simple" /> </jats:inline-formula>, JUNO can provide evidence of neutrino oscillation in the Earth at approximately the 3 <jats:inline-formula> <jats:tex-math><?CDATA $ \sigma $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M9.jpg" xlink:type="simple" /> </jats:inline-formula> (2 <jats:inline-formula> <jats:tex-math><?CDATA $ \sigma $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M10.jpg" xlink:type="simple" /> </jats:inline-formula>) level by measuring the non-zero signal rate variation with respect to the solar zenith angle. Moreover, JUNO can simultaneously measure <jats:inline-formula> <jats:tex-math><?CDATA $ \Delta m^2_{21} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M11.jpg" xlink:type="simple" /> </jats:inline-formula> using <jats:inline-formula> <jats:tex-math><?CDATA $ ^8 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M12.jpg" xlink:type="simple" /> </jats:inline-formula>B solar neutrinos to a precision of 20% or better, depending on the central value, and to sub-percent precision using reactor antineutrinos. A comparison of these two measurements from the same detector will help understand the current mild inconsistency between the value of <jats:inline-formula> <jats:tex-math><?CDATA $ \Delta m^2_{21} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023004_M13.jpg" xlink:type="simple" /> </jats:inline-formula> reported by solar neutrino experiments and the KamLAND experiment. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this study, we obtain the universal function corresponding to the diffractive process and show that the cross section exhibits geometrical scaling. It is observed that diffractive theory according to the color dipole approach at small-<jats:italic>x</jats:italic> is a convenient framework that reveals the color transparency and saturation phenomena. We also calculate the contribution of heavy quark production in the diffractive cross section at high energy that is determined by the small size dipole configuration. The ratio of the diffractive cross section to the total cross section in electron-proton collision is the other important quantity that is computed in this work. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The resonance state of the <jats:inline-formula> <jats:tex-math><?CDATA $\Delta$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023102_M1.jpg" xlink:type="simple" /> </jats:inline-formula> baryon, which exists in four isospin ( <jats:inline-formula> <jats:tex-math><?CDATA $I= {3}/{2}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023102_M2.jpg" xlink:type="simple" /> </jats:inline-formula>) states, has been studied using the hypercentral constituent quark model (hCQM) with a simple linear potential with added first order correction. The calculated data ranges for 1<jats:italic>S</jats:italic>-5<jats:italic>S</jats:italic>, 1<jats:italic>P</jats:italic>-5<jats:italic>P</jats:italic>, 1<jats:italic>D</jats:italic>-4<jats:italic>D</jats:italic> and 1<jats:italic>F</jats:italic>-2<jats:italic>F</jats:italic> are given, with possible spin-parity assignments for all the states. The magnetic moments have also been obtained for all four configurations. The <jats:inline-formula> <jats:tex-math><?CDATA $N\pi$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023102_M3.jpg" xlink:type="simple" /> </jats:inline-formula> decay channel width has been calculated for a few states. The linear nature of the data has been verified through Regge trajectories. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We study the scattering of <jats:inline-formula> <jats:tex-math><?CDATA $J/\psi$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023103_M3.jpg" xlink:type="simple" /> </jats:inline-formula> - <jats:inline-formula> <jats:tex-math><?CDATA $J/\psi$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023103_M4.jpg" xlink:type="simple" /> </jats:inline-formula> mesons using quadratic and Cornell potentials in our tetraquark ( <jats:inline-formula> <jats:tex-math><?CDATA ${{c\bar cc\bar c}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023103_M5.jpg" xlink:type="simple" /> </jats:inline-formula>) system. The system’s wavefunction in the restricted gluonic basis, which is written by utilizing the adiabatic approximation and Hamiltonian, is used via a quark potential model. The resonating group technique is used to obtain the integral equations, which are solved to obtain the unknown inter-cluster dependence of the total wavefunction of our tetraquark system. T-Matrix elements are calculated from the solutions, and eventually, the scattering cross sections are obtained using the two potentials. We compare these cross sections and find that the magnitudes of scattering cross sections of quadratic potential are higher than the Cornell potential. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>QCD theory predicts the existence of glueballs, but so far all experimental endeavors have failed to identify any such states. To remedy this discrepancy between QCD, which has proven to be a successful theory for strong interactions, and the failure of experimental searches for glueballs, one is tempted to accept the promising interpretation that the glueballs mix with regular <jats:inline-formula> <jats:tex-math><?CDATA $ q\bar q $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M1.jpg" xlink:type="simple" /> </jats:inline-formula> states of the same quantum numbers. The lattice estimate of the masses of pure <jats:inline-formula> <jats:tex-math><?CDATA $ 0^{++} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> glueballs ranges from 1 to 2 GeV, which is the region of the <jats:inline-formula> <jats:tex-math><?CDATA $ f_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M3.jpg" xlink:type="simple" /> </jats:inline-formula> family. Thus many authors suggest that the <jats:inline-formula> <jats:tex-math><?CDATA $ f_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M4.jpg" xlink:type="simple" /> </jats:inline-formula> mesonic series is an ideal place to study possible mixtures of glueballs and <jats:inline-formula> <jats:tex-math><?CDATA $ q\bar q $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M5.jpg" xlink:type="simple" /> </jats:inline-formula>. In this paper, following the strategy proposed by Close, Farrar and Li, we try to determine the fraction of glueball components in <jats:inline-formula> <jats:tex-math><?CDATA $ f_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M6.jpg" xlink:type="simple" /> </jats:inline-formula> mesons using the measured mass spectra and the branching ratios of <jats:inline-formula> <jats:tex-math><?CDATA $ J/\psi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M7.jpg" xlink:type="simple" /> </jats:inline-formula> radiative decays into <jats:inline-formula> <jats:tex-math><?CDATA $ f_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M8.jpg" xlink:type="simple" /> </jats:inline-formula> mesons. Since the pioneering papers by Close <jats:italic>et al</jats:italic>., more than 20 years have elapsed and more accurate measurements have been done by several experimental collaborations, so it is time to revisit this interesting topic using new data. We suppose <jats:inline-formula> <jats:tex-math><?CDATA $ f_0(500) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M9.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ f_0(980) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M10.jpg" xlink:type="simple" /> </jats:inline-formula> to be pure quark states, while for <jats:inline-formula> <jats:tex-math><?CDATA $ f_0(1370) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M11.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ f_0(1500) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M12.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ f_0(1710) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M13.jpg" xlink:type="simple" /> </jats:inline-formula>, to fit both the experimental data of <jats:inline-formula> <jats:tex-math><?CDATA $ J/\psi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M14.jpg" xlink:type="simple" /> </jats:inline-formula> radiative decay and their mass spectra, glueball components are needed. Moreover, the mass of the pure <jats:inline-formula> <jats:tex-math><?CDATA $ 0^{++} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023104_M15.jpg" xlink:type="simple" /> </jats:inline-formula> glueball is phenomenologically determined. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Measuring the fermion Yukawa coupling constants is important for understanding the origin of the fermion masses and their relationship with spontaneously electroweak symmetry breaking. In contrast, some new physics (NP) models change the Lorentz structure of the Yukawa interactions between standard model (SM) fermions and the SM-like Higgs boson, even in their decoupling limit. Thus, the precise measurement of the fermion Yukawa interactions is a powerful tool of NP searching in the decoupling limit. In this work, we show the possibility of investigating the Lorentz structure of the bottom-quark Yukawa interaction with the 125 GeV SM-like Higgs boson for future <jats:inline-formula> <jats:tex-math><?CDATA $e^+e^-$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023105_M1.jpg" xlink:type="simple" /> </jats:inline-formula> colliders. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Neutrinos stand out among the elementary particles because of their unusually small masses. Various seesaw mechanisms attempt to explain this fact. In this work, applying insights from matrix theory, we are in a position to treat variants of seesaw mechanisms in a general manner. Specifically, using Weyl's inequalities, we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos. We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos, shifted at most by the maximal strength of the coupling to the light neutrino sector. We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy. For higher-dimensional cases the inverse eigenvalue methods are used. In particular, for the <jats:italic>CP-</jats:italic>invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones, i.e. if the respective mass submatrix is positive definite, then large masses are provided by matrices with large elements accumulated on the diagonal. Finally, the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis. This general observation concerning neutrino mixing, together with results on the mass spectrum properties, opens directions for further neutrino physics studies using matrix analysis. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams. We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the interaction Hamiltonian in all cases, including that of Feynman diagrams with symmetry factors.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We consider the positivity bounds on dimension-8 four-electron operators and study two related phenomenological aspects at future lepton colliders. First, if positivity is violated, probing such violations will revolutionize our understanding of the fundamental pillars of quantum field theory and the <jats:italic>S</jats:italic>-matrix theory. We observe that positivity violation at scales of 1-10 TeV can potentially be probed at future lepton colliders even if one assumes that dimension-6 operators are also present. Second, the positive nature of the dimension-8 parameter space often allows us to either directly infer the existence of UV-scale particles together with their quantum numbers or exclude them up to certain scales in a model-independent way. In particular, dimension-8 positivity plays an important role in the test of the Standard Model. If no deviations from the Standard Model are observed, it allows for simultaneous exclusion limits on all kinds of potential UV-complete models. Unlike the dimension-6 case, these limits apply regardless of the UV model setup and cannot be removed by possible cancellations among various UV contributions. This thus consists of a novel and universal test to confirm the Standard Model. We demonstrate with realistic examples how all the previously mentioned possibilities, including the test of positivity violation, can be achieved. Hence, we provide an important motivation for studying dimension-8 operators more comprehensively. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass, we calculate the decay constants of <jats:inline-formula> <jats:tex-math><?CDATA $ D_{s}^{(*)} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ D^{(*)} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M2.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $ \phi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M3.jpg" xlink:type="simple" /> </jats:inline-formula>. The lattice size is <jats:inline-formula> <jats:tex-math><?CDATA $ 48^3\times96 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, which corresponds to a spatial extension of <jats:inline-formula> <jats:tex-math><?CDATA $ \sim5.5 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M5.jpg" xlink:type="simple" /> </jats:inline-formula> fm, with a lattice spacing of <jats:inline-formula> <jats:tex-math><?CDATA $ a\approx 0.114 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M6.jpg" xlink:type="simple" /> </jats:inline-formula> fm. For the valence light, strange, and charm quarks, we use overlap fermions at several mass points close to their physical values. Our results at the physical point are <jats:inline-formula> <jats:tex-math><?CDATA $ f_D = 213(5) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M7.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D_s} = 249(7) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M8.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D^*} = 234(6) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M9.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D_s^*} = 274(7) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M10.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, and <jats:inline-formula> <jats:tex-math><?CDATA $ f_\phi = 241(9) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M11.jpg" xlink:type="simple" /> </jats:inline-formula> MeV. The couplings of <jats:inline-formula> <jats:tex-math><?CDATA $ D^* $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M12.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ D_s^* $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M13.jpg" xlink:type="simple" /> </jats:inline-formula> to the tensor current ( <jats:inline-formula> <jats:tex-math><?CDATA $ f_V^T $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M14.jpg" xlink:type="simple" /> </jats:inline-formula>) can be derived from ratios <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D^*}^T/f_{D^*} = 0.91(4) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M15.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D_s^*}^T/f_{D_s^*} = 0.92(4) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M16.jpg" xlink:type="simple" /> </jats:inline-formula>, respectively, which are the first lattice quantum chromodynamics (QCD) results. We also obtain ratios <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D^*}/f_D = 1.10(3) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M17.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D_s^*}/f_{D_s} = 1.10(4) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M18.jpg" xlink:type="simple" /> </jats:inline-formula>, which reflect the size of heavy quark symmetry breaking in charmed mesons. Ratios <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D_s}/f_{D} = 1.16(3) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M19.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ f_{D_s^*}/f_{D^*} = 1.17(3) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_2_023109_M20.jpg" xlink:type="simple" /> </jats:inline-formula> can be taken as a measure of <jats:italic>SU</jats:italic>(3) flavor symmetry breaking. </jats:p>