arXiv subjects

A. M. Badalian

Publications and source records attributed to A. M. Badalian.

At least 37 records · Page 2Linked to original sources

arXiv2010

Radial Regge trajectories for higher $ψ(nS)$ and $ψ(nD)$ states

The masses of $ψ((n+1) {}^3S_1)$ and $ψ(n {}^3D_1)$ are calculated using the relativistic string Hamiltonian with "linear+gluon-exchange" potential. They occur in the range 4.5-5.8 GeV, in particular, $M(3D)=4.54$ GeV, $M(5S)=4.79$ GeV, $M(4D)=4.85$ GeV are calculated with accuracy $\sim 50$ MeV. Linear Regge trajectories: $M^2(nS)=M^2(ψ(4.42))+ 2.91$ GeV$^2 (n-4)$ $(n\geq 4) $ and $M^2(nD)=(4.54^2+ 2.88 (n-3))$ GeV$^2$ ($n\geq 3$) are obtained only for higher charmonium excitations. They have slopes two times larger than those of light mesons and give good description of calculated masses. These masses are compared with enhancements in some recent $e^+e^-$ experiments.

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arXiv2010

The Hyperfine Splittings in Heavy-Light Mesons and Quarkonia

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the $B_q$ (q=n,s) mesons are shown to be in full agreement with experiment if a universal coupling $α_{HF}=0.310$ is taken in perturbative spin-spin potential. It gives $M(B^*)-M(B)=45.7(3)$ MeV, $M(B_s^*)-M(B_s)=46.7(3)$ MeV ($n_f=4$), while in bottomonium $Δ_{HF}(b\bar b)=M(Υ(9460))-M(η_b(1S))=63.4$ MeV for $n_f=4$ and 71.1 MeV for $n_f=5$ are obtained; just latter agrees with recent BaBar data. For unobserved excited states we predict $M(Υ(2S))-M(η_b(2S))=36(2)$ MeV, $M(Υ(3S))-M(η(3S))=28(2)$ MeV, and also $M(B_c^*)=6334(4)$ MeV, $M(B_c(2S))=6868(4)$ MeV, $M(B_c^*(2S))=6905(4)$ MeV. The mass splittings between $D(2^3S_1)-D(2^1S_0)$, $D_s(2^3S_1)-D_s(2^1S_0)$ are predicted to be $\sim 70$ MeV, which are significantly smaller than in several other studies.

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arXiv2010

The Hyperfine Splittings in Bottomonium and the $B_q (q=n,s,c)$ Mesons

A universal description of the hyperfine splittings (HFS) in bottomonium and the $B_q (q=n,s,c)$ mesons is obtained with a universal strong coupling constant $α_s(μ)=0.305(2)$ in a spin-spin potential. Other characteristics are calculated within the Field Correlator Method, taking the freezing value of the strong coupling independent of $n_f$. The HFS $M(B^*)- M(B)=45.3(3)$ MeV, $M(B_s^*) - M(B_s)=46.5(3)$ MeV are obtained in full agreement with experiment both for $n_f=3$ and $n_f=4$. In bottomonium, $M(Υ(9460))- M(η_b)=70.0(4)$ MeV for $n_f=5$ agrees with the BaBar data, while a smaller HFS, equal to 64(1) MeV, is obtained for $n_f=4$. We predict HFS $M(Υ(2S))-M(η_b(2S))=36(1)$ MeV, $M(Υ(3S))- M(η(3S))=27(1)$ MeV, and $M(B_c^*) - M(B_c)= 57.5(10)$ MeV, which gives $M(B_c^*)=6334(1)$ MeV, $M(B_c(2 {}^1S_0))=6865(5)$ MeV, and $M(B_c^*(2S {}^3S_1))=6901(5)$ MeV.

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arXiv2009

Di-electron and two-photon widths in charmonium

The vector and pseudoscalar decay constants are calculated in the framework of the Field Correlator Method. Di-electron widths: $Γ_{ee}(J/ψ)=5.41$ keV, $Γ_{ee}(ψ'(3686))=2.47$ keV, $Γ_{ee}(ψ''(3770))=0.248$ keV, in good agreement with experiment, are obtained with the same coupling, $α_s=0.165$, in QCD radiative corrections. We show that the larger $α_s=0.191\pm 0.004$ is needed to reach agreement with experiment for $Γ_{γγ}(η_c)=7.22$ keV, $Γ_{γγ} (χ(^3P_0))=3.3$ keV, $Γ_{γγ}(χ(^3P_2))= 0.54$ keV, and also for $Γ(J/ψ\to 3g)=59.5$ keV, $Γ(J/ψ\to γ2g)=5.7$ keV. Meanwhile even larger $α_s=0.238$ gives rise to good description of $Γ(ψ'\to 3g)=52.7$ keV, $Γ(ψ'\to γ2g)= 3.5$ keV, and provides correct ratio of the branching fractions: $\frac{\mathcal{B}(J/ψ\to light hadrons)}{\mathcal{B}(ψ'\to light hadrons)}=0.24.$

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arXiv2009

On the possibility to observe higher $n^3D_1$ bottomonium states in the $e^+e^-$ processes

The possibility to observe new bottomonium states with $J^{PC}= 1^{--}$ in the region $10.7-11.1$ GeV is discussed. The analysis of the di-electron widths shows that the $(n+1)^3S_1$ and $n^3D_1$ states ($n\geq 3$) may be mixed with a rather large mixing angle, $θ\sim30^\circ$ and this effect provides the correct values of $Γ_{ee}(Υ(10580))$ and $Γ_{ee}(Υ(11020))$. On the other hand, the $S-D$ mixing gives rise to an increase by two orders of magnitude of the di-electron widths of the mixed $\tildeΥ(n^3D_1$) resonances ($n=3,4,5$), which originate from pure $D-$wave states. The value $Γ_{ee}(\tildeΥ(3D))=0.095^{+0.028}_{-0.025}$ keV is obtained, being only $\sim 3$ times smaller than the di-electron width of $Υ(10580)$, while $Γ_{ee}(\tildeΥ(5D))\sim 135$ eV appears to be close to $Γ_{ee}(Υ(11020))$ and therefore this resonance may become manifest in the $e^+e^-$ experiments. The mass differences between $M(nD)$ and $M((n+1)S) (n=4,5)$ are shown to be rather small, $50\pm 10$ MeV.

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arXiv2009

Dielectron widths of the S-, D-vector bottomonium states

The dielectron widths of $Υ(nS) (n=1,...,7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For $Υ(nS) (n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For $Υ(10580)$ and $Υ(11020)$ a good agreement with experiment is reached only if the 4S--3D mixing (with a mixing angle $θ=27^\circ\pm 4^\circ$) and 6S--5D mixing (with $θ=40^\circ\pm 5^\circ$) are taken into account. The possibility to observe higher "mixed $D$-wave" resonances, $\tildeΥ(n {}^3D_1)$ with $n=3,4,5$ is discussed. In particular, $\tildeΥ(\approx 11120)$, originating from the pure $5 {}^3D_1$ state, can acquire a rather large dielectron width, $\sim 130$ eV, so that this resonance may become manifest in the $e^+e^-$ experiments. On the contrary, the widths of pure $D$-wave states are very small, $Γ_{ee}(n{}^3 D_1) \leq 2$ eV.

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arXiv2009

The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $\mathbf{1^{--}}$ states

The di-electron widths of $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$, and their ratios are shown to be in good agreement with experiment, if in all cases the $S-D$ mixing with a large mixing angle $θ\approx 34^\circ$ is taken. Arguments are presented why continuum states give small contributions to the wave functions at the origin. We find that the Y(4360) resonance, considered as a pure $3 {}^3D_1$ state, would have very small di-electron width, $Γ_{ee}(Y(4360))=0.060$ keV. On the contrary, for large mixing between the $4 {}^3S_1$ and $3 {}^3D_1$ states with the mixing angle $θ=34.8^\circ$, $Γ_{ee}(ψ(4415))=0.57$ keV coincides with the experimental number, while a second physical resonance, probably Y(4360), has also a rather large $Γ_{ee} (Y(\sim 4400))=0.61$ keV. For the higher resonance Y(4660), considered as a pure $5 {}^3S_1$ state, we predict the di-electron width $Γ_{ee}(Y(4660))=0.70$ keV, but it becomes significantly smaller, namely 0.31 keV, if the mixing angle between the $5 {}^3S_1$ and $4 {}^3D_1$ states $θ=34^\circ$. The mass and di-electron width of the $6 {}^3S_1$ charmonium state are calculated.

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arXiv2008

Spin-dependent interactions in quarkonia

The spin-dependent interactions in mesons are considered in detail in the framework of the Field Correlator Method. Analytic expressions for the spin-dependent potentials in heavy and light quarkonia are derived with the QCD string moment of inertia taken into account. Recent lattice data are analysed using these formulae and the data are shown to be consistent with very small values of the gluonic correlation length, <0.1 fm. The Field Correlator and the Eichten-Feinberg definitions of the spin-dependent potentials in the lowest, Gaussian approximation for the QCD vacuum are compared to one another and the two approaches are shown to be equivalent in the limit of a vanishing vacuum correlation length, whereas for finite values of the latter the difference between these two approaches can be explained by the contribution of the higher-order field corelators, starting from the quartic one.

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arXiv2008

The coupled-channel analysis of $D_s$ and $B_s$ mesons

In the framework of the coupled channel model the mass shifts of the $P$--wave excitations of $D_s$ and $B_s$ mesons have been calculated. The corresponding coupling to $DK$ and $BK$ channels is provided by the effective chiral Lagrangian which is deduced from QCD and does not contain fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost at rest. Two factors are essential for large mass shifts: strong coupling of the $0^+$ and $1^{+'}$ states to the $S$-wave decay channel, containing a Nambu-Goldstone meson, and the chiral flip transitions due to the bispinor structure of both heavy-light mesons. The masses $M(B^*_s(0^+))=5710(15)$ MeV and $M(B_s(1^{+'}))=5730(15)$ MeV are predicted. Experimental limit on the width $Γ(D_{s1}(2536))<2.3$ MeV puts strong restrictions on admittable mixing angle between the $1^+$ and $1^{+'}$ states.

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arXiv2008

Chiral shifts in heavy-light mesons

The mass shifts of the $P$-wave $D_s$ and $B_s$ mesons due to coupling to $DK$ and $BK$ channels are calculated in the coupling channel model without fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost in situ. The masses of $0^+$ and ${1^+}'$ states of $B_s$ mesons have been predicted.

hep-ph↗

arXiv2008

Gluonic correlation length from spin-dependent potentials

The vacuum gluonic correlation length is extracted from recent lattice data on spin-dependent interquark potentials in heavy quarkonia. It is shown that the data are consistent with extremely small values of the correlation length, Tg<0.1 fm.

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arXiv2008

Dynamical suppression of the spin-orbit interaction in hadrons

Spin-dependent interaction in hadrons is considered in the approach of the QCD string. The string moment of inertia, which ensures the correct (inverse) Regge slope 2*pi*sigma, is found to suppress the spin-orbit interaction. For light quarks and moderate angular momenta the suppression constitutes around 25% whereas for large angular momenta the spin-orbit interaction is suppressed by the factor L^(-2/5). For heavy quarks the effect manifests itself as a string correction for the spin-dependent potential.

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arXiv2008

The running mass $m_s$ at low scalefrom the heavy-light meson decay constants

It is shown that a 25(20)% difference between the decay constants $f_{D_s}(f_{B_s})$ and $f_D(f_B)$ occurs due to large differences in the pole masses of the $s$ and $d(u)$ quarks. The values $η_D =f_{D_s}/f_D\approx 1.23(15)$, recently observed in the CLEO experiment, and $η_B=f_{B_s}/f_B\approx 1.20$, obtained in unquenched lattice QCD, can be reached only if the running mass $m_s$ at low scale is $m_s(\sim 0.5 $ GeV)$= 170 - 200$ MeV. Our results follow from the analytical expression for the pseudoscalar decay constant $f_{\rm P}$ based on the path-integral representation of the meson Green's function.

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arXiv2007

The chiral transitions in heavy-light mesons

The mass shifts of the $P$-wave $D_s$ and $B_s$ mesons due to coupling to $DK$, $D^*K$ and $BK$, $B^*K$ channels are studied using the chiral quark-pion Lagrangian without fitting parameters. The strong mass shifts down $\sim 140$ MeV and $\sim 100$ MeV for $D^*_s(0^+)$ and $D_s(1^{+'})$ and $\sim 100$ MeV for $B^*_s(0^+)$ and $B_s(1^{+'})$ are calculated. Two factors are essential for large mass shifts: strong coupling of the $0^+$ and $1^{+'}$ states to the $S$-wave decay channel, containing a Nambu-Goldstone meson, and the chiral flip transitions due to the bispinor structure of both heavy-light mesons. The masses $M(B^*_s(0^+))=5695(10)$ MeV and $M(B_s(1^{+'}))=5730(15)$ MeV,very close to $M(B(0^+))$ and $M(B(1^{+'}))$, are predicted. Experimental limit on the width $Γ(D_{s1}(2536))<2.3$ MeV puts strong restrictions on admittable mixing angle between the $1^+$ and $1^{+'}$ states, $|ϕ|<6^{\circ}$, which corresponds to the mixing angle $θ$ between the $^3P_1$ and $^1P_1$ states, $29^{\circ}<θ< 41^{\circ}$.

hep-ph↗

arXiv2007

Decay constants of the heavy-light mesons from the field correlator method

Meson Green's functions and decay constants $f_Γ$ in different channels $Γ$ are calculated using the Field Correlator Method. Both, spectrum and $f_Γ$, appear to be expressed only through universal constants: the string tension $σ$, $α_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5$ MeV. For the $D$ and $D_s$ mesons the values of $f_{\rm P} (1S)$ are equal to 210(10) and 260(10) MeV, respectively, and their ratio $f_{D_s}/f_D$=1.24(3) agrees with recent CLEO experiment. The values $f_{\rm P}(1S)=182, 216, 438$ MeV are obtained for the $B$, $B_s$, and $B_c$ mesons with the ratio $f_{B_s}/f_B$=1.19(2) and $f_D/f_B$=1.14(2). The decay constants $f_{\rm P}(2S)$ for the first radial excitations as well as the decay constants $f_{\rm V}(1S)$ in the vector channel are also calculated. The difference of about 20% between $f_{D_s}$ and $f_D$, $f_{B_s}$ and $f_B$ directly follows from our analytical formulas.

hep-ph↗

arXiv2006

Masses and decay constants of B_q mesons in the QCD string approach

The relativistic string Hamiltonian is used to calculate the masses and decay constants of $B_q$ mesons: they appear to be expressed through onlythree fundamental values: the string tension $σ$, $α_s$, and the quark pole masses. The values $f_B =186 $ MeV, $f_{B_s}= 222$ MeV are calculated while $f_{B_c}$ depends on the $c$-quark pole mass used, namely $f_{B_c}=440 (424)$ MeV for $m_c =1.40 (1.35)$ GeV. For the $1P$ states we predict the spin-averaged masses: $\bar M(B_J)=5730$ MeV and $\bar M(B_{sJ})=5830$ MeV which are in good agreement with the recent data of the D0 and CDF Collaborations, at the same time owning to the string correction being by $\sim 50$ MeV smaller than in other calculations.

hep-ph↗

arXiv2006

Masses of the η_c(nS) and η_b(nS) mesons

The hyperfine splittings in heavy quarkonia are studied using new experimental data on the di-electron widths. The smearing of the spin-spin interaction is taken into account, while the radius of smearing is fixed by the known $J/ψ-η_c(1S)$ and $ψ(2S)-η'_c(2S)$ splittings and appears to be small, $r_{ss} \approx 0.06$ fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings ($\sim 50%)$ is observed in bottomonium. For the $nS b\bar b$ states $(n=1,2,...6)$ the values we predict (in MeV) are 28, 12, 10, 6, 6, and 3, respectively. In single-channel approximation for the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

hep-ph↗

arXiv2006

Higher $η_c(nS)$ and $η_b (nS)$ mesons

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using the experimental data on di-electron widths. Relativistic correlations are taken into account together with the smearing of the spin-spin interaction. The radius of smearing is fixed by the known $J/ψ-η_c(1S)$ and $ψ(2S)-η'_c(2S)$ splittings and appears to be small, $r_{ss} \cong 0.06$ fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings ($\sim 50%)$ is observed in bottomonium. For the $nS~ b\bar b$ states $(n=1,2,...,6)$ we predict the values (in MeV) 28, 12, 10, 6, 6, and 3, respectively. For the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

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