arXiv subjects

A. M. Badalian

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

53 records · Page 3Linked to original sources

arXiv2004

The gluonic condensate from the hyperfine splitting $M_{\rm cog}(χ_{cJ})-M(h_c)$ in charmonium

The precision measurement of the hyperfine splitting $Δ_{\rm HF} (1P, c\bar c)=M_{\rm cog} (χ_{cJ}) - M(h_c) = -0.5 \pm 0.4$ MeV in the Fermilab--E835 experiment allows to determine the gluonic condensate $G_2$ with high accuracy if the gluonic correlation length $T_g$ is fixed. In our calculations the negative value of $Δ_{\rm HF} = -0.3 \pm 0.4$ MeV is obtained only if the relatively small $T_g = 0.16$ fm and $G_2 = 0.065 (3)$ GeV${}^4$ are taken. These values correspond to the ``physical'' string tension $(σ\approx 0.18 $ GeV$^2$). For $T_g \ge 0.2$ fm the hyperfine splitting is positive and grows for increasing $T_g$. In particular for $T_g = 0.2$ fm and $G_2 = 0.041 (2)$ GeV${}^4$ the splitting $Δ_{\rm HF} = 1.4 (2)$ MeV is obtained, which is in accord with the recent CLEO result.

hep-ph↗

arXiv2004

Leptonic widths of high excitations in heavy quarkonia

Agreement with the measured electronic widths of the $ψ(4040)$, $ψ(4415)$, and $Υ(11019)$ resonances is shown to be reached if two effects are taken into account: a flattening of the confining potential at large distances and a total screening of the gluon-exchange interaction at $r\ga 1.2$ fm. The leptonic widths of the unobserved $Υ(7S)$ and $ψ(5S)$ resonances: $Γ_{e^+e^-}(Υ(7S))=0.11$ keV and $Γ(ψ(5S))\approx 0.54$ keV are predicted.

hep-ph↗

arXiv2004

The vector coupling in IR region from splittings in bottomonium

The splittings $1D-1P, 1F-1P, 2D-2P$ are shown to be the most convenient characteristics to determine the vector coupling in IR region. In background perturbation theory the splitting $Δ=1D -1P$ appears to be in agreement with $Δ(\exp) =261.1 \pm 2.2$ MeV only for large freezing value, $α_{crit} \cong 0.60$, which corresponds to $Λ_{\bar{MS}} (2$-loop, $n_f=5)\cong 240$ MeV $(α_s(M_Z) =0.1193(2)$. The masses $M_{cog} (1F)=10362\pm 3$ MeV and $M_{cog} (2D) =10452\pm 4 $ MeV are predicted.

hep-ph↗

arXiv2004

The heavy-quark pole masses in the Hamiltonian approach

From the fact that the nonperturbative self-energy contribution $C_{\rm SE}$ to the heavy meson mass is small: $C_{\rm SE}(b\bar{b})=0$; $C_{\rm SE}(c\bar{c})\cong -40$ MeV \cite{ref.01}, strong restrictions on the pole masses $m_b$ and $m_c$ are obtained. The analysis of the $b\bar{b}$ and the $c\bar{c}$ spectra with the use of relativistic (string) Hamiltonian gives $m_b$(2-loop)$=4.78\pm 0.05$ GeV and $m_c$(2-loop)$=1.39 \pm 0.06$ GeV which correspond to the $\bar{\rm MS}$ running mass $\bar{m}_b(\bar{m}_b)=4.19\pm 0.04$ GeV and $\bar{m}_c(\bar{m}_c)=1.10\pm 0.05$ GeV. The masses $ω_c$ and $ω_b$, which define the heavy quarkonia spin structure, are shown to be by $\sim 200$ MeV larger than the pole ones.

hep-ph↗

arXiv2004

The static force in background perturbation theory

The static force $F_B(r)$ and the strong coupling $α_F(r)$, which defines the gluon-exchange part of $F_B(r)$, are studied in QCD background perturbation theory (BPT). In the region $r\la 0.6 $ fm $α_F(r)$ turns out to be essentially smaller than the coupling $α_B(r)$ in the static potential. For the dimensionless function $Φ_B(r) = r^2 F_B(r)$ the characteristic values $Φ_B(r_1) =1.0$ and $Φ_B(r_0)=1.65$ are shown to be reached at the following $Q\bar Q$ separations: $r_1\sqrtσ =0.77, r_0\sqrtσ =1.09$ in quenched approximation and $r_1\sqrtσ=0.72, r_0\sqrtσ=1.04$ for $n_f =3$. The numbers obtained appear to be by only 8% smaller than those calculated in lattice QCD while the values of the couplings $α_F(r_1)$ and $α_F(r_0)$ in BPT are by $\sim 30% (n_f =3)$ and $50% (n_f=0)$ larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained.

hep-ph↗

arXiv2004

The restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

The $b\bar b$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings $Δ_1= Υ({\rm 1D})-χ_b({\rm 1P})$ and other splittings are very sensitive to the QCD constant $Λ_V(n_f)$ which occurs in the Vector scheme, and good agreement with the experimental data is obtained for $Λ_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the conventional $Λ_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV, $α_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: $α_{\rm crit} (2$-loop, $q^2=0)=α_{\rm crit} (2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $α_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with $Δ_1({\rm exp})$ and $Δ_2({\rm exp})$ can be reached for the rather large value $α_{\rm static} =0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV.

hep-ph↗

arXiv2003

Is the a_0(1450) a candidate for the lowest q\bar{q} ^3P_0 state?

For the $a_0(1450)$, considered as the $q\bar{q} 1^3P_0$ state, "experimental" tensor splitting, $c_{exp}=(-150\pm 40$) MeV, appears to be in contradiction with conventional theory of fine structure. There is no such discrepancy if the $a_0(980)$ belongs to the $1^3P_J q\bar{q}$ multiplet. The hadronic shift of the $a_0(980)$ is shown to be strongly dependent on the value of the strong coupling in spin-dependent interaction.

hep-ph↗

arXiv2003

The $η_c(3654)$ and hyperfine splitting in charmonium

The hyperfine splitting for the 2S charmonium state is calculated and the predicted number is $Δ_{\rm HF}(2S) = 57 \pm 8$ MeV, being by derivation the lower bound of this splitting. It results in $M(η_c(2S))= 3630 \pm 8$ MeV, which is smaller by two standard deviations than found in the Belle experiment \cite{ref.01}, but close to the $η_c(2S)$ mass observed by the same group in the experiment $e^+e^- \to J/ψη_c$ \cite{ref.06} where $M(η_c(2S)) = 3622 \pm 12$ MeV was found.

hep-ph↗

arXiv2003

A short distance quark-antiquark potential

Leading terms of the static quark-antiquark potential in the background perturbation theory are reviewed, including perturbative, nonperturbative and interference ones. The potential is shown to describe lattice data at short quark-antiquark separations with a good accuracy.

hep-ph↗

arXiv2002

Light-meson orbital excitations in the QCD string approach

In the framework of the QCD string approach it is shown that the spin-averaged masses $\bar{M}(nL)$ of all low-lying light mesons are well described using the string tension $σ$ as the only parameter. The Regge slope $α'_L$ and the intercept $α_L(0)$ of the Regge L-trajectory for $\bar{M}(nL)$ are calculated analytically and turn out to be $α'_L = 0.80$ GeV${}^{-2}$ (for $L \leq 4$) and $α_L(0) = -0.34$, in good agreement with the experimental data: $α'_{L {\rm exp}} = 0.81 \pm 0.01$ GeV${}^{-2}$, $α_{L {\rm exp}}(0) = -0.30 \pm 0.02$. To obtain this strong agreement with the data the nonperturbative quark self-energy contributions to the meson masses must be taken into account, which appeared to be large and negative for small values of L, and are even for larger values of L important for a close fit. From the present analysis of the meson spectra the restriction $α_s \leq 0.40$ on the strong coupling is required.

hep-ph↗

arXiv2002

Light meson radial Regge trajectories

A new physical mechanism is suggested to explain the universal depletion of high meson excitations. It takes into account the appearance of holes inside the string world sheet due to $q\bar{q}$ pair creation when the length of the string exceeds the critical value $R_1 \simeq 1.4$ fm. It is argued that a delicate balance between large $N_c$ loop suppression and a favorable gain in the action, produced by holes, creates a new metastable (predecay) stage with a renormalized string tension which now depends on the separation r. This results in smaller values of the slope of the radial Regge trajectories, in good agreement with the analysis of experimental data in [Ref.3]

hep-ph↗

arXiv2001

Freezing of QCD coupling affects the short distance static potential

A striking contradiction between lattice short range static potential (nf=0) and standard perturbative potential, observed by Bali G.S., is investigated in the framework of the background perturbation theory. With the use of the background coupling which contains the only background parameter - mass mB, fixed by fine structure fit in bottomonium, the lattice data are nicely explained without introduction of exotic short range linear potential with large "string tension" approx. 1 GeV squared. A significant difference between the background coupling and standard perturbative coupling is found in the range 0.05 fm < r<0.15 fm, while at larger distances, r > 0.3 fm the background coupling fast approaches the freezing value. Some problems concerning the strong coupling properties at short and long distances are discussed and solutions are suggested.

hep-ph↗

arXiv2001

Nonperturbative hyperfine contribution to the $b_1$ and $h_1$ meson masses

Due to the nonperturbative contribution to the hyperfine splitting the mass of the $n^1P_1$ state is strongly correlated with the center of gravity $M_{\rm cog}(n^3P_J)$ of the $n^3P_J$ multiplet: $M(n^1P_1)$ is less than $M_{\rm cog}(n^3P_J)$ by about 40 MeV (20 MeV) for the 1P (2P) state. For $b_1(1235)$ the agreement with experiment is reached only if $a_0(980)$ belongs to the $1^3P_J$ multiplet. The predicted mass of $b_1(2^1P_1)$ is $\approx 1620$ MeV. For the isoscalar meson a correlation between the mass of $h_1$(1170) $(h_1(1380))$ and $M_{cog}(1^3P_J)$ composed from light (strange) quarks also takes place.

hep-ph↗

arXiv2000

Strong coupling constant from bottomonium fine structure

From a fit to the experimental data on the $b\bar{b}$ fine structure, the two-loop coupling constant is extracted. For the 1P state the fitted value is $α_s(μ_1) = 0.33 \pm 0.01(exp)\pm 0.02 (th)$ at the scale $μ_1 = 1.8 \pm 0.1$ GeV, which corresponds to the QCD constant $Λ^{(4)}(2-loop) = 338 \pm 30$ MeV (n_f = 4) and $α_s(M_Z) = 0.119 \pm 0.002. For the 2P state the value $α_s(μ_2) = 0.40 \pm 0.02(exp)\pm 0.02(th)$ at the scale $μ_2 = 1.02 \pm 0.2$ GeV is extracted, which is significantly larger than in the previous analysis of Fulcher (1991) and Halzen (1993), but about 30% smaller than the value given by standard perturbation theory. This value $α_s(1.0) \approx 0.40$ can be obtained in the framework of the background perturbation theory, thus demonstrating the freezing of $α_s$. The relativistic corrections to $α_s$ are found to be about 15%.

hep-ph↗

arXiv1999

Fine structure splittings of excited P and D states in charmonium

It is shown that the fine structure splittings of the $2 ^3P_J$ and $3 ^3P_J$ excited states in charmonium are as large as those of the $1^3P_J$ state if the same $α_s(μ)\approx 0.36$ is used. The predicted mass $M(2 ^3P_0)=3.84$ GeV appears to be 120 MeV lower that the center of gravity of the $2 ^3P_J$ multiplet and lies below the $D\bar D^*$ threshold. Our value of $M(2 ^3P_0)$ is approximately 80 MeV lower than that from the paper by Godfrey and Isgur while the differences in the other masses are $\la 20$ MeV. Relativistic kinematics plays an important role in our analysis.

hep-ph↗

arXiv1999

Determination of Alpha_s(1 GeV) from the charmonium fine structure

The strong coupling constant $α_s(μ)$ is extracted from the fits to charmonium spectrum and fine structure splittings. The relativistic kinematics is taken into account and relativistic corrections are shown to increase the matrix elements defining spin effects up to 40%. The value of $α_s(μ)$ at low-energy scale $μ=1.0 \pm 0.2 GeV$ was found to be $α_s(μ) = 0.38 \pm 0.03 (exp.) + 0.04 (theor.)$ which is about 50% lower than standard perturbative two-loop approximation and is in good agreement with the freezing $α_s$ behaviour.

hep-ph↗

arXiv1997

Running coupling constant of background perturbation theory and lattice interquark interaction

The conventional parametrizations of lattice static interquark force are shown to produce a mismatch of coupling constant near the matching point R_m \approx 0.2 fm. The running coupling constant of the background perturbation theory yields instead a selfconsistent description of lattice data over all interval of distances, 0.05 fm \la R \la 1.1.fm, and is an analytic function with the property of asymptotic freedom at small R and it is freezing at large R.

hep-lat↗