1S Mass Research Articles

P -wave fully charm and fully bottom tetraquark states

We have studied the mass spectra of the P-wave fully charm and fully bottom tetraquark states in the framework of quantum chromodynamics (QCD) sum rules. We construct the interpolating currents by inserting the covariant derivative operator D↔μ between the S-wave diquark and antidiquark fields. The excitation structures show that the pure λ-mode excited P-wave fully heavy tetraquarks exist for the quantum numbers JPC=1−−,1−+,2−−,2−+, and 3−−, while it is difficult to separate the λ-mode and ρ-mode excitations in the 0−+ channel. Within three Lorentz indices, there is no pure λ-mode excited P-wave fully charm/bottom tetraquark operators with JPC=0−− and 3−+. Our results support that the recent observed X(6900) and X(7200) resonances could be interpreted as the P-wave fully charm ccc¯c¯ tetraquark states with JPC=1−+ and 2−+, respectively. Some P-wave fully bottom bbb¯b¯ tetraquark states are predicted to be lower than the di-ηb(1S) and di-ϒ(1S) mass thresholds. Hopefully our calculations will be useful for identifying the nature of new exotic tetraquark states. Published by the American Physical Society 2024

The photon energy spectrum in B → Xsγ at N3LL′

We present predictions for the photon energy spectrum in inclusive B → Xsγ decays mediated by the electromagnetic penguin operator O7 to N3LL′. We use soft-collinear effective theory (SCET) to resum the singular contributions in the peak region at large photon energy. In the tail region the resummed predictions are matched to fixed order at N3LO, where we include the known fixed-order contributions for O7 up to mathcal{O} ( {alpha}_s^2 ). We develop a method to suitably parametrize the still unknown mathcal{O} ( {alpha}_s^3 ) nonsingular corrections in terms of theory nuisance parameters, whose variations provide an estimate of the associated theory uncertainty. In this context, we also study different ways to treat higher-order cross terms in the matching. Another important aspect of our analysis is the short-distance scheme used for the b-quark mass mb. We find that in the present context, the 1S mass scheme, which was previously used up to 2-loop order, fails to work at 3-loop order, because the mass scheme enters at a soft scale much smaller than mb here, for which the 1S scheme was not devised. Using instead the MSR mass scheme with R ~ 1 GeV, we obtain stable results with good perturbative convergence up to N3LL′.

Revision of results on ϒ(1S), ϒ(2S), and ϒ(3S) masses

We have reconsidered the results on the masses of the narrow bottomonium states ϒ(1S)–ϒ(3S) obtained in 1982–1986 at CESR, DORIS and VEPP-4 colliders in order to fix shortcomings of the mass determination procedures. For experiments at CESR and DORIS this includes the incorrect accounting of the radiative corrections and usage of the electron mass value revised in 1986. In analyses of all experiments the interference of the resonance production and the nonresonant process was ignored. The corrected mass values for five experiments are suggested. The corrections vary from 0.1 to 0.4 MeV. The discrepancy between CESR and VEPP-4 results on ϒ(1S) mass has been reduced from 3.3 to 1.8 standard deviations.

Determination of |Vcb| using N3LO perturbative corrections to Γ(B → Xcℓν) and 1S masses

We determine |Vcb| using the third-order perturbative series for the inclusive semileptonic B decay width and for the masses of the bottomonium 1S states. We use the masses of ηb(1S) and ϒ(1S) as short-distance masses and point out that there is a sizable difference of |Vcb| between the two 1S mass schemes. This is the dominant error of our determination and stems from insufficiency to describe theoretically the observed mass splitting of the bottomonium 1S states. We also study the significance of the O(ΛMS‾2) non-perturbative effects in HQET with respect to the current perturbative accuracy. Our result |Vcb|=0.0425(11) is consistent with the PDG value determined from the inclusive decays and has a slightly larger error.

Review of bottomonium studies at Belle

We review recent bottomonium studies at Belle. The results include the new measurement of the ηb(1S ) mass, the observation of the γ(4S ) → γ (1S )η’ transition, and the observation of the e+e−→ χbJ (1P)π+π−π0 process in the Υ(11020) region.

Measurement of ηc(1S) , ηc(2S) , and nonresonant η′π+π− production via two-photon collisions

We report the measurement of gamma gamma to eta_c(1S), eta_c(2S) to eta' pi+ pi- with eta' decays to gamma rho and eta pi+ pi- using 941 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. The eta_c(1S) mass and width are measured to be M = [2984.6\pm0.7 (stat.)\pm2.2 (syst.)] MeV/c^{2} and \Gamma = [30.8^{+2.3}_{-2.2}~(stat.) \pm 2.5~(syst.)] MeV, respectively. First observation of eta_c(2S) to eta' pi+ pi- with a significance of 5.5sigma including systematic error is obtained, and the eta_c(2S) mass is measured to be M = [3635.1\pm3.7~(stat.)\pm2.9~(syst.)] MeV/c^{2}. The products of the two-photon decay width and branching fraction (B) of decays to eta'pi+ pi- are determined to be \Gamma_{gamma gamma}B = [65.4\pm2.6~(stat.)\pm6.9~(syst.)] eV for eta_c(1S) and [5.6^{+1.2}_{-1.1}~(stat.)\pm1.1~(syst.)] eV for eta_c(2S). A new decay mode for the eta_c(1S) to eta'f_0(2080) with f_0(2080) to pi+ pi- is observed with a statistical significance of 20sigma. The f_0(2080) mass and width are determined to be M = [2083^{+63}_{-66}~(stat.)\pm 32~(syst.)] MeV/c^{2} and \Gamma = [178^{+60}_{-178}~(stat.) \pm 55~(syst.)] MeV. The cross sections for gamma gamma to eta' pi+ pi- and eta'f_{2}(1270) are measured for the first time.

Higher-order condensate corrections to \u03d2 masses, leptonic decay rates and sum rules

With the recent completion of NNNLO results, the perturbative description of the ϒ system has reached a very high level of sophistication. We consider the non-perturbative corrections as an expansion in terms of local condensates, following the approach pioneered by Voloshin and Leutwyler. The leading order corrections up to dimension eight and the potential NLO corrections at dimension four are computed and given in analytical form. We then study the convergence of the expansion for the masses, the leptonic decay rates and the non-relativistic moments of the ϒ system. We demonstrate that the condensate corrections to the ϒ(1S) mass exhibit a region with good convergence, which allows us to extract {overline{m}}_bleft({overline{m}}_bright)=4214pm 37 {left(mathrm{pert}.right)}_{-22}^{+20}left(mathrm{n}mathrm{o}mathrm{n}-mathrm{pert}.right) MeV, and show that non-perturbative contributions to the moments with n ≈ 10 are negligible.

Renormalization group improved bottom mass from $ \varUpsilon $ sum rules at NNLL order

We determine the bottom quark mass from non-relativistic large-n Upsilon sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of alpha_s ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic alpha_s ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling (alpha_s(M_Z) = 0.1183 +- 0.0010) we obtain M_b^{1S}=4.755 +- 0.057(pert) +- 0.009(alpha_s) +- 0.003(exp) GeV for the bottom 1S mass and m_b(m_b)= 4.235 +- 0.055(pert) +- 0.003(exp) GeV for the bottom MSbar mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.

Reduced branching ratio for H → AA → 4 τ from A − η b mixing

Models with an extended Higgs sector, as the NMSSM, allow for scenarios where the Standard Model-like CP-even Higgs boson H decays dominantly as H → AA → 4τ where A is a light CP-odd Higgs boson. Tight constraints on this scenario in the form of lower bounds on M H have recently been published by the ALEPH group. We show that, due to A − η b mixing, the branching ratio H → AA → 4τ is strongly reduced for M A in the range 9–10.5 GeV. This is the range of M A in which the tension between the observed η b (1S) mass and its prediction based on QCD can be resolved due to mixing, and which is thus still consistent with a light CP-even Higgs boson H satisfying LEP constraints with a masswellbelow114GeV. This result is practically independent from the coupling of A to b quarks.

Evidence for theηb(1S)Meson in RadiativeΥ(2S)Decay

We have performed a search for the ηb(1S) meson in the radiative decay of the Υ(2S) resonance using a sample of 91.6×106 Υ(2S) events recorded with the BABAR detector at the PEP-II B factory at the SLAC National Accelerator Laboratory. We observe a peak in the photon energy spectrum at Eγ=609.3−4.5+4.6(stat)±1.9(syst) MeV, corresponding to an ηb(1S) mass of 9394.2−4.9+4.8(stat)±2.0(syst) MeV/c2. The branching fraction for the decay Υ(2S)→γηb(1S) is determined to be [3.9±1.1(stat)−0.9+1.1(syst)]×10−4. We find the ratio of branching fractions B[Υ(2S)→γηb(1S)]/B[Υ(3S)→γηb(1S)]=0.82±0.24(stat)−0.19+0.20(syst).Received 6 March 2009DOI:https://doi.org/10.1103/PhysRevLett.103.161801©2009 American Physical Society

Measurement of the moments of the photon energy spectrum inB→Xsγdecays and determination of|Vcb|andmbat Belle

Using the previous Belle measurement of the inclusive photon energy in B→Xsγ decays, we determine the first and second moments of this spectrum for minimum photon energies in the B meson rest frame ranging from 1.8 to 2.3 GeV. Combining these measurements with recent Belle data on the lepton energy and hadronic mass moments in B→Xclν decays, we perform fits to theoretical expressions derived in the 1S and kinetic mass schemes and extract the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element Vcb, the b-quark mass, and other nonperturbative parameters. In the 1S scheme analysis we find |Vcb|=(41.56±0.68(fit)±0.08(τB))×10-3 and mb1S=(4.723±0.055)GeV. In the kinetic scheme, we obtain |Vcb|=(41.58±0.69(fit)±0.08(τB)±0.58(th))×10-3 and mbkin=(4.543±0.075)GeV. © 2008 The American Physical Society.

Observation of the Bottomonium Ground State in the DecayΥ(3S)→γηb

We report the results of a search for the bottomonium ground state ηb(1S) in the photon energy spectrum with a sample of (109±1) million of Υ(3S) recorded at the Υ(3S) energy with the BABAR detector at the PEP-II B factory at SLAC. We observe a peak in the photon energy spectrum at Eγ=921.2−2.8+2.1(stat)±2.4(syst) MeV with a significance of 10 standard deviations. We interpret the observed peak as being due to monochromatic photons from the radiative transition Υ(3S)→γηb(1S). This photon energy corresponds to an ηb(1S) mass of 9388.9−2.3+3.1(stat)±2.7(syst) MeV/c2. The hyperfine Υ(1S)-ηb(1S) mass splitting is 71.4−3.1+2.3(stat)±2.7(syst) MeV/c2. The branching fraction for this radiative Υ(3S) decay is estimated to be [4.8±0.5(stat)±1.2(syst)]×10−4.Received 7 July 2008DOI:https://doi.org/10.1103/PhysRevLett.101.071801©2008 American Physical Society

IMPROVEMENT OF RENORMALIZATION-SCALE UNCERTAINTIES WITHIN EMPIRICAL DETERMINATIONS OF THE b-QUARK MASS

Accurate determinations of the [Formula: see text]b-quark mass mb(mb) from σ(e+e-→ hadrons ) experimental data currently contain three comparable sources of uncertainty; the experimental uncertainty from moments of this cross-section, the uncertainty associated with αs(Mz), and the theoretical uncertainty associated with the renormalization scale. Through resummation of all logarithmic terms explicitly determined in the perturbative series by the renormalization-group (RG) equation, it is shown that the renormalization-scale dependence is virtually eliminated as a source of theoretical uncertainty in mb(mb). This resummation also reduces the estimated effect of higher-loop perturbative contributions, further reducing the theoretical uncertainties in mb(mb). Furthermore, such resummation techniques improve the agreement between the values of the [Formula: see text]b-quark mass extracted from the various moments of R(s) = σ(e+e-→ hadrons )/σpt [σpt = 4πα2/(3s)], obviating the need to choose an optimum moment for determining mb(mb). Based on this analysis, the resulting value of the b-mass is mb(mb) = 4.207 GeV ± 40 MeV , where the dominant uncertainty now arises from the experimental moments. Resummation techniques are also shown to reduce renormalization-scale dependence in the relation between b-quark [Formula: see text] and pole mass and in the relation between the pole and 1S mass.

MOMENTS OF THE HADRONIC MASS DISTRIBUTION IN SEMILEPTONIC B MESON DECAYS

We present a measurement of the first and second moments of the squared-mass distribution of charm hadrons in semileptonic decays of B mesons based on ~ 180 pb-1 of data taken with the CDF II detector at the Fermilab Tevatron. For a minimum lepton momentum of 0.7 GeV/c in the B meson rest frame, we measure the first two moments of the D** → D(*)π component to be [Formula: see text] and [Formula: see text]. Combining these values with known contributions from the D and D* components, we obtain the overall charm hadron moments [Formula: see text] and [Formula: see text] where [Formula: see text] is the spin-averaged D meson mass and the subscript "BR" denotes the uncertainty from the branching ratios used to combine the D, D* and D** components. From these moments we also determine the non-perturbative Heavy Quark Effective Theory parameters Λ and λ1 in the pole and 1S mass schemes.

Global analysis of inclusiveBdecays

In light of the large amount of new experimental data, we revisit the determination of |V{sub cb}| and m{sub b} from inclusive semileptonic and radiative B decays. We study shape variables to order {Lambda}{sub QCD}{sup 3}/m{sub b}{sup 3} and {alpha}{sub s}{sup 2}{beta}{sub 0}, and include the order {alpha}{sub s} {Lambda}{sub QCD}/m{sub b} correction to the hadron mass spectrum in semileptonic decay, which improves the agreement with the data. We focus on the 1S and kinetic mass schemes for the b quark, with and without expanding m{sub b}-m{sub c} in HQET. We perform fits to all available data from BABAR, BELLE, CDF, CLEO, and DELPHI, discuss the theoretical uncertainties, and compare with earlier results. We find |V{sub cb}| = (41.9 {+-} 0.6 {+-} 0.1{sub {tau}{sub B}}) x 10{sup -3} and m{sub b}{sup 1S} = 4.68 {+-} 0.04GeV, including our estimate of the theoretical uncertainty in the fit.

Reducing theoretical uncertainties inmbandλ1

We calculate general moments of the lepton energy spectrum in inclusive semileptonic B -> X_c l \nu decay. Moments which allow the determination of mb^{1S} and lambda1 with theoretical uncertainties Delta(mb^{1S}) ~ 0.04 GeV and Delta(lambda1) ~ 0.05 GeV^2 are presented. The short distance 1S mass is used to extract a mass parameter free of renormalon ambiguities. Moments which are insensitive to mb and lambda1 and therefore test the size of the 1/mb^3 matrix elements and the validity of the OPE are also presented. Finally, we give an expression for the total branching ratio with a lower cut on the lepton energy, which allows one to eliminate a source of model dependence in current determinations of |Vcb| from B -> X_c l \nu decay.

Dissociation of heavy quarkonia in the quark–gluon plasma

Using a temperature-dependent potential obtained from lattice gauge calculations of Karsch et al, we study the stability of heavy quarkonia in the quark–gluon plasma. We find that only the Υ(1S) and ηb(1S) are bound in the quark–gluon plasma, and have a small binding energy. The quark–gluon plasma may be revealed by an Υ(1S) dilepton peak with an invariant mass close to twice the current b quark mass, which is lower than the Υ(1S) mass in free space. The quarkonia Υ(1S) and ηb(1S) can dissociate by collision with quarks and gluons in the quark–gluon plasma. The Υ(1S) and the ηb(1S) can also dissociate spontaneously at temperatures above the dissociation temperature 1.11 Tc, where Tc is the quark–gluon plasma phase transition temperature. At temperatures slightly above the dissociation temperature these states appear as resonances, which provides another signature for the quark–gluon plasma.

Quarkonium spectroscopy and perturbative QCD: a new perspective

We study the energy spectrum of bottomonium in perturbative QCD, taking alpha_s(Mz)=0.1181 +/- 0.0020 as input and fixing m_b^{MSbar}(m_b^{MSbar}) on the Upsilon(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces reasonably well the gross structure of the spectrum as long as the coupling constant remains smaller than one. We perform a detailed analysis and discuss the size of non-perturbative effects. A new qualitative picture on the structure of the bottomonium spectrum is provided. The lowest-lying (c,cbar) and (b,cbar) states are also examined.

Top-quark pair production close to threshold: Top-quark mass, width, and momentum distribution

The complete NNLO QCD corrections to the total cross section $\sigma(e^+e^- \to Z*,\gamma*\to t\bar t)$ in the kinematic region close to the top-antitop threshold are calculated by solving the corresponding Schroedinger equations exactly in momentum space in a consistent momentum cutoff regularization scheme. The corrections coming from the same NNLO QCD effects to the top quark three-momentum distribution $d\sigma/d |\vec k_t|$ are determined. We discuss the origin of the large NNLO corrections to the peak position and the normalization of the total cross section observed in previous works and propose a new top mass definition, the 1S mass M_1S, which stabilizes the peak in the total cross section. If the influence of beamstrahlung and initial state radiation on the mass determination is small, a theoretical uncertainty on the 1S top mass measurement of 200 MeV from the total cross section at the linear collider seems possible. We discuss how well the 1S mass can be related to the $\bar{MS}$ mass. We propose a consistent way to implement the top quark width at NNLO by including electroweak effects into the NRQCD matching coefficients, which then can become complex.

Charmonium spectroscopy with heavy Kogut-Susskind quarks

Charmonium spectroscopy with Kogut-Susskind valence quarks are carried out for quenched QCD at $\beta=6.0$ and for two-flavor full QCD at $\beta=5.7$. Results for 1P--1S mass splitting and estimates of $\alpha^{(5)}_{\overline{MS}}(m_Z)$ are reported. Problems associated with flavor breaking effects and finite size effects of $1P$ states are discussed.