Mass Spectra of Charm-Strange Hadronic States in a Screened Potential Model

V from the hadronic invariant mass spectrum in semileptonic B decay

On the systematic errors of the pseudofermion algorithm

In this article, we utilise the non-relativistic potential model to calculate the mass-spectra of all bottom [ $$bb][{\bar{b}}{\bar{b}}$$ ] and heavy-light bottom [ $$bq][{\bar{b}}{\bar{q}}$$ ] (q = u,d) tetraquark states in diquark–antidiquark approximation. The four-body problem is reduced into two body problem by numerically solving the $$Schr\ddot{o}dinger$$ equation using a Cornell-inspired potential along with relativistic correction term. The splitting structure of the tetraquark spectrum is described using spin-dependent terms (spin-spin, spin-orbit, and tensor). We have successfully calculated and predicted the masses of bottom mesons, diquarks and tetraquarks. The masses of S and P-wave tetraquark states [ $$bb][{\bar{b}}{\bar{b}}$$ ] and [ $$bq][{\bar{b}}{\bar{q}}$$ ], respectively, are found to be between 18.7–19.4 GeV and 10.4–11.3 GeV, in which the masses of S-wave [ $$bb][{\bar{b}}{\bar{b}}$$ ] states are less than the 2 $$\eta _{b}$$ , $$\eta _{b}\Upsilon $$ , and 2 $$\Upsilon $$ threshold. Additionally, we have investigated the $$Z_b(10610)$$ and $$Z_ b(10650)$$ states in the current model and found that they are 150 MeV below the $$BB^{*}$$ and $$B^{*}B^{*}$$ thresholds.

We construct an extended version of the linear sigma model in such a way as to describe spin-1 hadrons as well as spin-0 hadrons in two-color QCD (QC2D) by respecting the Pauli-Gürsey SU(4) symmetry. Within a mean-field approximation, we therefrom examine a mass spectrum of the spin-1 hadrons at finite quark chemical potential (μq) and zero temperature. Not only mean fields of scalar mesons and scalar-diquark baryons but also of vector mesons and vector-diquark baryons are incorporated. As a result, we find that, unless all of those four types of mean fields are taken into account, neither lattice result for the critical μq that corresponds to the onset of baryon superfluidity nor for μq dependence of the pion mass can be reproduced. We also find that a slight suppression of the ρ meson mass in the superfluid phase, which was suggested by the lattice simulation, is reproduced by subtle mixing effects between spin-0 and spin-1 hadrons. Moreover, we demonstrate the emergence of an axial-vector condensed phase and possibly of a vector condensed phase by identifying the values of μq at which the corresponding hadron masses vanish. The possible presence of isotriplet 1− diquarks that may be denoted by a tensor-type quark bilinear field is also discussed. Published by the American Physical Society 2024

It is suggested that the general form of the hadronic mass spectrum can be determined by studying the decay of hot hadronic matter produced in very-high-energy nuclear collisions. In a thermodynamic model we find that at presently attainable energies the temperature and the hadron populations in the matter depend strongly on the form of the hadronic spectrum.

We present an extended discussion of the previously noted possibility to extract |V_{ub}| from an analysis of the hadronic recoil mass spectrum in B->X_u l nu decays. Invariant mass spectra containing perturbative as well as nonperturbative corrections are given; their shape is manifestly sensitive to the three basic quantities mu_pi^2, m_b, and alpha_s$, whereas the total integrated rate is much less so. Only a small fraction of b->u transitions generates a recoil mass M_X of at least M_D. We find that the fraction of events with M_X < 1.5 GeV (to reject leakage from b->c) exhibits fairly little dependence on mu_pi^2, m_b and alpha_s; |V_{ub}| can then be extracted in a largely model-insensitive way. This conclusion is based on the applicability of the OPE to actual semileptonic B decays. A direct cross-check of this assumption and a determination of the required basic parameters of the heavy quark expansion will be possible in the future with more experimental data.

Finite temperature lattice simulations of quantum chromodynamics (QCD) are sensitive to the hadronic mass spectrum for temperatures below the "critical" temperature T(c) ≈ 160 MeV. We show that a recent precision determination of the QCD trace anomaly shows evidence for the existence of a large number of hadron states beyond those known from experiment. The lattice results are well represented by an exponentially growing mass spectrum up to a temperature T=155 MeV. Using simple parametrizations of the hadron mass spectrum we show how one may estimate the total spectral weight in these yet undermined states.

Thermodynamics of hadronic matter at high density

In Chapter XI, we studied the problem of hadronic mass spectra and concluded that it is safe to believe that hadrons are quantum bound states of quarks having localized probability distribution. As in all bound state cases, this localization condition is reponsible for the existence of discrete mass spectra. Therefore the hadronic mass spectra plays a very important role in demonstrating that hadrons are quantum bound states of quarks.

Hadron collisions above ∼10 GeV/c primary laboratory momentum show an interesting global aspect (i.e. when averaged over all final channels): they can be described as a superposition of a rather special form of thermodynamics and of the kinematics of collective motions in the forward-backward direction. The thermodynamical behaviour is similar to that of boiling; the boiling temperatureT 0 is not exactly known but near to 160 MeV; its value and the whole thermodynamic behaviour of hadronic matter follow uniquely from the hadronic mass spectrum. Namely, in this model, as a consequence of a kind of asymptotic bootstrap involving all hadrons, the mass spectrum of hadrons turns out to grow necessarily like exp [m/T 0] whereT 0 is the highest possible temperature (boiling point of hadronic matter). Global aspects of hadron collisions from ∼10 GeV/c up to the highest cosmic-ray primary momenta (>105 GeV/c) namely: production rates, differential momentum spectra of secondaries, transverse-momentum distributions, etc., agree well with the calculations based on this model. The known part of the hadronic mass spectrum does indeed grow exponentially and the mean transverse momenta of pions produced between 10 and 105 GeV/c primary momentum correspond toT≈120 to 160 MeV. The following speculative picture emerges: these seems to exist a highest temperature (or boiling point of hadronic matter)T 0≈160 MeV; hadronic matter in collisions above some ten GeV/c primary momentum is in a state whereall hadrons melt by way of a universal hadronic bootstrap, into «boiling hadronic matter» in which strong collective motions in the direction of the collision axis coexist with local thermodynamical equilibrium.

We present, using the statistical model, a new analysis of hadron production in central collisions of heavy nuclei. This study is motivated by the availability of final measurements both for the SPS (beam energies 20–160 AGeV) and for the RHIC energies (sNN=130 and 200 GeV) and by updates in the hadron mass spectrum, which is a crucial input for statistical models. Extending previous studies by inclusion of very high-mass resonances (m>2 GeV), and the up-to-now neglected scalar σ meson leads to an improved description of the data. In particular, the hitherto poorly reproduced energy dependence of the K+/π+ ratio at SPS energies (“the horn”) is now well described through the connection to the hadronic mass spectrum and, implicitly, Hagedorn's limiting temperature. We thereby demonstrate the intimate connection between the horn and the QCD phase transition.

In this paper we investigate the hadronic mass spectra of inclusive B decays. Specifically, we study how an upper cut on the invariant mass spectrum, which is necessary to extract V_{ub}, results in the breakdown of the standard perturbative expansion due to the existence of large infrared logs. We first show how the decay rate factorizes at the level of the double differential distribution. Then, we present closed form expressions for the resummed cut rate for the inclusive decays B -&gt; X_s gamma and B -&gt; X_u e nu at next-to-leading order in the infrared logs. Using these results, we determine the range of cuts for which resummation is necessary, as well as the range for which the resummed expansion itself breaks down. We also use our results to extract the leading and next to leading infrared log contribution to the two loop differential rate. We find that for the phenomenologically interesting cut values, there is only a small region where the calculation is under control. Furthermore, the size of this region is sensitive to the parameter mass spectrum.

We investigate systematics of the freezeout surface in heavy ion collisions due to the hadron spectrum. The role of suspected resonance states that are yet to be confirmed experimentally in identifying the freezeout surface has been investigated. We have studied two different freezeout schemes - unified freezeout scheme where all hadrons are assumed to freezeout at the same thermal state and a flavor dependent sequential freezeout scheme with different freezeout thermal states for hadrons with or without valence strange quarks. The data of mean hadron yields as well as scaled variance of net proton and net charge distributions have been analysed. We find the freezeout temperature $T$ to drop by $\sim5\%$ while the dimensionless freezeout parameters $\mu_B/T$ and $VT^3$ ($\mu_B$ and $V$ are the baryon chemical potential and the volume at freezeout respectively) are insensitive to the systematics of the input hadron spectrum. The observed hint of flavor hierarchy in $T$ and $VT^3$ with only confirmed resonances survives the systematics of the hadron spectrum. It is more prominent between $\sqrt{s_{NN}}\sim10 - 100$ GeV where the maximum hierarchy in $T\sim10\%$ and $VT^3\sim40\%$. However, the uncertainties in the thermal parameters due to the systematics of the hadron spectrum and their decay properties do not allow us to make a quantitative estimate of the flavor hierarchy yet.

We calculate the hadronic tensor for inclusive semileptonic B decay to O(alpha_s). This allows O(alpha_s Lambda_{QCD}/mb) corrections to hadronic invariant mass observables to be directly evaluated with experimentally required cuts on phase space. Several moments of phenomenological interest are presented to O(alpha_s Lambda_{QCD}/mb) and O(Lambda_{QCD}^3/mb^3), allowing a consistent extraction of the HQET parameters up to O(Lambda_{QCD}^3/mb^3) and the b quark mass with theoretical error ~ 50 MeV. The hadronic invariant mass spectrum is examined with a general moment to obtain observables that test the theoretical error estimate assigned to these parameters; in particular, fractional moments that directly test the OPE for inconsistencies in the hadronic invariant mass spectrum are reported. The mb Lambda_{QCD}/mc^2 expansion present for fractional moments of the hadronic invariant mass spectum is discussed and shown to introduce a numerically suppressed uncertainty of O(mb^4 Lambda_{QCD}^4/mc^8).

We study the hadronic form factors of the τ lepton decays |$\tau \rightarrow K \pi (\eta) \nu $|⁠. We compute one-loop corrections to the form factors using the chiral Lagrangian including vector mesons. The counterterms that subtract the divergence of the one-loop amplitudes are determined by using the background field method. In the vector form factor, K* resonance behavior is reproduced because a diagram with a vector meson propagator is included. We fit the data of the hadronic invariant mass spectrum measured by Belle by determining some of the counterterms of the Lagrangian. Besides the hadronic invariant mass spectrum, forward–backward asymmetry is predicted. We also study the effect of CP violation of a two Higgs doublet model. In the model, CP violation of the neutral Higgs sector generates the mixing of CP-even Higgs and CP-odd Higgs. We show how the mixing leads to direct CP violation of the τ decays and predict the CP violation of the forward–backward asymmetry.