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eco warrior


- Joined on 01-11-2008

- Posts 377



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A bit more information about vacuum particles
In light of a previous article related to the subject of this paper, the first question that comes to mind is what is special about investigating the property of a meson f0(980) when we already have a list of 300 or so hadrons (or levels in the quark model)? The answer to this question lies in the fact that the meson shares its quantum number with that of vacuum. The light scalar meson having JPC (spin-parity-charge parity) = 0++ is unique among hadrons and has been an enigma in particle physics studies for 40 years. Theoretically, its interplay with vacuum calls for non-perturbative treatments. Experimentally, too many scalar mesons have been observed, and usually, they do not fit well to the simple Breit-Wigner (BW) formula (for a resonace scattering peak representing an unstable particle) with a constant width, a technique that otherwise works well in analyzing hadron data. Recently, however, a simple and unified interpretation of the 0++ scalar mesons has emerged .Although it would be presumptuous to claim that the view has been established, I like it, nevertheless, and will introduce it first; I will then discuss the role of the article in this context.
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According to the emerging interpretation, low-lying ( 1 − 1.5 GeV/c2) 0++ mesons exist not only in the ordinary quark model (qq in spin triplet and in P wave (L = 1 excitation)) but also in a deuteron-like model, drawn schematically in fig.1. Here, four quarks - qq and qq - form a spin singlet color triplet pair. In the color space, they behave exactly like q and q combined into a color singlet. The result is a multi-quark state forming a core of a hadron. However, at the periphery, the multi-quarks rearrange themselves to become a molecule, a bound state of mesons, rather than quarks. When the flavor degree of the quarks (q = u,d,s) are taken into account, they constitute a 0++ nonet. The level structure of the qqqq nonet is inverted as compared to that of the qq pair (fig.2). Gluons, the gauge particles in QCD, can form a bound state (glueball) by themselves because of their nonlinear interaction and further complicate the analysis of observed spectra. However, lattice QCD suggests a relatively large mass of above ∼ 1.5 GeV/c2, somewhat simplifying the picture below 1 GeV/c2.
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Level structure of two 0++ nonets, deuteron-like model (left), and ordinary quark model (right). For the observed states, notation a is used for isospin I=1 triplet, K* for an I =1/2 doublet (and its anti-particle), and f for I = 0 singlet. σ and κ are retained for the sake of old timers. The numbers in parenthesis indicate the mass value in MeV/c2. The level splitting is primarily caused by the mass of the s-quark. κ is not yet established experimentally and there are one too many f0's in the 0++ nonet above 1 GeV/c2, suggesting the existence of a glueball. The three f0's are considered as mixtures of the glueball and two I =0 members of the nonet.
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QCD is believed to be the framework of hadron and nuclear dynamics. QCD has almost exact chiral symmetry, but it is broken by (1) UA(1) anomaly, (2) dynamical symmetry breaking (DSB), and (3) explicit mass term (current mass) of the quarks (which, in turn, is a result of the DSB of the electroweak symmetry due to Higgs). The quarks behave as almost free and weakly interacting particles (asymptotic freedom) at high energies, but at low energies (temperature), they develop a dynamically enhanced mass (constituent mass) with a confining potential that forbids them to separate beyond ∼ 10−13 cm. It is these constituent quarks for which the non-relativistic quark model with spin-spin and spin-orbit interaction as the level splitting potential works well. DSB is induced when a qq pair (in the Nambu-Jona-Lasinio model) or equivalently, a scalar meson generically called σ (in the sigma model), acting as an order parameter in the terminology of condensed matter physics, condenses and develops a new vacuum state. This is analogous to the Cooper pair condensation of the superconductivity. In other words, the vacuum environment has gone through a phase transition at a low temperature. In particle physics, we say that the chiral symmetry has been spontaneously broken and the scalar field has acquired a vacuum expectation value. The observed scalar particles are the residual excitations of the condensed scalar field. The quarks and the scalar mesons acquire dynamical mass, which is a drag effect caused by swimming through the sea of condensed scalar particles.
The pions (or the pseudo-scalar 0−+ nonet when extended to three flavors) are considered as Nambu-Goldstone bosons of the chiral symmetry breaking (a magnon of the magnetic order parameter). Consequently, they have zero mass in principle but acquire additional mass by the explicit mass term of the quarks. This is the reason why 0−+ pseudo-scalar nonet are light and there are a plethora of combinations that can form a vacuum quantum number into which the 0++ scalar meson can decay. Their interplay produces a variety of side effects listed below that distort the shape of the BW formula and make it hard to establish a one-to-one correspondence between the position of the resonance and the scattering intensity (fig. 3).
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| Intensity of the I = J =0 ππ scattering. Notice that there are no simple one-to-one correspondences between the resonance position and the intensity. [The figure is taken from ref. 3] |
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| (a) Fit to the total cross section of γγ → π+π− between 0.8 and 1.5 GeV/c2 (see related article). (b) Contribution of the resonance σ(γγ → π+π−) (solid line) and the interference (dashed line). The cross section of σ(γγ → f0(980) → K+K−) is also shown (dotted line). [The figures are taken from ref.1] |
- The width of σ is very wide, casting the use of BW itself in doubt.
- Many resonances overlap each other.
- When the threshold of a certain combination of 0−+ mesons lies within a resonance width, the interference effect changes the spectral shape of the BW formula (fig. 4), narrowing it or sometimes even making a sharp dip (fig. 3).
- The mass and the width of the resonances are not constant, but change with the energy.
- The chiral symmetry forces the 0−+ − 0−+ meson scattering amplitudes to vanish at a certain low energy point (Adler zero), which also change the shape of the low-energy resonances.
An exact phenomenological treatment is yet to be established. The bottom line is one has to do multi-channel analysis taking all the above effects into account in extracting the resonances from the data.
The level (mass) structure of the scalar mesons is intricately interwoven with the dynamics of vacuum. Clarification of the vacuum dynamics is prerequisite for understanding the low-energy hadron and nuclear physics. If the described concept is correct, the lowest 0++ scalar meson nonet, with 0−+ nonet as its chiral partner, could be understood as the Higgs bosons of the strong interaction. Then the scalar meson dynamics could also be a prelude to the upcoming Higgs dynamics should the Large Hadron Collider (LHC) at CERN find it. This is why precise high-statistics data in a variety of specific channels like the one of the related article are important. There, a resonance is picked up in the γγ → π+π− channel where the charge parity C = + and no J = 1 state is allowed. It is a simple and clear reaction process where theoretical interpretation is easier. The acquired statistics is two orders of magnitude higher when compared to previous experiments. This allowed the authors to determine precisely the shape of the γγ → π+π− partial wave amplitude and extract the exact parameters of the f0(980) resonance from the distorted BW shape of the experimental data (fig. 4). It may be said we are one step closer to the understanding of vacuum.
Did this one for my science homework...............only joking.
Eco Warrior 
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The use of solar energy has not been opened up because the oil industry does not own the sun.
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