INTRODUCTION

Conventional wisdom has established the K*(892) meson as an excited (J = 1) state of the K meson. As such, the neutral mode of the K*(892), the K*(892)⁰, is thought to involve a bound state of the down (d) quark and the strange (s) anti-quark (s*). Its anti-particle, herein designated by [K*(892)⁰]*, involves, therefore, d* and s, again, by conventional wisdom (PDG (2004), p. 20). Meanwhile, the charged mode of the K*(892), the K*(892)^±, would be characterized by a bound state of the up (u) quark and the s* or vice versa, i.e., u* and s (PDG (2004), p.20). According to PDG (2004), p.28, the K*(892) decays nearly 100% into various πK products, and, presumably through the use of coincidence analysis, experiments indicate that decays involving no net charge associated with the decay products take place at essentially the same rate as decays involving one unit of charge associated with same, as the decay width, Γ₀, of the K*(892)⁰ is inferred to be essentially the same as the decay width, Γ_±, of the K*(892)^± ((50.7 ± 0.6) Mev vs. (50.8 ± 0.9) Mev, respectively). Also according to PDG (2004), p. 28, the neutral decay mode is associated with a meson mass of 896 Mev, the mass, M₀, of the K*(892)⁰, while the charged decay mode stems from a meson mass of 892 Mev, the mass, M_±, of the K*(892)^±.

Above is recounted, as noted, the conventional wisdom straight out of PDG (2004) and as it has been expressed in the literature for decades concerning the K*(892). Below, we wish to apply some “unconventional wisdom” to the situation, the results of which will show that a reinterpretation as to the structure of the K*(892) appears to be in order. Specifically, assuming the context of high-energy colliding beams as providing for meson production, we apply the Gluon Emission Model (GEM) to the situation involving the K*(892). (For literature as to the roots of the Gluon Emission Model and its early application to hadron production phenomena see Close (1979) and White (1985).) Since J = 1 for the K*(892), the stated application of GEM is valid, as we may assume that the K*(892) arises via quark spin-flip with accompanying gluon emission (see White (2008) and Dalitz (1977)).

The particular value realized through the application of GEM is that it yields a formula for the width of any J = 1 meson in its ground state, a formula which is highly sensitive to the assumed quark structure of the given J = 1 meson under consideration. Specifically, GEM–determined widths are each proportional to Σ_i (q_i)⁴, where i represents a generic quark type (u, d, or s herein) comprising the decay products common to the meson and q_i represents the basic unit of charge of the given quark type in units of the proton charge, i.e., q_u = 2/3, q_d = 1/3, and q_s = 1/3.

Hence, the conventionally–assumed quark structure of the K*(892)⁰ and the K*(892)^± can be used for GEM width formulas, the theoretical results then compared with experimental determinations. We will find significant discrepancies with “conventional wisdom”, to be sure. However, GEM will allow for a new picture as to the structure of the K*(892) – one that is as simple as it is reasonable.

APPLICATION OF GEM

From White (2008), Eq. 4, the GEM formula governing the width, Γ_v(GEM), of any conventional vector meson, v, of mass, m_v, in its ground state is given by:

Γ_v(GEM) ≅ (1960 Mev)(m_ρ/m_v)³(Σ_i(q_i)⁴)[ln(m_v/50 Mev)]^-1, (1)

where m_ρ = 776 Mev = mass of the ρ meson (PDG (2004), p. 4). As noted in White (2008), however, the K*(892) is not a “conventional” vector meson, because it has an isospin value of (1/2), and so unlike the “conventional” vector mesons such as the ρ, the φ, the J, and the ϒ, half of the K*(892)’s energetically allowed decay routes are forbidden, i.e., decays into a pion and a kaon are allowed, but decays into pion pairs are not. (For a discussion on isospin, see Ohanian (1987), pp. 439 – 441.) For the time being, considering the K*(892) as a composite structure of charged and neutral modes of average mass, 894 Mev, we postulate that its width is given by Eq. 1 above with the sum over q_i⁴ as q_u⁴ + q_d⁴ + q_s⁴ = 18/81, except that we must multiply the right hand side by (18/35), because, as a composite structure, u, d, and s quark types are common both to the meson and its collection of allowed decay products, whereas the forbidden route only involves u and d quarks in the decay products, so that the relevant sum over q_i⁴ would be 17/81. Hence, the allowed route is favored over the forbidden one by the factor 18 to 17 (see White (2008), Section IV). Denoting the width of the composite structure as determined by GEM as Γ_C(GEM), we find from Eq. 1

Γ_C(GEM) ≅ (18/35)(1960 Mev)(776/894)³(18/81)[ln(894/50)]^-1 ≅ 50.80 Mev, (2a)

a figure certainly well representative of the experimentally determined width of either the K*(892)⁰ or the K*(892)^± noted in the Introduction.

Now, building upon the composite structure idea, if we consider the K*(892)⁰ as a linear combination of u, d and s quark / anti-quark pairs – much in keeping with the description of the ρ as a linear combination of uu* and dd* objects, or of the ϕ as a linear combination of ss* (forming its kaon branch), uu* and dd* (together forming its non-kaon branch) objects – whose decay products bear no net charge, we can invoke GEM to obtain the theoretical width of the K*(892)⁰ under the above assumption. Specifically, denoting its GEM–determined width as Γ₀(GEM), we find:

Γ₀(GEM) ≅ (18/35)(1960 Mev)(776/896)³(18/81)[ln(896/50)]^-1 ≅ 50.42 Mev, (2b)

a figure well in accord with the experimental finding of (50.7 ± 0.6) Mev noted in the Introduction.

Proceeding similarly with the K*(892)^±, whose decay products would bear, of course, one unit of charge and denoting its GEM–determined width as Γ_±(GEM), we find:

Γ_±(GEM) ≅ (18/35)(1960 Mev)(776/892)³(18/81)[ln(892/50)]^-1 ≅ 51.18 Mev, (2c)

a figure also well in accord with the experimental finding of (50.8 ± 0.9) Mev noted above in the Introduction.

Obviously, to consider the K*(892)⁰ as a construction containing only the (conventionally assumed) d and s quark types would not lead to an accurate width determination of it via GEM by any stretch of the imagination. The term involving the sum over quark charges would be only “(2/81)”, thus producing the corresponding “weight factor” (scaling the allowed decay route) of “(2/(2 + 1))” = “(2/3)”, since only the d quark type would be common to both the forbidden decay products (pions) and the meson. The resulting width of the K*(892)⁰ as determined by GEM would thus be only 7.26 Mev. Neither would considering the K*(892)^± as a construction containing only the (conventionally assumed) u and s quark types give via GEM a determination of its width as accurate as seen in Eq. 2c. Here, the term involving the sum over quark charges would be “(17/81)”, thus producing a “weight factor” of “(17/(17 + 16))” = “(17/33)”, since, here, only the u quark type would be common to both the forbidden decay products (again, pions) and the meson. The resulting width of the K*(892)^± as determined via GEM would be 48.42 Mev, a figure lying outside the range of experimental uncertainty. The most reasonable and, in our view, correct assumption as to the actual structure of the K*(892), as indicated by GEM, therefore, would be that it comprises a composite structure of uu*, dd*, and ss* in equal measure.

DISCUSSION OF RESULTS

The structure indicated by GEM for the K*(892) – charged mode or uncharged mode - i.e., a linear combination of uu*, dd*, and ss* in equal measure, we will represent by

χ = (1/√3)(uu* + dd* + ss*). (3)

As such, the K*(892) would not be characterized as a “strange meson” in the usual sense, as said term usually denotes a structure of the form, χ_s = sx* (or s*x), where “x” denotes a given type of quark other than “s”. Indeed, χ is much more akin to the theoretical structures of the light, unflavored vector mesons, such as the ρ and the ϕ. If one assumes the decay of χ takes place via s (or s*) joining either u* (or u) or d* (or d) on a random basis, all possible Kπ decay products would show up with equal probability, such in keeping with the widths of the charged mode and neutral mode being essentially equal. Under our assumptions it is thus seen that all possible Kπ products are realized in all possible permutations with equal likelihood – consistent with experimental findings. Hence, it appears eminently evident that the K*(892) is not “strange” at all. Rather, it clearly should be regarded as just another one of the garden variety light, unflavored vector mesons – joining ρ, ω, and φ as the third most massive in the group of four such objects.

CONCLUDING REMARKS

In a sense, GEM has provided for the discovery (perhaps “uncovery” would be a better word) of a “missing link” between the ρ/ω and the φ. The ρ and ω, for instance, are theoretically constructed from linear combinations of uu* and dd* structures, and, in keeping with that, give rise to various π decay products (no Ks). The φ, on the other hand, is thought to be a linear combination of uu*, dd*, and ss* objects, similar to our suggested construction of the K*(892) (see Eq. 3), but the φ is massive enough to decay into two kaons, which it does predominately. So, the predominant decay mode of the φ is characterized by s joining u* and the associated s* joining u, for example, so that two Ks can be emitted. Where is the vector meson less massive than the φ but more massive than the ρ/ω which can give rise to the intermediate type of decay, i.e., a π plus a K? It’s quite a mystery once one begins to think about it! However, much as Arthur Conan Doyle’s famous purloined letter, we believe the missing meson can be found in plain view for anyone who really looks for it: It’s right there on page 28 of PDG (2004) for all to see.

REFERENCES

1) PDG (2004) “Mesons”, accessed online November 7, 2008, http://pdg.lbl.gov/2004/tables/mxxx.pdf

2) White, D. (2008) “The Gluon Emission Model for Hadron Production Revisited”, Journal of Interdisciplinary Mathematics, 11 (4), pp. 543 - 551.

3) Close, F. (1979) An Introduction to Quarks and Partons, Academic Press.

4) White, D. (1985) “Calculation of the Strong Coupling Constant, α_s, from Considerations of Virtual Synchrotron Radiation Resulting in Hadron Pair Emission”, International Journal of Theoretical Physics, 24 (2), pp. 201 - 216.

5) Dalitz, R. H. (1977) “Glossary for New Particles and New Quantum Numbers”, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 355 (1683), p. 601.

6) Ohanian, H. C. (1987) Modern Physics, Second Edition, Prentice Hall, pp. 439 – 44

This article was originally published in the Journal of Applied Global Research. It is reprinted here courtesy of Dr. David King and the IntellectBase International Consortium.