What "excites" Sigma, Xi' baryons ?

[Widdekind]

Please ponder the following "scalar" (S = 1/2) baryons (3 quarks):

 

[math]\Lambda^0 (uds)[/math] (

1116 MeV

)

[math]\Sigma^0 (uds)[/math] (

1193 MeV

)

 

Both are comprised of the same set of quarks (uds), and both have the same Spin (1/2). Yet, the latter is some 77 MeV more massive than the former, into which it typically decays by simple photon emission:

 

[math]\Sigma^0 \to \Lambda^0 + \gamma[/math]

 

This decay does not produce particles, like combinations of quarks or electrons + neutrinos, strongly suggesting that the [math]\Sigma^0[/math] state is a purely Electromagnetic excitation of the [math]\Lambda^0[/math].

 

 

Likewise, let us look at the charmed-Xi & charmed-Xi-prime pair(s) (also "scalar" (S=1/2) Spin (ground-)states):

 

[math]\Xi_c^{+} (usc)[/math] (

2468 MeV

)

[math]\Xi_c^{+'} (usc)[/math] (

2575 MeV

)

 

[math]\Xi_c^{0} (dsc)[/math] (

2471 MeV

)

[math]\Xi_c^{0'} (dsc)[/math] (

2578 MeV

)

 

Being about 107 MeV more massive, these "primed" particles also typically decay down into their respective "unprimed" partners, via apparently purely Electromagnetic photon emssion:

 

[math]\Xi_c^{+'} \to \Xi_c^{+} + \gamma[/math]

[math]\Xi_c^{0'} \to \Xi_c^{0} + \gamma[/math]

 

Without affecting the relative orientations of their constituent quarks' Magnetic Moments (arising from their Spins, which are fixed, for these "scalar" ground-states (S=1/2)), what kind of Electromagnetic interaction could account for these [math]\Sigma^0[/math] & [math]\Xi_c^{'}[/math] "excited" states ??

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Decay from "lateral re-arrangement" of Quarks ?

 

Arguing from a completely classical picture, the lowest energy state, both Electrostatically & Magnetically, would be "charge (& Magnetic Moment) symmetric":

 

[math]\Lambda^0 (d \uparrow u \downarrow s \uparrow)[/math]

 

[math]\Xi_c^0 (d \uparrow c \downarrow s \uparrow)[/math]

 

But, were one to "laterally rearrange" those quarks:

 

[math]\Lambda^0 (d \uparrow u \downarrow s \uparrow) \to (d \uparrow s \uparrow u \downarrow )[/math]

 

[math]\Xi_c^0 (d \uparrow c \downarrow s \uparrow) \to (d \uparrow s \uparrow c \downarrow)[/math]

 

then one could conceivably construct a purely Magnetically excited state, somewhat less Electromagnetically bound, and so somewhat more massive. The following figure attempts to illustrate this simple suggestion (completely qualitatively):

 

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Note that the [math]\Xi_c^0 (dcs)[/math] is a "Generational excitation" of the [math]\Lambda^0 (dus)[/math], where the 1^st Generation u [math]\to[/math] 2^nd Generation c. And, both behave somewhat similarly. So, "going with the flow", one could start to suspect, that a further "Generational excitation", of the [math]\Xi_c^0 (dcs) \to \Omega_c^0 (scs)[/math] (or [math]\to \Xi_{cb}^0 (dcb)[/math]), might mean, that that charmed Omega-zero baryon (or charmed-bottom-Xi-zero) might also display some sort of similar excited state, producing a purely photon emission decay. However, it seems that this suggested decay has not been observed in the [math]\Omega_c^0[/math]. Yet, the [math]\Xi_{cb}^{0'}[/math] has been observed, as the "charmed-bottom-Xi-zero-prime", although its particular properties yet await measurement. (Then, since "Generational excitations" seem to work, why not consider a "Generational de-excitation", from the [math]\Lambda^0 (uds)[/math] to the neutron (udd) ?? Are there any unusual excitation states of the neutron , based upon the pattern, w/ probable mass about 1000 MeV ??)

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List of the "neutron-like" neutral baryons

 

[math]n^0[/math]

(

udd

) (

940 MeV

)

 

[math]\Lambda^0[/math] (

ud

s

) (

1116 MeV

)

[math]\Sigma^0[/math] (

ud

s

) (

1193 MeV

)

 

[math]\Xi_c^{+}[/math] (

u

sc

) (

2468 MeV

)

[math]\Xi_c^{+'}[/math] (

u

sc

) (

2575 MeV

)

 

[math]\Xi_c^{0}[/math] (

d

sc

) (

2471 MeV

)

[math]\Xi_c^{0'}[/math] (

d

sc

) (

2578 MeV

)

 

[math]\Omega_c^0[/math]

(

scs

) (

2698 MeV

)

 

[math]\Xi_{cb}^0[/math] (

d

c

b

)

[math]\Xi_{cb}^{0'}[/math] (

d

c

b

)

 

From this, one can quickly see, that the "Generationally symmetric" neutral baryons -- those whose quarks come all from the same Generation ([math]n^0, \Omega_c^0[/math]) -- show no ~100 MeV excitation state.

 

In the case of the neutron, Magnetic Moment interactions demand that all 3 quarks' Magnetic Moments are parallel, produced when the lone up quark Spins anti-parallel: [math]n^0 (d \uparrow u \downarrow d \uparrow)[/math]. But, in the more massive, "Generationally asymmetric", neutral baryons, perhaps the more massive quarks aren't quite as constrained, leading to excited (S=1/2) spin states, along the lines of [math]\Sigma^0 (d \uparrow u \downarrow s \downarrow)[/math] vs. [math]\Lambda^0 (d \uparrow u \downarrow s \uparrow)[/math] ???

Edited June 12, 2010 by Widdekind
Consecutive posts merged.