We study the loosely bound Skyrme model with the addition of two different pion mass terms; this is the most general potential of polynomial form up to second order in the trace of the Skyrme field. The two pion mass terms are called the standard pion mass term and the modified pion mass term. We find that the binding energies are not reduced by the introduction of the modified pion mass, but it is analogous to the standard pion mass term with a decrease in the value of the mass parameter of the loosely bound potential (for large values of the latter parameter). We find by increasing the overall pion mass that we can reduce the classical binding energy of the 4-Skyrmion to the 2.7% level and the total binding energy including the contribution from spin-isospin quantization is reduced to the 5.8% level.
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