  Recently, the ALICE collaboration analyzed the three- and four-pion Hanbury
Brown-Twiss (HBT) correlations in Pb-Pb collisions at the Large Hadron Collider
(LHC). The measured suppressions of three- and four-pion correlations may
originate from a substantial coherence of the particle-emitting sources. In
this work we investigate the normalized three- and four-pion HBT correlation
functions for evolving pion gas (EPG) sources with Bose-Einstein condensation.
We find that the intercepts of the normalized correlation functions at zero
relative momentum are sensitive to source condensation and particle momentum.
The normalized correlation functions in low average-momentum regions of three
and four pions decrease with decreasing temperature and increasing particle
number of the source, indicating a dependence of the normalized correlation
functions on source condensation. However, this dependence becomes weak in an
intermediate average-momentum region because particles with high momenta are
likely emitted from excited states incoherently in the EPG model, even if the
source has a considerable condensation fraction. For a wide momentum range, the
normalized correlation functions for low source temperatures are enhanced at
larger relative momenta because of a rapid increase of two-pion chaoticity
parameter with increasing particle momentum. We hope the significant
enhancement of the normalized four-pion correlation function at high relative
momentum will be identified through future analyses of experimental data.
