^{1}

^{2}

^{3}

^{3}.

We study the thermodynamics of the strange baryon system by using an

It was conjectured a long time ago that thermodynamics of hadrons can be understood in terms of the hadron resonance gas (HRG) model

Around the time of the original Hagedorn proposal, a more systematic approach to study thermodynamics of hadrons was proposed by Dashen, Ma, and Bernstein—the

The

It is natural to expand the previous

We show that the proper treatment of resonances in the

Before getting into the details of extracting an effective phase shift from a full-fledged coupled-channel PWA for the

Consider the following fact of a unitary

Using

The determinant operation makes this quantity invariant under any unitary rotation

In the single-channel case

In this parametrization,

A direct calculation shows that the phase-shift function

We see that

This means that the “observed”

Note that

To obtain other channel-specific quantities, we compare the model

The inelasticity parameter

In Fig.

(a) Phase shifts [Eq.

Furthermore, we examine the effective and standard spectral functions of the model, defined as

The effective spectral functions within a channel can be computed via
^{1}

Note that

We briefly summarize the key features of the effective spectral function

One observes irregularities in the

(a) Total and channel-specific effective and (b)standard spectral functions defined in Eq.

The apparent “shift” of the strength towards lower invariant masses of

The parametrization for the resonance decay presented in Eqs.

Note that the definition for energy dependent branching fractions in Eq.

In an actual PWA, the

The simple example just presented motivates a robust way to extract, for a coupled-channel system, an effective phase shift function

According to the

In the

The interaction contribution

In this paper we are interested in the pressure of strange baryons. The dominant contribution to the strange baryon pressure comes from

The

Taking into account that

Here

The first term in Eq.

To evaluate the effective phase shift function

In terms of PWA one can write

The generalized phase shift function

The effective spectral functions

With the extracted effective spectral functions

The pressure (normalized to

The contributions to

Pole masses and widths of the

We also investigated the question to what extent taking into account the width of the resonances as constants via a simple B-W parametrization, i.e.,

Note that the HRG approximation discussed above and labeled as HRG PWA is different from standard HRG model which uses only well-established resonances, i.e., four and three star resonances, from PDG

So far, we did not discuss the contribution of

The contribution from different partial waves to

In the previous section we compared the pressure of

The second-order baryon strangeness correlations,

However the agreement remains incomplete, and we see that further interaction strength in the strange baryon system is needed to reproduce the LQCD results. This may come from an improved analysis of the

The enhancement may also come from an improved treatment of the

Previously

It would be interesting to study higher-order baryon strangeness correlations, e.g.,

In this paper the partial pressure of strange baryons and baryon-strangeness correlations have been discussed within the

C.F.R. was partly supported by PAPIIT-DGAPA (UNAM, Mexico) Grant No. IA101717 and CONACYT (Mexico) Grant No. 251817. P.M.L. was partly supported by the Polish National Science Center (NCN), under Maestro Grant No. DEC-2013/10/A/ST2/00106 and by the Short Term Scientific Mission (STSM) program under COST Action CA15213 (Ref. No. 41977). P.P. was supported by U.S. Department of Energy under Contract No. DE-SC0012704. We used the web interface of the DATA analysis Center at George Washington University (