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Register a new userPFA(S)[S] for the masses
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Franklin D. Tall
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We present S. Todorcevics method of forcing with a coherent Souslin tree over restricted iteration axioms as a black box usable by those who wish to avoid its complexities but still access its power.
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We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of omega_1 and in which all separable closed subspaces are Lindelof.
We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of every locally compact, perfectly normal space is paracompact.
In this work, we perform a systematical investigation about the possible hidden and doubly heavy molecular states with open and hidden strangeness from interactions of $D^{(*)}{bar{D}}^{(*)}_{s}$/$B^{(*)}{bar{B}}^{(*)}_{s}$, ${D}^{(*)}_{s}{bar{D}}^{(*)}_{s}$/${{B}}^{(*)}_{s}{bar{B}}^{(*)}_{s}$, ${D}^{(*)}D_{s}^{(*)}$/${B}^{(*)}B_{s}^{(*)}$, and $D_{s}^{(*)}D_{s}^{(*)}$/$B_{s}^{(*)}B_{s}^{(*)}$ in a quasipotential Bethe-Salpeter equation approach. The interactions of the systems considered are described within the one-boson-exchange model, which includes exchanges of light mesons and $J/psi/Upsilon$ meson. Possible molecular states are searched for as poles of scattering amplitudes of the interactions considered. The results suggest that recently observed $Z_{cs}(3985)$ can be assigned as a molecular state of $D^*bar{D}_s+Dbar{D}^*_s$, which is a partner of $Z_c(3900)$ state as a $Dbar{D}^*$ molecular state. The calculation also favors the existence of hidden heavy states $D_sbar{D}_s/B_sbar{B}_s$ with spin parity $J^P=0^+$, $D_sbar{D}^*_s/B_sbar{B}^*_s$ with $1^{+}$, and $D^*_sbar{D}^*_s/B^*_sbar{B}^*_s$ with $0^+$, $1^+$, and $2^+$. In the doubly heavy sector, the bound states can be found from the interactions $(D^*D_s+DD^*_s)/(B^*B_s+BB^*_s)$ with $1^+$, $D_sbar{D}_s^*/B_sbar{B}_s^*$ with $1^+$, $D^*D^*_s/B^*B^*_s$ with $1^+$ and $2^+$, and $D^*_sD^*_s/B^*_sB^*_s$ with $1^+$ and $2^+$. Some other interactions are also found attractive, but may be not strong enough to produce a bound state. The results in this work are helpful for understanding the $Z_{cs}(3985)$, and future experimental search for the new molecular states.
Isochronous mass spectrometry has been applied in the storage ring CSRe to measure the masses of the $T_z=-3/2$ nuclei $^{27}$P and $^{29}$S. The new mass excess value $ME$($^{29}$S) $=-3094(13)$~keV is 66(52)~keV larger than the result of the previous $^{32}$S($^3$He,$^{6}$He)$^{29}$S reaction measurement in 1973 and a factor of 3.8 more precise. The new result for $^{29}$S, together with those of the $T=3/2$ isobaric analog states (IAS) in $^{29}$P, $^{29}$Si, and $^{29}$Al, fit well into the quadratic form of the Isobaric Multiplet Mass Equation IMME. The mass excess of $^{27}$P has been remeasured to be $ME(^{27}$P$)=-685(42)$ keV. By analyzing the linear and quadratic coefficients of the IMME in the $T_z=-3/2$ $sd$-shell nuclei, it was found that the ratio of the Coulomb radius parameters is $Rapprox0.96$ and is nearly the same for all $T=3/2$ isospin multiplets. Such a nearly constant $R$-value, apparently valid for the entire light mass region with $A>9$, can be used to set stringent constraints on the isovector and isotensor components of the isospin non-conserving forces in theoretical calculations.
The branching fraction of the decay $B_{s}^{0} rightarrow D_{s}^{(*)+}D_{s}^{(*)-}$ is measured using $pp$ collision data corresponding to an integrated luminosity of $1.0fb^{-1}$, collected using the LHCb detector at a centre-of-mass energy of $7$TeV. It is found to be begin{align*} {mathcal{B}}(B_{s}^{0}rightarrow~D_{s}^{(*)+}D_{s}^{(*)-}) = (3.05 pm 0.10 pm 0.20 pm 0.34)%, end{align*} where the uncertainties are statistical, systematic, and due to the normalisation channel, respectively. The branching fractions of the individual decays corresponding to the presence of one or two $D^{*pm}_{s}$ are also measured. The individual branching fractions are found to be begin{align*} {mathcal{B}}(B_{s}^{0}rightarrow~D_{s}^{*pm}D_{s}^{mp}) = (1.35 pm 0.06 pm 0.09 pm 0.15)%, ewline{mathcal{B}}(B_{s}^{0}rightarrow~D_{s}^{*+}D_{s}^{*-}) = (1.27 pm 0.08 pm 0.10 pm 0.14)%. end{align*} All three results are the most precise determinations to date.
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