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Register a new userNuclides as a liquid phase of $SU(2)_L times SU(2)_R$ chiral perturbation theory I: emergence of pion-less SU(2) $chi$ PT
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The Standard Model of particle physics, augmented with neutrino mixing, is at least very nearly the complete theory of interactions of known particles at energies accessible to Nature on Earth. Candidate effective theories of nuclear structure must therefore reflect SM symmetries, especially the chiral global $SU(2)_L times SU(2)_R$ symmetry of two-massless-quark QCD. For ground-state nuclei, SU(2) chiral perturbation theory (XPT) enables perturbation in inverse powers of $Lambda_{XSB}simeq 1 GeV$, with analytic operators renormalized to all loop orders. We show that pion-less Static Chiral Nucleon Liquids (SXNL) emerge as a liquid phase of SU(2) XPT of protons, neutrons and 3 Nambu-Goldstone boson pions. Far-IR pions decouple from SXNL, simplifying the derivation of saturated nuclear matter and microscopic liquid drops (ground-state nuclides). We trace to the global symmetries of two-massless-quark QCD the power of pion-less SU(2) XPT to capture experimental ground-state properties of certain nuclides with even parity, spin zero, even proton number Z, and neutron number N. We derive the SXNL effective SU(2) XPT Lagrangian, including all order $Lambda_{XSB},Lambda^0_{XSB}$ operators. These include: all 4-nucleon operators that survive Fierz rearrangement in the non-relativistic limit, and effective Lorentz-vector iso-vector neutral $rho$-exchange operators. SXNL motivate nuclear matter as non-topological solitons at zero pressure: the Nuclear Liquid Drop Model and Bethe-Weizsacker Semi-Empirical Mass Formula emerge in an explicit Thomas-Fermi construction provided in the companion paper. For chosen nuclides, nuclear Density Functional and Skyrme models are justified to order $Lambda_{chi SB}^0$. We conjecture that inclusion of higher order operators will result in accurate natural Skyrme, No-Core-Shell, and neutron star models.
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We study effective field theories (EFT) of nuclear structure based on spontaneously broken global $SU(2)_Ltimes SU(2)_R$ chiral symmetry of QCD with two massless quarks, i.e. $SU(2)chi PT$. For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of $Lambda_{chi SB}simeq 1 GeV$, with analytic operators renormalized to all loop orders. We derive the EFT Lagrangian to order $Lambda^0_{chi SB}$. We show that $SU(2)chi PT$ of protons, neutrons and pions admits a semi-classical Static Chiral Nucleon Liquid (Static$chi$NL) phase and that Pion-less $SU(2)chi PT$ emerges in this liquid: far-infrared pions decouple from Static$chi$NL, vastly simplifying the derivation of saturated nuclear matter (the infinite liquid phase) and of finite microscopic liquid drops (ground-state nuclides). Static$chi$NL are made entirely of nucleons with even parity, total spin zero, and even $Z$ and $N$; local expectation values for spin and momenta vanish. They explain the power of pion-less $SU(2)chi PT$ to capture experimental ground-state properties of certain nuclides, this explanation following directly from the global symmetries of QCD with two massless quarks. Mean-field Static$chi$NL non-topological solitons are true solutions of $SU(2)chi PT$s semi-classical symmetries: they obey all CVC and PCAC conservation laws and they have zero internal and external pressure. The nuclear liquid-drop model and the semi-empirical mass formula emerge -- with correct nuclear density and saturation and asymmetry energies -- in an explicit Thomas-Fermi construction. We relate our work to compatible and complementary work in pionless and in halo/ cluster EFTs, also composed entirely of nucleons and applied to light ($Aleq 6$) nuclei, which might provide important (<12.5%) corrections to Static$chi NL$.
We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry $SU(4)_c times SU(2)_L times SU(2)_R$. A $U(1), R$ symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include $p rightarrow e^{+}(mu^+) + pi^0$, $p rightarrow bar{ u} + pi^{+}$, $p rightarrow K^0 + e^+(mu^{+})$, and $p rightarrow K^+ + bar{ u}$, with a lifetime estimate of order $10^{34}-10^{36}$ yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale $M_{rm GUT}$ ($sim 10^{16}$ GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.
We explore the sparticle mass spectra including LSP dark matter within the framework of supersymmetric $SU(4)_c times SU(2)_L times SU(2)_R$ (422) models, taking into account the constraints from extensive LHC and cold dark matter searches. The soft supersymmetry-breaking parameters at $M_{GUT}$ can be non-universal, but consistent with the 422 symmetry. We identify a variety of coannihilation scenarios compatible with LSP dark matter, and study the implications for future supersymmetry searches and the ongoing muon g-2 experiment.
Motivated by the ongoing searches for new physics at the LHC, we explore the low energy consequences of a D-brane inspired $ SU(4)_Ctimes SU(2)_L times SU(2)_R$ (4-2-2) model. The Higgs sector consists of an $SU(4)$ adjoint, a pair $H+bar H$ in $(4,1,2)+(bar 4,1,2)$, and a bidoublet field in $h(1,2,2)$. With the $SU(4)$ adjoint the symmetry breaks to a left-right symmetric $SU(3)_Ctimes U(1)_{B-L} times SU(2)_L times SU(2)_R$ model. A missing partner mechanism protects the $SU(2)_R$ Higgs doublets in $H,bar H$, which subsequently break the symmetry to the Standard Model at a few TeV scale. An inverse seesaw mechanism generates masses for the observed neutrinos and also yields a sterile neutrino which can play the r^ole of dark matter if its mass lies in the keV range. Other phenomenological implications including proton decay are briefly discussed.
Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the $19$ low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order~cite{Ren:2014vea} is supported by comparing the effective parameters (the combinations of the $19$ couplings) with the corresponding low-energy constants in the SU(2) sector~cite{Alvarez-Ruso:2013fza}. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.~cite{Alvarez-Ruso:2013fza}.
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