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The discovery of topological phases of matter forced condensed matter physicists to question and reexamine some of the basic notions of their discipline. Wen reviews the progress of the field that took a sharp turn from Landau's broken symmetry paradigm to arrive at the modern notions of topological order and quantum entanglement in many-body systems. This development was made possible by using increasingly sophisticated mathematical formalisms. Science , this issue p. eaal3099 It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.

Symmetry-protected topological (SPT) states have boundary ’t Hooft anomalies that obstruct the effective boundary theory realized in its own dimension with UV completion and with an on-siteG-symmetry. In this work, yet we show that a certain anomalous non-on-siteG-symmetry along the boundary becomes on-site when viewed as an extendedH-symmetry, via a suitable group extension1→K→H→G→1. Namely, a nonperturbative global (gauge or gravitational) anomaly inGbecomes anomaly free inH. This guides us to construct an exactly soluble lattice path integral and Hamiltonian of symmetric gapped boundaries applicable to any SPT state of any finite symmetry group, including on-site unitary and antiunitary time-reversal symmetries. The resulting symmetric gapped boundary can be described either by anH-symmetry extended boundary in any spacetime dimension or, more naturally, by a topological emergentK-gauge theory with a global symmetryGon a3+1Dbulk or above. The excitations on such a symmetric topologically ordered boundary can carry fractional quantum numbers of the symmetryG, described by representations ofH. (Applying our approach to a1+1Dboundary of2+1Dbulk, we find that a deconfined gauge boundary indeed has spontaneous symmetry breaking with long-range order. The deconfined symmetry-breaking phase crosses over smoothly to a confined phase without a phase transition.) In contrast to known gapped boundaries or interfaces obtained via symmetry breaking (either global symmetry breaking or the Anderson-Higgs mechanism for gauge theory), our approach is based on symmetry extension. More generally, applying our approach to SPT states, topologically ordered gauge theories, and symmetry enriched topologically ordered (SET) states leads to generic boundaries or interfaces constructed with a mixture of symmetry breaking, symmetry extension, and dynamical gauging.

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in1+1Dbosonic systems, there is no nontrivial topological order, while in2+1Dbosonic systems, the topological orders are classified by the following pair: a modular tensor category and a chiral central charge. In this paper, following a new line of thinking, we find that in3+1Dthe classification is much simpler than it was thought to be; we propose a partial classification of topological orders for3+1Dbosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair(G,ω4): a finite groupGand its group 4-cocycleω4∈H4[G;U(1)](up to group automorphisms). Furthermore, all such3+1Dtopological orders can be realized by Dijkgraaf-Witten gauge theories.

Motivated by the LHCb observation of exotic states X 0 , 1 ( 2900 ) with four open quark flavors in the D - K + invariant mass distribution in the decay channel B ± → D + D - K ± , we study the spectrum and decay properties of the open charm tetraquarks. Using the two-body chromomagnetic interactions, we find that the two newly observed states can be interpreted as a radial excited tetraquark with J P = 0 + and an orbitally excited tetraquark with J P = 1 - , respectively. We then explore the mass and decays of the other flavor-open tetraquarks made of s u d ¯ c ¯ and d s u ¯ c ¯ , which are in the 6 ¯ or 15 representation of the flavor SU(3) group. We point that these two states can be found through the decays: X d s u ¯ c ¯ ( ′ ) → ( D - K - , D s - π - ) , and X s u d ¯ c ¯ ( ′ ) → D s - π + . We also apply our analysis to open bottom tetraquark X b and predict their masses. The open-flavored X b can be discovered through the following decays: X u d s ¯ b ¯ → B 0 K + , X d s u ¯ b ¯ ( ′ ) → ( B 0 K - , B s 0 π - ) , and X s u d ¯ b ¯ ( ′ ) → B s 0 π + .

Analyses of heavy mesons and baryons hadronic charmless decays using the flavor SU(3) symemtry can be formulated in two different forms. One is to construct the SU(3) irreducible representation amplitude by decomposing effective Hamiltonian, and the other is to draw the topological diagrams. In the flavor SU(3) limit, we study various B / D → P P , V P , V V , B c → D P / D V decays, and two-body nonleptonic decays of beauty/charm baryons, and demonstrate that when all terms are included these two ways of analyzing the decay amplitudes are completely equivalent. Furthermore we clarify some confusions in drawing topological diagrams using different ways of describing beauty/charm baryons.

Arrestins recognize different receptor phosphorylation patterns and convert this information to selective arrestin functions to expand the functional diversity of the G protein-coupled receptor (GPCR) superfamilies. However, the principles governing arrestin-phospho-receptor interactions, as well as the contribution of each single phospho-interaction to selective arrestin structural and functional states, are undefined. Here, we determined the crystal structures of arrestin2 in complex with four different phosphopeptides derived from the vasopressin receptor-2 (V2R) C-tail. A comparison of these four crystal structures with previously solved Arrestin2 structures demonstrated that a single phospho-interaction change results in measurable conformational changes at remote sites in the complex. This conformational bias introduced by specific phosphorylation patterns was further inspected by FRET and 1 H NMR spectrum analysis facilitated via genetic code expansion. Moreover, an interdependent phospho-binding mechanism of phospho-receptor-arrestin interactions between different phospho-interaction sites was unexpectedly revealed. Taken together, our results provide evidence showing that phospho-interaction changes at different arrestin sites can elicit changes in affinity and structural states at remote sites, which correlate with selective arrestin functions. The interaction between a GPCR, such as the vasopressin receptor-2 (V2R), and arrestin depends on the receptors’ phosphorylation pattern. Here authors use FRET and NMR to analyze the phosphorylation patterns of the V2R-arrestin complex and show that phospho-interactions are the key determinants of selective arrestin conformational states and correlated functions.

A bstract We consider decays of B and K mesons into a pseudo-scalar or vector meson plus missing energy. Within the SM, these modes originate from flavor changing neutral current (FCNC) processes with two neutrinos in the final state. In this paper we consider the experimental upper bounds on these modes and interpret the difference between these bounds and the SM prediction as a window into new light invisible particles. In particular we consider the case where some new symmetry requires the new particles to be produced in pairs. We first construct the general low energy effective Lagrangian coupling an FCNC with two dark sector particles of spin zero, one-half and one. We then present numerical estimates for the constraints that can be placed on these interactions, finding that an effective new physics scale from O (10)- O (10 11 ) GeV can be probed, with the exact value strongly depending on the interaction structure as well as the mass of the invisible particle. For we incorporate into our constraints the effect of using only the signal regions of NA62, and for the q 2 -dependent efficiency of Belle II.

A bstract We explore simple Higgs-portal models of dark matter (DM) with spin 1/2, 3/2, and 1, respectively, applying to them constraints from the LUX and PandaX-II direct detection experiments and from LHC measurements on the 125-GeV Higgs boson. With only one Higgs doublet, we find that the spin-1/2 DM having a purely scalar effective coupling to the doublet is viable only in a narrow range of mass near the Higgs pole, whereas the vector DM is still allowed if its mass is also close to the Higgs pole or exceeds 1.4 TeV, both in line with earlier analyses. Moreover, the spin-3/2 DM is in a roughly similar situation to the spin-1/2 DM, but has surviving parameter space which is even more restricted. We also consider the two-Higgs-doublet extension of each of the preceding models, assuming that the expanded Yukawa sector is that of the two-Higgs-doublet model of type II. We show that in these two-Higgs-doublet-portal models significant portions of the DM mass regions excluded in the simplest scenarios by direct search bounds can be reclaimed due to suppression of the effective DM interactions with nucleons at some ratios of the CP -even Higgs bosons’ couplings to the up and down quarks. The regained parameter space contains areas which can yield a DM-nucleon scattering cross-section that is far less than its current experimental limit or even goes below the neutrino-background floor.

A bstract In this paper we systematically consider the baryon ( B ) and lepton ( L ) number violating dinucleon to dilepton decays ( pp → ℓ + ℓ ′ + , pn → ℓ + ν ¯ ′ , nn → ν ¯ ν ¯ ′ ) with ∆ B = ∆ L = − 2 in the framework of effective field theory. We start by constructing a basis of dimension-12 (dim-12) operators mediating such processes in the low energy effective field theory (LEFT) below the electroweak scale. Then we consider their standard model effective field theory (SMEFT) completions upwards and their chiral realizations in baryon chiral perturbation theory (B χ PT) downwards. We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions, and express the decay rates in terms of the Wilson coefficients associated with the dim-12 operators in the SMEFT and the low energy constants pertinent to B χ PT. We find the current experimental limits push the associated new physics scale larger than 1 − 3 TeV, which is still accessible to the future collider searches. Through weak isospin symmetry, we find the current experimental limits on the partial lifetime of transitions pp → ℓ + ℓ ′ + , pn → ℓ + ν ¯ ′ imply stronger limits on nn → ν ¯ ν ¯ ′ than their existing lower bounds, which are improved by 2 − 3 orders of magnitude. Furthermore, assuming charged mode transitions are also dominantly generated by the similar dim-12 SMEFT interactions, the experimental limits on pp → e + e + , e + μ + , μ + μ + lead to stronger limits on pn → ℓ α + ν ¯ β with α, β = e, μ than their existing bounds. Conversely, the same assumptions help us to set a lower bound on the lifetime of the experimentally unsearched mode pp → e + τ + from that of pn → e + ν ¯ τ , i.e., Γ pp → e + τ + − 1 ≳ 2 × 10 34 yr.