Vacuum phase transition at nonzero baryon density

It is argued that the dominant contribution to the interaction of quark–gluon plasma at moderate T?Tc$T?T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark–gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons Lfund(T),Ladj(T)=(Lfund)^9/4$L_{\mathrm{fund}}(T),L_{\mathrm{adj}}(T)={(L_{\mathrm{fund}})}^{9/4}$ known from lattice and analytic calculations. Phase transition at any μ   is described as a transition due to vanishing of one of correlators, DE(x)$D^E(x)$, which implies the change of gluonic condensate ΔG₂$\mathrm{\Delta }{G}_2$. Resulting transition temperature Tc(μ)$T_c(\mu )$ is calculated in terms of ΔG₂$\mathrm{\Delta }{G}_2$ and Lfund(Tc)$L_{\mathrm{fund}}(T_c)$. The phase curve Tc(μ)$T_c(\mu )$ is in a good agreement with lattice data. In particular Tc(0)=0.27$T_c(0)=0.27$; 0.19; 0.17 GeV$0.17\text{ GeV}$ for nf=0,2,3$n_f=0,2,3$ and fixed ΔG₂=0.0035 GeV⁴$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

The anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of a longitudinal field on a bcc lattice

In this work we study the critical behavior of the quantum spin-1/2 anisotropic Heisenberg antiferromagnet in the presence of a longitudinal field on a body centered cubic (bcc) lattice as a function of temperature, anisotropy parameter (Δ)$(\Delta )$ and magnetic field (H  ), where Δ=0$\Delta =0$ and 1 correspond the isotropic Heisenberg and Ising models, respectively. We use the framework of the differential operator technique in the effective-field theory with finite cluster of N  =4 spins (EFT-4). The staggered _ms=(_mA−_mB)/2$m_s=(m_A-m_B)/2$ and total m=(_mA+_mB)/2$m=(m_A+m_B)/2$ magnetizations are numerically calculated, where in the limit of _ms→0$m_s\to 0$ the critical line _TN(H,Δ)$T_N(H,\Delta )$ is obtained. The phase diagram in the T−H$T-H$ plane is discussed as a function of the parameter Δ$\Delta$ for all values of H∈[0,_Hc(Δ)]$H\in [0,H_c(\Delta )]$, where _Hc(Δ)$H_c(\Delta )$ correspond the critical field (_TN=0)$(T_N=0)$. Special focus is given in the low temperature region, where a reentrant behavior is observed around of H=_Hc(Δ)≥_Hc(Δ=1)=8J$H=H_c(\Delta )\ge H_c(\Delta =1)=8J$ in the Ising limit, results in accordance with Monte Carlo simulation, and also was observed for all values of Δ∈[0,1]$\Delta \in [\mathrm{0,1}]$. This reentrant behavior increases with increase of the anisotropy parameter Δ$\Delta$. In the limit of low field, our results for the Heisenberg limit are compared with series expansion values.     

Isomer-tagged differential-plunger measurements in proton-unbound Ho

The lifetime of an excited state above a weakly populated isomer in the proton-unbound odd–odd nucleus ¹⁴⁴Ho has been measured using the recoil distance Doppler shift method. This measurement represents the first differential-plunger lifetime measurement to utilize recoil-isomer tagging. The first excited Iπ=(¹⁰⁺)$I^{\pi }=({10}^{+})$ state above the two-quasiparticle πh_11/2⊗νh_11/2(⁸⁺)$\pi h_{11/2}\otimes \nu h_{11/2}(8^{+})$ isomer was determined to have a lifetime of τ=6(1) ps$\tau =6(1)\text{ps}$. Potential energy surface calculations, based on the configuration-constrained blocking method, predict the isomeric state to have γ  -soft triaxial-nuclear shape with |γ|≈24°$|\gamma |\approx 24\text{°}$. The lifetime of the (¹⁰⁺)$({10}^{+})$ state can be understood from these calculations if there is a degree of rotational alignment in this band, with the K value being lower than the bandhead spin. However, the validity of the K quantum number with large predicted triaxiality and gamma softness requires further theoretical study.     

Fixed point resolution in extensions of permutation orbifolds

We determine the simple currents and fixed points of the orbifold theory CFT⊗CFT/Z₂$\mathit{CFT}\otimes \mathit{CFT}/{\mathbb{Z}}_2$, given the simple currents and fixed point of the original CFT  . We see in detail how this works for the SUk₍₂₎$\mathit{SU}{(2)}_k$ WZW model, focusing on the field content (i.e. h  -spectrum of the primary fields) of the theory. We also look at the fixed point resolution of the simple current extended orbifold theory and determine the SJ$S^J$ matrices associated to each simple current for SU₂₍₂₎$\mathit{SU}{(2)}_2$ and for the B_1(n)$B{(n)}_1$ and D_1(n)$D{(n)}_1$ series.     

Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I²〉$〈I^2〉$ as a function of the n-th iteration of the map as well as the parameters K and γ  , controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K?1$K?1$. In this regime and for large initial action _I0?K$I_0?K$, we prove that dissipation produces an exponential decay for the average action 〈I〉$〈I〉$. Also, for _I0≅0$I_0\cong 0$, we describe the behavior of 〈I²〉$〈I^2〉$ using a scaling function and analytically obtain critical exponents which are used to overlap different curves of 〈I²〉$〈I^2〉$ onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action ω.     

Long-range memory elementary 1D cellular automata: Dynamics and nonextensivity

We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state _σi(t)∈{0,1}${\sigma }_i(t)\in \{0,1\}$ of a cell i   does not only depend on the states in its local neighborhood at time t-1$t-1$, but also on the memory of its own past states _σi(t-2),_σi(t-3),…,_σi(t-τ),…${\sigma }_i(t-2),{\sigma }_i(t-3),\dots ,{\sigma }_i(t-\tau ),\dots$ . We assume that the weight of this memory decays proportionally to τ^-α${\tau }^{-\alpha }$, with α?0$\alpha ?0$ (the limit α→∞$\alpha \to \infty$ corresponds to the usual CA). Since the memory function is summable for α>1$\alpha >1$ and nonsummable for 0?α?1$0?\alpha ?1$, we expect pronounced changes of the dynamical behavior near α=1$\alpha =1$. This is precisely what our simulations exhibit, particularly for the time evolution of the Hamming distance H   of initially close trajectories. We typically expect the asymptotic behavior H(t)∝t^1/(1-q)$H(t)\propto t^{1/(1-q)}$, where q   is the entropic index associated with nonextensive statistical mechanics. In all cases, the function q(α)$q(\alpha )$ exhibits a sensible change at α?1$\alpha ?1$. We focus on the class II rules 61, 99 and 111. For rule 61, q=0$q=0$ for 0?α?_αc?1.3$0?\alpha ?{\alpha }_c?1.3$, and q<0$q<0$ for α>_αc$\alpha >{\alpha }_c$, whereas the opposite behavior is found for rule 111. For rule 99, the effect of the long-range memory on the spread of damage is quite dramatic. These facts point at a rich dynamics intimately linked to the interplay of local lookup rules and the range of the memory. Finite size scaling studies varying system size N   indicate that the range of the power-law regime for H(t)$H(t)$ typically diverges ∝N^z$\propto N^z$ with 0?z?1$0?z?1$.     

Thermodynamic geometry of a kagome Ising model in a magnetic field

We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive thermodynamic curvature and its components near the criticality. According to standard scaling, scalar curvature R   behaves as |β−_βc|^α−2${|\beta -{\beta }_c|}^{\alpha -2}$ for α>0$\alpha >0$ where β is the inverse temperature and α is the critical exponent of specific heat. In the model considered here in which α is zero, we found that R   behaves as |β−_βc|^α−1${|\beta -{\beta }_c|}^{\alpha -1}$.     

On DBI Textures with generalized Hopf fibration

In this Letter we show numerical existence of O(4)$O(4)$ Dirac–Born–Infeld (DBI) Textures living in (N+1)$(N+1)$ dimensional spacetime. These defects are characterized by S^N→S³$S^N\to S^3$ mapping, generalizing the well-known Hopf fibration into _πN(S³)${\pi }_N(S^3)$, for all N>3$N>3$. The nonlinear nature of DBI kinetic term provides stability against size perturbation and thus renders the defects having natural scale.     

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈?²〉$〈{?}^2〉$ and 〈T_μν〉$〈T_{\mu \nu }〉$, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s   in a qualitatively different way: while 〈?²〉$〈{?}^2〉$ becomes convergent for a sufficiently large value of s  , the number of divergent terms in the adiabatic expansion of 〈T_μν〉$〈T_{\mu \nu }〉$ increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.     

Topology and phase transitions II. Theorem on a necessary relation

In this second paper, we prove a necessity theorem about the topological origin of phase transitions. We consider physical systems described by smooth microscopic interaction potentials VN(q)$V_N(q)$, among N   degrees of freedom, and the associated family of configuration space submanifolds _{Mv}v∈R${\{M_v\}}_{v\in \mathbb{R}}$, with Mv={q∈RN|VN(q)?v}$M_v=\{q\in {\mathbb{R}}^N|V_N(q)?v\}$. On the basis of an analytic relationship between a suitably weighed sum of the Morse indexes of the manifolds _{Mv}v∈R${\{M_v\}}_{v\in \mathbb{R}}$ and thermodynamic entropy, the theorem states that any possible unbound growth with N   of one of the following derivatives of the configurational entropy S(−)(v)=(1/N)logMv_∫dNq$S^{(-)}(v)=(1/N)\log {\int }_{M_v}{d}^{N}q$, that is of |k^∂S(−)(v)/∂vk|$|{\partial }^k{S}^{(-)}(v)/\partial v^k|$, for k=3,4$k=3,4$, can be entailed only by the weighed sum of Morse indexes. Since the unbound growth with N of one of these derivatives corresponds to the occurrence of a first- or of a second-order phase transition, and since the variation of the Morse indexes of a manifold is in one-to-one correspondence with a change of its topology, the Main Theorem of the present paper states that a phase transition necessarily stems from a topological transition in configuration space. The proof of the theorem given in the present paper cannot be done without Main Theorem of paper I.     

Probing photon helicity in radiative B decays via charmonium resonance interference

We investigate a new method to probe the helicity of the photon emitted in the b→sγ$b\to s\gamma$ transition. The method relies on the observation of interference effects between two resonance contributions, B→K^∗(Kγ)γ$B\to K^{\ast }(K\gamma )\gamma$ and B→ηc(γγ)K$B\to {\eta }_c(\gamma \gamma )K$ or B→χ_c0(γγ)K$B\to {\chi }_{c0}(\gamma \gamma )K$ to the same final state Kγγ  . Decays of the type B→Kres(Kγ)γ$B\to K_{\mathrm{res}}(K\gamma )\gamma$ dominate the B→Kγγ$B\to K\gamma \gamma$ yield throughout most of the phase space, and may be accessible at current B meson facilities already.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

FCNC-induced heavy-quark events at the LHC from supersymmetry

We analyze the production and subsequent decay of the neutral Higgs bosons h≡h⁰,H⁰,A⁰$h\equiv h^0,H^0,A^0$ of the MSSM into electrically neutral quark pairs of different flavors (qq^′≡tc,bs$q{q}^{\prime }\equiv tc,bs$, depending on h  ) at the LHC, i.e. σ(pp→h→qq^′)$\sigma (pp\to h\to q{q}^{\prime })$, and compare with the direct FCNC production mechanisms σ(pp→qq^′)$\sigma (pp\to q{q}^{\prime })$. The cross-sections are computed in the unconstrained MSSM with minimal flavor-mixing sources and taking into account the stringent bounds from b→sγ$b\to s\gamma$. We extend the results previously found for these FCNC processes, which are singularly uncommon in the SM. Specifically, we report here on the SUSY-EW part of σ(pp→h→qq^′)$\sigma (pp\to h\to q{q}^{\prime })$ and the SUSY-QCD and SUSY-EW contributions to σ(pp→bs)$\sigma (pp\to bs)$. In this way, the complete map of MSSM predictions for the qq^′$q{q}^{\prime }$-pairs produced at the LHC becomes available. The upshot is that the most favorable channels are: (1) the Higgs boson FCNC decays into bs, and (2) the direct production of tc   pairs, both of them at the ∼1 pb$\sim 1\text{pb}$ level and mediated by SUSY-QCD effects. If, however, the SUSY-QCD part is suppressed, we find a small SUSY-EW yield for σmax_{(pp→h→tc)}∼¹⁰⁻⁴ pb$\sigma {(pp\to h\to tc)}_{\max }\sim {10}^{\mathrm{-4}}\text{pb}$ but, at the same time, σmax_{(pp→h→bs)}∼0.1–1 pb$\sigma {(pp\to h\to bs)}_{\max }\sim 0.1\text{–}1\text{pb}$, which implies a significant number (∼¹⁰⁴–¹⁰⁵$\sim {10}^4\text{–}{10}^5$) of bs   pairs per 100 fb⁻¹$100{\text{fb}}^{\mathrm{-1}}$ of integrated luminosity.