Reaction pp \rightarrow pp \pi \pi \pi as a background for hadronic decays of the \eta^{{\prime}}_{} meson

Isospin violating hadronic decays of the $ \eta$ and $ \eta{^\prime}$ mesons into 3 $ \pi$ mesons are driven by a term in the QCD Lagrangian proportional to the mass difference of the d and u quarks. The source giving large yield of the mesons for such decay studies are pp interactions close to the respective kinematical thresholds. The most important physics background for $ \eta$ , $ \eta{^\prime}$ $ \rightarrow$ $ \pi$ $ \pi$ $ \pi$ is coming from direct three-pion production reactions. In case of the $ \eta$ meson the background for the decays is relatively low ( $ \approx$ 10% . The purpose of this article is to provide an estimate of the direct pion production background for the $ \eta{^\prime}$ $ \rightarrow$ 3 $ \pi$ decays. Using the inclusive data from the COSY-11 experiment we have extracted the differential cross-section for the pp $ \rightarrow$ pp -multipion production reactions with the invariant mass of the pions equal to the $ \eta{^\prime}$ meson mass and estimated an upper limit for the signal to background ratio for studies of the $ \eta{^\prime}$ $ \rightarrow$ $ \pi^{+}_{}$ $ \pi^{-}_{}$ $ \pi^{0}_{}$ decay.     

Semileptonic form factors D \rightarrow \pi, K and B \rightarrow \pi, K from a fine lattice

We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a = 0.04 fm (corresponding to a ^-1 = 4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy-quark expansion. For decays of D and D_s mesons, our results for the physical form factors at $\ensuremath q^2 = 0$ are as follows: $\ensuremath f_+^{D\rightarrow\pi}(0) = 0.74(6)(4)$ , $\ensuremath f_+^{D \rightarrow K}(0) = 0.78(5)(4)$ and $\ensuremath f_+^{D_s \rightarrow K} (0) = 0.68(4)(3)$ . Similarly, for B and B_s we find $\ensuremath f_+^{B\rightarrow\pi}(0) = 0.27(7)(5)$ , $\ensuremath f_+^{B\rightarrow K} (0) = 0.32(6)(6)$ and $\ensuremath f_+^{B_s\rightarrow K}(0) = 0.23(5)(4)$ . We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.     

Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$

We present a dispersive analysis of the decay amplitude for \(\eta '\rightarrow \eta \pi \pi \) that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the \({\pi \pi }\) and \({\pi }\eta \) scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.     

Comprehensive Bayesian analysis of rare (semi)leptonic and radiative \varvec{B} decays

The available data on \(|\Delta B| = |\Delta S| = 1\) decays are in good agreement with the Standard Model when permitting subleading power corrections of about \(15\,\%\) at large hadronic recoil. Constraining new-physics effects in \(\mathcal {C}_{7}^{\mathrm {}}\) , \(\mathcal {C}_{9}^{\mathrm {}}\) , \(\mathcal {C}_{10}^{\mathrm {}}\) , the data still demand the same size of power corrections as in the Standard Model. In the presence of chirality-flipped operators, all but one of the power corrections reduce substantially. The Bayes factors are in favor of the Standard Model. Using new lattice inputs for \(B\rightarrow K^*\) form factors and under our minimal prior assumption for the power corrections, the favor shifts toward models with chirality-flipped operators. We use the data to further constrain the hadronic form factors in \(B\rightarrow K\) and \(B\rightarrow K^*\) transitions.     

Split supersymmetry under GUT and current dark matter constraints

There are four types of two-Higgs doublet models under a discrete \(Z_2\) symmetry imposed to avoid tree-level flavor-changing neutral current, i.e. type-I, type-II, type-X, and type-Y models. We investigate the possibility to discriminate the four models in the light of the flavor physics data, including \(B_s\) – \(\bar{B}_s\) mixing, \(B_{s,d} \rightarrow \mu ^+ \mu ^-\) , \(B\rightarrow \tau \nu \) and \(\bar{B} \rightarrow X_s \gamma \) decays, the recent LHC Higgs data, the direct search for charged Higgs at LEP, and the constraints from perturbative unitarity and vacuum stability. After deriving the combined constraints on the Yukawa interaction parameters, we have shown that the correlation between the mass eigenstate rate asymmetry \(A_{\Delta \Gamma }\) of \(B_{s} \rightarrow \mu ^+ \mu ^-\) and the ratio \(R=\mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{exp}/ \mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{SM}\) could be a sensitive probe to discriminate the four models with future precise measurements of the observables in the \(B_{s} \rightarrow \mu ^+ \mu ^-\) decay at LHCb.     

The process\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma as an alternative to\pi ^0 \to v\bar v

The process \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) is investigated as an alternative to \(\pi ^0 \to v\bar v\) . It is shown that the experimental bound on the branching fraction for missing energy (in the form of \(\lambda _\gamma \bar \lambda _\gamma \) and/or \(v\bar v\) ) may be understood in terms of \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) for the kinematically allowed photino mass, if the squark mass is >8 GeV.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Suggestion for Einstein-Podolsky-Rosen experiments using reactions likee^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p

Since weakly decaying particles are their own polarimeters, reactions like \(\eta _c \to \Lambda \bar \Lambda , \psi \to \Lambda \bar \Lambda ,e^ + e^ - \to \mu ^ + \mu ^ -\) , etc. are interesting for testing the non-locality of quantum mechanical predictions. Although such reactions, in principle, do not exclude all classes of hidden variable theories, they can be used to complement current experiments with external polarimeters. The reaction \(\eta _c \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^{ + - } \bar p\) is conceptually the simplest and most useful as agedanken experiment, although it has not yet been seen experimentally. The reaction \(e^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p\) near threshold or at the φ resonance can be used for essentially the same test. This is feasible with presently available data and would be the first EPR experiment involving weak interactions.     

Tracy–Widom at High Temperature

We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature \(\beta \) tends to \(0\) . We prove that the minimal eigenvalue, whose fluctuations are governed by the Tracy–Widom \(\beta \) law, converges weakly, when properly centered and scaled, to the Gumbel distribution. More generally we obtain the convergence in law of the marginal distribution of any eigenvalue with given index \(k\) . Those convergences are obtained after a careful analysis of the explosion times process of the Riccati diffusion associated to the stochastic Airy operator. We show that the empirical measure of the explosion times converges weakly to a Poisson point process using estimates proved in Dumaz and Virág (Ann Inst H Poincaré Probab Statist 49(4):915–933, 2013). We further compute the empirical eigenvalue density of the stochastic Airy ensemble on the macroscopic scale when \(\beta \rightarrow 0\) . As an application, we investigate the maximal eigenvalues statistics of \(\beta _N\) -ensembles when the repulsion parameter \(\beta _N\rightarrow 0\) when \(N\rightarrow +\infty \) . We study the double scaling limit \(N\rightarrow +\infty , \beta _N \rightarrow 0\) and argue with heuristic and numerical arguments that the statistics of the marginal distributions can be deduced following the ideas of Edelman and Sutton (J Stat Phys 127(6):1121–1165, 2007) and Ramírez et al. (J Am Math Soc 24:919–944, 2011) from our later study of the stochastic Airy operator.     

DGP cosmological model with generalized Ricci dark energy

The Higgs-boson decay \(h \rightarrow \gamma \ell ^+ \ell ^-\) for various lepton states \(\ell = (e, \, \mu , \, \tau )\) is analyzed. The differential decay width and forward–backward asymmetry are calculated as functions of the dilepton invariant mass in a model where the Higgs boson interacts with leptons and quarks via a mixture of scalar and pseudoscalar couplings. These couplings are partly constrained from data on the decays to leptons, \(h \rightarrow \ell ^+ \ell ^-\) , and quarks \(h \rightarrow q \bar{q} \) (where \(q = (c, \, b)\) ), while the Higgs couplings to the top quark are chosen from the two-photon and two-gluon decay rates. Nonzero values of the forward–backward asymmetry will manifest effects of new physics in the Higgs sector. The decay width and asymmetry integrated over the dilepton invariant mass are also presented.     

Absolute E3 and M2 transition probabilities for the electromagnetic decay of the \mathrm{\ensuremath I^{\pi}=K^{\pi}=8^{-}} isomeric state in 132Ce

The decay of the $\ensuremath I^{\pi}=K^{\pi}=8^{-}$ isomeric state at 2340keV in ¹³²Ce has been investigated in the ¹²⁰Sn(¹⁶O, 4n)¹³²Ce reaction. The measurements were carried out in e - $ \gamma$ and $ \gamma$ - $ \gamma$ coincidence modes using an electron spectrometer coupled to the OSIRIS II gamma-ray array at the Heavy Ion Laboratory of the University of Warsaw. Experimentally obtained internal conversion coefficients for the $\ensuremath 8^{-} \rightarrow 6^{+}$ and $\ensuremath 8^{-} \rightarrow 5^{+}$ transitions allowed the multipolarities, mixing ratios, reduced transition probabilities and hindrance factors to be determined.     

Harmonic Oscillator Trap and the Phase-Shift Approximation

The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts \(\delta \) of the particles by a formula first published by Busch et al. It is here used to find an expression for the shift of the energy levels, caused by the interaction, rather than the perturbed spectrum itself. In the limit of high energy (large quantum number \(n\) of the H.O.) this shift (in H.O. units) is shown to be given by \(\Delta =-2\frac{\delta }{\pi }\) , also exact in the limit of infinite scattering length ( \(\delta =\pm \frac{\pi }{2}\) ) in which case \(\Delta =\mp 1\) . Numerical investigation shows that this expression otherwise differs from the exact result of Busch et al., by less than \(\frac{1}{2}\,\%\) except for \(n=0\) when it can be as large as \(\approx \) 2.5 %. This result for the energy-shift is well known from another exactly solvable model, namely that of two particles interacting in a spherical infinite square-well trap (or box) of radius \(R\) in the limit \(R\rightarrow \infty \) , and/or in the limit of large energy. It is in solid state physics referred to as Fumi’s theorem. It can be (and has been) used in (infinite) nuclear matter calculations to calculate the two-body effective interaction in situations where in-medium effects can be neglected. It is in this context referred to as the phase-shift approximation a term also used throughout this report.     

Antiproton low-energy collisions with Ps-atoms and true muonium atoms (μ + μ −)

Three-charge-particle collisions with participation of ultra-slow antiprotons ( \(\overline {\rm {p}}\) ) is the subject of this work. Specifically we compute the total cross sections and corresponding thermal rates of the following three-body reactions: \(\overline {\rm p}+(e^+e^-) \rightarrow \overline {\rm {H}} + e^-\) and \(\overline {\rm p}+(\mu ^+\mu ^-) \rightarrow \overline {\rm {H}}_{\mu } + \mu ^-\) , where \(e^-(\mu ^-)\) is an electron (muon) and \(e^+(\mu ^+)\) is a positron (antimuon) respectively, \(\overline {\rm {H}}=(\overline {\rm p}e^+)\) is an antihydrogen atom and \(\overline {\rm {H}}_{\mu }=(\overline {\rm p}\mu ^+)\) is a muonic antihydrogen atom, i.e. a bound state of \(\overline {\rm {p}}\) and μ ⁺. A set of two-coupled few-body Faddeev-Hahn-type (FH-type) equations is numerically solved in the framework of a modified close-coupling expansion approach.     

Pesin’s Entropy Formula for Systems Between C^1 and C^{1+\alpha }

In this article we give a new observation of Pesin’s entropy formula, motivated from Mañé’s proof of (Ergod Theory Dyn Sys 1:95–102, 1981). Let \(M\) be a compact Riemann manifold and \(f:\,M\rightarrow M\) be a \(C^1\) diffeomorphism on \(M\) . If \(\mu \) is an \(f\) -invariant probability measure which is absolutely continuous relative to Lebesgue measure and nonuniformly-H \(\ddot{\text {o}}\) lder-continuous(see Definition 1.1), then we have Pesin’s entropy formula, i.e., the metric entropy \(h_\mu (f)\) satisfies $$\begin{aligned} h_{\mu }(f)=\int \sum _{\lambda _i(x)> 0}\lambda _i(x)d\mu , \end{aligned}$$ where \(\lambda _1(x)\ge \lambda _2(x)\ge \cdots \ge \lambda _{dim\,M}(x)\) are the Lyapunov exponents at \(x\) with respect to \(\mu .\) Nonuniformly-H \(\ddot{\text {o}}\) lder-continuous is a new notion from probabilistic perspective weaker than \(C^{1+\alpha }.\)      

The Colored Hofstadter Butterfly for the Honeycomb Lattice

We rely on a recent method for determining edge spectra and we use it to compute the Chern numbers for Hofstadter models on the honeycomb lattice having rational magnetic flux per unit cell. Based on the bulk-edge correspondence, the Chern number \(\sigma _\mathrm{H}\) is given as the winding number of an eigenvector of a \(2 \times 2\) transfer matrix, as a function of the quasi-momentum \(k\in (0,2\pi )\) . This method is computationally efficient (of order \(\mathcal {O}(n^4)\) in the resolution of the desired image). It also shows that for the honeycomb lattice the solution for \(\sigma _\mathrm{H}\) for flux \(p/q\) in the \(r\) -th gap conforms with the Diophantine equation \(r=\sigma _\mathrm{H}\cdot p+ s\cdot q\) , which determines \(\sigma _\mathrm{H}\mod q\) . A window such as \(\sigma _\mathrm{H}\in (-q/2,q/2)\) , or possibly shifted, provides a natural further condition for \(\sigma _\mathrm{H}\) , which however turns out not to be met. Based on extensive numerical calculations, we conjecture that the solution conforms with the relaxed condition \(\sigma _\mathrm{H}\in (-q,q)\) .     

The CMSSM and NUHM1 after LHC Run 1

We analyze the impact of data from the full Run 1 of the LHC at 7 and 8 TeV on the CMSSM with \(\mu > 0\) and \(<0\) and the NUHM1 with \(\mu > 0\) , incorporating the constraints imposed by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment. We use the following results from the LHC experiments: ATLAS searches for events with \({E\!\!/}_{T}\) accompanied by jets with the full 7 and 8 TeV data, the ATLAS and CMS measurements of the mass of the Higgs boson, the CMS searches for heavy neutral Higgs bosons and a combination of the LHCb and CMS measurements of \(\mathrm{BR}(B_s \rightarrow \mu ^+\mu ^-)\) and \(\mathrm{BR}(B_d \rightarrow \mu ^+\mu ^-)\) . Our results are based on samplings of the parameter spaces of the CMSSM for both \(\mu >0\) and \(\mu <0\) and of the NUHM1 for \(\mu > 0\) with 6.8 \(\times 10^6\) , 6.2 \(\times 10^6\) and 1.6 \(\times 10^7\) points, respectively, obtained using the MultiNest tool. The impact of the Higgs-mass constraint is assessed using FeynHiggs 2.10.0, which provides an improved prediction for the masses of the MSSM Higgs bosons in the region of heavy squark masses. It yields in general larger values of \(M_h\) than previous versions of FeynHiggs, reducing the pressure on the CMSSM and NUHM1. We find that the global \(\chi ^2\) functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs-mass and the \({E\!\!/}_{T}\) searches, with best-fit values that are comparable to the \(\chi ^2/\mathrm{dof}\) for the best Standard Model fit. We provide 95 % CL lower limits on the masses of various sparticles and assess the prospects for observing them during Run 2 of the LHC.     

Electroweak radiative corrections to $$W^+W^-\gamma $$ production at the ILC

We consider holographic superconductors in a rotating black string spacetime. In view of the mandatory introduction of the \(A_\varphi \) component of the vector potential we are left with three equations to be solved. Their solutions show that the rotation parameter \(a\) influences the critical temperature \(T_\mathrm{c}\) and the conductivity \(\sigma \) in a simple but non-trivial way.     

Quantum Measures on Finite Effect Algebras with the Riesz Decomposition Properties

One kind of generalized measures called quantum measures on finite effect algebras, which fulfil the grade-2 additive sum rule, is considered. One basis of vector space of quantum measures on a finite effect algebra with the Riesz decomposition property (RDP for short) is given. It is proved that any diagonally positive symmetric signed measure \(\lambda \) on the tensor product \(E\otimes E\) can determine a quantum measure \(\mu \) on a finite effect algebra \(E\) with the RDP such that \(\mu (x)=\lambda (x\otimes x)\) for any \(x\in E\) . Furthermore, some conditions for a grade-2 additive measure \(\mu \) on a finite effect algebra \(E\) are provided to guarantee that there exists a unique diagonally positive symmetric signed measure \(\lambda \) on \(E\otimes E\) such that \(\mu (x)=\lambda (x\otimes x)\) for any \(x\in E\) . At last, it is showed that any grade- \(t\) quantum measure on a finite effect algebra \(E\) with the RDP is essentially established by the values on a subset of \(E\) .     

QCD analysis of forward neutron production in DIS

Observing light-by-light scattering at the large hadron collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the process \({{pp}}\rightarrow {{p}}\gamma \gamma {{p}}\rightarrow {{p}}\gamma \gamma {{p}}\) through graviton exchange in the large extra dimension (LED) model. Typically, when we do the background analysis, we also study the double Pomeron exchange of \(\gamma \gamma \) production. We compare its production in the quark–quark collision mode to the gluon–gluon collision mode and find that contributions from the gluon–gluon collision mode are comparable to the quark–quark one. Our result shows, for extra dimension \(\delta =4\) , with an integrated luminosity \(\mathcal{L} = 200\,\mathrm{fb}^{-1}\) at the 14 TeV LHC, that diphoton production through graviton exchange can probe the LED effects up to the scale \({M}_{S}=5.06 (4.51, 5.11)\,\mathrm{TeV}\) for the forward detector acceptance \(\xi _1 (\xi _2, \xi _3)\) , respectively, where \(0.0015<\xi _1<0.5\) , \(0.1<\xi _2<0.5\) , and \(0.0015<\xi _3<0.15\) .