The quest for <Emphasis Type="Italic">μ</Emphasis> → <Emphasis Type="Italic">e</Emphasis><Emphasis Type="Italic">γ</Emphasis>: present and future

The quest for μ → eγ is one of the most important endeavors to search for New Physics beyond the Standard Model. In this talk I will review the current status of the experimental searches by the MEG Collaboration at PSI. I will also present a study of the experimental limiting factors that will define the ultimate performances, and hence the sensitivity, in the search for μ → eγ with continuous muon beams of extremely high rate (one or even two orders of magnitude larger than the present beams), whose construction is under consideration for the next decade.     

Process <Emphasis Type="Italic">γ</Emphasis>*<Emphasis Type="Italic">γ</Emphasis> → <Emphasis Type="Italic">σ</Emphasis> at large virtuality of <Emphasis Type="Italic">γ</Emphasis>*

The process γ*γ → σ is investigated in the framework of the SU(2)×SU(2) chiral NJL model. The form factor of the process is derived for arbitrary virtuality of γ* in the Euclidean kinematic domain. The asymptotic behavior of this form factor resembles the asymptotic behavior of the γ*γ → π form factor.     

The cusp effect in <Emphasis Type="Italic">η</Emphasis>′→<Emphasis Type="Italic">η</Emphasis><Emphasis Type="Italic">π</Emphasis><Emphasis Type="Italic">π</Emphasis> decays

Strong final-state interactions create a pronounced cusp in η′→η π ⁰ π ⁰ decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of π π scattering lengths from K→3π decays to this case. The cusp effect is predicted to have an effect of more than 8% on the decay spectrum below the π ⁺ π ⁻ threshold.     

Roy–Steiner equations for <Emphasis Type="Italic">γγ</Emphasis>→<Emphasis Type="Italic">ππ</Emphasis>

Starting from hyperbolic dispersion relations, we derive a system of Roy–Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on high-energy input, we also consider once- and twice-subtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equations are valid. As an application, we consider the resolution of the γγ→ππ partial waves by a Muskhelishvili–Omnès representation with finite matching point. We find a sum rule for the isospin-two S-wave, which, together with chiral constraints, produces an improved prediction for the charged-pion quadrupole polarizability (a₂-b₂)^p±=(15.3±3.7)×10^-4(\alpha_{2}-\beta_{2})^{\pi^{\pm}}=(15.3\pm3.7)\times 10^{-4} fm⁵. We investigate the prediction of our dispersion relations for the two-photon coupling of the σ-resonance Γ _σγγ . The twice-subtracted version predicts a correlation between this width and the isospin-zero pion polarizabilities, which is largely independent of the high-energy input used in the equations. Using this correlation, the chiral perturbation theory results for pion polarizabilities, and our new sum rule, we find Γ _σγγ =(1.7±0.4) keV.     

Eight resonances and a half for the reaction <Emphasis Type="Italic">γ</Emphasis> + <Emphasis Type="Italic">p</Emphasis>→<Emphasis Type="Italic">η</Emphasis> + <Emphasis Type="Italic">p</Emphasis>

On the basis of the dynamical model for meson photoproduction on nucleons, it is shown that only eight broad resonances (of width in excess of 120 MeV), of which two belong to the class of missing resonances, are required for reproducing experimental data from the threshold for the reaction γp → ηp to the photon energy of 3 GeV.     

Inclusive <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis> photoproduction and polarization at HERA in the <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>-factorization approach

We investigate the inclusive photoproduction of J/ψ mesons at HERA within the framework of the k _T -factorization QCD approach. Our study is based on the color singlet model supplemented with the relevant off-shell matrix elements and the CCFM and KMR unintegrated gluon densities in a proton and in a photon. Both the direct and resolved photon contributions are taken into account. Our predictions are compared with the recent experimental data taken by the H1 and ZEUS collaborations. Special attention is put on the J/ψ polarization parameters λ and ν, which are sensitive to the production dynamics.     

Contribution of final-state interaction to the branching ratio of <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis><Emphasis Type="Italic">D</Emphasis>

To test the validity of perturbative QCD (pQCD) and investigate its range of application, one should look for a suitable process. B→J/ψ D is a promising candidate. The linear momentum of the products is relatively small, so that there may exist a region where exchanged gluons are soft and the perturbative treatment may fail, so that the non-perturbative effect would be significant. We attribute such non-perturbative QCD effects to the long-distance final-state interaction (FSI) which is estimated in this work. We find that the contribution from the FSI to the branching ratio is indeed sizable and may span the rather wide range of 10⁻⁶∼10⁻⁵ and cover a region where the pQCD prediction is of the same order. A more accurate measurement of its branching ratio may provide important information about the application region of pQCD and help to clarify the picture of inelastic rescattering (i.e. FSI), which is generally believed to play an important role in B decays.     

Probing unparticle theory via lepton-flavor violating process <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis>→<Emphasis Type="Italic">ll</Emphasis>′ at BESIII

The lepton-flavor violating process J/ψ→ll′(l≠l′) serves as an ideal place to probe the unparticle theory. Such a process can only occur at loop level in the Standard model (SM), so that should be very suppressed; by contrast, in the unparticle scenario, it happens at tree level and its contribution may be sizable for practical measurement. Moreover, the BESIII will offer the largest database on J/ψ, which makes more accurate measurements possible. Furthermore, for such purely leptonic decays the background is relatively low and the signal would be cleaner. Our work carefully investigates the possibility of observing such processes from both theoretical and experimental aspects.     

Temperature-dependent resonant tunneling in disordered quasi-one-dimensional <Emphasis Type="Italic">N</Emphasis>–<Emphasis Type="Italic">I</Emphasis>–<Emphasis Type="Italic">N</Emphasis> junctions

Formulas are obtained for the current–voltage characteristics and conductance of a quasi-one-dimensional N–I–N junction (where N is an ordinary metal and I is an insulator) with quantum resonance percolation trajectories (QRPTs) in a disordered I-layer at temperatures T > 0 K and the energy of local single-impurity electron level being equal to the Fermi energy ε₀ = ε_F. Under these conditions, the impact QRPTs have on the current through the junctions weakens as the temperature grows, and the conductance drops; this is in contrast to the rise in conductance of an empty junction (with no impurities in the I-layer).     

<Emphasis Type="Italic">α</Emphasis>-cluster and <Emphasis Type="Italic">α</Emphasis>-binucleon states of 1<Emphasis Type="Italic">p</Emphasis>-shell nuclei

States that exhibit the properties of an α-cluster or an α-binucleon condensate are studied in 1p-shell nuclei. The generalized Hamiltonian of the Elliott SU(3) model is used to classify these states and to calculate their spectra. The results of the calculations are found to be in good agreement with experimental data. States not observed so far in the cluster spectra of the ¹²C, ¹⁶O, ¹⁰Be, and ¹²Be nuclei are predicted.     

Revised Spherically Symmetric Solutions of <Emphasis Type="Italic">R</Emphasis>+<Emphasis Type="Italic">ε</Emphasis>/<Emphasis Type="Italic">R</Emphasis> Gravity

We study spherically symmetric static empty space solutions in R+ε/R model of f(R) gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general solutions which are perturbed Schwarzschild metric and viable for solar system. Our results for large scale contains a logarithmic term with a coefficient producing a repulsive gravity force which is in agreement with the positive acceleration of the universe.     

Final state interactions in the decays <Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis>→<Emphasis Type="Italic">VPP</Emphasis>

We investigate the interplay between crossed channel final state interactions and the constraints from two-particle unitarity for the reactions J/ψ→V π π and VK[`(K)]VK\bar{K} , where V is either ω or φ. Using a model where the parameters are largely constrained by other sources, we find that, although small, crossed channel final state interaction can influence the amplitudes considerably, in special areas of phase space. These results cast doubt on the inapplicability of unitarity constraints on production amplitudes as recently claimed in the literature.     

<Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis> suppression and <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript> spectra in RHIC and LHC energy collisions

In a hydrodynamic model, we have studied J/ψ production in Au+Au/Cu+Cu collisions at RHIC energy, GeV. At the initial time, J/ψ’s are randomly distributed in the fluid. As the fluid evolves in time, the free streaming J/ψ’s are dissolved if the local fluid temperature exceeds a threshold temperature T _J/ψ . Sequential melting of charmonium states (χ _c , ψ ^′ and J/ψ), with melting temperatures , T _J/ψ ≈2T _c and feed-down fraction F≈0.3, explains the PHENIX data on the centrality dependence of J/ψ suppression in Au+Au collisions. J/ψ p _T spectra and the nuclear modification factor in Au+Au collisions are also well explained in the model. The model however overpredicts the centrality dependence of J/ψ suppression in Cu+Cu collisions by 20–30%. The J/ψ p _T spectra are underpredicted by 20–30%. The model predicts that in central Pb+Pb collisions at LHC energy,  GeV, J/ψ’s are suppressed by a factor of ∼10. The model predicted a J/ψ p _T distribution in Pb+Pb collisions at LHC is similar to that in Au+Au collisions at RHIC.     

Universal Characters and <Emphasis Type="Italic">q</Emphasis>-Painlevé Systems

We propose an integrable system of q-difference equations satisfied by the universal characters and regard it as a q-analogue of the UC hierarchy; see [10]. Via a similarity reduction of this integrable system, rational solutions of the q-Painlevé systems are constructed in terms of the universal characters.     

Bottomonium γ(5<Emphasis Type="Italic">S</Emphasis>) decays into <Emphasis Type="Italic">BB</Emphasis> and <Emphasis Type="Italic">BB</Emphasis>π

Two-and three-body decays of γ(5S) into BB, BB*, B*B*, B _s B _s , B _s B _s ^*, and BB*π, B*B*π are evaluated using the theory developed earlier for dipion-bottomonium transitions. The theory contains only two parameters—vertex masses M _br and M _ω—known from the dipion spectra and width. Predicted values of Γ_tot(5S) and six partial widths Γ _k (5S), k = BB, BB*, ... are in agreement with the experiment. The decay widths Γ_5S (πBB*) and Γ_5S (πB*B*) are also calculated and found to be on the order of 10 keV. The text was submitted by the authors in English.