Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

Remarks on Hamiltonian structures of the KP hierarchy and W KP( q ) algebra

It is known that second Hamiltonian structures of the KP hierarchy are parameterized by a continuous complex parameter q and correspond to the W-infinite algebra of W _infKP ^sup(q) . In this Letter, by constructing a Miura map, we first show a generalized decomposition theorem to the second Hamiltonian structures and then establish a relation between those structures which corresponds to values (q+1) and q of the parameter, respectively. This discussion also gives a better understanding to the structures of W _infKP ^sup(q) , its reduced algebras, and their free fields realizations.     

Geometrical Tools for Quantum Euclidean Spaces

We apply one of the formalisms of noncommutative geometry to ℝ ^N _q , the quantum space covariant under the quantum group SO _q (N). Over ℝ ^N _q there are two SO _q (N)-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in a previous article for the case of ℝ³ _q . As in the case N=3, one has to slightly enlarge the algebra ℝ ^N _q ; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N=3 there is a conformal ambiguity in the natural metrics on the differential calculi over ℝ ^N _q . While in our previous article the frame was found “by hand”, here we disclose the crucial role of the quantum group covariance and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of ℝ ^N _q with U _q so(N) into ℝ ^N _q , an interesting result in itself. Received: 4 March 2000 / Accepted: 11 October 2000     

Hadronic weak decays of heavy mesons and nonfactorization

The parametersχ _1,2, which measure nonfactorizable soft gluon contributions to hadronic weak decays of mesons, are updated by extracting them from the data ofD, B→PP, VP decays (P: pseudoscalar meson,V: vector meson). It is found thatχ ₂ ranges from −0.36 to −0.60 in the decays fromD→Kπ toD ⁺→φπ ⁺,D→K*π, while it is of order 10% with a positive sign inB→ψK, Dπ, D*π, Dρ decays. Therefore, the effective parametera ₂ is process dependent in charm decay, whereas it stays fairly stable inB decay. This is in accordance with the picture that nonfactorizable soft gluon effects become stronger when the relative momentum of the decay particles becomes smaller. As forD, B→VV decays, the presence of nonfactorizable terms in general prevents a possible definition of effectivea ₁ anda ₂. This is reinforced by the observation of a large longitudinal polarization fraction inB→ψK* decay, implying nonfactorizable effects contributing differently toS-, P- andD-wave amplitudes. We found thatA ₁ ^nf /A ₁>0>A ₂ ^nf /A ₂,V ^nf/V (nf standing for nonfactorization) forB→ψK* decay and 0>A ₁ ^nf /A ₁>A ₂ ^nf /A ₂,V ^nf/V forD→K*ρ decay. A measurement of longitudinally and transversely polarized decay rates Γ _L and Γ _T in color-suppressed decay modesB ⁰→D*⁰ ρ ⁰,D*⁰ ω andD ⁺→φρ ⁺ is urged.     

Screening Length of Rotating Heavy Meson from AdS/CFT

In this paper we consider a quark-antiquark (q[`(q)]q\bar{q}) pair which can be interpreted as a meson in N=4{\mathcal{N}}=4 SYM thermal plasma. We assume that the string moves at speed v and rotates around its center of mass simultaneously. By using the AdS/CFT correspondence, we obtain the momentum densities of the rotating string and determine its motion for small angular velocities. Then in general case, we calculate the screening length of q[`(q)]q\bar{q} pair numerically and show that its velocity dependance is in consistent with the well known formula L _s T∼(1−v ²)^1/4 in the literature.     

A natural framework for the minimal supersymmetric gauge theories

We show that the sequence of Jordan algebras M _inf3 ^sup1 , M _inf3 ^sup2 , M _inf3 ^sup4 , and M _inf3 ^sup8 , whose elements are in the 3×3 Hermitean matrices over , , , and O, respectively, provide an elegant and natural framework in which to describe supersymmetric gauge theories. The four minimal supersymmetric gauge theories are in a one-to-one correspondence with these four Jordan algebras and, hence, with the four division algebras.     

New neutrino experiments

Following incredible recent progress in understanding neutrino oscillations, many new ambitious experiments are being planned to study neutrino properties. The most important may be to find a non-zero value of θ₁₃. The most promising way to do this appears to be to measurev _μ →v _e oscillations with anE/L near Δm _atmo ² . Future neutrino experiments are great.     

L p -Boundedness of Wave Operators for¶Two Dimensional Schrödinger Operators

Let be the two dimensional Schr?dinger operator with the real valued potential V which satisfies the decay condition at infinity for . We show that the wave operators , , are bounded in for any 1<p<∞ under the condition that H has no zero bound states or zero resonance, extending the corresponding results for higher dimensions. As W _± intertwine H ₀ and the absolutely continuous part H P _ac of H : f(H)P _ac=W _± f(H ₀ )W _± ^* for any Borel function f on ℝ¹, this reduces the various L ^p -mapping properties of f(H)P _ac to those of f(H)₀), the convolution operator by the Fourier transform of the function f(ξ²). Received: 5 April 1999 / Accepted: 26 May 1999     

Charged Higgs bosons in the next-to MSSM (NMSSM)

The charged Higgs boson decays H^±→W^±A₁ and H^±→W^±H_i are studied in the framework of the next-to-minimal supersymmetric standard model (NMSSM). It is found that the decay rate for H^±→W^±A₁ can exceed the rates for the τ^±ν and tb channels both below and above the top–bottom threshold. The dominance of H^±→W^±A₁ is most readily achieved when A₁ has a large doublet component and small mass. We also study the production process pp→H^±A₁ at the LHC followed by the decay H^±→W^±A₁, which leads to the signature W^±A₁A₁. We suggest that pp→H^±A₁ is a promising discovery channel for a light charged Higgs boson in the NMSSM with small or moderate tanβ and dominant decay mode H^±→W^±A₁. This W^±A₁A₁ signature can also arise from the Higgsstrahlung process pp→W^±H₁ followed by the decay H₁→A₁A₁. It is shown that there exist regions of parameter space where these processes can have comparable cross sections and we suggest that their respective signals can be distinguished at the LHC by using appropriate reconstruction methods. PACS  12.60.Fr; 14.80.Cp     

Study of the semileptonic decays B→<Emphasis Type="Italic">π</Emphasis>, D→<Emphasis Type="Italic">π</Emphasis> and D→K

The semileptonic decay B→π is studied starting from a simple quark model that takes into into account the effect of the B^*-resonance. A novel, multiply subtracted, Omnès dispersion relation has been implemented to extend the predictions of the quark model to all q² values accessible in the physical decay. By comparison to the experimental data, we extract | V _ub| = (3.4±0.2(exp.)±0.7(theory))0^-3. As a further test of the model, we have also studied D→π and D→K decays for which we get good agreement with experiment.     

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

Possible generalization of Boltzmann-Gibbs statistics

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS _q k [1 – _i=1 ^W p _i ^q ]/(q-1), whereq characterizes the generalization andp _i are the probabilities associated withW (microscopic) configurations (W). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq1 limit.     

Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph

For the kernel of the Laplace operator Δ^Λ with potential Σ _j=1 ^k c _j δ _{q j} (x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ ^k ⊕ ℂ ^k ), an isomorphism Γ: ker Δ^Λ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH ^Λ)) are found. Dedicated to the memory of V. A. Geyler     

Two-neutrino double β decay of96Zr to excited 2+ state of96Mo

The two-neutrino double beta decay of⁹⁶Zr isotope for 0⁺ → 2⁺ transition has been studied in the PHFB model. In our earlier work, the reliability of the intrinsic wave functions of⁹⁶Zr and⁹⁶Mo isotopes has been established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties as well as half-lives of 2vββ decay for 0⁺ → 0⁺ transition and the available experimental data. In the present work, the half-life of 2vββ decay for 0⁺ ar 2⁺ transition T ₁ ^2/2v (0⁺ →²⁺) has been calculated using the same set of intrinsic wave functions.     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Neutrino mixing and masses in a left–right model with mirror fermions

In the framework of a left–right model containing mirror fermions with gauge group SU(3) _C ⊗SU(2) _L ⊗SU(2) _R ⊗U(1) _Y′, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes μ→eγ, τ→μγ and τ→eγ. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels N→W ^± l ^∓, N→Zν _l and N→Hν _l , which are roughly equal for large values of the heavy neutrino mass. Starting from the most general Majorana neutrino mass matrix, the smallness of active neutrino masses turns out from the interplay of the hierarchy of the involved scales and the double application of seesaw mechanism. An appropriate parameterization on the structure of the neutrino mass matrix imposing a symmetric mixing of electron neutrino with muon and tau neutrinos leads to tri-bimaximal mixing matrix for light neutrinos.     

Asymptotics of Determinants of Bessel Operators

 For aL ^∞ (ℝ₊)∩L ¹ (ℝ₊) the truncated Bessel operator B _τ (a) is the integral operator acting on L ² [0,τ] with the kernel

Pointwise bounds for Schrödinger eigenstates

In a different paper we constructed imaginary time Schrödinger operatorsH _q=–1/2+V acting onL ^q( ⁿ ,dx). The negative part of typical potential functionV was assumed to be inL +L ^q for somep>max{1,n/2}. Our proofs were based on the evaluation of Kac's averages over Brownian motion paths. The present paper continues this study: using probabilistic techniques we prove pointwise upper bounds forL ^q-Schrödinger eigenstates and pointwise lower bounds for the corresponding groundstate. The potential functionsV are assumed to be neither smooth nor bounded below. Consequently, our results generalize Schnol's and Simon's ones. Moreover probabilistic proofs seem to be shorter and more informative than existing ones.Laboratoire de Mathématiques de Marseille associé au C.N.R.S. L.A.225     

On Lieb-Thirring inequalities for higher order operators with critical and subcritical powers

Let ϰ _i (H _l (V)) denote the negative eigenvalues of the operatorH _l u≔(−Δ) ^l u−V≧0,x ℝ ^d onL ₂(ℝ ^d ). We prove the two-sided estimate . We discuss bounds on the Riesz means . The first author was supported by the EPSRC grant GR/J 32084. The second author was supported byDeutsche Forschungsgemeinschaft grant We 1964-1.