NLL QCD contribution of the electromagnetic dipole operator to B -> Xs gamma gamma with a massive strange quark

We calculate the O(αs) corrections to the double differential decay width dΓ77/(ds1ds2) for the process B¯→Xsγγ, originating from diagrams involving the electromagnetic dipole operator O7. The kinematical variables s1 and s2 are defined as si=(pb−qi)2/m2b, where pb, q1, q2 are the momenta of the b quark and two photons. We introduce a nonzero mass ms for the strange quark to regulate configurations where the gluon or one of the photons become collinear with the strange quark and retain terms which are logarithmic in ms, while discarding terms which go to zero in the limit ms→0. When combining virtual and bremsstrahlung corrections, the infrared and collinear singularities induced by soft and/or collinear gluons drop out. By our cuts the photons do not become soft, but one of them can become collinear with the strange quark. This implies that in the final result a single logarithm of ms survives. In principle, the configurations with collinear photon emission could be treated using fragmentation functions. In a related work we find that similar results can be obtained when simply interpreting ms appearing in the final result as a constituent mass. We do so in the present paper and vary ms between 400 and 600 MeV in the numerics. This work extends a previous paper by us, where only the leading power terms with respect to the (normalized) hadronic mass s3=(pb−q1−q2)2/m2b were taken into account in the underlying triple differential decay width dΓ77/(ds1ds2ds3).

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

A Ladder Operator Solution to the Particle in a Box Problem

A ladder operator solution to the particle in a box problem of elementary quantum mechanics is presented, although the pedagogical use of this method for this problem is questioned.

Operator and replicability bias in comparative taphonomic studies

The operator effect is a well-known methodological bias already quantified in some taphonomic studies. However, the replicability effect, i.e., the use of taphonomic attributes as a replicable scientific method, has not been taken into account to the present. Here, we quantified for the first time this replicability bias using different multivariate statistical techniques, testing if the operator effect is related to the replicability effect. We analyzed the results reported by 15 operators working on the same dataset. Each operator analyzed 30 biological remains (bivalve shells) from five different sites, considering the attributes fragmentation, edge rounding, corrasion, bioerosion and secondary color. The operator effect followed the same pattern reported in previous studies, characterized by a worse correspondence for those attributes having more than two levels of damage categories. However, the effect did not appear to have relation with the replicability effect, because nearly all operators found differences among sites. Despite the binary attribute bioerosion exhibited 83% of correspondence among operators it was the taphonomic attributes that showed the highest dispersion among operators (28%). Therefore, we conclude that binary attributes (despite showing a reduction of the operator effect) diminish replicability, resulting in different interpretations of concordant data. We found that a variance value of nearly 8% among operators, was enough to generate a different taphonomic interpretation, in a Q-mode cluster analysis. The results reported here showed that the statistical method employed influences the level of replicability and comparability of a study and that the availability of results may be a valid alternative to reduce bias.

A FEM-BEM coupling procedure through the Steklov-Poincarè operator

Many advantages can be got in combining finite and boundary elements.It is the case, for example, of unbounded field problems where boundary elements can provide the appropriate conditions to represent the infinite domain while finite elements are suitable for more complex properties in the near domain. However, in spite of it, other disadvantages can appear. It would be, for instance, the loss of symmetry in the finite elements stiffness matrix, when the combination is made. On the other hand, in our days, with the strong irruption of the parallel proccessing the techniques of decomposition of domains are getting the interest of numerous scientists. With their application it is possible to separate the resolution of a problem into several subproblems. That would be beneficial in the combinations BEM-FEM as the loss of symmetry would be avoided and every technique would be applicated separately. Evidently for the correct application of these techniques it is necessary to establish the suitable transmission conditions in the interface between BEM domain and FEM domain. In this paper, one parallel method is presented which is based in the interface operator of Steklov Poincarè.

Analysis of the operator action and the single failure criteria in a SGTR sequence using best estimate assumptions with TRACE 5.0

Steam Generator Tube Rupture (SGTR) sequences in Pressurized Water Reactors are known to be one of the most demanding transients for the operating crew. SGTR are a special kind of transient as they could lead to radiological releases without core damage or containment failure, as they can constitute a direct path from the reactor coolant system to the environment. The first methodology used to perform the Deterministic Safety Analysis (DSA) of a SGTR did not credit the operator action for the first 30 min of the transient, assuming that the operating crew was able to stop the primary to secondary leakage within that period of time. However, the different real SGTR accident cases happened in the USA and over the world demonstrated that the operators usually take more than 30 min to stop the leakage in actual sequences. Some methodologies were raised to overcome that fact, considering operator actions from the beginning of the transient, as it is done in Probabilistic Safety Analysis. This paper presents the results of comparing different assumptions regarding the single failure criteria and the operator action taken from the most common methodologies included in the different Deterministic Safety Analysis. One single failure criteria that has not been analysed previously in the literature is proposed and analysed in this paper too. The comparison is done with a PWR Westinghouse three loop model in TRACE code (Almaraz NPP) with best estimate assumptions but including deterministic hypothesis such as single failure criteria or loss of offsite power. The behaviour of the reactor is quite diverse depending on the different assumptions made regarding the operator actions. On the other hand, although there are high conservatisms included in the hypothesis, as the single failure criteria, all the results are quite far from the regulatory limits. In addition, some improvements to the Emergency Operating Procedures to minimize the offsite release from the damaged SG in case of a SGTR are outlined taking into account the offsite dose sensitivity results.