Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points

This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on using generalized power series expansions near singular points of the differential system, solving difference equations for the corresponding coefficients in these expansions and using matching to connect series expansions at two neighboring points. Here we use our algorithm and the corresponding code for our example of four-loop generalized sunset diagrams with three massive and two massless propagators, in order to obtain new analytical results. We analytically evaluate the master integrals at threshold, $p^2=9 m^2$, in an expansion in $\epsilon$ up to $\epsilon^1$. With the help of our code, we obtain numerical results for the threshold master integrals in an $\epsilon$-expansion with the accuracy of 6000 digits and then use the PSLQ algorithm to arrive at analytical values. Our basis of constants is build from bases of multiple polylogarithm values at sixth roots of unity.Comment: Discussion extende

Four-loop quark form factor with quartic fundamental colour factor

We analytically compute the four-loop QCD corrections for the colour structure $(d_F^{abcd})^2$ to the massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in the top sector. We compute the master integrals by introducing a second mass scale and solving differential equations with respect to the ratio of the two scales. We present details of our calculational procedure. Analytical results for the cusp and collinear anomalous dimensions, and the finite part of the form factor are presented. We also provide analytic results for all master integrals expanded up to weight eight.Comment: 16 pages, 2 figure

Three-loop massive form factors: complete light-fermion and large-NcN_c corrections for vector, axial-vector, scalar and pseudo-scalar currents

We compute the three-loop QCD corrections to the massive quark form factors with external vector, axial-vector, scalar and pseudo-scalar currents. All corrections with closed loops of massless fermions are included. The non-fermionic part is computed in the large-$N_c$ limit, where only planar Feynman diagrams contribute.Comment: 33 page

Core formation on Mars and differentiated asteroids

Meteorite chronometry based on the Hf-182-W-182 system can provide powerful constraints on the timing of planetary accretion and differentiation(1-4), although the full potential of this method has yet to be realized. For example, no measurements have been made on the silicate-rich portions of planets and planetesimals other than the Earth and Moon. Here we report tungsten isotope compositions for two eucrites, thought to be derived from asteroid 4 Vesta, and from eight other basaltic achondritic meteorites that are widely considered to be from Mars. The eucrites, which are among the oldest differentiated meteorites, yield exceedingly radiogenic tungsten, indicating rapid accretion, differentiation and core formation on Vesta within the first 5-15 Myr of Solar System history, whereas the range of radiogenic tungsten measurements on the martian meteorites points towards tungsten depletion via melting and core formation within the first 30 Myr of the Solar System. The survival of tungsten isotope heterogeneity in the martian upper mantle implies that no giant impacts or large-scale convective mixing took place since this time, These results contrast with those obtained for the Earth-Moon system(2,3) for which accretion and core formation related to giant impacts appears to have continued for at least an additional 20 Myr.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62720/1/388854a0.pd

Behavioral interventions for asthma self-management in South Asian populations: a systematic review

Objective: Asthma outcomes are significantly worse for minority groups, including South Asians (SAs), in high-income settings. Despite this, comparatively few existing studies have focused on SAs when studying the effectiveness of behavioral interventions on asthma self-management, and no prior study has synthesized these findings. We review the effectiveness of behavioral interventions on asthma management in adults and children of SA origin across low- (LICs), middle- (MICs), and high-income countries (HICs). // Methods: Data sources included EMBASE, MEDLINE, Cochrane Library and Trial registries: WHO, ICTRP and ClinicalTrials.gov. Eligibility criteria: randomized controlled trials (RCTs), quasi-RCTs and non-RCTs (controlled before-after [CBA] studies), published in English, with no publication year or country restrictions in adults and children of South Asian origin. Exclusion criteria: those focusing solely on pharmacological interventions. Search terms were “asthma” and “South Asian”. // Results: We included 33 studies, 27 from MICs and 6 from HICs (education [n = 10], self-management plans [n = 6], yoga/breathing exercises [n = 10]) organizational interventions [n =1], diet therapy [n = 1] and combined interventions [n = 5]). Outcome measures included: blood biochemistry, lung function, healthcare utilization and quality of life. A meta-analysis was not performed due to significant study heterogeneity. // Conclusion: Behavioral interventions for asthma management in SAs are effective. Educational interventions that aim to optimize asthma knowledge, control, and inhaler technique, and yoga/breathing exercises are most effective for improved long-term outcomes in adults and children across LICs and MICs. Further research is needed to evaluate the effectiveness of all behavioral interventions for SAs in HICs to better inform current guidance by policy makers and health care providers

Inelastic scattering of photon pairs in qubit arrays with subradiant states

We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded in a waveguide. Our analysis reveals strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering such as superradiant, subradiant, and twilight states, being a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to a storage and processing of quantum information

Pressure dependence of upper critical fields in FeSe single crystals

We investigate the pressure dependence of the upper critical fields ({\mu}$_0$$H$$_{c2}$) for FeSe single crystals with pressure up to 2.57 GPa. The superconducting (SC) properties show a disparate behavior across a critical pressure where the pressure-induced antiferromagnetic phase coexists with superconductivity. The magnetoresistance for $H//ab$ and $H//c$ is very different: for $H//c$, magnetic field induces and enhances a hump in the resistivity close to the $T_c$ for pressures higher than 1.2 GPa, while it is absent for $H//ab$. Since the measured {\mu}$_0$$H$$_{c2}$ for FeSe samples is smaller than the orbital limited upper critical field ($H$$^{orb}$$_{c2}$) estimated by the Werthamer Helfand and Hohenberg (WHH) model, the Maki parameter ({\alpha}) related to Pauli spin-paramagnetic effects is additionally considered to describe the temperature dependence of {\mu}$_0$$H$$_{c2}$($T$). Interestingly, the {\alpha} value is hardly affected by pressure for $H//ab$, while it strongly increases with pressure for $H//c$. The pressure evolution of the {\mu}$_0$$H$$_{c2}$(0)s for the FeSe single crystals is found to be almost similar to that of $T_c$($P$), suggesting that the pressure-induced magnetic order adversely affects the upper critical fields as well as the SC transition temperature.Comment: 23 pages, 6 figures, 1 tabl

Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in ϵ\epsilon

Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of dimensional regularization, $d$. The method was used to obtain analytical expressions for two missing constants in the $\epsilon$-expansion of the most complicated master integrals contributing to the three-loop massless quark and gluon form factors and thereby present the form factors in a completely analytic form. To illustrate its power we present, at transcendentality weight seven, the next order of the $\epsilon$-expansion of one of the corresponding most complicated master integrals. As a further application, we present three previously unknown terms of the expansion in $\epsilon$ of the three-loop non-planar massless propagator diagram. Only multiple $\zeta$ values at integer points are present in our result.Comment: Talk given at the International Workshop `Loops and Legs in Quantum Field Theory' (April 25--30, 2010, W\"orlitz, Germany)