Boomerang webs up to three-loop order

Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm of the amplitude and their ultraviolet renormalization encodes its infrared structure. In this paper, we consider the particular class of boomerang webs, consisting of multiple gluon exchanges, but where at least one gluon has both of its endpoints on the same Wilson line. First, we use the replica trick to prove that diagrams involving self-energy insertions along the Wilson line do not contribute to the web, i.e. their exponentiated colour factor vanishes. Consequently boomerang webs effectively involve only integrals where boomerang gluons straddle one or more gluons that connect to other Wilson lines. Next we classify and calculate all boomerang webs involving semi-infinite non-lightlike Wilson lines up to three-loop order, including a detailed discussion of how to regulate and renormalize them. Furthermore, we show that they can be written using a basis of specific harmonic polylogarithms, that has been conjectured to be sufficient for expressing all multiple gluon exchange webs. However, boomerang webs differ from other gluon-exchange webs by featuring a lower and non-uniform transcendental weight. We cross-check our results by showing how certain boomerang webs can be determined by the so-called collinear reduction of previously calculated webs. Our results are a necessary ingredient of the soft anomalous dimension for non-lightlike Wilson lines at three loops.

Colour Preference for Two-Colour Combinations

What determines which colour combinations will be attractive to a person and which will not? Is colour attractiveness only a subjective human experience, or can we predict it based on physical colour parameters? One of the pioneers of the attraction of colour theories was Michel Eugène Chevreul (1786–1889). He distinguished two types of colour harmony – analog colour and contrast – and tried to describe what harmonics are based on physical colour parameters. This was later done by other scientists. Later, semantic evaluation of colours was introduced and factor analysis attempted to identify emotions caused by colours or combinations of colours. The aim of this research is to test whether there is a consistent pattern of judgments of colour combinations under controlled conditions and, if so, to what extent they are influenced by the objective physical characteristics of those combinations. Subjects. The study involved 40 students (20 men, 20 women). All subjects had normal colour vision and were not related to fine art. Research tools. The study used 8 colours: 4 opponent (green, red, yellow and blue) and 4 additional (orange, lettuce, blue and purple). The 28 colour combinations (made up of two different colours) were composed of those 8 colours and printed onto cardboard card where each colour had area of 80 mm x 80 mm. Questionnaire of 40 adjectives consisting of 20 pairs of antonyms were used for semantic colour assessment. Procedure. The investigation was conducted in a dark room. Initially, all 28 cards with colour combinations were placed randomly on a desk lit by a 40 cm high fluorescent lamp (4000K correlated colour temperature). The subject was asked to select one of the cards with the most preferable colour combination, to write its code on the questionnaire and to mark all the epithets in the questionnaire which suits this colour combination. The same procedure was applied to the all other cards. One experiment lasted 35–50 minutes. Results and conclusions. Independent component analysis distinguished 4 dimensions describing colours: pleasure, energy, purple color and strength. Logistic regression analysis was run on colour factor loadings to discriminate colour combinations into two groups: liked and disliked colour combinations. It shows that that colour combination could be predicted as being liked or disliked with 85% probability. Adding physical colour parameters to the regression increases prognostic probability to 92 %. Also a relationship between subjective factors and physical characteristics of colour combinations was found. Pleasure correlates with hue contrast and strength with saturation contrast. It can be argued that the reliability of colour combinations is determined by both subjective and physical factors.

Quality of Visual Aesthetic Facets in Designing Christian and Islamic Religious Websites

This study considers visual aesthetics as a significant contributor to involving the user in online visual communication. It argues that religious websites as an online environment require attention to the impressive communication process. In this study, we focus on how Christian and Islamic religious websites use the five visual aesthetic facets, including Simplicity, Diversity (visual richness), Colourfulness, Typography, and Image on homepages. To address this issue, 10 Christian and Islamic religious websites are selected from the Alexa top religious websites. Using a descriptive-analytics approach, evaluation of visual aesthetics is conducted through a checklist based on the theoretical and empirical literature reviewed on visual aesthetics and website design. It is included some criteria about visual aesthetic items in web design. The results show that Christian and Islamic religious websites have different types of visual aesthetics. Furthermore, Christian websites with high simplicity, low diversity, paying attention to the colour factor, appropriate typography and high-quality images, received the highest overall aesthetics ratings. While Islamic websites, with low simplicity, low diversity, little attention to the colour and typography characteristics, as well as low-quality images, received the low scores.

NON-UNIVERSALITY AND EVOLUTION OF THE SIVERS FUNCTION

We examine the large-x QCD evolution of the twist-three gluonic-pole strength defining an effective T -odd Sivers function, where evolution of the T -even transverse-spin DIS structure function g2 is multiplicative. The result corresponds to a colour-factor modified spin-averaged twist-two evolution.

ON THE COLOUR FACTOR RATIO CA/CF

From the fractal properties of the hadron suggested by the statistical model, the colour factor ratio [Formula: see text] has been derived and is found to be in exact agreement with the corresponding QCD prediction.