Digamma, what next?
نویسندگان
چکیده
If the 750 GeV resonance in the diphoton channel is confirmed, what are the measurements necessary to infer the properties of the new particle and understand its nature? We address this question in the framework of a single new scalar particle, called digamma (z). We describe it by an effective field theory, which allows us to obtain general and model-independent results, and to identify the most useful observables, whose relevance will remain also in model-by-model analyses. We derive full expressions for the leading-order processes and compute rates for higher-order decays, digamma production in association with jets, gauge or Higgs bosons, and digamma pair production. We illustrate how measurements of these higher-order processes can be used to extract couplings, quantum numbers, and properties of the new particle. ar X iv :1 60 4. 06 44 6v 2 [ he pph ] 1 1 M ay 2 01 6
منابع مشابه
Infinite family of approximations of the Digamma function
The aim of this work is to find “good” approximations to the Digamma function Ψ. We construct an infinite family of “basic” functions {Ia, a ∈ [0, 1]} covering the Digamma function. These functions are shown to approximate Ψ locally and asymptotically, and that for any x ∈ R, there exists a such that Ψ (x) = Ia (x). Local and global bounding error functions are found and, as a consequence, new ...
متن کاملThe integrals in Gradshteyn and Ryzhik. Part 10: The digamma function
The table of Gradshteyn and Rhyzik contains some integrals that can be expressed in terms of the digamma function ψ(x) = d dx log Γ(x). In this note we present some of these evaluations.
متن کاملTranscendental values of the digamma function
Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler’s -function. Let q be a positive integer greater than 1 and γ denote Euler’s constant. We show that all the numbers ψ(a/q)+ γ, (a, q)= 1, 1 a q, are transcendental. We also prove that at most one of the numbers γ, ψ(a/q), (a, q)= 1, 1 a q, is algebraic. © 2007 Elsevier Inc. All rights reserved. MSC: primary 11J81...
متن کاملThe Laplace Transform of the Digamma Function: an Integral Due to Glasser, Manna and Oloa
The definite integral M(a) := 4 π ∫ π/2 0 x2 dx x2 + ln2(2e−a cosx) is related to the Laplace transform of the digamma function L(a) := ∫ ∞ 0 e−asψ(s+ 1) ds, by M(a) = L(a) + γ/a when a > ln 2. Certain analytic expressions for M(a) in the complementary range, 0 < a ≤ ln 2, are also provided.
متن کاملA harmonic mean inequality for the digamma function and related results
We present some inequalities and a concavity property of the digamma function ψ = Γ′/Γ, where Γ denotes Euler’s gamma function. In particular, we offer a new characterization of Euler’s constant γ = 0.57721.... We prove that −γ is the minimum of the harmonic mean of ψ(x) and ψ(1/x) for x > 0. Mathematics Subject Classification (2010). 33B15, 39B62, 41A44.
متن کامل