Gemeinschaftliches Wohnen – gestern und heute / Community Housing – Past and Present

Kühn, Gerd; Harlander, Tilman

doi:10.11129/detail.9783955530068.12

Cited by 1 publication

(4 citation statements)

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“…Z-boson exchange is only relevant at high energies. There, however, apart from the QCD corrections 2 , also the electro-weak corrections become important [2]; these will not be addressed in this paper. Nevertheless, rhad can be used to evaluate the vector contribution to the production of top quarks in the same way as for charm and bottom production.…”

Section: General Structure Of R(s)mentioning

confidence: 99%

“…At leading order (LO) perturbative QCD (pQCD), the cross section as a function of the squared center-of-mass (c.m.s.) energy, s, has thresholds at the points s = 4m 2 Q with Q = d, u, s, c, b, t. However, close to threshold, fixed-order pQCD is no longer applicable. Below threshold, non-perturbative effects lead to the formation of bound states of the quark-anti-quark pair, which appear as more or less sharp peaks in the cross section.…”

Section: General Structure Of R(s)mentioning

confidence: 99%

“…However, a peak in the cross section remains around s = 4m 2 t . 2 For a discussion of corrections to the axial-vector correlator see Ref. [1].…”

Section: General Structure Of R(s)mentioning

confidence: 99%

“…Furthermore we need r db V (s, M 1 , 0) up to the quadratic mass terms which enters the evaluation of R (2) c in the limit s > s thr b . It is given by…”

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confidence: 99%

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: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD

Harlander

Steinhauser

2003

Computer Physics Communications

102

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This paper describes the fortran program rhad which performs a numerical evaluation of the photon-induced hadronic R-ratio, R(s), related to the cross section for electron-positron annihilation, for a given center-of-mass energy √ s. In rhad the state-of-the-art perturbative corrections to R(s) are implemented and the running and decoupling of the strong coupling constant and the quark masses is automatically treated consistently. Several options allow for a flexible use of the program. PROGRAM SUMMARY Title of program: rhad Nature of physical problem:The hadronic R-ratio R(s) is a fundamental quantitiy in high energy physics. It is defined as the ratio of the inclusive cross section σ(e + e − → hadrons) and the point cross section σ pt = 4πα 2 /(3s). It is well-defined both from the experimental and the theoretical side. R(s) belongs to the few physical quantities for which high-order perturbative calculations have been performed (partial results up to order α 4 s exist!). Mass effects from real and virtual quarks, the evolution of the MS parameters, in particular in the presence of thresholds, and other subtleties lead to fairly complex results in high orders. Thus it is important to provide a comprehensive collection of formulas in order to make them available to non-experts. Method of solution:rhad is a compilation of all currently available perturbative QCD corrections to the quantity R(s). Several options are provided which allow for a flexible use. In addition, rhad contains routines which perform the running and decoupling of the strong coupling constant. Thus only the center-of-mass energy has to be provided in order to determine R(s). Restrictions on the complexity of the problem:The applicability of rhad is restricted to the perturbative energy regions and does not cover the narrow and broad resonances. Typical running time:The typical runtime is of the order of fractions of a second. LONG WRITE-UP General structure of R(s)We are considering the fully inclusive production of quark pairs in e + e − annihilation (for a review see Ref.[1]). The tree-level diagram for this process in shown in Fig. 1 (a). At leading order (LO) perturbative QCD (pQCD), the cross section as a function of the squared center-of-mass (c.m.s.) energy, s, has thresholds at the points s = 4m 2 Q with Q = d, u, s, c, b, t. However, close to threshold, fixed-order pQCD is no longer applicable. Below threshold, non-perturbative effects lead to the formation of bound states of the quark-anti-quark pair, which appear as more or less sharp peaks in the cross section. 1 In our perturbative framework of charm and bottom production, these narrow resonances cannot be described, and are therefore not included in rhad. In addition, we have to spare out the region between the physical threshold s low Q and the beginning of the more or less flat continuum region at s thr Q , where the cross section exhibits rapid variations. In the case of charm production, for example, the limits would be s low c ≈ 2m D ≈ 3.73 GeV and s thr c ≈ 4.8 G...

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Section: General Structure Of R(s)mentioning

confidence: 99%

Section: General Structure Of R(s)mentioning

confidence: 99%

“…However, a peak in the cross section remains around s = 4m 2 t . 2 For a discussion of corrections to the axial-vector correlator see Ref. [1].…”

Section: General Structure Of R(s)mentioning

confidence: 99%

“…Furthermore we need r db V (s, M 1 , 0) up to the quadratic mass terms which enters the evaluation of R (2) c in the limit s > s thr b . It is given by…”

mentioning

confidence: 99%

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