rpp2010-rev-cross-section-formulae

rpp2010-rev-cross-section-formulae - 40. Cross-section...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
40. Cross-section formulae for speciFc processes 1 40. CROSS-SECTION FORMULAE FOR SPECIFIC PROCESSES Revised October 2009 by H. Baer (University of Oklahoma) and R.N. Cahn (LBNL). PART I: STANDARD MODEL PROCESSES Setting aside leptoproduction (for which, see Sec. 16 of this Review ), the cross sections of primary interest are those with light incident particles, e + e , γγ , q q , gq , gg , etc. , where g and q represent gluons and light quarks. The produced particles include both light particles and heavy ones - t , W , Z , and the Higgs boson H .W ep rov id eth e production cross sections calculated within the Standard Model for several such processes. 40.1. Resonance Formation Resonant cross sections are generally described by the Breit-Wigner formula (Sec. 16 of this Review ). σ ( E )= 2 J +1 (2 S 1 + 1)(2 S 2 +1) 4 π k 2 · Γ 2 / 4 ( E E 0 ) 2 2 / 4 ¸ B in B out , (40 . 1) where E is the c.m. energy, J is the spin of the resonance, and the number of polarization states of the two incident particles are 2 S 1 +1 and 2 S 2 + 1. The c.m. momentum in the initial state is k , E 0 is the c.m. energy at the resonance, and Γ is the full width at half maximum height of the resonance. The branching fraction for the resonance into the initial-state channel is B in and into the Fnal-state channel is B out . ±or a narrow resonance, the factor in square brackets may be replaced by π Γ δ ( E E 0 ) / 2. 40.2. Production of light particles The production of point-like, spin-1/2 fermions in e + e annihilation through a virtual photon, e + e γ f f ,atc .m . energysquared s is given by d Ω = N c α 2 4 s β £ 1+cos 2 θ +(1 β 2 )sin 2 θ ¤ Q 2 f , (40 . 2) where β is v/c for the produced fermions in the c.m., θ is the c.m. scattering angle, and Q f is the charge of the fermion. The factor N c is 1 for charged leptons and 3 for quarks. In the ultrarelativistic limit, β 1, σ = N c Q 2 f 4 πα 2 3 s = N c Q 2 f 86 . 8nb s (GeV 2 ) . (40 . 3) The cross section for the annihilation of a q q pair into a distinct pair q ± q ± through a gluon is completely analogous up to color factors, with the replacement α α s . Treating all quarks as massless, averaging over the colors of the initial quarks and deFning t = s sin 2 ( θ/ 2), u = s cos 2 ( 2), one Fnds [1] d Ω ( q q q ± q ± α 2 s 9 s t 2 + u 2 s 2 . (40 . 4) K. Nakamura et al. ,JPG 37 , 075021 (2010) (http://pdg.lbl.gov) July 30, 2010 14:36
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 40. Cross-section formulae for speciFc processes Crossing symmetry gives d Ω ( qq ± ± )= α 2 s 9 s s 2 + u 2 t 2 . (40 . 5) If the quarks q and q ± are identical, we have d Ω ( q q q q α 2 s 9 s · t 2 + u 2 s 2 + s 2 + u 2 t 2 2 u 2 3 st ¸ , (40 . 6) and by crossing d Ω ( α 2 s 9 s · t 2 + s 2 u 2 + s 2 + u 2 t 2 2 s 2 3 ut ¸ . (40 . 7) Annihilation of e + e into γγ has the cross section d Ω ( e + e α 2 2 s u 2 + t 2 tu . (40 . 8) The related QCD process also has a triple-gluon coupling. The cross section is d Ω ( q q gg 8 α 2 s 27 s ( t 2 + u 2 ) Ã 1 tu 9 4 s 2 . (40 . 9) The crossed reactions are d Ω ( qg α 2 s 9 s ( s 2 + u 2 )( 1 su + 9 4 t 2 )( 4 0 . 10) and d Ω ( q q α 2 s 24 s ( t 2 + u 2 )( 1 tu
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 24

rpp2010-rev-cross-section-formulae - 40. Cross-section...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online