# QCD and Collider Physics

by

R. Keith Ellis ( ellis@fnal.gov )

W. James Stirling ( w.j.stirling@imperial.ac.uk )

Bryan R. Webber ( webber@hep.phy.cam.ac.uk )

Updates and corrections

We maintain an approved list of updates and corrections here, so please send us
a note of any errors that you think you have found.  Here are those reported so far:
 Page Eqn. or Figure Number Correction Thanks to: 3 4th line, last paragraph such muons --> such as muons 14 Eq.(1.48) Eq.(1.50) +m should read -m_j, +M should read -M. (The correct form is given in Eq. (1.9)) Stefano Catani 25 Fig.(2.2) The statement describing Fig.(2.2) is not literally correct. The curve including the 3-loop coefficient is distinguishable from the curve with the 2-loop coefficient. For an updated figure see Fig 2.2_updated Richard Ball 33 Eqs.(2.40)  and (2.41) Eq. (9) of the paper Nucl.Phys.B438:278,1995 (e-Print Archive: hep-ph/9411260) by S.A. Larin,T. van Ritbergen and J.A.M. Vermaseren corrects the paper by W. Bernreuther and W. Wetzel, Nucl.Phys.B197:228,1982, as confirmed by the erratum Nucl.Phys.B513:758(1998). Our Eq. (2.40) should read C_2(x)=\frac{1}{72 \pi^2} (2 x^2 +33 x -11) and hence our Eq. (2.41) becomes \alpha_{+}(m_q^2) = \alpha_{-}(m_q^2) -\frac{11}{72\pi^2}[\alpha_{-}(m_q^2)]^3 The difference between \alpha_{+} and \alpha_{-} remains small. 41 Eq.(2.69) The first integration should be from x to y, not from z to y Gavin Salam 55 Eq.(3.2) In the definition of kappa, the 16 pi alpha should be 4 pi alpha. Note that 1 >> |chi_1| >> chi_2, (rather than 1 >> chi_1 >> chi_2 as stated in text between Eqs.(3.3) and (3.4)). Thomas Hadig 56 Eq.(3.10) The RHS of Eq.(3.10) should be divided by 4 (ie the numerical factor is 6 not 24) Mike Seymour 57,58 Eqs.(3.12-3.15) These equations contain errors, although the final result Eq.(3.16) is correct, For the corrected equations see replacement text Carlo Ewerz Ugo Aglietti 78 Eq.(3.52) Eq.(3.53) The subscripts 2 and 3 should be interchanged; . The denominator should be |p_1 x p_2|.|p_3 x p_4|. In the last sentence in Sec 3.5 former should read latter. Mark Smith Thomas Hadig 87 Eq.(4.1) nu should be M(E-E') Mrinal Dasgupta 91 midpage "Note that in the QCD-improved parton model F_L is only non-zero at leading order in perturbation theory", should read "Note that in the QCD-improved parton model F_L is only non-zero beyond leading order in perturbation theory." Thomas Hadig 91 Eq.(4.19) There is a factor of x missing in the third term. F3(x,Q^2) should read x F3(x,Q^2) 91 Eq.(4.21) There is a factor of the ratio of the Z coupling to the photon coupling missing in the last line of Eqn. (4.21). The corrected version is given here Thomas Hadig 95 Eq.(4.29) The term involving W_1 should have an overall minus sign Mrinal Dasgupta 95,100,101 The notation for the square of vectors in the transverse plane is confusing. q_T^2, k_T^2 and q_T.k_T should be interpreted as 2-vector products, i.e. q_T^2 = -q_T^\mu q_{T \mu} > 0, etc. Thomas Hadig 106 Fig.4.8c,d Figures 4.8 c and d have incorrect arrows on fermion lines, For an updated figure see Fig 4.8_updated Thomas Hadig 107 4th line, last paragraph been so far been --> been so far Thomas Hadig 112 Eq.(4.110,4.116,4.117) Unfortunately we have used a mixed notation in describing the singlet NLO branching of a gluon into a quark. This leads to some confusion in the placement of factors of 2 n_f. Eqs.(4.109-4.112) satisfy Eqs.(4.116,4.117), after including the endpoint contributions as described in Eqs.(4.118-4.120). However the notation established in Eq.(4.92) suggests that they should satisfy an equation like the leading order momentum conservation relation, Eq.(4.93). 114 Eq.(4.122) The third equation  for P_{gq} is missing a factor of 9 in the denominator of the second term  The correct formulae are given in Zeit. Phys. C27,Page 623, Eq. (30). Richard Ball 115 Fig.(4.9) The upper-right (qg) plot includes the factor of 2n_f (with n_f=4) that is shown explicitly in Eq.(4.128). Peter Landshoff 136 Eqs. at foot of page The first bullet should read (n=0;m=0) + P^{(0)} : LO Thomas Hadig 145 Eqs.(4.216,4.218) The factor of u in the numerator of the integrand should be replaced by du 155 Ref. 34 Phys. Rev. 10 should read Phys. Rev. D10 Carlo Ewerz 161 Eq.(5.11) The = sign on the second line should be proportional to Dave Soper 162 Eq.(5.15) A factor of g is missing from the middle and right hand side. 162,163 Tables 5.2,5.3 These tables show the values of 2F, not F Dave Soper Eqs.(5.16,5.19) The factor of 4 should be replaced by 2 Dave Soper 164 Eqs.(5.26,5.28) In the case g -> gg, we define the n+1 particle cross section to include an identical particle factor 1/2. With this factor, the equations are correct as printed. Dave Soper 180 Eq.(5.79) The term on the right-hand side of the equal sign has the wrong sign 181 Eq.(5.88) It should have been mentioned that the first approximation in (5.90) has already been applied Junya Nakamura 184 Eq.(5.100) The right-hand sides of both equations should be multiplied by 2. The expression for p_T^2 is in fact only a small-angle approximation. Eq.(5.101) is still valid as it only aims to keep the leading soft and/or collinear singularities, so constant factors can be neglected. Junya Nakamura 202 Eq.(6.26) Eq.(6.27) The lower limit of integration should be 0, not x . There should be a tilde over the D Mrinal Dasgupta 210 5th line dot-dashed should read long-dashed Thomas Hadig 215 Eq.(6.57) The 3/4 should be 3/2, and the last two occurrences of phi_q should be phi_g Mark Smith 215 Eq.(6.61) The first occurrence of phi_q should again be phi_g, and the two occurrences of Delta_q should be Delta_g Mike Seymour 225 Eq.(6.91) s should read tau s Mike Seymour 234 Ref.(29) The page number of the second paper should be 323, not 353 245 Fig.(7.4) The qq luminosity shown is for identical flavours, i.e. (u*u+d*d+s*s+c*c+ubar*ubar+dbar*dbar+sbar*sbar+cbar*cbar). A plot for (q+qbar)*(q+qbar), including all flavour combinations, may be found here. Michael Peskin 253 Eq.(7.33) The factor of tau_J multiplying the parton luminosity should be removed. Howie Haber 260 2nd line amplitudes should read cross sections Timothy Thomas 280 Eq.(8.53) contains a typo ig_W \cdot T \slash{W} should read ig_W T \cdot \slash{W} 284 Eq.(8.67) q_f should read Q_f 294 Eq.(8.108) The right-hand side should be divided by s. John Campbell 307 Eq.(9.19) The factor of alpha_s/2pi in the second term on the right-hand side should be omitted, as it appears explicitly in Eq.(9.20). Marco Bonvini 317 Eq.(9.42) Assuming the bar over the sum on the left-hand side of Eq. (9.42) implies a colour average, the right-hand side should be divided by 3. 322 Eq.(9.53) pi should read 4 pi (both equations). 351 Eqs.(10.59,10.60) The short distance cross section is a function not of s but of s_hat, defined in Eq. (10.48) Florent Fayette 389 Eq.(11.1) The LEP Higgs mass limit given is out of date. The October 2005 LEP limit was M_H > 114.4 GeV (95% c.l.). See the page of the LEP Higgs Working Group for details. The mass listed in the 2013 Review of Particle Physics is M_H=125.9+/-0.4 GeV 391 Eq.(11.9) The factor of M_W^2/M_Z^2 in the Higgs -> ZZ partial width should be deleted, i.e., the ZZ width should be one half of the WW width with M_W replaced by M_Z. Stefano Forte 397 Eq.(11.19) 4 should read 16. The expansion of I(x) in inverse powers of x is 1 + 7/(120 x) + 1/(168 x^2) + ... 400 Eq.(11.22) C_1^W = 0, C_2^W = 1 should read C_1^W = 1, C_2^W = 0. Peter Williams 424 Eq.(12.25) The Review of Particle Physics updates measurements of the strong coupling constant, and other topics in quantum chromodynamics, regularly. The September 2005 value given there, replacing that in Eq. (12.25), is alpha_s(M_Z^2) = 0.1176 +/- 0.002.

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Bryan Webber

Last modified: Wed March 26 00:50:23 GMT 2014