Erratum to: The LPM effect in sequential bremsstrahlung

The denominator Xy(XyXȳ − X2 yȳ) on the far right-hand side of (5.44d) should be Xȳ(XyXȳ−X yȳ). Analogously, the denominator Xȳ(XyXȳ−X yȳ) on the far right-hand side of (5.44e) should be Xy(XyXȳ−X yȳ). These errors propagate to the following corrections to the rest of the paper and significantly change the infrared behavior of the result. The behavior α2 s/x 3y3/2 shown on the right-hand side of (1.7) and (9.11) should instead be α2 s ln(y)/xy 3/2. But both here and in (1.6), it would be more precise and informative to write ln(y/x) instead of ln(y). The x −5/2 min in the text following (9.11) then becomes x −1/2 min ln 2 xmin, and so this divergence is almost as mild as the single-splitting divergence mentioned in the next sentence of the text. There is another error in the paper concerning the calculation of the pole terms in section 7. Section 7 successfully calculates a subset of the pole contributions associated with ∆t = 0 but misses others. This error requires a lengthy analysis to explain and correct, which may be found in ref. [41] below. The effects of the above correction to (5.44) and the correction [41] to the pole terms are that the number 10.437054610798 in footnote 35 should be −10.892657927744, the corresponding statement in the main text that [dΓ/dx dy]crossed is positive for (x, y) = (0.3, 0.6) is no longer true, and figure 27 and its caption should be replaced by those below. There are some purely typographic errors. In eqs. (5.7), (5.8) and (5.9a), all occurrences of B1 in those equations should be replaced by B ′. Eq. (6.10) should include a factor of E on the right-hand side. The Ω± appearing on the right-hand side of (E.9) should be Ω−.

The denominator X y (X y Xȳ − X 2 yȳ ) on the far right-hand side of (5.44d) should be Xȳ(X y Xȳ−X 2 yȳ ). Analogously, the denominator Xȳ(X y Xȳ−X 2 yȳ ) on the far right-hand side of (5.44e) should be X y (X y Xȳ − X 2 yȳ ). These errors propagate to the following corrections to the rest of the paper and significantly change the infrared behavior of the result.
The behavior α 2 s /x 3 y 3/2 shown on the right-hand side of (1.7) and (9.11) should instead be α 2 s ln(y)/xy 3/2 . But both here and in (1.6), it would be more precise and informative to write ln(y/x) instead of ln(y). The x −5/2 min in the text following (9.11) then becomes x −1/2 min ln 2 x min , and so this divergence is almost as mild as the single-splitting divergence mentioned in the next sentence of the text.
There is another error in the paper concerning the calculation of the pole terms in section 7. Section 7 successfully calculates a subset of the pole contributions associated with ∆t = 0 but misses others. This error requires a lengthy analysis to explain and correct, which may be found in ref.
The effects of the above correction to (5.44) and the correction [41] to the pole terms are that the number 10.437054610798 in footnote 35 should be −10.892657927744, the corresponding statement in the main text that [dΓ/dx dy] crossed is positive for (x, y) = (0.3, 0.6) is no longer true, and figure 27 and its caption should be replaced by those below.
There are some purely typographic errors. In eqs. (5.7), (5.8) and (5.9a), all occurrences of B 1 in those equations should be replaced by B . Eq. (6.10) should include a factor of E on the right-hand side. The Ω ± appearing on the right-hand side of (E.9) should be Ω − . The dΓ ∝ y −3/2 ln(y/x) dashed line shows the y −3/2 ln(y/x) behavior of the y x 1 power law quoted in (9.11). The dΓ ∝ y −1 ln(x/y) dashed line shows the x −1 ln(y/x) behavior of the same power law if one switches the labels x and y. We have only shown results for y ≤ 0.5; results for y > 0.5 are given by the permutation symmetry y ↔ z ≡ 1−x−y of the problem.
Finally, an embarrassingly misleading choice of notation was made in section 2.2, starting in (2.16). The d 2 Γ el /d 2 b ⊥ defined in (2.17) is not a "differential rate with respect to impact parameter" and should not have been called that, and the notation d 2 Γ el /d 2 b ⊥ should not have been used. A better notation is to replace d 2 Γ el /d 2 b ⊥ and d 2Γ el /d 2 b ⊥ by simply Γ el andΓ el throughout this section. In the new notation, Γ el (0, t) is the rate of elastic scattering from the medium, and Γ el (b, t) is the Fourier transform of the differential rate d 2 Γ el /d 2 q ⊥ with respect to transverse momentum transfer q ⊥ .
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