II-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Non-global logarithms in hadron collisions at Nc = 3†
Y. Hatta∗1,∗2 and T. Ueda∗3
Recently, there have been a lot of activities in developing Monte Carlo algorithms for simulating parton showers beyond the large-Nc (leading-Nc ) approximation where Nc = 3 is the number of colors. Traditionally, in most event generators, the large-Nc approximation has been the only practical way to keep
track of the color indices of many partons involved.
Among other observables, the ﬁnite-Nc corrections are
particularly important but diﬃcult to quantify for theso-called non-global observables1) which are sensitive
to the wide-angle emission of soft gluons in restricted
regions of phase space. In Ref. 2), we have developed a framework to resum non-global logarithms at
Nc = 3 by improving and completing the earlier attempt.3) Numerical results are so far available only
for two observables in e+ e− annihilation: interjet energy ﬂow2) and the hemisphere jet mass distribution.4)
In this work we demonstrate that our approach canbe practically applied to hadron collisions where it isprobably most useful. We do so by explicitly computing the rapidity gap survival (or ‘veto’) probabilities in
Higgs plus dijet production pp → HjjX. The relevant
logarithms are of the form (αs ln Q/Eout )n where Q is
the hard scale (Higgs mass or jet transverse momentum) and Eout ≪ Q is the veto scale.
Consider quark-quark scattering qi (p1 )qj (p2 ) →qk (p3 )ql (p4 )H where i, j, k, l = 1, 2, 3 are color indices.
The outgoing quarks with momenta p3 , p4 are backto-back and detected as two jets in the forward andbackward directions. We are interested in the probability that the energy emitted in the central rapdiity
region π − θin > θ > θin is less than Eout .
The leading-order amplitude can be written as
Mijkl = M1 δki δlj + M8 taki talj .

Fig. 1. Gap survival probability in qq → qqH, color-octetchannel.

⟩1 ⟨tr(U3 U1† )tr(U4 U2† ) ,(3)2Nc⟩⟨tr(U3 U1† )tr(U4 U2† )tr(U3 U2† )tr(U4 U1† )−2
Nc
8, (4)=Pqq
Nc2 − 11Pqq=

where Uα is the fundamental Wilson line in the direction of α. We compute these probabilities as a functionofτ=

Nc2 − 1 2 8M8 Pqq .
4Nc2(1)(2)

References

P 1,8 are the gap survival probabilities in the singlet
and octet channels.
†∗1
∗2
∗3(5)

8for θin = π/3 is shown in Fig. 1 toThe result for Pqq
gether with its various approximations. Surprisingly,
we ﬁnd a very good agreement with the large-Nc approximation in which P is simply computed from thesolution of the Banﬁ-Marchesini-Smye equation.5) A
similar conclusion is reached for other channels including gluons in the initial state. While we do not fully
understand the reason of this agreement at the moment, if it turns out to be a robust feature, it is goodnews because one can approximately get full-Nc resultsin hadron collisions using the known large-Nc frameworks.1,5)

where M1,8 are amplitudes in the singlet and octet
channel. We dress up (1) by attaching soft gluons toexternal legs in the eikonal approximation. We thensquare it and average over color indices to get the crosssection
1M12 Pqq+PT
αsln.
πEout

1) M. Dasgupta, G. Salam, Phys. Lett. B 512, 323 (2001).
2) Y. Hatta, T. Ueda, Nucl. Phys. B 874, 808 (2013).
3) H. Weigert, Nucl. Phys. B 685, 321 (2004).
4) Y. Hagiwara, Y. Hatta, T. Ueda, Phys. Lett. B 756,254 (2016).
5) A. Banfi, G. Marchesini, G. Smye, J. High Energy Phys.
08, 006 (2002).

Condensed from the article in Nucl. Phys. B 962, 115273(2021)RIKEN Nishina Center
Physics Department, Brookhaven National Laboratory
Faculty of Science and Technology, Seikei University- 65 -1