Photon-initiated processes at high mass

We consider the influence of photon-initiated processes on high-mass particle production. We discuss in detail the photon parton distribution function (PDF) at relatively high parton $x$, relevant to such processes, and evaluate its uncertainties. In particular we show that, as the dominant contribution to the input photon distribution is due to coherent photon emission, at phenomenologically relevant scales the photon PDF is already well determined in this region, with the corresponding uncertainties under good control. We then demonstrate the implications of this result for the example processes of high-mass lepton and $W$ boson pair production at the LHC and FCC. While for the former process the photon-initiated contribution is expected to be small, in the latter case we find that it is potentially significant, in particular at larger masses.

Figure 1

(Left) The coherent [Eq. (6)] and incoherent [Eq. (11)] components of the photon PDF at the starting scale $Q_0^2=2{\mathrm{GeV}}^2$. (Right) The minimum photon $Q^2$ vs the momentum fraction $x$ carried for the coherent [Eq. (6)] and incoherent [Eq. (11)] emission processes.

Figure 2

The photon PDF at the scales ${\mu }_F=100$ and 2000 GeV, with the breakdown between coherent, incoherent and evolution components, defined as in Eqs. (3) and (10) given. Also shown is the NNPDF3.0 [10] result, with the corresponding 68% C.L. uncertainty bands, and the LUXqed [20] prediction. In the lower plots the ratios of the different components to the total photon PDF are shown.

Figure 3

The $\gamma \gamma$, $gg$, $q\overline{q}$ and $qq$ PDF luminosities. The $\gamma \gamma$ case is shown for the NNPDF3.0 [10] set and following the approach of Sec. 2b, while all other luminosities correspond to the NNPDF set. The corresponding 68% C.L. uncertainty bands are shown in the NNPDF cases, while an uncertainty band due to varying the incoherent component between $x\gamma (x,Q_0)=0$ and the upper bound of Eq. (11) is shown, although barely visible, for our prediction. The LUXqed [20] prediction is also shown.

Figure 4

The differential lepton pair production cross sections at $\sqrt{s}=13$ and 100 TeV with respect to the invariant mass of the pair $M_{ll}$, for lepton $|\eta |<2.5$ and $p_{\perp }>20\mathrm{GeV}$. The photon-initiated contributions predicted following the approach of Sec. 2 and the NNPDF3.0QED [10] set, including the 68% C.L. uncertainty bands are shown, in addition to the NLO Drell-Yan cross section, calculated with MCFM [25]. An uncertainty band due to varying the incoherent component between $x\gamma (x,Q_0)=0$ and the upper bound of Eq. (11) is shown for our prediction.

Figure 5

The differential $W$ boson pair production cross sections at $\sqrt{s}=13$ and 100 TeV with respect to the invariant mass of the pair $M_{WW}$, for $W$ pseudorapidity $|\eta |<4$. The photon-initiated contributions predicted following the approach of Sec. 2b and the NNPDF3.0QED [10], including the 68% C.L. uncertainty bands are shown, in addition to the NLO QCD cross section, calculated with MCFM [25], and including the gluon-initiated box contribution. An uncertainty band due to varying the incoherent component between $x\gamma (x,Q_0)=0$ and the upper bound of Eq. (11) is shown for our prediction.

Figure 6

The differential lepton pair-production cross section at $\sqrt{s}=8\mathrm{TeV}$ with respect to the invariant mass of the pair $M_{ll}$, calculated as in Fig. 4.