Measurements are presented of the single-diffractive dijet cross section and the diffractive cross section as a function of the proton fractional momentum loss $\xi$ and the four-momentum transfer squared $t$. Both processes pp$\to$pX and pp$\to$Xp, ie with the proton scattering to either side of the interaction point, are measured, where X includes at least two jets; the results of the two processes are averaged. The analyses are based on data collected simultaneously with the CMS and TOTEM detectors at the LHC in proton-proton collisions at $\sqrt{s}$= 8 TeV during a dedicated run with $\beta^{\ast} =$ 90 m at low instantaneous luminosity and correspond to an integrated luminosity of 37.5 nb$^{-1}$. The single-diffractive dijet cross section $\sigma^\mathrm{pX}_{\mathrm{jj}}$, in the kinematic region $\xi \lt$ 0.1, 0.03 $\lt |$t$| \lt 1$ GeV$^2$, with at least two jets with transverse momentum $p_\mathrm{T} >$ 40 GeV, and pseudorapidity $|\eta| \lt$ 4.4, is 21.7$\pm$0.9 (stat)$^{+3.0}_{-3.3}$ (syst) $\pm$ 0.9 (lum) nb. The ratio of the single-diffractive to inclusive dijet yields, normalised per unit of $\xi$, is presented as a function of $x$, the longitudinal momentum fraction of the proton carried by the struck parton. The ratio in the kinematic region defined above, for $x$ values in the range $-$2.9 $\leq \log_{10} x \leq$$-$1.6, is $R = (\sigma^\mathrm{pX}_{\mathrm{jj}}/\Delta\xi)/\sigma_{\mathrm{jj}} =$ 0.025$\pm$0.001 (stat) $\pm$ 0.003 (syst), where $\sigma^\mathrm{pX}_{\mathrm{jj}}$ and $\sigma_{\mathrm{jj}}$ are the single-diffractive and inclusive dijet cross sections, respectively. The results are compared with predictions from models of diffractive and nondiffractive interactions. Monte Carlo predictions based on the HERA diffractive parton distribution functions agree well with the data when corrected for the effect of soft rescattering between the spectator partons.
A search for exclusive two-photon production via photon exchange in proton-proton collisions, pp $\to$ p$\gamma\gamma$p with intact protons, is presented. The data correspond to an integrated luminosity of 9.4 fb$^{-1}$ collected in 2016 using the CMS and TOTEM detectors at a center-of-mass energy of 13 TeV at the LHC. Events are selected with a diphoton invariant mass above 350 GeV and with both protons intact in the final state, to reduce backgrounds from strong interactions. The events of interest are those where the invariant mass and rapidity calculated from the momentum losses of the forward-moving protons matches the mass and rapidity of the central, two-photon system. No events are found that satisfy this condition. Interpreting this result in an effective dimension-8 extension of the standard model, the first limits are set on the two anomalous four-photon coupling parameters. If the other parameter is constrained to its standard model value, the limits at 95% CL are $\lvert\zeta_1\rvert$ $\lt$ 2.9 $\times$ 10$^{-13}$ GeV$^{-4}$ and $\lvert\zeta_2\rvert$ $\lt$ 6.0 $\times$ 10$^{-13}$ GeV$^{-4}$.