UC Berkeley

Using the known resummation of virtual corrections together with knowledge of the

leading-log structure of real radiation in a parton shower, we derive analytic expressions

for the resummed real radiation after they have been integrated over all of phase space.

Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV pp collider, we

show that resummation of the real corrections is at least as important as resummation of

the virtual corrections, and that this resummation has a sizable eect for partonic center of

mass energies exceeding

p

s = O(few TeV). For partonic center of mass energies

p

s & 10

TeV, which can be reached at a 100 TeV collider, resummation becomes an O(1) eect and

needs to be included even for rough estimates of the cross-sections.

We compute the leading-order evolution of parton distribution functions for all Standard

Model fermions and bosons up to energy scales far above the electroweak scale, where electroweak

symmetry is restored. Our results include the 52 PDFs of the unpolarized proton,

evolving according to the SU(3), SU(2), U(1), mixed SU(2)U(1) and Yukawa interactions.

We illustrate the numerical eects on parton distributions at large energies, and show that

this can lead to important corrections to parton luminosities at a future 100 TeV collider.

We present a resummation of those double-logarithmically enhanced electroweak correction

that arise in pp colliders because protons are not SU(2) singlets, by solving DGLAP

equations in the full Standard Model. We then show how to match these results with those

of xed-order electroweak calculations. At a 100 TeV pp collider, contributions beyond order

are 10% at partonic center-of-mass energies of a few TeV. These are mainly due to

initial states with massive vector bosons.