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Intrinsic Fluctuations of the Proton Saturation Momentum Scale in High Multiplicity p+p Collisions

High multiplicity events in p+p collisions are studied using the theory of the Color Glass Condensate. We show that intrinsic fluctuations of the proton saturation momentum scale are needed in addition to the sub-nucleonic color charge fluctuations to explain the very high multiplicity tail of distributions in p+p collisions. The origin of such intrinsic fluctuations are presumably non-perturbative in nature. Classical Yang Mills simulations using the IP-Glasma model are performed to make quantitative estimations. We find that fluctuations as large as $\cal O$(1) of the average values of the saturation momentum scale can lead to rare high multiplicity events seen in p+p data at RHIC and LHC energies. Using the available data on multiplicity distributions we try to constrain the distribution of the proton saturation momentum scale and make predictions for the multiplicity distribution in 13 TeV p+p collisions.