We present a study of the inexplicit connection between radio jet activity and γ-ray emission of BL Lacertae (BL Lac; 2200+420). We analyze the long-term millimeter activity of BL Lac via interferometric observations with the Korean VLBI Network (KVN) obtained at 22, 43, 86, and 129 GHz simultaneously over three years (from January 2013 to March 2016); during this time, two γ-ray outbursts (in November 2013 and March 2015) can be seen in γ-ray light curves obtained from Fermi observations. The KVN radio core is optically thick at least up to 86 GHz; there is indication that it might be optically thin at higher frequencies. To first order, the radio light curves decay exponentially over the time span covered by our observations, with decay timescales of 41185 days, 352±79 days, 310±57 days, and 283±55 days at 22, 43, 86, and 129 GHz, respectively. Assuming synchrotron cooling, a cooling time of around one year is consistent with magnetic field strengths B ∼ 2 μT and electron Lorentz factors γ ∼ 10 000. Taking into account that our formal measurement errors include intrinsic variability and thus over-estimate the statistical uncertainties, we nd that the decay timescale  scales with frequency τ ν - 0.2. This relation is much shallower than the one expected from opacity effects (core shift), but in agreement with the (sub-)mm radio core being a standing recollimation shock. We do not find convincing radio flux counterparts to the γ-ray outbursts. The spectral evolution is consistent with the `generalized shock model' of Valtaoja et al. (1992). A temporary increase in the core opacity and the emergence of a knot around the time of the second -ray event indicate that this γ-ray outburst might be an `orphan' are powered by the `ring of fire' mechanism.

Abstract
1. INTRODUCTION
2. OBSERVATIONS AND DATA REDUCTION
3. RESULTS
    3.1. Radio Morphology of BL Lac
    3.2. Radio Light Curves
    3.3. Spectral Indices and Spectrum of the Core
4. DISCUSSION
    4.1. Variability and Cooling Time Scales
    4.2. Shock Evolution in the Core Region
    4.3. The Radio – -Ray Connection
5. SUMMARY
REFERENCES

• Dae-Won Kim(Department of Physics and Astronomy, Seoul National University)
• Sascha Trippe(Department of Physics and Astronomy, Seoul National University) Corresponding author
• Sang-Sung Lee(Korea Astronomy and Space Science Institute/Korea University of Science and Technology)
• Jong-Ho Park(Department of Physics and Astronomy, Seoul National University)
• Jae-Young Kim(Max-Planck-Institut fur Radioastronomie)
• Juan-Carlos Algaba(Department of Physics and Astronomy, Seoul National University)
• Jeffrey A. Hodgson(Korea Astronomy and Space Science Institute)
• Motoki Kino(National Astronomical Observatory of Japan/Kogakuin University, Academic Support Center)
• Guang-Yao Zhao(Korea Astronomy and Space Science Institute)
• Kiyoaki Wajima(Korea Astronomy and Space Science Institute)
• Sincheol Kang(Korea Astronomy and Space Science Institute/Korea University of Science and Technology)
• Junghwan Oh(Department of Physics and Astronomy, Seoul National University)
• Taeseok Lee(Department of Physics and Astronomy, Seoul National University)
• Do-Young Byun(Korea Astronomy and Space Science Institute/Korea University of Science and Technology)
• Soon-Wook Kim(Korea Astronomy and Space Science Institute/Korea University of Science and Technology)
• Jeong-Sook Kim(National Astronomical Observatory of Japan)