Constraints on differential Shapiro delay between neutrinos and photons
  from IceCube-170922A
  On 22nd September 2017, the IceCube Collaboration detected a neutrino with
energy of about 290 TeV from the direction of the gamma-ray blazar TXS
0506+056, located at a distance of about 1.75 Gpc. During the same time,
enhanced gamma-ray flaring was also simultaneously observed from multiple
telescopes, giving rise to only the second coincident astrophysical
neutrino/photon observation after SN 1987A. We point out that for this event,
both neutrinos and photons encountered a Shapiro delay of about 6300 days along
the way from the source. From this delay and the relative time difference
between the neutrino and photon arrival times, one can constrain violations of
Einstein's Weak Equivalence Principle (WEP) for TeV neutrinos. We constrain
such violations of WEP using the Parameterized Post-Newtonian (PPN) parameter
$\gamma$, which is given by $|\gamma_{\rm {\nu}}-\gamma_{\rm{EM}}|<5.5 \times
10^{-2}$, after assuming time difference of 175 days between neutrino and
photon arrival times.
