2 Space-time correlations between GRBs and upward-going muons

We look for correlations with 2233 GRBs in the Batse Catalogs 3B and 4B (Meegan [1997]) collected since 21 Apr. 1991 to 5 Oct. 1998 and 894 of the 909 upward-going muons detected by MACRO during this period (see Fig. 1). Considering Batse angular accuracy, we estimate that a half-cone of $20^{\circ }$ ( $10^{\circ }$) contains 99.8$\%$ (96.8$\%$) of $\nu$ sources (if GRB sources are $\nu$ sources, too). The same percentages of upward-going muons are contained in these half-cones from the GRB sources. As a matter of fact, we calculate via Monte Carlo the fraction of signal lost, which depends on the $\nu$ spectral index, multiple scattering of muons during propagation in the rock and MACRO angular resolution. Using various cone apertures, we estimate that this fraction is negligible for $\ge 10^{\circ}$. The area for upgoing muon detection in the direction of the GRBs averaged over all the bursts is 119 m². Its value is small because MACRO is sensitive to neutrinos only in the lower hemisphere and because it was incomplete in the period 1991-1994. We find no statistically significant correlation between neutrino event and GRB directions and detection times. As shown in Fig. 2, we find no events in a window of $\pm 200$ s inside $10^{\circ }$ from GRB directions and 1 event inside $20^{\circ }$, which was measured after 39.4 s from the Batse GRB of 22 Sep. 1995 (4B 950922). For this burst the radius of the positional error box in the Batse catalog is 3.86$^{\circ}$, much smaller than the angular distance of 17.6$^{\circ}$ at which we find the neutrino event. The expected number of atmospheric $\nu$ events is computed with the delayed coincidence technique. We expect 0.035 (0.075) events in $10^{\circ }$ ( $20^{\circ }$). The corresponding upper limits (90$\%$ c.l.) for the upward-going muon flux are 0.87 10^-9 cm^-2 ( 1.44 10^-9 cm^-2) upward-going muons per average burst. These limits exclude an extreme cosmic string-type model reported in (Halzen [1996]), which results in $10^{-1} \, \mu$ cm^-2, while according to a fireball scenario model in (Waxman [1997]), a burst at a distance of 100 Mpc producing 0.4 10⁵¹ erg in neutrinos of around 10¹⁴ eV would produce $\sim 6~10^{-11}$ cm^-2 upward-going muons.

Figure 1: MACRO upward-going muon (dashed line) and Batse GRB (solid line) distributions versus year

Figure 2: Difference in detection times vs. cosine of angular separation between Batse GRBs and upward-going $\mu$s. a) and b) have different time scales. In a) the $\pm 200$ s - $10^{\circ }$, $20^{\circ }$ windows are indicated