| Summary: | IceCube measures a diffuse neutrino flux comparable to the Waxman-Bahcall bound, which suggests the possibility that the ultra-high energy cosmic rays (UHECRs) have a common origin with diffuse high energy neutrinos. We propose high energy gamma-ray and/or neutrino observations toward the arrival directions of UHECRs to search for the sources and test this possibility. We calculate the detection probability of gamma-ray/neutrino sources, and find that the average probability per UHECR of >10 EeV is ∼10% if the sensitivity of the gamma-ray or neutrino telescope is ∼10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>12</mn></mrow></msup></semantics></math></inline-formula> erg cm<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></semantics></math></inline-formula> s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and the source number density is ∼10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></semantics></math></inline-formula> Mpc<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula>. Future gamma-ray and neutrino observations toward UHECRs, e.g., by LHAASO-WCDA, CTA, IceCube/Gen2, are encouraged to constrain the density of UHECR sources or even identify the sources of UHECRs.
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