diff --git a/tests/test_2637_jax_tracer_error.py b/tests/test_2637_jax_tracer_error.py
new file mode 100644
index 0000000000..9b23fba060
--- /dev/null
+++ b/tests/test_2637_jax_tracer_error.py
@@ -0,0 +1,37 @@
+# BSD 3-Clause License; see https://github.com/scikit-hep/awkward/blob/main/LICENSE
+from __future__ import annotations
+
+import pytest
+
+import awkward as ak
+
+jax = pytest.importorskip("jax")
+
+
+def test():
+    ak.jax.register_and_check()
+
+    jets = ak.Array(
+        [
+            [
+                {"pt": 1.0, "eta": 1.1, "phi": 0.1, "mass": 0.01},
+                {"pt": 2, "eta": 2.2, "phi": 0.2, "mass": 0.02},
+            ],
+            [
+                {"pt": 4.0, "eta": 4.4, "phi": 0.4, "mass": 0.04},
+                {"pt": 5.0, "eta": 5.5, "phi": 0.5, "mass": 0.05},
+                {"pt": 6.0, "eta": 6.6, "phi": 0.6, "mass": 0.06},
+            ],
+        ],
+        backend="jax",
+    )
+
+    def correct_jets(jets, alpha):
+        new_pt = jets["pt"] + 25.0 * alpha
+        jets["pt"] = new_pt
+        return ak.sum(jets["pt"])
+
+    val, grad = jax.value_and_grad(correct_jets, argnums=1)(jets, 0.1)
+
+    assert val == 30.5
+    assert grad == 125.0