Many width parameters are invented to capture the tractability of CSP (and its equivalent problem, conjunctive queries (CQ) evaluation): treewidth, hypertree width, generalized hypertree width, fractional hypertree width, submodular width. Every width parameter besides treewidth seems to be motivated by the $V(H)$ can be unbounded given $H = (V(H),E(H))$ being a hypergraph representation of a problem instance, i.e., treewidth of $H$ can become unbounded but the problem instance with $H$ can be evaluated in polynomial-time. In other words, a class of hypergraphs with bounded treewidth fails to capture all the tractable problem instances. I can imagine this works for CSP where an arity of constraint can be unbounded but it's hard for me to imagine this assumption holds for conjunctive queries, which essentially suggests that an arity of a relation can be unbounded, which contradicts with the general assumption .
My question is
When does bounded treewidth fail to capture all tractable CQs? Is there any example? Such example (query) needs to have bounded arity of each relation appearing in the query and at the same time, the treewidth is unbounded.
One example, described in CSP, is given in  at the end of section 2. Translated into query context, effectively, it says that for a query with one relation, $R$, if arity of $R$ goes to $\infty$, associated $H$ has unbounded treewidth but it can be evaluated polynomial-time: we just simply return $R$ as the query result (Please correct me if I understand wrong). Thus, this specific example does not address my question. Gottlob et al.  mention the following in the paper "Each query having treewidth $k$ or degree of cyclicity $k$ has also query width $\le k$, but for some queries the converse does not hold [9, 18]. There are even classes of queries with bounded query width but unbounded treewidth." However, I haven't been able to find such query with unbounded treewidth but bounded hypertree width (or a closely-related query width) in the cited references of the sentence.
 Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases, volume 8. Addison-Wesley Reading, 1995.
 Martin Grohe and Dániel Marx. Constraint Solving via Fractional Edge Covers. ACM Transactions on Algorithms (TALG), 11(1):1–20, 2014.
 Georg Gottlob, Nicola Leone, and Francesco Scarcello. Hypertree Decompositions and Tractable Queries. Journal of Computer and System Sciences, 64(3):579–627, 2002.
 Ch. Chekuri and A. Rajaraman. Conjunctive Query Containment Revisited. In Proc. International Conference on Database Theory 1997 (ICDT’97), Delphi, Greece, Jan. 1997, Springer LNCS, Vol. 1186, pp.56-70, 1997.
 G. Gottlob, N. Leone, and F. Scarcello. The Complexity of Acyclic Conjunctive Queries. Technical Report DBAI-TR-98/17, available on the web as: http://www.dbai.tuwien.ac.at/staff/gottlob/acyclic.ps, or by email from the authors. An extended abstract concerning part of this work has been published in Proc. of the IEEE Symposium on Foundations of Computer Science (FOCS’98), pp.706-715, Palo Alto, CA, 1998.