Decay widths of theX(1835)as anN¯Nbound state

Abstract

Partial decay widths of various decay channels of the X(1835) are evaluated in the 3 P0 quark model, assuming that the X(1835) is a N N bound state with the quantum number assignmentIt is found that the decays to the ρρ, ωω and πa0(1450) states dominate over other channels, and that the product branching fractions Br(J/ψ → γX)Br(X → ππη) and Br(J/ψ → γX)Br(X → ππη ′ ) are in the same order. We suggest that the X(1835) may be searched in the πa0(1450) channel.

Spanning tree generating functions and Mahler measures

“…We note that Rogers gave a slightly different version of (41), and that this form of the identity was first observed by Samart [36]. Rodriguez-Villegas and Stienstra proved similar modular expansions for two-variable Mahler measures [39], [31].…”

“…The integral on the right is analytic when |w| < 1, so it is easy to see that formula (36) is valid on a somewhat larger domain than formula (35). Formula (36) is an intermediate step in the derivation of (35), but is not actually stated in [32]. The two identities coincide if w ∈ [0, 1 2 ], because Clausen's identity allows us to perform the integration [9]:…”

“…Since 4w(1 − w) = 256u 9(1+3u) 4 , we recover (35). Clausen's identity fails when w > 1/2, so we need an additional method to simplify (36).…”

“…If we wish to compare formulas (36) and (48) numerically, it is sufficient to set r = 4p (1+p) 2 in (36). The left-hand side of (48) equals g 1 (6) when p = 1 2 2 + 3 √ 2 − 2 √ 3 − √ 6 .…”

“…However it could have been derived that way, as the relevant Mahler measure is given by equation ( 18) above. The value of the spanning tree constant is obtained by evaluating the STGF at z = 1, and this evaluation is given by Samart in terms of L functions [36] as…”