Dual parametrization of GPDs versus the double distribution Ansatz

We establish a link between the dual parametrization of GPDs and a popular parametrization based on the double distribution Ansatz, which is in prevalent use in phenomenological applications. We compute several first forward-like functions that express the double distribution Ansatz for GPDs in the framework of the dual parametrization and show that these forward-like functions make the dominant contribution into the GPD quintessence function. We also argue that the forward-like functions $Q_{2 \nu}(x)$ with $\nu \ge 1$ contribute to the leading singular small-$x_{Bj}$ behavior of the imaginary part of DVCS amplitude. This makes the small-$x_{Bj}$ behavior of \im A^{DVCS} independent of the asymptotic behavior of PDFs. Assuming analyticity of Mellin moments of GPDs in the Mellin space we are able to fix the value of the $D$-form factor in terms of the GPD quintessence function $N(x,t)$ and the forward-like function $Q_0(x,t)$.Comment: 18 pages, 5 figures. A version that appeared in Eur. Phys. J. A. Some of the statements were refined and misprints in the formulas were correcte

Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.Comment: 12 page

Pentaquarks with hidden charm as hadroquarkonia

We consider hidden charm pentaquarks as hadroquarkonium states in a QCD inspired approach. Pentaquarks arise naturally as bound states of quarkonia excitations and ordinary baryons. The LHCb $P_c(4450)$ pentaquark is interpreted as a $\psi'$-nucleon bound state with spin-parity $J^P=3/2^-$. The partial decay width $\Gamma(P_c(4450)\to J/\psi+N)\approx 11$ MeV is calculated and turned out to be in agreement with the experimental data for $P_c(4450)$. The $P_c(4450)$ pentaquark is predicted to be a member of one of the two almost degenerate hidden-charm baryon octets with spin-parities $J^{P}=1/2^-,3/2^-$. The masses and decay widths of the octet pentaquarks are calculated. The widths are small and comparable with the width of the $P_c(4450)$ pentaquark, and the masses of the octet pentaquarks satisfy the Gell-Mann-Okubo relation. Interpretation of pentaquarks as loosely bound $\Sigma_c\bar D^*$ and $\Sigma_c^*\bar D^*$ deuteronlike states is also considered. We determine quantum numbers of these bound states and calculate their masses in the one-pion exchange scenario. The hadroquarkonium and molecular approaches to exotic hadrons are compared and the relative advantages and drawbacks of each approach are discussed.Comment: 33 pages, 2 figures, 3, tables; Minor changes, 2 references added; Version published in Eur. Phys. J.

New LHCb pentaquarks as hadrocharmonium states

New LHCb Collaboration results on pentaquarks with hidden charm [1] are discussed. These results fit nicely in the hadrocharmonium pentaquark scenario [2,3]. In the new data the old LHCb pentaquark $P_c(4450)$ splits into two states $P_c(4440)$ and $P_c(4457)$. We interpret these two almost degenerate hadrocharmonium states with $J^P=1/2^-$ and $J^P=3/2^-$ as a result of hyperfine splitting between hadrocharmonium states predicted in [2]. It arises due to QCD multipole interaction between color-singlet hadrocharmonium constituents. We improve the theoretical estimate of hyperfine splitting [2,3] that is compatible with the experimental data. The new $P_c(4312)$ state finds a natural explanation as a bound state of $\chi_{c0}$ and a nucleon, with $I=1/2$, $J^P=1/2^+$ and binding energy 42 MeV. As a bound state of a spin-zero meson and a nucleon, hadrocharmonium pentaquark $P_c(4312)$ does not experience hyperfine splitting. We find a series of hadrocharmonium states in the vicinity of the wide $P_c(4380)$ pentaquark that can explain its apparently large decay width. We compare the hadrocharmonium and molecular pentaquark scenarios and discuss their relative advantages and drawbacks.Comment: 10 page