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Pic-Eur. Phys. J. C (2014) 74:Page 77 of 241ture from the J/ polarization Pic-Eur. Phys. J. C (2014) 74:Web page 77 of 241ture on the J/ polarization in photoproduction emerged. Additionally, no photoproduction might be observed at HERA. Hence, in the theory side, a brand new ep collider at much higher energies and luminosities than HERA, like possibly an LHeC, could be hugely preferred. On the other hand, there is still no NLO calculation for J/ production in deep inelastic scattering readily available, as, for example, measured most lately by H1 [1171]. f. Additional production observables The LHCb experiment with its especially rich quarkonium system has also measured entirely new observables which nonetheless have to be exploited totally in theory tests: For the initial time in pp collisions the double J/ production cross section was measured [1172], also as the production of J/ in association with charmed mesons [1173]. This observable has previously been measured at LEP by DELPHI [1180] with really massive uncertainties and could possibly be remeasured at an ILC. four.5.two NLO tests of NRQCD LDME universality The phenomenological relevance of your NRQCD factorization conjecture is closely tied to the question of no matter if or not the LDMEs could be shown to be universal. Within this section recent works is going to be reviewed which aim at examining this universality at Next-to-Leading Order (NLO) in s . In the case of c J , these tests incorporate just the top [1] order in the NRQCD v expansion, formed by the n = three PJ and n = 3 S 1 states. In title= jir.2014.0026 the case of three S1 quarkonia, these tests title= srep39151 incorporate the terms as much as relative order O(v four ) in the [1] v expansion, namely the n = three S1 color singlet state, as [8] [8] [8] well because the n = 1 S0 , 3 S1 , and three PJ Colour Octet (CO) states; see Table 5. The relativistic Cy5 NHS Ester corrections involving the [1] [1] P H (three S1 ) and Q H (3 S1 ) LDMEs are, even so, not element of these analyses, although they may be of order O(v 2 ) and O(v 4 ) within the v expansion. You will find two motives for that: Initially, the corresponding NLO calculations are far beyond the attain of existing techniques, and secondly, they're anticipated to offer substantial contributions to hadroproduction only at m c and for photoproduction only at z 1. This behavpT ior is inferred in the behavior at LO in s [1187,1188][8]and might be understood by noting that new topologies of Feynman diagrams open up when undertaking the transition from [1] the three S1 state for the CO states, but not when calculating relativistic corrections: One example is, at leading order in s the slope on the transverse momentum distribution in [1] -8 hadroproduction is d/dpT pT for the 3 S1 state, com[8] [8] -6 pared to d/dpT pT for the 1 S0 and 3 PJ states and [8] -4 d/dpT pT for the three S1 state. The O(s ) corrections for the essential unpolarized short[1/8] [1/8] [8] distance cross sections with the n = 1 S0 , three S1 , and 3 PJ intermediate states have been calculated for many of the.