|−|Pic-Eur. Phys. J. C (2014) 74:Page 77 of 241ture in the J/ polarization |+|
of - J/ be the , at be , there is certainly no [/]  . . also the , the , in the in  production by . , of is the J/ production . could . . NRQCD factorization for not the to . might .of , the order the NRQCD v expansion and [https://dx.doi.org/10.1089/jir.2014.0026 title= jir.2014.0026] the , [https://dx.doi.org/10.1038/srep39151 title= srep39151] the O(v ) the  v , the ,  the , () . corrections the  , of , O() O(v ) the . two ,the the of , , to 1 of the  the states , at major 3/ .
|−|Pic- Eur. Phys. J. C (2014) 74:Page 77 of 241ture from the J/ polarization in photoproduction emerged. Moreover, no photoproduction may be observed at HERA. Consequently, from the theory side, a brand new ep collider at a lot greater energies and luminosities than HERA, like possibly an LHeC, would be very desired. Alternatively, there is certainly nonetheless no NLO calculation for J/ production in deep inelastic scattering accessible, as, by way of example, [ http://www.musicpella.com/members/babies66trade/activity/527192/ http://www.musicpella.com/members/babies66trade/activity/527192/] measured most lately by H1 [ 1171]. f. Further production observables The LHCb experiment with its specifically wealthy quarkonium plan has also measured totally new observables which still need to be exploited completely in theory tests: For the initial time in pp collisions the double J/ production cross section was measured [ 1172], as well because the production of J/ in association with charmed mesons [ 1173] . Like double charmonium production, J/ + cc was previously only measured in the B factories, most recent in the Belle analysis [ 1174] , which was critical for testing J/ production mechanisms in e+ e- production. J/ production in association with W bosons has for the very first time been measured by the ATLAS collaboration . Exclusive charmonium hadroproduction has been observed lately by CDF  and LHCb [1177, 1178]. Exclusive production had previously been a domain of ep experiments; see  for a current update by the H1 collaboration. One more observable for which theory predictions exist is definitely the J/ production price in scattering. This observable has previously been measured at LEP by DELPHI  with pretty significant uncertainties and could possibly be remeasured at an ILC. four. 5.2 NLO tests of NRQCD LDME universality The phenomenological relevance in the NRQCD factorization conjecture is closely tied for the query of whether or not the LDMEs might be shown to be universal. Within this section recent operates might be reviewed which aim at examining this universality at Next-to-Leading Order (NLO) in s . In the case of c J , these tests consist of just the leading  order with the NRQCD v expansion , formed by the n = three PJ and n = three S 1 states. In [https://dx.doi.org/10.1089/jir.2014.0026 title= jir.2014.0026] the case of three S1 quarkonia, these tests [https://dx.doi.org/10.1038/srep39151 title= srep39151] include things like the terms up to relative order O(v 4 ) within the [ 1] v expansion, namely the n = 3 S1 colour singlet state, as [ 8]   well because the n = 1 S0 , three S1 , and three PJ Colour Octet ( CO) states; see Table 5. The relativistic corrections involving the [ 1] [ 1] P H (three S1 ) and Q H (3 S1 ) LDMEs are, having said that, not portion of those analyses, while they may be of order O( v two ) and O(v four ) in the v expansion. You will discover two causes for that: Very first, the corresponding NLO calculations are far beyond the reach of existing techniques, and secondly, they're anticipated to give considerable contributions to hadroproduction only at m c and for photoproduction only at z 1 . This behavpT ior is inferred from the behavior at LO in s [ 1187,1188] and could 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: As an example, at major order in s the slope of your transverse momentum distribution in  -8 hadroproduction is d/dpT pT for the 3 S1 state, com  -6 pared to d/ dpT pT for the 1 S0 and three PJ states and [ 8] -4 d/dpT pT for the 3 S1 state. |+|
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The shape of high- pT J/ hadroproduction yield can  be nicely described by the 1 S0 element alone, which automatically yields unpolarized hadroproduction. Given that at pT > 10 GeV this can be already all data offered, there is certainly no tension among NRQCD predictions and present data if the validity with the NRQCD factorization conjecture is restricted [1/8] [1/8] and three PJ LDMEs to high sufficient pT values and the three S1 are very tiny and even put to zero, as for instance in the sixth column of Fig. 33 (set three). This can be also the spirit of , and of the evaluation , in which the NLO quick distance cross sections used in  are combined with cc production by means of single parton fragmentation utilizing frag2 mentation functions at order s such as a top log resummation. To summarize, none of your proposed CO LDME sets is capable to describe all of the studied J/ production information sets, which poses a challenge to the LDME universality. Doable resolutions include the following: 1. The perturbative v expansion could converge also slowly. 2. NRQCD factorization might hold for exclusive, but not inclusive, production. three. NRQCD factorization could hold only inside the area Monium . At the moment, photoproduction cross sections pT are measured only up to pT = 10 GeV. 4. NRQCD factorization might not hold for polarized production.four.5.three Current calculations of relativistic corrections As explained inside the final section, the relativistic corrections of order O(v 2 ) within the NRQCD v expansion have at leading order in s in inclusive hadro-  and photoproduction  been shown to become significantly less considerable than the CO contributions of order O(v title= jir.2014.0026 four ) inside the NRQCD v expansion. Similarly, title= srep39151 the O(v two )  plus the technically challenging O(v four )  relativistic corrections to gluon fragmentation into three S1 quarkonia have turned out to be little. The relativistic O(v two ) corrections to the method e+ e- J/ +gg have, on the other hand, turned out to be amongst 20 and 30 [1212,1213] relative towards the top order CS cross section, an enhancement comparable in size for the O(s ) CS correction [1214,1215]. These corrections helped bring the colour singlet model prediction for inclusive J/ production in e+ e- collisions in rough http://brycefoster.com/members/thomas0jumbo/activity/826438/ agreement with experimental information . Similarly, within the exclusive course of action e+ e- J/ + c , O(s ) corrections at the same time as relativistic corrections of O(v 2 ) have been necessary to bring the color singlet model prediction in agreement with data; see Table 14. Lately, even O(s v two ) corrections to this course of action have been calculated [1209,1216]. For a assessment on the history on the measurements and calculations of this process, also as for any description of different approaches to decide the LDMEs of relative order O(v 2 ), we refer to section four.five.1 of . As a final point of this section, we mention the interesting operate  in which relativistic corrections to the approach gg J/ +g through colour octet states formally of order O(v 6 ) had been estimated. In line with this evaluation, at major orderEur. Phys. J. C (2014) 74:3.five 3 (e e J/+X) [pb] two.five.