Pentaquark photoproduction confronting with new LHCb observation

The newly measurement of production fractions of $P_c$ states by LHCb collaboration have put restriction on their decay branching ratios of $J/\psi p$ channel, so their photoproduction in $\gamma p\to J/\psi p$ reaction. We show the tension between LHCb results and the current experiments in search of $P_c$ photoproduction. We also find that present information of branching ratios of $P_c\to J/\psi p$ has already constrained the models which study the nature of $P_c$.

Very recently, the LHCb collaboration reported their new results of pentaquarks in Λ 0 b → J/ψpK − decay [1], soon after the first presentation at the Rencontres de Moriond QCD Conference [2], with nine times data sample more than that used in previous analysis [3].A new narrow pentaquark state, named as P c (4312), was observed with a statistical significance of 7.3 σ, and the previously reported P c (4440) resonance was resolved into two narrower states, P c (4440) and P c (4457), where the statistical significance of this two-peak interpretation is 5.4σ.The measured resonance parameters are summarized in Table I.
The pentaquark photoproduction, e.g.γp → J/ψp has attracted wide interest soon after their discovery at LHCb.The anomalous triangle singularity can not be present in this reaction, so the states which are photo-produced will be definitely genuine resonances.The calculation in various models give sizable peaks upon the non-resonant t-channel process in the cross sections with moderate partial width of P c → J/ψp [24][25][26][27].Several experimental proposals have been put forward, where some groups are analyzing the data and have released the preliminary results [28][29][30].The sensitivity of these planned experiment is usually in the order of several percentage for the branching ratio B(P + c → J/ψp).The production of exotic state candidate P c in γp → J/ψp can be written as [25,26], where s 1 is the spin of initial proton.The J is the total spin of P c , √ s the center of mass (c.m.) energy, and k in the magnitude of three momentum of initial states in c.m. frame.If assuming P c → γp is dominated by the vector meson (VMD), its branching ratio B(P c → γp) is proportional to B(P c → J/ψp) [25]: where α is the fine structure constant, L the quantum number of orbital excitation between J/ψ and proton, k out the magnitude of three momentum of final states in c.m. frame.The f L , whose value can be found in Ref. [25], is the fraction of decays P c → J/ψp in a relative partial wave L that goes into transversally polarized J/ψ.Thus the main uncertainty of the calculated cross section of γp → J/ψp is from the B(P c → J/ψp).
independent of the spin and parity of corresponding P c .LHCb group has measured the B(Λ 0 b → J/ψpK − ) several years ago [31], so if the branching ratio of Λ 0 b → P + c K − is known, one would obtain the value of B(Λ 0 b → J/ψpK − ).However, the B(Λ 0 b → P + c K − ) is dependent on the nature of P c and even the intrinsic component of Λ 0 b [32], which is not fully determined yet, therefore its value is hardly ever calculated and reported in the literature.
As a compromise, we can only speculate a range of B(Λ 0 b → P + c K − ) and B(P + c → J/ψp).LHCb has given the results [31]: whose accuracy is anticipated to be improved with the new LHCb data set.We will use the Particle Data Group (PDG) average value [33]: After combining it with R in Table I, we obtain GlueX at JLab Hall-D proposed an experiment to study the P c photoproduction and gave their preliminary result as [28]: P c (4312) + 4311.9 ± 0.7  challenging the partial widths with the value of above 1 MeV in dynamically generated coupled-channel unitary approach [14,15] and the updated version with further considering heavy quark symmetry [13,20].This upper limit is also much smaller than the calculation in molecular picture [7][8][9][10].A very recent calculation in the molecular scenario conclude that the B(P + c → J/ψp) for all P c is well above 10.0%[10].With this upper limit we have, which means that P + c K − is a very important decay channel for Λ 0 b , whose branching fraction is at least the same level with B(Λ 0 b → J/ψpK − ) in Eq. ( 5).The values in Eq. ( 6) are nearly one order smaller than previous LHCb results [31]: If we sum B(Λ b → P + c K − )B(P + c → J/ψp) of the P c (4440) + and P c (4457) + in Eq. ( 6), we find that it is in fact compatible with that of P c (4450) + in Eq. ( 9) within errors.This is consistent with the observation that P c (4450) + is decomposed into P c (4440) + and P c (4457) + states in the new LHCb data sample.If regardless of this problem at the moment, we adopt these values in Eq. ( 9) and GlueX's upper limit in Eq. (7), it means that, confronting with values in Eq. (8).In this case it is expected that B(Λ ), only smaller than the leptonic branching decay ratio of Λ 0 b , which is in the value of several percentage [33].This deduction challenges our understanding of Λ 0 b properties.Moreover, due to the narrow width of P c , if B(Λ b → P + c K − ) is big as indicated in Eq. ( 10), we can easily observe it from the K − recoil mass spectrum at BELLE or BELLE II.So the old LHCb results in Eq. ( 9) are confronting sharply with GlueX's upper limit in Eq. ( 7) and unreasonable.A reasonable and very loose upper limit of B(Λ b → P + c K − ) would be 10 −3 , which is consistent with Eq. ( 8).Therefore we have from Eq. ( 6): As a result, we roughly expect B(P + c → J/ψp) for all P c , 2% > B(P + c → J/ψp) > 0.05% (12) which is a tight constrain at the moment, spanning only within two order.A naive postulation is that B(Λ b → P + c K − ) shall be not bigger than B(Λ 0 b → J/ψpK − ) in Eq. ( 4).If we match this postulation and use an upper limit 10 −4 for B(Λ b → P + c K − ), the lower limit of B(P + c → J/ψp) would be 0.5%.However, we will adopt the conservative range in Eq. ( 12).Several models with molecular picture favor the assignment of 1/2 − , 1/2 − , and 3/2 − for P c (4312) + , P c (4440) + , and P c (4457) + , respectively [7-10, 13, 18].This assignment is supported by QCD sum rule [4] but different from the interpretation of hidden-charm diquarkdiquark-antiquark baryons [12].If the first two states have the same spin-parity as expected by the most of models, one may safely assume that their B(Λ b → P + c K − ) are roughly the same.From Table I, we have B(P c (4312) + → J/ψp) : B(P c (4440) + → J/ψp) = 1 : 3.7 +1.9 −4.4 .
If at the moment we neglect the small difference of phase space from P c mass and assume the decay of two P c states proceeding in the same partial wave in Eq. ( 2) (usually the lowest partial wave is dominant), the P c photoproduction at the peak position σ Pc is, Apparently above values imply that P c (4440) is much easier to be found in γp → J/ψp.So if we do not find P c (4440) + in the γp → J/ψp and use the GlueX's upper limit in Eq. ( 7), the upper limit of B(P c (4312) + → J/ψp) would be 0.54 +3.2 −0.18 %, very close to the lower limit in Eq. ( 12).So we expect roughly that: 2% > B(P c (4440 As stated above, this conclusion is dependent on two assumptions: FIG. 1: The cross section of γp → J/ψp as a function of √ s.The solid squares represent the GlueX preliminary data [28], and the open circles is the old data from the compilation in Ref. [34]. The grey band is from the range of the B(P c → J/ψp).
(1) The production mechanism of P c (4312) and P c (4440) is the same in the Λ b decay; (2) The decay of two P c states to J/ψp is proceeding in the same partial wave.
both of which depend critically on the nature of P c (4312) and P c (4440).The second one is trivially understandable because usually the dominance of the lowest partial wave.The first one about the P c production is rarely studied by the models, though their decay is explored widely.Eq. ( 16) tells us that P c (4312) photoproduction is out of reach of current cross section measurements, which is only sensitive to a few percentage of B(P c → J/ψp).
In other word, If the peak of P c (4312) is observed in γp → J/ψp by experiment, then the first assumption above would be most doubtful and the nature of P c (4312) and P c (4440) is quite different.
For P c (4440) and P c (4457), the situation is more complicated because of the closeness of two states.If the experiments do not find any peak around their mass, one possibility is that their couplings to J/ψp is really inconspicuous as shown by the lower limit in Eq. ( 16) and Eq.(12).However, another possible reason maybe the destructive interference between P c (4440) and P c (4457) + , even they both have strong coupling to J/ψp.
We plot the cross section of γp → J/ψp as a function of √ s in Fig. 1.We use the non-resonant contribution from soft dipole pomeron model [34].The resonant contribution is calculated by Eq. ( 1) with the range of B(P c → J/ψp) in Eq. ( 15) for P c (4312), Eq. ( 16) for P c (4440) and Eq. ( 12) for P c (4457), respectively.The grey error band is from the range of these B(P c → J/ψp).We use the central values of the parameters of P c states in Tab.I and do not consider the interference among various contributions here.As can be seen, it is really challenging to hunt for such narrow P c states in their photoproduction.
The Hall-C at JLab is analyzing the new data of γp → J/ψp and expected to released the results soon.It can identify the P c photoproduction if the partial decay ratios of J/ψp are of several percentage [29,30].If the upper limit of GlueX at Hall-D in Eq. ( 7) is confirmed, then it is not easy to study the P c peaks in the unpolarized cross section of γp → J/ψp.
However, the measurement of double polarization asymmetries at Hall-A would still be encouraged.With the lower limit in Eq. ( 12), Eq. ( 15) and Eq. ( 16), we optimistically expect that P c , at least for P c (4440), is noticeable in the polarization observables if they are real resonant states.The possible complex interference would be also differentiated by polarization measurements.
In a short conclusion, we give a range of B(P c → J/ψp) based on the measured branching ratios and fractions by LHCb and GlueX collaborations.The small B(P c → J/ψp) are confronting sharply with the up-to-date information of P c photoproduction.It is anticipated that the polarization observables in γp → J/ψp would be more appreciate for in searching of P c photoproduction and determine the assignment of their spin parity, considering the sensitivity of JLab experiments.Other final states, e.g.D0 Λ c in photoproduction, would be also crucial for looking for the P c states.We would like to address that the couplings of P c to J/ψp will disentangle various models of the P c , some of which have given the calculated values but well above the present range.On the other hand, we have limited information on P c production mechanism, especially the B(Λ b → P + c K − ) decay, so it needs more theoretical and experimental attention in the future.