New Spectroscopy with PANDA at FAIR: X, Y, Z and the F-wave Charmonium States
aa r X i v : . [ h e p - e x ] D ec New Spectroscopy with PANDA at FAIR:X, Y, Z and the F-wave Charmonium States.
Elisabetta Prencipe , Jens S ¨oren Lange and Alexander Blinov Forschngszentrum J¨ulich, J¨ulich (DE) Justus-Liebig-Universit¨at, Giessen (DE) Budker Institute of Nuclear Physics and Novosibirsk State University, Novosibirsk (RUS) a) [email protected] behalf of the PANDA collaboration. Abstract.
Charm and charmonium physics have gained renewed interest in the past decade. Recent spectroscopic observationsstrongly motivate these studies. Among the several possible reactions, measurements in proton-antiproton annihilation play animportant role, complementary to the studies performed at B-factories. The fixed target PANDA experiment at FAIR (Darmstadt,Germany) will investigate fundamental questions of hadron and nuclear physics in the interactions of antiprotons with nucleonsand nuclei. With reaction rates as large as 2 × interactions / s, and a mass resolution 20 times better as compared with the mostrecent B-factories, PANDA is in a privileged position to successfully perform the measurement of the width of narrow states,such as the X (3872). PANDA will investigate also high spin particles, whose observation was forbidden at B-factories, i.e. F-wavecharmonium states. In this report extrapolations on cross sections and rates with PANDA are given. INTRODUCTION
In the past decade many new, narrow states have been observed in the charmonium and bottomonium mass regions,which do not fit into a spectroscopical scheme as predicted by a static quark-antiquark potential model [1].The X (3872) [2, 3, 4, 5], for example, is found very narrow and close to the DD ∗ threshold. Recently the quan-tum numbers have been determined to J PC = ++ by LHCb [6]. However, its nature is not understood, yet. The Y (4260) [7, 8, 9] is found far above the open-charm thresholds; however no decay into D ( ∗ ) D ( ∗ ) has been observedso far. Therefore it is being discussed e.g. as a possible hybrid with gluonic excitation. Z states have raised attentionafter the discovery of the Z (4430) [10, 11], because many of those Z states are charged, which is in contradictionto conventional charmonium, inevitably being neutral. In the past 2 years several resonant structures, namely the Z c (3900) [12, 13], the Z c (4020) [14], the Z c (3885) [15], and the Z c (4025) [16], have been observed. Their nature isstill unclear.The transition Y (4260) → Z (3900) − π + has been seen by BES III [17]; the transition Y (4260) → X (3872) γ hasalso been seen [18]. But no experiment until now looked for the transition X → Z , or vice versa. Some Z states areobserved decaying to DD ∗ or D ∗ D ∗ . The mass values of the Z c (3885), the Z c (3900), and the Z c (4020), published byBESIII, are close to the DD ∗ and D ∗ D ∗ thresholds, respectively. Assuming that the Z states contain S-wave DD ∗ and D ∗ D ∗ components, the spin parity J P of the Z c (3885) and the Z c (3900) would be J P = + , and the spin parity of the Z c (4020) is expected to be J P = + , 1 + , or 2 + . The former is confirmed by BESIII experimental data. One can expectalso similar S-wave resonances in the ¯ DD system, with J P = + (C =+ / c , which are not observed yet.In this context, the contribution of a ¯ pp machine has to be considered as essential, because it can either confirmthe above BES III measurements, and look for the non-observed 0 + Z states at the ¯ DD threshold, as ¯ pp annihilation is agluon rich process with direct access to various quantum numbers in production processes. In addition, the possibilityof F-wave charmonium state search has been explored, as a test of flavor independence to understand the quark-antiquark potential. stimates for the X (3872) at PANDA. The future PANDA experiment at FAIR (Facility for Antiproton and Ion Research) is well suited for charmoniumstudies, thanks to the high capability rate and the excellent mass resolution, that allows high precision measurementsand energy scan. The experimental setup is described elsewhere [19].One of the most striking advantages of the PANDA experiment is the opportunity to search for direct productionof exotic resonant states with various quantum numbers, including charged ones in ¯ pd collisions. In e + e − experimentsonly neutral J PC = −− resonances can be directly produced, and production of exotic charmed states through othermechanisms is suppressed.Using the detailed balance method, we can evaluate the cross section as: σ [ ¯ pp → R ] · BR ( R → f ) = (2 J + · π s − m p · BR ( R → ¯ pp ) · BR ( R → f ) · Γ R √ s − m R ) + Γ R (1)where f is the final state of the decay channel, Γ is the total width of a resonance R , and √ s the center ofmass energy. For example, in order to evaluate the cross section of the process ¯ pp → X (3872), we make use of theEquation (1), and obtain: σ [ ¯ pp → X (3872)] · BR ( X (3872) → f ) = · π s − m p · BR ( X (3872) → ¯ pp ) · BR ( X (3872) → f ) · Γ X (3872) √ s − m X (3872) ) + Γ X (3872) . (2)We know that the spin parity of the X (3872) is J P = + . We assume here a non-polarized incident beam. Downbelow we will use the decay channel J / ψπ + π − as f for the case of the X (3872). If we run at √ s = m X (3872) = / c the Equation (2) simplifies: σ [ ¯ pp → X (3872)] = · π m X (3872) − m p · BR ( X (3872) → ¯ pp ). Here we assume c = ~ = BR (( X (3872) → ¯ pp ), then, enters the formula of Equation (2). We estimate it from the available experimentalmeasurements in the PDG [20], and those published by the LHCb experiment [21]. The combination of both leadsto an upper limit at 95% confidence level (c.l.): σ ( ¯ pp → X (3872)) < (68 ± σ ( ¯ pp → X (3872)) =
50 nb. Therefore, inPANDA we use to evaluate the expected X (3872) yield by using the above cross section estimate. This value should beinterpreted as an upper limit. A lower limit estimate to the X (3872) cross section cannot be quoted yet, simply becauseits very narrow width leads to unreasonable lower limits, by using standard methods for cross section evaluations.PANDA could start in di ff erent operation modes, involving di ff erent antiproton beam resolution and luminosityvalues. Assuming the X (3872) cross section in ¯ pp annihilation equal to 50 nb [22, 23], we are expected to produce432000 X (3872) per day in high luminosity mode (average luminosity L = cm − s − ), and 43200 X (3872) perday in high resolution mode (average luminosity L = cm − s − ). Thus, PANDA can be considered as a ”mini- X (3872) factory”. In the latter situation, the mass scan in 100-keV-steps, that is needed to measure the X (3872) width,can be performed in about 3 weeks, collecting 15 points above and below the mass threshold, as detailed explained inRef. [24]. In high resolution mode, PANDA is designed to have ∆ p / p = · − . Estimates for the Y (4260) at PANDA. We calculate the number of produced Y (4260) by multiplying the expected luminosity and the cross section of theprocess ¯ pp → Y (4260). We assume BR ( Y (4260) → J /ψπ + π − ) = • the decay Y (4260) → J /ψπ + π − was the discovery mode [7]; • for all known Y (4260) decay channels, the PDG [20] quotes “seen” with no numbers reported; • all searches for decays to open charm performed at B factories, in ISR and B decay modes, lead to upper limitsonly. In the PDG [20], these upper limits are all normalized to the BR( Y (4260) → J /ψπ + π − ) [25, 26, 27, 28,29, 30, 31, 32]; • recently, the BESIII experiment published the observation of the transition Y (4260) → γ X (3872) [18], fromwhich it can be concluded that the BR ( Y (4260) → γ X (3872), with X (3872) → J /ψπ + π − , contributes in negligi-ble way to the total BR ( Y (4260)), i.e. ≤ pp → Y (4260) can be estimated using detailed balance (Equation (1)). However,if the poorly known upper limit BR ( Y (4260) → ¯ pp ) / BR ( Y (4260) → J /ψπ + π − ) < pp , is known, we can directly apply the detailed balance method toevaluate the cross section. However, if this BR is not known, at first we use the ansatz that partial width is identicalfor states R , R of the same quantum number [19]. BR ( R → pp ) = BR ( R → pp ) · Γ total ( R ) Γ total ( R ) . (3)This method assumes that the partial widths Γ ( R → ¯ pp ) of all charmonium states are identical, where R refers tothe state. Although we might have indication that the Y (4260) is not a charmonium state, no model exists to evaluatethe cross section for exotic states. In absence of any explanation of the Y (4260) nature, thus we perform our calculationunder the naive assumption that it is a charmonium state. As a reference state for the Y (4260) estimates, we choose the ψ (3770), for which the following numbers have been recently measured [35]: BR ( ψ (3770) → ¯ pp ) = (7 . + . − . ) · − ,and σ ( ¯ pp → ψ (3770)) = (9 . + . − . ) nb . We start our calculation from Equation (3), using ψ (3770) as a reference, andobtain: BR ( Y (4260) → pp ) = BR ( ψ (3770) → pp ) · Γ total ( ψ (3770)) Γ total ( Y (4260)) . (4)We can write again Equation (4), using the detailed balance principle, as: σ ( pp → Y (4260)) = σ ( pp → ψ (3770)) · Γ total ( ψ (3770)) Γ total ( Y (4260)) = . nb · . MeV
MeV = . nb . (5)We assume the cross section of Equation (5) as an upper limit. In order to estimate a lower limit for the cross section¯ pp → Y (4260), we use the assumption that the annihilation part, which manifests in the decay into e + e − and the decayinto ¯ pp , are identical: σ ( pp → Y (4260)) = . nb · Γ ee ( Y (4260)) Γ ee ( ψ (3770)) = . nb · Γ ee ( Y (4260)) BR ( ψ (3770) → e + e − ) · Γ total ( ψ (3770)) = . nb . (6)This result is obtained by using the partial width Γ ee ( Y (4260)) and Γ total from PDG [20], and BR ( ψ (3770) → ¯ pp )from Ref. [35]. As a word of caution, the scaling in Equation (4) is only an approximation as well, as e + and e − are point-like particles, but p and ¯ p are not. When scaling the partial width Γ ( R → ¯ pp ) (or the branching fraction BR ( R → ¯ pp )) for a decay to ¯ pp of a resonance R = R with a mass m to another resonance R = R with a mass m , onewould have to take into account, that the proton formfactor G has an energy dependence G ( √ s ) and is changing from √ s = m to √ s = m . However, we do not have to apply this correction here for the evaluation of the lower cross sectionlimit for the Y (4260), as the formfactor is already implicitely included in the measured BR ( ψ (3770) → ¯ pp )).The cross section σ ( ¯ pp → Y (4260)) could be compared to the cross section σ ( e + e − → Y (4260)) = (62.9 ± pp process is a factor of about 35 larger thanthe cross section measured in e + e − collisions. Estimation of the produced Z c (3900) at PANDA. The number of expected Z c (3900) events in PANDA can be estimated from Refs. [17], [23], and [34]: in the decay e + e − → J /ψπ + π − the BESIII experiment observed the Z c (3900) [17], using the full dataset collected near the Y (4260)energy. The observed Z c (3900) yield is 307, and the ratio R = σ ( e + e − → Z c (3900) + π − → J /ψπ + π − ) σ ( e + e − → J /ψπ + π − ) = . . (7)All measurements are based on 1.9 fb − , which is presently the world largest dataset collected at the Y (4260)energy. We can extrapolate how many produced Z c (3900) are expected at PANDA, assuming that [66 − Y (4260)states are expected to be produced per day in high resolution mode. The calculation is based upon the cross sectionrange [77 − σ ( ¯ pp → Z c (3900)) = σ ( ¯ pp → Y (4260)) · . = . nb . (8)For the lower limit evaluation we find: σ ( ¯ pp → Z c (3900)) = σ ( ¯ pp → Y (4260)) · . = . nb . (9)Based on these estimates, we would be able to produce [14 − Z c (3900) events / day in high resolution mode,when running at a center-of-mass energy for Y (4260) peak resonance production. We note that of course there canbe non-resonant production ¯ pp → J /ψπ + π − at the same energy, and the according non-resonant cross section can beeven larger than the resonant cross section, although the indication from BESIII and the ISR measurements at the Bfactories is that non-resonant e + e − → J /ψπ + π − is small ( O < Z ↔ X transitions at PANDA. Observations of transitions of X, Y and Z states are very important for understanding the spectroscopical pattern, andpossibly conclude similarities in the nature of these states. Two recent BESIII publications connect the X (3872) to the Y (4260) [18], and the Y (4260) to the Z c (3900) [17]. However, up to now, no experimental measurement connects the X (3872) to the Z structures. Thus, we propose to search for the transitions X to Z (or Z to X). PANDA would be wellsuited for this search because of the following reasons: • about possible Z to X transitions, the decay Z (3900) → X (3872) π is kinematically forbidden. The decay Z (4020) → X (3872) π is allowed, however suppressed as a P-wave decay close to threshold, since both the X (3872) and the Z (4020) have positive parity (assuming S-wave D ∗ D ∗ content of the Z (4020)). Two pion tran-sitions between the Z (4020) and the X (3872) would go in S-wave, but they are kinematically forbidden; • Z (4020) + → J /ψπ π + is allowed, but no signal for the Z (4020) was observed in the investigation of the accord-ing final state in searches for the charged partner of the X (3872) at BaBar [36] and Belle [37]; • PANDA will collect a data set of X (3872) (see above), with a statistics larger than other experiments by one ortwo orders of magnitude. Thus, rare decays of the X(3872), e.g. isospin forbidden decays or radiative decays,become accessible; • as the Z (3900) was observed in close vicinity of the DD ∗ threshold, and the Z (4020) was observed in closevicinity of the D ∗ D + threshold, it is intriguing to assume the existance of another yet unboserved Z (3730) inclose vicinity of the ¯ DD threshold. Assuming S-wave, this state would have J P = + , and thus it cannnot decayto J / ψπ due to parity conservation. In fact, neither charged or neutral structure have been observed around thismass in this final state. Using the future X (3872) data sample at PANDA, X (3872) → Z (3730) π representsa candidate decay channel. The latter decay is suppressed due to isospin violation; however, isospin violatingdecays of the X (3872), such as X (3872) → J / ψρ , have been observed with significant branching fractions. Inaddition, the requirement of a J / ψ in the final state provides a tool to reduce the hadronic background at PANDA.Simulations performed at the X (3872) energy scan have already shown that the ratio signal over background is6:1 [24]; therefore, a favorable ratio S / B is expected also for the search of the Z (3730) resonant structures; • due to the observation of the Z (3900) and the Z (4020) , Z c states have been interpreted as isospin tripletswith charged and neutral partners at the same mass. Thus, we may search for the Z (3730) , which could bereconstructed from J /ψγ and χ c π decays. In fact, in these transitions the parity flips from J P = + (the X (3872))to J P = + × − . Although radiative decays are suppressed by α / π , the observation of this decay would be of veryhigh importance, as it would provide a way to measure the C-parity of the Z (3730) ; • in an additional stage, we could also search for the charged Z (3730) + candidate, decaying to χ c π + , with subse-quent χ c → J /ψγ and J /ψ → leptons (with L = Z (3730) → DD in e.g. pp → DD π are also possible, but would su ff er of higher background. Again, it should be noted that a dedicateddata taking run at the center of mass energy of Z (3730) is not required for the proposed study.To summarize, PANDA would be unique to search for X → Z π transitions involving yet unobserved neutral andcharged Z (3730) states in the processes: • ¯ pp → Z (3730) π , Z (3730) → J /ψγ , with J /ψ → leptons and π → γγ ; ABLE 1.
Summary of the expected X, Y, and Z production rates per day in PANDA, assuming di ff erent operation modes (e.g.di ff erent rates L / day). The calculation is performed by multiplying luminosity and cross sections. The cross section upper limitsare used in these calculations, and in parenthesis the corresponding lower limit is reported. For the X (3872), only an upper limitwas evaluated in this short report, and thus we omit a second number. Resonance L = pb − / day L = pb − / day L = pb − / dayX (3872) 432000 43200 21600 Y (4260) 19000 (665) 1900 (67) 950 (7) Z (3900) + • ¯ pp → Z (3730) π , Z (3730) → χ c π , with π → γγ , χ c → J /ψγ and J /ψ → leptons; • ¯ pp → Z (3730) ± π ∓ , Z (3730) ± → χ c π ∓ , with χ c → J /ψγ and J /ψ → leptons.We also note, that the Z c (3900) and the Z c (4020) have not been observed in B decays, yet. Thus, we expect highdiscovery potential for PANDA. F-wave charmonium states
A unique feature for PANDA can be the search for high spin states. Based on theoretical predictions as in Ref. [38],we simulated the multiple radiative cascade 1 F ( J PC = ++ ) → D ( J PC = −− ) → χ c ( J PC = ++ ) → J /ψ ( J PC = −− ), as detailed reported in Ref. [23]. PANDA is designed to perform an excellent photon reconstruction, and oursimulations have already demonstrated that physics channels reconstructed from one J /ψ and three γ have clearsignature, and a background suppression factor of about 10 [23]. The static heavy quark anti-quark ( ¯ QQ ) potentialof the Cornell-type [38, 39, 40] can be expressed by V ( r ) = α s r + k · r , with a chromo-electric Coulomb-type term,and a linear confinement term. It predicts many of the experimentally observed charmonium and bottomonium statesup to a precision of ≈ h c , the h b and the h ′ b , or η b and η ′ b . By the mass measurements of these new states,a comparison of the level spacings between charmonium (mass region 3-4 GeV / c ) and bottomonium (mass region9-10 GeV / c ) became available for the first time. For example, the following spin-averaged mass di ff erences: m ( h c ) − · m ( J /ψ ) + m ( η c )4 = . ± . MeV (10) m ( h b ) − · m ( Υ (1 S ) + m ( η b )4 = . ± . MeV (11)are identical to a level of better than 10 − , which is quite surprising and points to flavor independence of the quarkanti-quark potential. In other words, the potential does not seem to depend on the di ff erent quark mass of the charmor the bottom quark, although in the Cornell potential the quark mass is explicitly one of the adjustable parameters.However, as already found in the 1970’s [41], flavor independence is not fulfilled for a Cornell-type potential.Potentials, for which identical level spacings for charmonium and bottomonium are fulfilled, are logarithmic potentialsof the type V ( r ) = r ln ( c r ).One of the important tasks of future experiments such as PANDA is the search for additional, yet unobservedstates (e.g. the h ′ c or F state), which could be used to obtain additional level spacings and further test the flavorindepedence, and possibly a logarithmic shape of the potential. Simulations in this sense were performed with thePANDA full reconstruction framework [42], and they are promising, as detailed in Ref. [23, 34]. Summary
In summary, Table 1 reports our estimates for X, Y, Z production rates at PANDA, assuming di ff erent luminosityaverage values L = cm − s − , L = cm − s − , and L = × cm − s − , respectively. Rates must be interpreteds educated guess, due to the ¯ pp cross sections, which have not been measured, yet. The expected large statistics atPANDA will help to address many open questions about X, Y, and Z states, in order to unravel their nature. A highdiscovery potential exists, in particular for new states with quantum numbers unobservable in production processes atother experimental facilities. REFERENCES [1] N. Brambilla et al. , CERN Yellow Report , hep-ph / et al. , Eur. Phys. J. C 71 (2011) 1534[arXiv:1010.5827 [hep-ph]]; N. Brambilla et al. , arXiv:1404.3723 (2014) [hep-ph].[2] S.K. Choi et al. (BES III), Phys.Rev.Lett. 91 (2003) 262001.[3] B. Aubert et al. (BaBar), Phys.Rev. D71 (2005) 071103[4] D. Acostaet et al. (CDF), Phys. Rev. Lett. 93 (2004) 072001.[5] V.N. Abazovet et al. (D0), Phys. Rev. Lett. 93 (2004) 162002.[6] R. Aaij et al. (LHCb), Eur. Phys. J. C72 (2012) 1972, arXiv:1112.5310 [hep-ex].[7] B. Aubert et al. (BaBar), Phys. Rev. Lett. 95 (2005) 142001; Conf. note 08 / et al. (BaBar), Phys. Rev. D 86 (2012) 051102.[8] Q. He et al. (CLEO-c) Phys. Rev. D 74 (2006) 091104.[9] C. Z. Yuan et al. (Belle) Phys. Rev. Lett. 99 (2007) 182004.[10] R. Aaij et al. (LHCb), Phys. Rev. Lett. 112 (2014) 222002.[11] S.K. Choi et al. (Belle), Phys. Rev. Lett. 100 (2008) 142001.[12] Z. Q. Liu et al. (Belle), Phys. Rev. Lett. 110 (2013) 252002.[13] M. Ablikim et al. (BESIII), Phys. Rev. Lett. 110 (2013) 252001.[14] M. Ablikim et al. (BES III), arXiv:1309.1896 [hep-ex][15] M. Ablikim et al. (BES III), Phys. Rev. Lett. 112 (2014) 022001.[16] M. Ablikim et al. (BES III), Phys. Rev. Lett. 112 (2014) 132001.[17] M. Ablikim et al. (BESIII), Phys. Rev. Lett. 110 (2013) 252001.[18] M. Ablikim et al. (BESIII), Phys. Rev. Lett. 112 (2014) 092001.[19] W. Erni et al. (PANDA), arXiv:0903.3905.[20] K.A. Olive et al. (Particle Data Group), Chin. Phys. C, 38 (2014) 090001.[21] R. Aaij et al. (LHCb), Phys. Rev. Lett. 110 (2013) 222001.[22] From a private communication with Eric Braaten, and Phys. Rev. D 77 (2008) 034019.[23] J. S. Lange et al . , arXiv:1311.7597 (2013) [hep-ex].[24] M. Galuska et al . , PoS (Bormio 2012) 018.[25] G. Pakhlova et al. (Belle), Phys. Rev. D 80 (2009) 091101.[26] B. Aubert et al. (BaBar), Phys. Rev. D 79 (2009) 092001.[27] D. Crinin-Hennessy et al. (CLEO), Phys. Rev. D 80 (2009) 072001.[28] B. Aubert et al. (BaBar), Phys. Rev. D 76 (2007) 111105.[29] B. Aubert et al. (BaBar), Phys. Rev. D 73 (2006) 012005.[30] B. Aubert et al. (BaBar), Phys. Rev. D 86 (2012) 051102.[31] M. Ablikim et al. (BES III), Phys. Rev. Lett. 110 (2013) 252001.[32] M. Ablikim et al. (BES III), Phys. Rev. Lett. 112 (2014) 092001.[33] B. Aubert et al. (BaBar), Phys. Rev. D 37 (2006) 012005.[34] E. Prencipe et al. , arXiv:1410.5201 (2014) [hep-ex].[35] M. Ablikim et al. (BES III), Phys. Lett. B 735 (2014) 101.[36] B. Aubert et al. (BaBar), Phys. Rev. D 71 (2005) 031501.[37] S.K. Choi et al. Phys. Rev. Lett. 111 (2013) 032001.[38] E. S. Swanson et al. , Phys. Rev. D 72 (2005) 054026.[39] E. Eichten et al. , Phys. Rev. D 17 (1978) 3090.[40] S. Godfrey et al. , Phys. Rev. D 32 (1985) 189.[41] C. Quigg et al. , Phys. Lett. B 71 (1977) 153.[42] S. Spataro et all ..