QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 1/36 Narrow States Near Thresholds: X(3872) Estia Eichten X(3872) at Threshold Charmonium Missing States K. Lane, C. Quigg Including Light Quark Effects Open Issues and Opportunities Summary
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 2/36 X(3872) at Threshold Belle ψ ψ X
Belle QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 3/36
2 Number of Candidates/ 5 MeV/c 2500 2000 1500 1000 500 Run II --- CDF Preliminary 3678 ± 99 ψ(2s) Mass: 3685.67 ± 0.08 (stat) MeV/c 2 σ: 3.41 ± 0.09 (stat) MeV/c 704 ± 67 Candidates Mass: 3871.4 ± 0.7 (stat) MeV/c σ 2 (Fixed): 4.3 MeV/c 2 ~220 pb M(ππ) > 500 MeV/c -1 2 2 0 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 2 ψπ + hep-ex/0312021 Mass of J/ π - Candidates [GeV/c ] Fit: QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 4/36
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 5/36 No. of Candidates / 14 MeV/ 2 900 800 700 600 500 400 300 200 100!(2S) (3872) < " < " < 1.0 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ( µ + µ $ # + # $ ) $ ( µ + µ $ ) [GeV/ 2]
,QYHVWLJDWLRQRIQDUURZVWDWHV ;K F %D%DU SUHOLPLQDU\ P ; 0H9F P-"## %5%!;. [%5;!-"## [ K F!(2V) &URVVFKHFNVHSDUDWLQJ-" Æ HHµµ HH%5 [ µµ%5 [ ;,QDGGLWLRQOLPLWVVHWRQK F!-"## DQGRQ%!-"' $ # %5%!K F. [%5K F!-"##[ ² %5%!-"' $ #[ ² &/ &/ QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 6/36
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 7/36 What we know about X(3872) Mass: DØ impose cuts of M ππ > (500, 520) MeV, respectively. Experiment Sample Events Mass (MeV) Belle 152M Υ(4S) B B 35.7 ± 6.8 3872.0 ± 0.8 CDF 220 pb 1 730 ± 90 3871.4 ± 0.8 DØ 230 pb 1 522 ± 100 3871.8 ± 4.3 BaBar 117M Υ(4S) B B 25.4 ± 8.7 3873.4 ± 1.4 Average 3871.9 ± 0.6 3871.9 ± 0.6 MeV higher than expected (3815 MeV) DD* thresholds: (3871.3 ± 1.0 MeV) (3878.6 ± 1.0 MeV) Width: 1.4 ± 0.7 MeV Belle
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 8/36 0 *0 D D Belle Threshold PRL 91, 262001 (2003) [hep-ex/0309032] CDF II D0 PRL 93, 072001 (2004) [hep-ex/0312021] [hep-ex/0405004] BaBar [hep-ex/0406022] 3865 3870 3875 2 3880 X(3872) Mass (MeV/c ) 2 Candidates/ 5 MeV/c 3000 2500 2000 1500 1000 CDF II 1400 1300 1200 1100 1000 900 3.80 3.85 3.90 3.95 500 2 M(π + π - ) > 0.5 GeV/c 2 M(π + π - ) < 0.5 GeV/c I. Kravchenko, CDF, ICHEP04, Aug 16-22, 2004 0 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 2 J/ψπ + π - Mass (GeV/c )
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 9/36 Decay: X(3872) π + π ψ Perhaps a sighting? X(3872) ω + ψ Only seen in discovery mode All other channels limits only Offshell - needs confirmation Production: Belle and BaBar - Produced in B decays. CDF and D0 - Significant prompt production. Expect Charmonium D wave state, BUT: Charmonium issues: Mass Splitting from ψ (3770) too large. Radiative transition rates too small.
Belle X(3872) ω + ψ 6 6 Events/bin 4 2 4 2 0 5.200 5.250 5.300 0-0.20 0.00 0.20 bc and (b) E distributions for candidate M bc (GeV) B Kπ + π π 0 J/ψ decays!e (GeV) with GeV. The curves are the result of the fit described in the text. FIG. 8: (a) The M bc and (b) E distributions for candidate B Kπ + π π 0 J/ψ decays with M(π + π π 0 ) > 0.75 GeV. The curves are the result of the fit described in the text. d (b) show the M bc and E projections for events with M(π + π π 0 ) > d by the arrow in Fig. 7(c)). Here a B meson signal is evident on a small ignal yield from a simultaneous fit is 10.0 ± 3.6 events and S/B = 5. The detection efficiencies: nce of the signal, determined from 2 ln(l 0 /L max ), where L max and L 0 alues for the best-fit and for zero-signal-yield, Γ(X ωj/ψ) respectively, is 5.8σ. This ion of an X(3872) decay mode other Γ(X than π + π + J/ψ) π J/ψ. of the signal events with π + π π 0 invariant mass greater than 0.75 GeV compute the ratio of ωj/ψ and π + π J/ψ partial widths by comparing this to the number of X π + π J/ψ in the sample data sample, corrected by the relative = 0.8 ± 0.3(stat) ± 0.1(syst), (5) where the systematic error reflects the uncertainty in the relative acceptance. The properties of the X π + π π 0 J/ψ decays are in good agreement with expectations of ref. [13]. The π + π π 0 invariant masses cluster near the upper kinematic limit, and its QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 10/36
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 11/36 µm Candidates per 20 10 3 10 2 10 CDF II Preliminary + ψ(2s) J/ψ π π - ±2.5σ Projection Around ψ(2s) -1 Data ~220 pb Prompt ψ(2s) Long-Lived ψ(2s) Prompt Background Long-Lived Background 1-0.1 0 0.1 0.2 0.3 Uncorrected Proper Time (cm) µm Candidates per 20 + X(3872) J/ψ π π- 10 3 10 2 10 CDF II Preliminary ±2.5σ Projection Around X(3872) -1 Data ~220 pb Prompt X(3872) Long-Lived X(3872) Prompt Background Long-Lived Background 1-0.1 0 0.1 0.2 0.3 Uncorrected Proper Time (cm) I. Kravchenko, CDF, ICHEP04, Aug 16-22, 2004
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 12/36 Missing Charmonium States D s D s + D sd s D D D s D s DD + D D + DD
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 13/36 Assignment for X? Charmonium TABLE I: c c spectrum in the Coulomb + linear potential (1). { 3415.0 ± 0.8 State } Mass (MeV) { Remarks 1 1 S 0 η c 2979.8 ± 1.8 1 3 c.o.g. 3067. S 1 J/ψ 3096.87 ± 0.04 1 1 P 1 1 3 P 0 h c 3526. } χ c0 1 3 P 1 χ c1 c.o.g. 3526. a 3510.51 ± 0.12 1 3 P 2 χ c2 } { 3556.18 ± 0.13 2 1 S 0 η 2 3 c 3654. ± 10. S 1 ψ c.o.g. 3678. 3685.96 ± 0.09 1 1 D 2 η c2 3815. D D (parity) } { 1 3 D 1 ψ 3769.9 ± 2.5 1 3 D 2 1 3 D 3 ψ 2 ψ 3 c.o.g. 3815. D D (parity) D D 2P 3968. 1F 4054. 3S 4118. D 0 D0 3729.0 threshold D + D 3738.6 threshold D 0 D 0 or D 0 D0 3871.2 threshold D ± D 3879.3 threshold D s + Ds 3973.2 threshold 0 D D 0 4013.4 threshold D + D 4020.0 threshold D D s 4099.0 threshold D + s s or Ds + D + s D a Input values. s 4224.8 threshold ELQ 2002 Molecular State S wave: P wave: pion exchange 1 ++ Other 1 ++ or, 1 + (0, 1, 2) ± Tornqvist hybrid M > 4200 MeV LQCD Braaten Large couplings near threshold 0 + Liao, Manke Juge, Kuti, Morningstar
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 14/36 Expectations circa 2002 TABLE II: Hadronic decay widths of charmonium states. c c state Decay Partial Width 1 1 S 0 η c gg 17.4 ± 2.8 MeV [21] 1 3 S 1 J/ψ ggg 52.8 ± 5 kev [22] 1 1 P 1 h c ggg 720 ± 320 kev a 1 3 P 0 χ c0 gg 14.3 ± 3.6 MeV b 1 3 P 1 χ c1 ggg 0.64 ± 0.10 MeV b 1 3 P 2 χ c2 gg 1.71 ± 0.21 MeV b 2 1 S 0 η c gg 8.3 ± 1.3 MeV c η c ππη c 160 kev d 2 3 S 1 ψ ggg 23 ± 2.6 kev [22] ψ ππj/ψ 152 ± 17 kev [22] ψ ηj/ψ 6.1 ± 1.1 kev [22] 1 1 D 2 η c2 gg 110 kev e η c2 ππη c 45 kev d 1 3 D 1 ψ ggg 216 kev f ψ ππj/ψ 43 ± 15 kev g 1 3 D 2 ψ 2 ggg 36 kev f ψ 2 ππj/ψ 45 kev d 1 3 D 3 ψ 3 ggg 102 kev f ψ 3 ππj/ψ 45 kev d a Computed from 3 P J rates using formalism of [23]; also see [24]. b Compilation of data analyzed by Maltoni, Ref. [23]. c Scaled from Γ(η c gg). d Computed using Eqn. (3.5) of Ref. [20]. e Computed using Eqn. (3). f Computed using Eqn. (2). g From rates compiled in Table X of Ref. [20]. TABLE III: Calculated and observed rates for radiative transitions among charmonium levels in the potential (1). γ energy Partial width (kev) Transition k (MeV) Computed Measured a ψ M1 η c γ 115 1.92 1.13±0.41 χ c0 χ c1 χ c2 h c η c ψ ψ ψ ψ ψ E1 J/ψγ 303 120 (105) b 98±43 E1 J/ψγ 390 242 (215) b 240±51 E1 J/ψγ 429 315 (289) b 270±46 E1 η c γ 504 482 E1 h c γ 126 51 E1 χ c2 γ 128 29 (25) b 22±5 E1 χ c1 γ 171 41 (31) b 24±5 E1 χ c0 γ 261 46 (38) b 26±5 M1 η cγ 32 0.04 M1 η c γ 638 0.91 0.75±0.25 ψ(3770) E1 χ c2 γ 208 3.7 ψ(3770) E1 χ c1 γ 250 94 ψ(3770) E1 χ c0 γ 338 287 η c2 η c2 ψ 2 ψ 2 E1 ψ(3770)γ 45 0.34 E1 h c γ 278 303 E1 χ c2 γ 250 56 E1 χ c1 γ 292 260 a Derived from Ref. [22]. b Corrected for coupling to decay channels as in Ref. [16].
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 15/36 Belle M bc M!"!"c1 No signals!! M bc M!"!"c2 #(X!!"!" c1 ) #(X!$ + $ % J/& /&) <0.9 #(X!!"!" c2 ) #(X!$ + $ % J/& /&) <1.1
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 16/36 Including Light Quark Effects. NRQCD (without couplings light quarks) Cornell model (CCCM) light quark pair creation Vacuum Pair Creation model (QPC) meson pair interactions
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 17/36 The Nature of H 2 Qq + qq Qq + qq dominant at large one pion exchange strong for S wave QQ separation Tornqvist General formulation at large scattering length Braaten and Kusunoki Qq + qq QQ + qq mainly at small QQ separation constituent exchange terms Swanson emphasizes that there are other nearby states J/ψ + ρ J/ψ + ω
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 18/36 Charmonium or Molecule? Including light quark effects seems to blur the distinction between charmonium and molecules. Not true for narrow states near thresholds. A molecular state exists only if an addition narrow state is seen in a given channel. Purely counting states. Levinson s theorem Schwinger
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 19/36 Coupling to open-charm channels Phenomenological approach: H ρ a = cγ 0 t a c + qγ 0 t a q CCCM Calculate pair-creation amplitudes, < 3 D 2 H I D D > Evaluate, etc. ELQ Solve coupled-state system ψ = ψ 0 + ψ 2 solve cc DD for ω and ψ 0
Decays into open charm QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 20/36
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 21/36
Γ(1 3 D 2 D 0 D 0 ) Γ(1 3 D 2 ππj/ψ) QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 22/36
TABLE III: Charmonium spectrum, including the influence of open-charm channels. All masses are in MeV. The penultimate column holds an estimate of the spin splitting due to tensor and spin-orbit forces in a single-channel potential model. The last column gives the spin splitting induced by communication with M(D*) open-charm > M(D) states, for an initially unsplit multiplet. Splitting State Mass Centroid (Potential) 1 1 S 0 2 979.9 a 1 3 S 1 3 096.9 a 3 067.6 b 90.5 +30.2 1 3 P 0 1 3 P 1 1 1 P 1 1 3 P 2 3 415.3 a 3 510.5 a c 3 525.3 3 525.3 3 556.2 a 114.9 e 11.6 e +1.5 e 31.9 e 2 1 S 0 3 637.7 a 2 3 S 1 3 686.0 a 3 673.9 b 50.4 +16.8 1 3 D 1 1 3 D 2 1 1 D 2 1 3 D 3 2 3 P 0 2 3 P 1 2 1 P 1 2 3 P 2 Effects on the spectrum Coupling to virtual channels induces spin-dependent forces in charmonium near threshold, because 3 769.9 ab 3 830.6 3 838.0 3 868.3 3 931.9 4 007.5 3 968.0 3 966.5 40 (3 815) d 0 0 +20 90 3 968 d 8 0 +25 Splitting (Induced) +2.8 0.9 +5.9 2.0 +0.5 0.3 +15.7 5.2 39.9 2.7 +4.2 +19.0 +10 +28.4 11.9 33.1 are those required to r are not predictions. F adopted as representa To reproduce the o we shift the bare 1D c other 1D masses are th In our model calcula channels increases th 20 MeV, but does no 102 MeV separation b is noteworthy that th turns out to be very c els, we have no expe bare centroid so that of the potential-mode have more to learn a channels. The 2 1 P 1 level has tive assignment for X ππ transition to J/ψ sition to the 1P levels places this state nearl As we shall see in qu lowed s-wave decay to large width, unless X( The wave functions are linear combination QWG3 a Observed mass, IHEP from Beijing, Review China ofoct. Particle 12-15, Physics, 2004 Ref. [13]. Eichten 23/36
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 24/36 Checks Decay widths: ψ (3770) width agrees with experiment. Mass shifts: M(η c) = 3637.7 ± 4.4 Hyperfine splitting: c ± M(ψ ) M(η c) = 32πα s Ψ(0) 2 /9m 2 c Normalize to ( ) ( M(J/ψ) ) = 117 MeV M(η c ) = 117 MeV Observed Shift M(ψ ) M(η c) = 67 MeV ±(48.3 ± 4.4) MeV 20.9MeV Agrees
Suppression of radiative decay rates (reduced overlap between initial & final states) Ψ(1 3 S 1 ) = 0.983 1 3 S 1 0.050 2 3 S 1 0.009 3 3 S 1 +... ; 96.8%(c c) Ψ(1 3 P 1 ) = 0.914 1 3 P 1 0.075 2 3 P 1 0.015 3 3 P 1 +... ; 84.1%(c c) Ψ(1 3 D 2 ) = 0.754 1 3 D 2 0.084 2 3 D 2 0.011 3 3 D 2 +... ; 57.6%(c c) Transition Partial width (kev) (γ energy in MeV) Computed 1 3 D 1 (3770) χ c0 γ(338) 254 225 1 3 D 2 (3831) χ c2 γ(266) 59 45 1 3 D 2 (3831) χ c1 γ(308) 264 212 1 3 D 2 (3872) χ c2 γ(303) 85 45 1 3 D 2 (3872) χ c1 γ(344) 362 207 1 3 D 3 (3868) χ c2 γ(303) 329 286 1 3 D 3 (3872) χ c2 γ(304) 341 299 QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 25/36
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 26/36 three gluon annihilation D Dbar decays total (exp) photon transitions pion transitions bound from photon transitions Γ(MeV) 2.4 1.8 1.2 0.6 3 D 2 3 D 3 Γ(MeV) 2.4 1.8 1.2 0.6 0.16.24.32.40.48.56.64 0.24.32.40.48.56.64 H.23 < Γ(X π + π J/ψ) < 1.18(MeV).27 < Γ(X π + π J/ψ) <.63(MeV)
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 27/36 Near 3872 MeV Γ(1 3 D 2 D 0 D 0 ) Γ(1 3 D 2 ππj/ψ) Γ(1 3 D 3 π + π J/ψ) 1 4 Γ(13 D 3 D D) Γ(1 3 D 3 γχ c2 ) 1 3 Γ(13 D 3 D D) Belle: B(X D 0 D0 ) 4B(X π + π J/ψ) B(X D + D ) 3B(X π + π J/ψ) Already approaches interesting range
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 28/36 Still issues with charmonium interpretation? Olsen s Summary - Krakow [hep-ex/0407033] Table 2. Status of the candidate charmonium assignments. State nickname J P C comment 1 3 D 2 ψ 2 2 Mass wrong; Γ γχc1 too small 2 1 P 1 h c 1 + Ruled out by cos θ J/ψ distribution 1 3 D 3 ψ 3 3 Γ γχc2 too small; spin seems too high 2 3 p 1 χ c1 1 ++ Γ γj/ψ too small 1 1 D 2 η c2 2 + B(π + π J/ψ) expected to be very small 3 1 S 0 η c 0 + Mass and width are wrong go slow stop fix float X(3872) π + π ψ Only viable for J PC = 2 and 3
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 29/36 Open Issues and Opportunities Further study with X(3872) Determine J PC, isospin and decay modes Missing Charmonium States Find them. Analog states? bb Threshold Nearby state B0 B 0 + B 0 B 0 = 10, 604 (MeV) M(Υ(4S)) = 10.580 and Γ = 20 (MeV) K exchange? M(D 0 D 0 ) = 142.1, M(Ds + D + s ) = 143.8 (MeV)
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 30/36 Following up X(3872) Verify I=0: look for charged partner, check dipion angular distribution, see π 0 π 0 Determine (or at least restrict) J PC Look for radiative decays: γχ c1, γχ c2 Measure prompt vs B-decay at CDF, DØ Look for D 0 D0 π 0 and D 0 D0 γ
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 31/36 Following up X(3872) Measure ππ mass distribution Look for structure in D D, D D, D D Find structures or set limits on other π + π J/ψ Examine J/ψ + (π ±, η, K ±, K S, p, Λ,...) Measure rates for b (c c) + anything Similar studies in b b
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 32/36 (ππ angular distribution) Another ππ diagnostic Isospin of dipion: charmonium + other contenders interpret X(3872) as I=0 R 0 Γ(X π 0 π 0 J/ψ)/Γ(X π + π J/ψ) measures dipion isospin Γ I Γ(X (π + π ) I J/ψ) : R 0 = 1 2 /(1 + Γ 1/Γ 0 ) Deviations from 1/2 signal I-violating decay of an isoscalar, or I-conserving decay of an isovector Significant π 0 π 0 C(X) : odd
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 33/36 Decay angular distributions Spin-2 X(3872) decaying through s-wave ππ: angular distribution of J/ψ sin 2 θ cos 2 θ θ : X line of flight vs J/ψ direction J/ψ l + l angular distribution 1 + cos 2 ϑ ϑ : angle of l + wrt J/ψ flight direction The classic: J. D. Jackson, Les Houches, 1965 also see Pakvasa & Suzuki, hep-ph/0309294
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 34/36 2 1 P 1 : dn d cos θ J/ψ sin 2 θ! 2 =75/9 cos" J/# Belle: ruled out!
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 35/36 SUMMARY Naive potential model limitations Failure to include light quark pair dynamics Narrow heavy-heavy states: X(3872) All three remaining low-lying L=2 charmonium states are narrow. A proper calculation for the masses and decay rates of these states must include the large effects from nearby (real/virtual) open charm decay channels. Detailed predictions for masses, mixings and decays using the Cornell Model reduce (but not eliminate) the difficulties with identifying the X as 3 D 2 3 D 3 a or state. 1 3 D 2, 1 1 D 2, 1 3 D 3
QWG3 IHEP Beijing, China Oct. 12-15, 2004 Eichten 36/36 If X(3872) is a molecular state: Unambiguous state not expected within the naive quark model. New spectroscopy Look for partner states if isospin is not zero. Possible analog states in the bb system. Need more precise tools to compute spectrum and decay properties.
EXTRA SLIDES
Toolbox for QCD Dynamics NRQCD for Heavy-Heavy Systems Q 1 Q 2 m Q >> Λ QCD v c HQET for Heavy-Light Systems j l = l+s Chiral Symmetry for Light Quarks Lattice QCD