C.H. Chang, ITP, AS Beijing1 Chao-Hsi Chang ( 张肇西 Zhao-XiZhang) I.T.P., Chinese Academy of Sciences 1.Introduction (the meson Bc & its mass) 2.Decay (lifetime, …) 3.Production (Tevatron vs LHC) 4.Outlook Production and decay of the meson Bc —— A brief review of theoretical studies —— (Based on the collaboration with Y.-Q. Chen, X.-Q. Li, C.-D. Lu, C.- F. Qiao, G.-L. Wang, J.-X. Wang, X.-G. Wu, et al)

C.H. Chang, ITP, AS Beijing2 1. Introduction (the meson Bc & its mass) Of the six quarks u c t d s b - u, d, s, light - c, b, t, heavy (top lifetime τ too short to form hadrons) Bc: double heavy-flavor mesons (unique in SM) (weak decay only) Very similar to, and very different from, hidden flavored heavy quarkonium J/ψ, η c, …,Υ,η b …. Good and new object for tests of PM, NRQCD, Lattice results etc.

C.H. Chang, ITP, AS Beijing3 1. Introduction (the meson Bc & its mass) Bc mass : Lattice QCD : I.F. Allison et al, PRL PM: Y.Q. Chen &Y.P. Kuang, PRD 46, 1165; Eichten & C.Quigg, PRD 49, 5845;…. : A. Kronfeld’s talk

C.H. Chang, ITP, AS Beijing4 1. Introduction (the meson Bc & its mass) Theoretical estimate & LEP-I (ALAPH, PLB 402, 213; DELPHI PLB 398, 207) : experimental studies of Bc can be carry out at Tevatron and LHC only! Theoretical estimate at Z resonance (LEP-I) : OPAL result PLB 420, 157 : The “early” day’s results

C.H. Chang, ITP, AS Beijing5 1. Introduction (the meson Bc & its mass) CDF discovery (1998 Observation) PRD 58, Pb -1 data E CM =1.8 TeV RunI Bc ±  J/  (  +  - )  ± - The only previous evidence by CDF RunI CDF new Observation hep-ex/ Bc ±  J/  (  +  - )  ± Pb -1 data E CM =1.96 TeV, RunII m Bc =6287.0±4.8(stat)±1.1(syst) MeV/c 2, 18.9±5.7 events D0 new Observation ICHEP-04 & Fermilab 4539-CONF Pb -1 data E CM =1.96 TeV, RunII Bc ±  J/  (  +  - )  ± Mass: 5.95 ± 0.34 GeV/c 2 Events: 95 ± 12± Lifetime: ± ps Br~2.4% + trilepton final state + easy to trigger Note: even Br( Bc ±  J/  (  +  - )  ± )/Br( Bc ±  J/  (  +  - )  ± ) not available ! Present experimental status:

C.H. Chang, ITP, AS Beijing6 2. Decay Bc lifetime : weak decay only (no strong &EM direct decay) according to spectator model and B & D mesons’ lifetime and annihilation: one may estimate More careful estimate: vertex detector is useful in observation Decay: Pure (radiative) leptonic Semoleptonic Nonleptonic

C.H. Chang, ITP, AS Beijing7 2. Decay : : Bc lifetime (non-spectator effects involved) : : ( ) In comparison with D & B mesons (input), we obtain:

C.H. Chang, ITP, AS Beijing8 2. Decay Pure leptonic (radiative) decay ( about measurement of the decay constant f Bc ): Pure leptonic (tree) decay : ( chiral suppression) Radiative leptonic decay (decay constant) : (escaped from chiral suppression) QED corrections (one-loop):

C.H. Chang, ITP, AS Beijing9 2. Decay Radiative leptonic decay (QED correction to the tree level) in total : Photon spectrum: It is quite difficult for hadronic expt. to measure the decay constant!

C.H. Chang, ITP, AS Beijing10 2. Decay Leptonic decay with light hadrons ( color-singlet vs color-octet ): Color-singlet: Short distance: Long distance: Charge lepton spectrum: In the decay

C.H. Chang, ITP, AS Beijing11 2. Decay Color-octet: P-wave (color- octet) S-wave (color-octet) Color-singlet Near the endpoint of the charged lepton in the decay to observe the color-octet components! Charged lepton spectrum:

C.H. Chang, ITP, AS Beijing12 2. Decay Semileptonic decays : Transitions (decays with great momentum recoil) The key factor:

C.H. Chang, ITP, AS Beijing13 2. Decay Mandelstam formulation (or say composite quantum field theory) to deal with the recoil effects in transitions: The ‘wave function’ of bound state equation: To cover a great range of momentum transfer (recoil), BS equation seems to be one of good choices for the problem.

C.H. Chang, ITP, AS Beijing14 2. Decay Carry out the contour integrations & :

C.H. Chang, ITP, AS Beijing15 2. Decay The semileptonic decays (S-wave) : One I-W function

C.H. Chang, ITP, AS Beijing16 2. Decay The semileptonic decays (P-wave or ) : Two I-W functions Recoil one Normal one Spectrum of charged lepton in the decays:

C.H. Chang, ITP, AS Beijing17 2. Decay Nonleptonic decays (S-wave product): EFT+Factorrization

C.H. Chang, ITP, AS Beijing18 2. Decay Nonleptonic decays (P-wave product or ):

C.H. Chang, ITP, AS Beijing19 2. Decay The lifetime is ‘quite long’ that the vertices of production and decay can be measured by vertex detector experimentally Sizable decay channels are rich The branch ratio of the decay to is quite great (form factors) The branch ratio of decay to or is very large Study two flavor ‘simultaneously’ (V cb & V cs ) Radiative pure leptonic decays escape from chiral suppression, but to measure the decay constant is still difficult The color-octet component might be observable through …….

C.H. Chang, ITP, AS Beijing20 3. Production (Tevatron & LHC) Gluon-gluon fusion mechanism dominant 36 Feynman diagrams for complete calculations ‘ Complete LO computation ’: information about the accompany quark-jets is kept QCD factorization: Subprocess:

C.H. Chang, ITP, AS Beijing21 3. Production (Tevatron & LHC) The lowest order calculations: uncertainties from The cross-section at LHC is greater than that at Tevatron S-wave state production

C.H. Chang, ITP, AS Beijing22 3. Production (Tevatron & LHC) LHC Tevatron Uncertainty from m C

C.H. Chang, ITP, AS Beijing23 3. Production (Tevatron & LHC) and Uncertainty from PDFs

C.H. Chang, ITP, AS Beijing24 3. Production (Tevatron & LHC) Uncertainties: quite great; sensitive to Q 2, m c. High order calculation can suppress them but it is too complicated. Uncertainty from

C.H. Chang, ITP, AS Beijing25 3. Production (Tevatron & LHC) P-wave excited state production To match the wave functions correctly (special attention on the spin structure), we start with the Mandelstam formulation on BS solution:

C.H. Chang, ITP, AS Beijing26 3. Production (Tevatron & LHC) 1P11P1 3P13P1 3P23P2 3P03P0 3P03P0 3P13P1 1P11P1 3P23P2 LHC TEVATRON P-wave production ( color-singlet) To see the contributions to Bc & the P-wave characters

C.H. Chang, ITP, AS Beijing27 | | 2 3. Production (Tevatron & LHC) Color octet may be comparable with that of color singlet Color-singlet (P-wave) M.E. Color-octet (S-wave) M.E. Scaling rule of NRQCD:

C.H. Chang, ITP, AS Beijing28 3. Production (Tevatron & LHC) LHC Tevatron Color-octet 1 S 0 Color-octet 3 S 1 Color-singlet 3 P 2 Color-singlet 1 P 1 Color-singlet 3 P 0 Color-singlet 3 P 1 P-wave production color-singlet vs color-octet Color-octet

C.H. Chang, ITP, AS Beijing29 The cross section of Bc at LHC is greater than that at Tevatron by one and more order of magnitude The uncertainties are quite big for LO PQCD The cross section is at the order (less) of B meson production 3. Production (Tevatron & LHC) Experimental needs of the M.C. generator: Difficulties of the experiments in Hadronic Collider High efficiency for the generator Generator: BCVEGPY1.0 (S-wave, helicity techniques ) BCVEGPY2.0 (S,P-wave, Color-octet,…& Mixture) Signals for feasibility studies CPC Lib. & hppt://

C.H. Chang, ITP, AS Beijing30 3. Production (Tevatron & LHC) (ours) another The generator is tested by comparing with PYTHIA The generator is proved to be suitable for the original purpose.

C.H. Chang, ITP, AS Beijing31 3. Production (Tevatron & LHC) - Bc  Bs + h + + X? beam ※ PV Bc: 140  m 6.4GeV ? Bs: 438  m 5.4GeV Oscilla. h + : , , ,e( ) tracks: pT~ MeV, too soft, off-line only ※ Ds - : 147  m 1.968GeV ※ K 0* - - K+K+ K -   (36%) (8%) (3.3%) (100 %) - Bc  Bs associated h + (as a tag for Bs). - Br[ Bc  B s +h + +X ] as Bs CP violation source ? Bc decay vertex is crucial. To be a possible source for tagged Bs (at LHC) ?

C.H. Chang, ITP, AS Beijing32 3. Production (Tevatron & LHC) beam - - ※ PV Bc: 140  m 6.4GeV Bs: 438  m 5.4GeV oscillation h + : , , ,e( ) tracks: pT~ MeV, too soft, off-line only ※ Ds - : 147  m 1.968GeV ※ K 0* K+K+ K -  (36%) (13%) (3.3%) (100%) ※ b-jet (B 0,B + )  (pT>1) Br~10%! - Bs  decay: the Bc decay vertex might be fixed with soft h + tracks, Br increases by 50%  The  from the other side b-quark fragmentation  Muon + opposite 2 nd VTX ( on Ds ) under feasibility investigation !

C.H. Chang, ITP, AS Beijing33 4. Outlook Experimental studies on Bc meson have been started at Tevatron already, and fresh results will be issued ‘from time to time’. The production cross-section at LHC is greater than that at Tevatron, so further experimental studies at LHC can be expected. Some model predictions will be tested. Theoretical estimates are requested to decrease the uncertainties and to increase the precision with data being accumulated. Bc studies may solve some puzzles relating to charmonium e.g. the observation may clarify up some of contents in, in meson there are more charm quarks than in meson. and some ‘unexpected things’ might be found. ……

C.H. Chang, ITP, AS Beijing34 Thank s