This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. FERMILAB-SLIDES-19-067-T Department of Energy, Office of Science, Office of High Energy Physics. Narrow ( c ¯ c ) above Flavor Threshold B c excited states (Stable) Doubly Heavy Tetraquarks Chris Quigg Fermilab & TUM Deciphering strong interactions . . . · MIAPP / Garching · October 25, 2019
Narrow ( c ¯ c ) states above flavor threshold LHC b : M ≈ 3842 . 71 MeV Γ = 2 . 79 ± 0 . 51 ± 0 . 35 MeV Eichten, Lane, Quigg, Phys. Rev. D 69 , 094019 (2004) / hep-ph/0401210. Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 1 / 17 q
LHC b observation of 3 D 3 candidate Can we find 3 F 4 , perhaps near 4054 MeV? Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 2 / 17 q
Reconstruction of B c meson (CDF, 2006) M ( B c ) = 6274 . 9 ± 0 . 8 MeV (Test of lattice QCD prediction) Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 3 / 17 q
Mesons with beauty and charm: stress test for NRQM, LQCD B c : weak decays only c → W − b → c c → s b ¯ 12–15 narrow levels ψπ : ( Q ¯ 7600 B c → J / Q ) transmutation 7400 Rich ( b ¯ c ) excitation spectrum; interpolates J / ψ, Υ ( � = masses) 7200 Mass [MeV] Excited states below BD → B c + . . . 7000 B c (2 S ) → B c (1 S ) + ππ 6800 P states: γ transitions 6600 Many states observable at LHC, Tera Z 6400 Lattice: ∆ = 54 MeV Update: Eichten & CQ (2019) 6200 using “frozen- α s ” potential, new approach to spin splittings Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 4 / 17 q
Observing the B c spectrum: ππ transitions 2.0 Combine predicted production rates (BCVEGPY2.2) with calculated 1.5 branching fractions to obtain d σ /dM [nb/MeV] 1.0 expectations for ππ transition rates ❀ peak heights: B ∗′ c / B ′ c ≈ 2 . 5 0.5 M1 B ∗ c → / γ B c unobserved 0 6820 6840 6850 6860 6870 6880 6890 6830 M( B c π + π – ) [MeV] [ M ( B ∗′ c ) − M ( B ′ c )] − [ M ( B ∗ c ) − M ( B c )] B ∗′ ≈ − 23 MeV: c lower peak 2S → ππ + 1S transitions observed by ATLAS, CMS, LHC b CMS separation: − 29 MeV LHC b : − 31 MeV Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 5 / 17 q
Observing the B c spectrum: ππ transitions 2.0 Combine predicted production rates (BCVEGPY2.2) with calculated 1.5 branching fractions to obtain d σ /dM [nb/MeV] 1.0 expectations for ππ transition rates ❀ peak heights: B ∗′ c / B ′ c ≈ 2 . 5 0.5 M1 B ∗ c → / γ B c unobserved 0 6820 6840 6850 6860 6870 6880 6890 6830 M( B c π + π – ) [MeV] [ M ( B ∗′ c ) − M ( B ′ c )] − [ M ( B ∗ c ) − M ( B c )] B ∗′ ≈ − 23 MeV: c lower peak 2S → ππ + 1S transitions observed by ATLAS, CMS, LHC b CMS separation: − 29 MeV LHC b : − 31 MeV Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 5 / 17 q
Mesons with beauty and charm: states near flavor threshold 3 S states above threshold have significant decay widths 3 1 S 0 3 3 S 1 3 P states just below threshold; J = 1 may have significant mixing 3 3 P 0 3 P ( ′ )1 3 3 P 2 Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 6 / 17 q
Observing the B c spectrum: E1 transitions 3.5 E1 spectroscopy in the ( b ¯ b ) family: 3.0 LHC experiments discovered χ ′′ b 1 , χ ′′ b 2 . 2.5 σ B [nb/MeV] 2.0 Incentive for the search: 2 S → 2 P and 1.5 2 P → 1 S transitions, assuming missing 1.0 B ∗ c → B c / γ in the reconstruction. 0.5 0.0 100 150 200 250 300 350 400 450 500 k [MeV] 3 S , 3 P yields ≈ 1 4 × 2 P → 1 S lines, but higher γ energies may aid detection. 3 3 P 2 (7154) → B ∗ c γ (777 MeV) Encourage search for (3 , 2) P ( b ¯ c ). Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 7 / 17 q
Heavy quark symmetry ⇒ stable heavy tetraquarks Q i Q j ¯ q k ¯ q l ¯ q ¯ q q ¯ q ¯ (QQ) (QQ) (QQ) Q Q q ¯ q ¯ ¯ q ¯ q HQS relates DHTQ mass to masses of QQq, Qqq, Q ¯ q. u ¯ s, bb ¯ Lightest bb ¯ d, bb ¯ u ¯ d ¯ s states: (likely) no strong decays. Heavier bb ¯ q k ¯ q l , cc ¯ q k ¯ q l , bc ¯ q k ¯ q l → Q ¯ q + Q ¯ q might be seen as “double-flavor” resonances near threshold. Observing a weakly decaying double-beauty state would establish the existence of tetraquarks and illuminate the role of heavy color- ¯ 3 diquarks as hadron constituents. Eichten & CQ 1707.09575 Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 8 / 17 q
Stability in the heavy-quark limit 1) Dissociation into two heavy-light mesons is kinematically forbidden. Q ≡ m ( Q i Q j ¯ q k ¯ q l ) − [ m ( Q i ¯ q k ) + m ( Q j ¯ q l )] = � 2 � 2 [1 + O ( v 2 )] M + O (1 / M ) , − 1 ∆( q k , q l ) 3 α s 2 � �� � light d.o.f. M ≡ (1 / m Qi + 1 / m Qj ) − 1 : reduced mass of Q i and Q j M →∞ ∆( q k , q l ) − − − → independent of heavy-quark masses For large enough M , QQ Coulomb binding dominates, Q < 0 Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 9 / 17 q
Stability in the heavy-quark limit 2) Decay to doubly heavy baryon and light antibaryon? ( Q i Q j ¯ q k ¯ q l ) → ( Q i Q j q m ) + (¯ q k ¯ q l ¯ q m ) 3 , same as ¯ Core Q i Q j is color- ¯ Q x . Up to contributions from Q motion and spin interactions, m ( Q i Q j ¯ q k ¯ q l ) − m ( Q i Q j q m ) = m ( Q x q k q l ) − m ( Q x ¯ q m ) (spin configurations matter) RHS has generic form ∆ 0 + ∆ 1 / M Qx Using m (Λ c ) − m ( D ) = 416 . 87 MeV and m (Λ b ) − m ( B ) = 340 . 26 MeV, we estimate ∆ 0 ≈ 330 MeV (asymptotic mass difference). All < m (¯ p ) = 938 MeV Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 10 / 17 q
No open strong decay channels in the heavy-quark limit! ¯ q (QQ) ¯ q As M → ∞ , stable Q i Q j ¯ q k ¯ q l mesons must exist Implications for the real world? ¯ q (QQ) ¯ q � r 2 � 1 / 2 = 0 . 28 fm( cc ) , 0 . 24 fm( bc ) , 0 . 19 fm( bb ) Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 11 / 17 q
HQS relations for ground-state tetraquark masses Assumed: compact diquark, light degrees of freedom “same” for all ( QQ ) m ( Q i Q j ¯ q k ¯ q l ) − m ( Q i Q j q m ) = m ( Q x q k q l ) − m ( Q x ¯ q m ) + finite-mass corrections RHS is determined from data One doubly heavy baryon observed, Ξ cc ; others from model calculations ⋆ LHC b : M (Ξ ++ cc ) = 3621 . 40 ± 0 . 78 MeV ⋆ We adopt Karliner & Rosner, PRD 90 , 094007 (2014) Strong decays ( Q i Q j ¯ q k ¯ q l ) �→ ( Q i Q j q m ) + (¯ q k ¯ q l ¯ q m ) ∀ ground states Consider decays to pairs of heavy–light mesons case-by-case Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 12 / 17 q
Expectations for ground-state tetraquark masses, in MeV J P State m ( Q i Q j ¯ q k ¯ q l ) Decay Channel Q [MeV] D + D ∗ 0 3876 u ¯ 1 + { cc } [¯ d ] 3978 102 1 + D + D ∗ + { cc } [¯ q k ¯ s ] 4156 3977 179 s D + D 0 , D + D ∗ 0 3734 , 3876 0 + , 1 + , 2 + { cc }{ ¯ q k ¯ q l } 4146 , 4167 , 4210 412 , 292 , 476 B − D + / B 0 D 0 7146 u ¯ 0 + [ bc ][¯ d ] 7229 83 0 + [ bc ][¯ q k ¯ s ] 7406 B s D 7236 170 B ∗ D / BD ∗ 7190 / 7290 1 + [ bc ] { ¯ q k ¯ q l } 7439 249 B ∗ D / BD ∗ 7190 / 7290 u ¯ 1 + { bc } [¯ d ] 7272 82 1 + { bc } [¯ q k ¯ s ] 7445 DB ∗ s 7282 163 0 + , 1 + , 2 + { bc }{ ¯ q k ¯ q l } 7461 , 7472 , 7493 BD / B ∗ D 7146 / 7190 317 , 282 , 349 B − ¯ B ∗ 0 10603 u ¯ 1 + { bb } [¯ d ] 10482 − 121 B ∗ 10695 / 10691 B ¯ ¯ s / ¯ B s ¯ 1 + { bb } [¯ q k ¯ s ] 10643 − 48 B ∗ B − B 0 , B − B ∗ 0 10559 , 10603 0 + , 1 + , 2 + { bb }{ ¯ q k ¯ q l } 10674 , 10681 , 10695 115 , 78 , 136 Cf. M. Karliner & J. L. Rosner model, Phys. Rev. Lett. 119 , 202001 (2017) [arXiv:1707.07666]. Estimate deeper binding, so additional bc and cc candidates. Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 13 / 17 q
Real-world candidates for stable tetraquarks J P = 1 + { bb } [¯ u ¯ d ] meson, bound by 121 MeV (77 MeV below B − ¯ B 0 γ ) T { bb } d ] (10482) − → Ξ 0 p , B − D + π − , and B − D + ℓ − ¯ bc ¯ ν u ¯ [¯ � �� � manifestly weak! J P = 1 + { bb } [¯ s ] and { bb } [ ¯ u ¯ d ¯ s ] mesons, bound (?) by 48 MeV (3 MeV below BB s γ ) − 0 ) T { bb } T { bb } bc (¯ s ] (10643) − → Ξ 0 s ] (10643) 0 → Ξ 0 bc Σ Λ , Σ [ ¯ [¯ u ¯ d ¯ Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 14 / 17 q
Unstable doubly heavy tetraquarks Resonances in “wrong-sign” (double flavor) combinations DD , DB , BB ? J P = 1 + T { cc } ++ (4156) → D + D ∗ + s : prima facie evidence for non- q ¯ q level [ ¯ d ¯ s ] Double charge / double charm (New kind of resonance: no attractive force at the meson–meson level.) Also, 1 + T { bb } 1 + T { bc } q l } (10681) 0 , − , −− , Q = +78 MeV d ] (7272) 0 , Q = +82 MeV u ¯ { ¯ q k ¯ [¯ 0 + T [ bc ] 1 + T { cc } d ] (7229) 0 , Q = +83 MeV d ] (3978) + , Q = +102 MeV u ¯ u ¯ [¯ [¯ Chris Quigg Narrow open charm, Excited B c , QQ ¯ q ¯ MIAPP · 25.10.2019 15 / 17 q
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