Theoretical Overview of B Physics → personal perspectives ← Xin-Qiang Li Central China Normal University Talk given at HFCPV-2018, Zhengzhou, 2018/10/26
Outline Introduction Theoretical tools for B physics B − ¯ B mixings: ∆ M s,d , ∆Γ s,d , a s,d fs B s,d → µ + µ − : powerful model killing Semi-leptonic decays: | V ub | , | V cb | and R ( D ( ∗ ) ) Exclusive b → sℓ + ℓ − decays: several anomalies Non-leptonic decays: higher-order pert. corrs Conclusion 2 / 35
Why B physics: ◮ What is B physics: properties, productions and decays of vari- ous hadrons containing at least one bottom quark; B u,d,s,c mesons, Λ b baryon ◮ Why study B physics: three main motivations; 3 / 35
Dedicated B-physics experiments: ◮ Past: first observation of B → X s γ by CLEO in 1994; continued by Tevatron @ Fermilab and the two B-factories: BaBar @ SLAC and Belle @ KEK with many key measurements; [ A. J. Bevan et al., “The Physics of the B Factories,” 1406.6311 ] ◮ Current: dedicated LHCb (also ATLAS and CMS) @ LHC with many exciting results; [ I. Bediaga et al., “Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era,” arXiv:1808.08865 ] ◮ Future: besides LHCb @ LHC, also Belle II @ SuperKEKB expected to start data taking in 2018, designed to find NP beyond the SM of particle physics; [ https://confluence.desy.de/display/BI/B2TiP+WebHome; 1808.10567 ] LHCb LHCb ±10.0 ±2.6 ±90 ±33.0 × 10 4 ±5.4 ±49 ±28.0 × 10 5 Current Current Belle II Belle II ±1.5 ±35.0 × 10 ±3.6 5 ±0.50 ATLAS/CMS ATLAS/CMS ±10.0 × 10 4 ±1.5 ±14 ±4.3 × 10 ±2.2 5 ±0.72 ±34 LHCb LHCb 2025 2025 ±22 ±21 ±3.0 × 10 4 ±0.35 ±4 ±1.0 × 10 ±0.70 5 ±0.20 ±10 R ( D * ) [%] ( B 0 + ) ) [%] a s [ ] s [ mrad ] R K [%] A HL-LHC HL-LHC ( B 0 + sl s 4 / 35
Theoretical tasks for B physics: ◮ Main task: try to improve the theory predictions to match the more and more precise exp. data; ◮ Many dynamical frameworks developed: HQET, SCET, NRQCD, QCDF, pQCD, · · · ֒ → based on QCD, and separate pert. from non- pert. strong interaction effects ↔ factorization theorem; ◮ For the non-pert. objects: mostly from Lattice QCD and LCSR, [ for reviews see: http://flag.unibe.ch/, and https://hflav.web.cern.ch/ ] · · · ; + = + + FLAG average for + ETM 13E HPQCD 13 = FLAG average for = + RBC/UKQCD 141 RBC/UKQCD 142 + RBC/UKQCD 14A RBC/UKQCD 13A (stat. err. only) = HPQCD 12 HPQCD 12 / 11A FNAL/MILC 11 HPQCD 09 FLAG average for = ALPHA 14 ALPHA 13 ETM 13B, 13C = ALPHA 12A ETM 12B ALPHA 11 ETM 11A ETM 09D 160 175 190 205 220 235 250 MeV 5 / 35
Current status of B physics: ◮ The CKM mechanism of flavor & CP violation well established! ֒ → 2008 Nobel Prize for Kobayashi and Maskawa; ◮ Information on UT from tree- and loop-level processes well consistent! 6 / 35
Current status of B physics: ◮ Remember: O (20%) NP contributions to most FCNC processes still allowed by the current data; ◮ Several intriguing tensions/anomalies do observed in flavour physics, might be any BSM signals? † all of them not yet conclu- sive: theo. uncertainties or exp. fluctuations? † except for theo. cleanest modes, more cross-checks needed; † exp. measurements of re- Br(B->pi^0 pi^0) A_CP(B->pi K) lated observables needed; Z.Ligeti,1606.02756 † indep. theory and lattice calculations needed; 7 / 35
How to describe B-hadron weak decays: ◮ At the quark level: B-hadron weak decays mediated by weak charged-current J µ cc coupled to W ± ; d L L cc = − g 2 t L ) γ µ V CKM J µ J µ cc W † c L , ¯ √ µ + h.c. , cc = (¯ u L , ¯ s L 2 b L ֒ → V CKM : describes flavor violation, and very predictive, especially for CPV! ◮ In the real world: no free quarks due to confinement; quarks always confined inside hadrons through soft-gluon exchanges; ֒ → In B physics, simple weak decays overshadowed by complex strong interactions! 8 / 35
Typical features for B-hadron weak decays: ◮ A typical multi-scale problem and scales are highly hierarchical; EW interaction scale ≫ ext. mom’a in B rest frame ≫ QCD-bound state effects m W ∼ 80 . 4 GeV ≫ m b ∼ 4 . 8 GeV ≫ Λ QCD ∼ 1 GeV ◮ Starting point L eff : integrate out heavy d.o.f. ( m W,Z,t ≫ m b ), physics [ A. J. Buras, 1102.5650 ] above (below) µ ∼ m b contained in C i ( �O i � ); ◮ C i : RG-improved pert. calculable; matching at µ 0 and running to µ b ; NNLL accuracy available! 9 / 35
Hadronic matrix elements for B-hadron weak decays: ◮ How to evaluate � f |O i | B � : � 0 |O i | B � , � π |O i | B � , � ππ |O i | B � , � ¯ B |O i | B � , · · · ; ◮ � M 1 M 2 |O i | B � : not yet possible in lattice QCD; expressed in terms of (few) universal non-pert. hadronic quantities with pert. calculable coefficients; - dynamical approaches based on factorization theorems: PQCD, QCDF, [ Keum, Li, Sanda, L¨ SCET, · · · ; u, Yang ’00; Beneke, Buchalla, Neubert, Sachrajda, ’00; Bauer, Flemming, Pirjol, Stewart, ’01 ] - (approximate) symmetries of QCD: Isospin, U-Spin, V-Spin, and flavor [ Zeppenfeld, ’81; SU(3) symmetries, · · · ; London, Gronau, Rosner, Chiang, Cheng et al. ] 10 / 35
B − ¯ B mixings: ◮ Motivation: strongly suppressed in SM; highly sensitive to BSM effects; ֒ → Λ ≥ 10 3 TeV ◮ ∆ M s,d . = 2 | M s,d 12 | : calculated from box diagrams with internal virtual par- B q B ( i ) ticles; main uncertainty from Bag parameters � B q |O i | ¯ B q � ∝ f 2 B q ; ∆ M SM = (0 . 53 +0 . 03 − 0 . 04 ) ps − 1 d ∆ M HFAG = (0 . 5065 ± 0 . 0019) ps − 1 d ∆ M SM = (18 . 1 +1 . 1 − 1 . 2 ) ps − 1 s ∆ M HFAG = (17 . 757 ± 0 . 021) ps − 1 s [ Kirk, Lenz and Rauh, 1711.02100; T. Rauh, talk given at CKM2018 ] 11 / 35
B − ¯ B mixings: ◮ ∆Γ s,d . = 2 | Γ s,d 12 | cos φ s,d 12 : arise from absorptive part of box diagrams, dom- cs ( d ) transitions; [ Artuso/Borissov/Lenz, 1511.09466 ] inated by tree-level b → c ¯ � α s 12 = Λ 3 � + α s � � 2 b s Γ s, (0) 4 π Γ s, (1) Γ s, (2) Γ s c + + ... 3 3 3 m 3 4 π b + Λ 4 � Γ s, (0) � + ... + ... [H. M. Asatrian et al , 1709.02160] 4 c m 4 s b b Quark Expansion (HQE) . Γ s,d � � ◮ a s,d � sin φ s,d = 12 12 : motivated by 2013 D0 dimuon charge asymmetry! � � fs M s,d � 12 ) 2 = 1 0 0.01 ∆ χ s (B LHCb SL 0 (*) B → D µ X ∆Γ s [ps − 1 ] A (s) (s) HFLAV 0.14 D0 8 fb − 1 Theory × 10 PDG 2018 0 68% CL contours World average ( ∆ log L = 1.15) 0.12 CMS 19.7 fb − 1 -0.01 0.10 Combined CDF 9.6 fb − 1 D 0 D 0 (*) muons B 0 → D µ X (s) SM (s) 0.08 D 0 -0.02 LHCb 3 fb − 1 average HFLAV B factory average ATLAS 19.2 fb − 1 PDG 2018 0.06 -0.02 -0.01 0 0.01 0.02 0 -0.4 -0.2 -0.0 0.2 0.4 A (B ) SL φ c ¯ cs s [rad] 12 / 35
B − ¯ B mixing: ◮ ∆ M s,d vs ∆Γ s,d : state-of-the-art comparison; [ Kirk, Lenz and Rauh, 1711.02100; T. Rauh, talk given at CKM2018 ] ◮ SM predictions and exp. averages consistent with each other! ֒ → Large NP effect in B s,d mixings now closed! 13 / 35
B s,d → µ + µ − : ◮ Facts about B s,d → µ + µ − : highly suppressed within the SM; - helicity suppressed, by a factor of ( m µ /m B ) 2 ; - FCNC process, forbidden at tree-level, proceed only via loop diagrams; - CKM suppressed by | V tb V ∗ ts | 2 ; ֒ → very sensitive to NP, especially from O S ( P ) ; ◮ Theory status: C A now to NNLO QCD + NLO EW; enhanced EM correction included; [ Bobeth et al., 1311.0903; Beneke, Bobeth and Szafron, 1708.09152 ] A,S,P H eff = − G F α � � � V tb V ∗ C i O i + C ′ i O ′ √ � � + h . c . tq i 2 πs 2 W i qγ µ P L b ) (¯ qP R b ) [¯ ℓγ µ γ 5 ℓ ) , O A = (¯ O S ( P ) = m b (¯ ℓ ( γ 5 ) ℓ ] B ( B s → µ + µ − ) = (3 . 57 ± 0 . 17) × 10 − 9 , B ( B d → µ + µ − ) = (1 . 06 ± 0 . 09) × 10 − 10 14 / 35
B s,d → µ + µ − : ◮ CMS + LHCb and LHCb updated results: [ 1411.4413, 1703.05747 ] 10 − 9 × 0.9 ) − µ 0.8 LHCb B ( B s → µ + µ − ) = (3 . 0 ± + µ 0.7 → 0 . 6 +0 . 3 − 0 . 2 ) · 10 − 9 ( 7 . 8 σ ); 0.6 0 BF(B 0.5 0.4 0.3 9 B ( B d → µ + µ − ) = (3 . 9 +1 . 6 9 9 . − 1 . 4 ) · 9 9 9 . 6 5 7 9 . 0.2 8 4 3 % . 2 5 % 7 % % 10 − 10 ( 3 . 0 σ ); 0.1 SM 10 − 9 × 0 0 2 4 6 8 BF(B 0 − ) → µ + µ s ◮ Powerful in model killing: good consistency between SM and exp. data; [ D. Straub, 1205.6094 ] 15 / 35
B s,d → µ + µ − : ◮ Time-dependent observables: due to sizeable ∆Γ s ; [ De Bruyn et al., 1204.1737; Fleischer et al., 1703.10160; 1709.04735 ] ◮ With the updated LHC: these observables provide new d.o.f. for NP [ Fleischer, Jaarsma, Tetlalmatzi-Xolocotzi, 1703.10160; 1709.04735 ] searches; 16 / 35
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