The B → D ( ∗ ) τ ¯ ν & B → τ ¯ ν decays, Theoretical status thereof Marat Freytsis University of Oregon FPCP 2016 — Caltech, June 6, 2016
Massive leptons in (semi-)leptonic B decays unique windows into both NP and the SM via B → ( X ) τ ¯ ν decays • Standard Model ◮ B → D ( ∗ ) transitions both depend on FFs whose contribution vanishes as m ℓ → 0 ◮ B − → τ − ¯ ν only decay sensitive to f B measurable in the near future • New Physics ◮ NP often presumed to couple preferentially to 3rd generation ◮ A reason to persue B → X s ν ¯ ν and B ( s ) → ( X ) ττ for years [Hewitt, hep-ph/9506289; Grossman, Ligeti, Nardi, hep-ph/9510378 & hep-ph/9607473]] • somewhere in between (focus of most of this talk) ◮ high-precision in B → X u,c ℓ ¯ ν critical to extraction of | V ub | , | V cb | ◮ ratios are great venue for tests of lepton flavor universality (LFU) standard diclaimers: . . . general overview, but colored by my biases . . . . . . apologies to any recent work I might have missed . . . 1/ 18
Plan • Introduction • Precise SM predictions ◮ complimentary, CKM-parameter-free families of ratio observables for LFU sensitivity • Quantifying NP sensitivity ◮ redundant effective operator bases for identification of UV physics • NP descriminators ◮ more differential distributions for discrimination of scenarios • Consequences and Conclusions 1/ 18
B − → τ − ¯ ν Pure leptonic decays In the SM: � 2 ν ) = | V ub | 2 G 2 1 − m 2 � Γ( B − → τ − ¯ F f 2 B m 2 τ τ m B m 2 8 π B either measure | V ub | f B in data or use f B from lattice to extract | V ub | (e.g., latest lattice world average: f B = (190 . 5 ± 4 . 2) MeV [FLAG, 1310.8555] ) • only P -odd currents contribute: � 0 | ¯ b ( γ µ ) γ 5 c | B � � = 0 • new pseudoscalar couplings typically proportional to fermion mass: Γ( B − → τ − ¯ ν ) = | 1 + r NP | 2 Γ( B − → τ − ¯ ν ) SM B C P | 2 Γ( B − → τ − ¯ = | 1 + C A V + m 2 ν ) SM � b � � B � � u � e 2/ 18 � e b c 0 + B D d d d � � u b c 0 + B D d d
B − → τ − ¯ ν Eliminating | V ub | dependence | V ub | drops out of ratio, but NP independent of lepton mass overall rate can still be affected/act as a bound [Hou, PRD48, 2342 (1993)] Γ( B − → τ − ¯ ν ) = Γ( B − → τ − ¯ ν ) ν ) SM Γ( B − → µ − ¯ Γ( B − → µ − ¯ ν ) SM • B − → µ − ¯ νγ correction complicates situation – no helicity suppression an alternative: compare to helicity unsuppressed decay B ( B − → τ − ¯ R π = τ B 0 ν ) ν ) = 0 . 73(13) from here ℓ = avg. of µ + e B ( ¯ B 0 → π + ℓ − ¯ τ B − [Fajfer, Kamenik, Niˇ sandˇ zi´ c, Zupan, 1206.1872] R π SM = 0 . 31(6) requires (improvable) decay constants and FFs from the lattice I have nothing else to add about B − → τ − ¯ ν , will now focus on b → cτ ¯ ν transitions 3/ 18
B → D ( ∗ ) τ ¯ ν An R ( X ) reminder R ( X ) = Γ( B → Xτ ¯ ν ) Γ( B → Xℓ ¯ ν ) original goal: 2HDM H ± • deviation first seen at BaBar, later results from Belle and LHCb BaBar/Belle full datasets τ → ℓν ¯ ν to minimize lepton reco systematics 0.5 R ( D ∗ ) R(D*) R ( D ) BaBar, PRL109,101802(2012) ∆ χ 2 = 1.0 Belle, PRD92,072014(2015) BaBar 0 . 440 ± 0 . 058 ± 0 . 042 0 . 332 ± 0 . 024 ± 0 . 018 0.45 LHCb, PRL115,111803(2015) Belle, arXiv:1603.06711 Belle ( B (had) χ HFAG Average, P( 2 ) = 67% ) 0 . 375 ± 0 . 064 ± 0 . 026 0 . 293 ± 0 . 038 ± 0 . 015 0.4 SM prediction tag Belle ( B ( ℓ ) tag ) 0 . 302 ± 0 . 030 ± 0 . 011 0.35 LHCb 0 . 336 ± 0 . 027 ± 0 . 030 0.3 Exp. average 0 . 397 ± 0 . 040 ± 0 . 028 0 . 316 ± 0 . 016 ± 0 . 010 0.25 HFAG R(D), PRD92,054510(2015) SM expectation 0 . 300 ± 0 . 010 0 . 252 ± 0 . 005 R(D*), PRD85,094025(2012) Prel. Winter 2016 0.2 Belle II, 50/ab ± 0 . 010 ± 0 . 005 0.2 0.3 0.4 0.5 0.6 R(D) ◮ clean SM observables: heavy quark symmetry relates FFs Caprini, Lellouch, Neubert, hep-ph/9712417 cancellation of hadronic uncertainties, | V cb | in ratios lattice QCD for R ( D ) only [MILC, 1503.07237; HPQCD, 1505.03925] ◮ R ( D ) — 1 . 9 σ , R ( D ∗ ) — 3 . 3 σ total significance — 4 . 0 σ largest deviation from SM right now! • similar ratios before Belle II: LHCb: R ( D ) ? Λ b → Λ ( ∗ ) c τ ¯ ν ? BaBar/Belle: hadronic τ decays? 4/ 18
Evading unquantified systematics in SM calculations Complementary theory predictions • inclusive B → X c τ ¯ ν rate bounded by known exclusive modes [MF, Ligeti, Ruderman, 1506.08896] ◮ form-factor independent OPE-based analysis – complementary theory systematics ◮ Corrections up to O (Λ QCD /m b , α 2 s ) R ( X c ) = 0 . 223 ± 0 . 004 theory B ( B − → X c ℓ ¯ ν ) = (10 . 92 ± 0 . 16)% inclusive ℓ data ⇒ B ( B − → X c τ ¯ ν ) = (2 . 42 ± 0 . 05)% prediction + ν ) = (2 . 41 ± 0 . 23)% ) (LEP: B ( b → Xτ • isospin-constrained fit: B ( ¯ ν ) + B ( ¯ B → D ∗ τ ¯ B → Dτ ¯ ν ) = (2 . 78 ± 0 . 25)% • estimate rate to excited B ( B → D ∗∗ τ ¯ ν ) � 0 . 2% get conservative limit: B ( B → D ∗∗ ℓ ¯ ν ) / B ( B → D ( ∗ ) ℓ ¯ ν ) ∼ 0 . 3 • deviation � 3 σ in inclusive calculation (minimal non-perturbative inputs) ◮ complementary to SM calculation of R ( D ( ∗ ) ) and LEP data 5/ 18
Leveraging inclusive spectra ν ) /dq 2 predictions Precision d Γ( B → X c τ ¯ • no measurements since LEP, ◮ papers in ‘90s used m pole , no study of spectra (new data needed, in progress @ Belle) b ◮ large 1 /m 2 OPE corrections • we’ve been told Belle analysis in progress 0 . 3 0 . 025 [GeV − 1 ] B → X c τν 0 ) dΓ / d q 2 [GeV − 2 ] B → X c τν 0 . 25 0 . 02 0 . 2 0 . 015 0 . 15 0 ) dΓ / d E τ 0 . 01 LO 0 . 1 LO NLO 0 . 005 NLO NLO+1 /m 2 0 . 05 b (1 / Γ (1 / Γ NLO+1 /m 2 NLO+1 /m 2 b +SF b 0 0 3 4 5 6 7 8 9 10 11 12 1 . 8 2 2 . 2 2 . 4 2 . 6 q 2 [GeV 2 ] E τ [GeV] 1 1 B → X c τν B → X c τν 0 . 9 0 . 9 0 . 8 0 . 8 0 . 7 0 . 7 cut ) Γ( E cut ) 0 . 6 0 . 6 Γ( q 2 0 . 5 0 . 5 � 0 . 4 � 0 . 4 LO LO 0 . 3 0 . 3 NLO NLO 0 . 2 NLO+1 /m 2 0 . 2 NLO+1 /m 2 b 0 . 1 b 0 . 1 NLO+1 /m 2 b +SF 0 0 3 4 5 6 7 8 9 10 11 12 1 . 8 2 2 . 2 2 . 4 2 . 6 q 2 cut [GeV 2 ] E cut [GeV] [Ligeti, Tackmann, 1406.7013] 6/ 18
leveraging inclusive spectra All τ modes. . . b → uτ ¯ ν ? • if deviation clearly established, huge motivation to study all decay modes with τ ν with a few × 10 6 B - ¯ ◮ if LEP could measure B → X c τ ¯ B pairs . . . ν with 5 × 10 10 B - ¯ ◮ . . . “surely” Belle II can measure B → X u τ ¯ B pairs • no inclusive distributions currently availible ◮ m τ � = 0 , m u = 0 – complications from different kinematic endpoints ◮ 1 . 8 GeV < E τ < 2 . 9 GeV – Subtleties with shape function; match onto u jet? [Ligeti, Luke, Tackmann, in progress] • phase space suppression is smaller in b → u : Γ( B → X u τ ¯ ν ) Γ( B → X c τ ¯ ν ) ν ) ≃ 0 . 333 ν ) ≃ 0 . 222 Γ( B → X u ℓ ¯ Γ( B → X c ℓ ¯ • can LHCb/Belle II measure b → uτ ¯ ν decay modes? ratios of τ/µ and/or c/u ? ◮ Other exclusive modes: Λ b → Λ ( c ) τ ¯ ν ? B → πτ ¯ ν ? B → ρτ ¯ ν ? 7/ 18
Plan • Introduction • Precise SM predictions • Quantifying NP sensitivity • NP descriminators • Consequences and Conclusions 7/ 18
Redundant four-fermion operator analysis • Fits to different fermion orderings convenient to understand allowed mediator Operator Fierz identity Allowed Current δ L int q L τ γ µ q L + g ℓ ¯ τγ µ P L ν ) ℓ L τ γ µ ℓ L ) W ′ O V L (¯ cγ µ P L b ) (¯ ( 1 , 3 ) 0 ( g q ¯ µ τγ µ P L ν ) O V R (¯ cγ µ P R b ) (¯ � O S R (¯ cP R b ) (¯ τP L ν ) q L u R iτ 2 φ † + λ ℓ ¯ ( 1 , 2 ) 1 / 2 ( λ d ¯ q L d R φ + λ u ¯ ℓ L e R φ ) O S L (¯ cP L b ) (¯ τP L ν ) cσ µν P L b ) (¯ O T (¯ τσ µν P L ν ) q L τ γ µ ℓ L U µ � ( 3 , 3 ) 2 / 3 λ ¯ O ′ cγ µ P L ν ) (¯ τγ µ P L b ) (¯ ↔ O V L V L � q L γ µ ℓ L + ˜ λ ¯ d R γ µ e R ) U µ ( 3 , 1 ) 2 / 3 ( λ ¯ O ′ cγ µ P L ν ) (¯ τγ µ P R b ) (¯ ↔ − 2 O S R V R O ′ − 1 (¯ τP R b ) (¯ cP L ν ) ↔ 2 O V R S R u R ℓ L + ˜ O ′ − 1 2 O S L − 1 (¯ τP L b ) (¯ cP L ν ) ↔ 8 O T ( 3 , 2 ) 7 / 6 ( λ ¯ λ ¯ q L iτ 2 e R ) R S L O ′ τσ µν P L b ) (¯ − 6 O S L + 1 (¯ cσ µν P L ν ) ↔ 2 O T T τγ µ P L c c ) (¯ O ′′ b c γ µ P L ν ) (¯ ↔ −O V R V L τγ µ P R c c ) (¯ ( λ ¯ R γ µ ℓ L + ˜ O ′′ b c γ µ P L ν ) (¯ d c q c L γ µ e R ) V µ (¯ ↔ − 2 O S R 3 , 2 ) 5 / 3 λ ¯ V R (¯ � q c 3 , 3 ) 1 / 3 λ ¯ L iτ 2 τ ℓ L S O ′′ τP R c c ) (¯ b c P L ν ) 1 (¯ ↔ 2 O V L S R � (¯ q c L iτ 2 ℓ L + ˜ u c 3 , 1 ) 1 / 3 ( λ ¯ λ ¯ R e R ) S τP L c c ) (¯ O ′′ b c P L ν ) − 1 2 O S L + 1 (¯ ↔ 8 O T S L O ′′ τσ µν P L c c ) (¯ b c σ µν P L ν ) − 6 O S L − 1 (¯ ↔ 2 O T T ◮ O parametrize all possible dim-6 contributions, O ′ , O ′′ related by Fierzing ◮ δ L int only for dim-6 gauge-inv. O ’s with mediator spin ≤ 1 8/ 18
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