Precision calculations of semileptonic B decays Yu-Ming Wang Technische Universität München The 10th TeV Physics Workshop 09. 08. 2015 Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 1 / 22
Where do we stand now? Big success of the SM and no evidences of NP = ⇒ Precision physics (Higgs, flavor ...). LQ1(ej) x2 stopped gluino (cloud) LQ1(ej)+LQ1( ν j) stopped stop (cloud) Long-Lived LQ2( μ j) x2 HSCP gluino (cloud) Leptoquarks LQ2( μ j)+LQ2( ν j) HSCP stop (cloud) Particles LQ3( ν b) x2 q=2/3e HSCP q=3e HSCP LQ3( τ b) x2 neutralino, ctau=25cm, ECAL time LQ3( τ t) x2 LQ3(vt) x2 0 1 2 3 4 0 1 2 3 4 j+MET, SI DM=100 GeV, Λ j+MET, SD DM=100 GeV, Λ RS1( γγ ), k=0.1 RS Gravitons γ +MET, SI DM=100 GeV, Λ RS1(ee,uu), k=0.1 Dark Matter γ +MET, SD DM=100 GeV, Λ RS1(jj), k=0.1 l+MET, ξ =+1, SI DM=100 GeV, Λ RS1(WW → 4j), k=0.1 l+MET, ξ =+1, SD DM=100 GeV, Λ 0 1 2 3 4 l+MET, ξ =-1, SI DM=100 GeV, Λ CMS Preliminary l+MET, ξ =-1, SD DM=100 GeV, Λ 0 1 2 3 4 Heavy Gauge SSM Z'( ττ ) Bosons SSM Z'(jj) ADD ( γγ ), nED=4, MS Large Extra SSM Z'(bb) ADD (ee, μμ ), nED=4, MS Dimensions SSM Z'(ee)+Z'(µµ) ADD (j+MET), nED=4, MD ADD ( γ +MET), nED=4, MD SSM W'(jj) QBH, nED=4, MD=4 TeV SSM W'(lv) NR BH, nED=4, MD=4 TeV SSM W'(WZ → lvll) Jet Extinction Scale SSM W'(WZ → 4j) String Scale (jj) 0 1 2 3 4 0 2 4 5 7 9 Excited Compositeness Fermions e* (M= Λ ) dijets, Λ + LL/RR μ * (M= Λ ) dijets, Λ - LL/RR q* (qg) dimuons, Λ + LLIM q* (q γ ) dimuons, Λ - LLIM b* dielectrons, Λ + LLIM 0 1 2 3 4 dimuons, Λ - LLIM single e, Λ HnCM coloron(jj) x2 Multijet single μ , Λ HnCM coloron(4j) x2 gluino(3j) x2 inclusive jets, Λ + Resonances gluino(jjb) x2 inclusive jets, Λ - 0 1 2 3 4 0 4 8 13 17 21 CMS Exotica Physics Group Summary – ICHEP , 2014 Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 2 / 22
Triumphs of flavor physics 1963: concept of flavor mixing [Cabibbo]. 1973: quark-flavor mixing with 3 generations incudes CP violation [KM mechanism]. 1974: prediction of the charm mass from K 0 − K 0 mixing. [Gaillard and Lee]. 1987: prediction of the top mass from B 0 − B 0 mixing observed by AUGUS (DESY) and UA1 (CERN). 2001: large CP violation in B meson decays [BaBar and Belle]. 2004: direct CP violation in B meson decays [BaBar and Belle]. Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 3 / 22
Why flavor matters in the LHC era? Indirect probe of BSM physics beyond direct reach. ◮ EFT parametrization of BSM physics: 1 dim 4 + ∑ Λ n − 4 Q ( n ) L = L SM z n n > 4 ∑ . ( i ) i i ◮ Dimension- n operator Q ( n ) is SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y gauge invariant. i ◮ Higher dimension operator Q ( n ) suppressed by the large scale. i ◮ Two examples: (a) leading NP operators of D = 6 for ∆ F = 2 processes � � � � Q ( 6 ) q i Γ A q j q i Γ B q j AB , ij = ⊗ , ¯ ¯ 1.5 (b) unitarity of the CKM triangles. excluded at CL > 0.95 excluded area has CL > 0.95 γ 1.0 ∆ m & ∆ m s d sin 2 β 0.5 ∆ m d ε α K γ β η 0.0 α V α ub -0.5 ε -1.0 K CKM γ sol. w/ cos 2 β < 0 f i t t e r (excl. at CL > 0.95) Winter 14 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 ρ Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 4 / 22
Why flavor matters in the LHC era? Find the underlying principle for the flavor structure. Suggestive pattern of masses and mixings. S. Stone, 1212.6374 ◮ Why are the quark masses (except the top) so small compared with the vev? ◮ Why is the CKM matrix hierarchical? ◮ Why is CKM so different from the PMNS? ◮ Why do we have three families? ◮ Sources of flavor symmetry and violation? Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 5 / 22
Why flavor matters in the LHC era? Excellent opportunities to explore the strong interaction dynamics: SM/CKM New Physics y Hadronic B 0 Penguins B B CP violation CP i l ti Mixing Semi-leptonic p Tree B s B Lifetime decays decays D 0 B c Radiative Pure-leptonic D D s Penguins Penguins Electroweak El t k b D decays Penguins LFV New K K 0 K Production Production resonances resonances QCD factorization theorems, effective field theories, resummation techniques, non-perturbative QCD dynamics, QCD sum rules. Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 6 / 22
Theory tools for precision flavor physics New Physics: L NP Aim: � f | Q i | ¯ B � = ? ↓ QCD factorization EW scale ( m W ): L SM + L D > 4 [BBNS approach]. ↓ TMD factorization. SCET factorization. Heavy-quark scale ( m b ): L eff = − G F 2 ∑ √ C i Q i + L eff , D > 6 (Light-cone) QCD i sum rules. ↓ Lattice QCD. QCD scale ( Λ QCD ) Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 7 / 22
Ten years of flavour factories 2004 = ⇒ 2014 1.5 1.5 excluded at CL > 0.95 excluded area has CL < 0.05 excluded area has CL > 0.95 γ ∆ m d 1 1.0 ∆ m & ∆ m sin 2 β sin 2 β d s sin 2 β ∆ m s & ∆ m d 0.5 0.5 m ∆ d B → ρρ ε α α K ε K β γ β γ η 0.0 0 η α | V ub /V cb | V α ub -0.5 -0.5 ε K ε -1.0 K -1 CKM γ sol. w/ cos 2 β < 0 f i t t e r CK M (excl. at CL > 0.95) Winter 14 f i t t e r B → ρρ Winter 2004 -1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1 -0.5 0 0.5 1 1.5 2 ρ ρ Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 8 / 22
Anomalies in FCNC processes A few “anomalies" exist in B → K ( ∗ ) ℓ + ℓ − . [LHCb-CONF-2015-002] 1 ' 5 P ) ) LHCb µ − e − LHCb-TALK-2014-108 preliminary µ + e + 0.5 K + K + SM from DHMV [1407.8526] → → 0 B + B + ( ( r r B B -0.5 = 2.6 σ R K -1 0 5 10 15 2 2 [GeV / 4 ] q c Indication of BSM physics or ignorance of QCD dynamics? P ′ 5 anomaly below 6GeV 2 more serious [power corrections]. Violation of lepton flavor universality [QED corrections]. Need more data and theoretical efforts. Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 9 / 22
| V ub | puzzle 3 σ tension between exclusive and inclusive | V ub | . CLEO (E ) e ± 4.28 0.50 + 0.31 - 0.36 2 2 BELLE sim. ann. (m , q 2 ) Khodjamirian et al. q < 12 GeV X ± 4.49 0.47 + 0.28 - 0.30 ± BELLE (E ) 3.41 0.06 + 0.37 - 0.32 e ± 4.93 0.46 + 0.27 - 0.29 BABAR (E ) e 2 2 ± Ball-Zwicky q < 16 GeV 4.54 0.26 + 0.27 - 0.33 max BABAR (E , s ) e h ± ± 3.58 0.06 + 0.59 - 0.40 4.53 0.22 + 0.33 - 0.38 BELLE multivariate (p*) ± 4.49 0.27 + 0.20 - 0.22 BABAR (m <1.55) 2 2 HPQCD q > 16 GeV X ± 4.30 0.20 + 0.28 - 0.27 ± BABAR (m <1.7) 3.52 0.08 + 0.61 - 0.40 X ± ± 4.04 0.22 0.23 2 BABAR (m <1.7, q >8) X 2 2 ± FNAL/MILC q > 16 GeV 4.30 0.23 + 0.26 - 0.28 BABAR (P + <0.66) ± ± 4.15 0.25 + 0.28 - 0.27 3.36 0.08 + 0.37 - 0.31 BABAR (p*>1GeV) ± 4.32 0.24 + 0.19 - 0.21 BABAR (p*>1.3GeV) ± 4.32 0.27 + 0.20 - 0.21 Average +/- exp + th. - th. HFAG ± 4.45 0.16 + 0.21 - 0.22 HFAG χ 2 /dof = 9.0/11 (CL = 62.00 %) PDG 2014 Bosch, Lange, Neubert and Paz (BLNP) Phys.Rev.D72:073006,2005 PDG14 2 4 6 0 2 4 × -3 -3 |V | [ 10 ] |V | [10 ] ub ub BSM physics or ignorance of the strong interaction dynamics? Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 10 / 22
Semileptonic B → π ℓ ν decays ν ℓ Hadronic matrix element: � � ℓ p B + p − m 2 B − m 2 B ( p + q ) � = f + B π ( q 2 ) π u γ µ b | ¯ � π ( p ) | ¯ q q 2 b u µ B π ( q 2 ) m 2 B − m 2 π + f 0 q µ . B ¯ π q 2 Lepton spectrum: G 2 F | V ub | 2 d Γ ( q 2 − m 2 l ) 2 | = � p π | 24 π 3 q 4 m 2 dq 2 B �� � � 1 + m 2 B π ( q 2 ) | 2 + 3 m 2 p π | 2 | f + π ) 2 | f 0 l m 2 8 q 2 ( m 2 l B − m 2 B π ( q 2 ) | 2 × B | � . q 2 Still the best way to determine | V ub | exclusively in the continuum approach! Λ b → p ℓ ν decays also become important now [ LHCb, arXiv:1504.01568]. � � × 10 − 3 . | V ub | = 3 . 27 ± 0 . 23 Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 11 / 22
B → π form factors from the B -meson LCSR Starting point: vacuum-to- B -meson correlation function � � ¯ � d 4 x e ip · x � 0 | T | ¯ Π µ ( p , q ) = d ( x ) n / γ 5 u ( x ) , ¯ u ( 0 ) γ µ b ( 0 ) B ( p + q ) � n · p ) n µ + � = Π ( n · p , ¯ Π ( n · p , ¯ n · p ) ¯ n µ , m 2 B + m 2 π − q 2 p + q ≡ m B v = m B n · p = , n · p ∼ O ( Λ QCD ) , 2 ( n + ¯ n ) . ¯ m B Inserting complete set of pion states → hadronic sum: B B � h π h � Π ( n · p , ¯ n · p ) = π π h π p p q q � n · p � � + ∞ ρ h ( n · p , ω ′ ) d ω ′ � f π ( n · p ) m B f + B π ( n · p )+ f 0 B π ( n · p ) ω ′ − ¯ 2 ( m 2 π − p 2 ) n · p m B ω s � �� � relative sign changes for Π ( n · p , ¯ n · p ) Yu-Ming Wang (TUM) B decays Beijing, 09. 08. 2015 12 / 22
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