Precision flavour physics Tobias Huber Universität Siegen CRC colloquium, July 13th, 2020 T. Huber Precision flavour physics 1 Outline Introduction / motivation Charged-current semileptonic decays Radiative decays FCNC semileptonic decays Mixing and lifetimes Nonleptonic decays SMEFT Conclusion and outlook T. Huber Precision flavour physics 2 Have to make a selection: Will focus on B mesons, because . Description of B-meson system contains many essential features of (precision) flavour physics Global fits driven by B meson anomalies [Arbey et al.,’19] Introduction The majority of the SM parameters resides in the Yukawa sector Quarks and leptons are the principal actors of flavour physics Many aspects of flavour physics Heavy (top, bottom, charm) and light quarks Mesons and baryons Charged leptons, neutrinos T. Huber Precision flavour physics 3 Introduction The majority of the SM parameters resides in the Yukawa sector Quarks and leptons are the principal actors of flavour physics Many aspects of flavour physics Heavy (top, bottom, charm) and light quarks Mesons and baryons Charged leptons, neutrinos Have to make a selection: Will focus on B mesons, because . Description of B-meson system contains many essential features of (precision) flavour physics Global fits driven by B meson anomalies [Arbey et al.,’19] T. Huber Precision flavour physics 3 Indirect search for new physics Look for virtual effects of new phenomena Mostly looked for in rare processes Requires precision in theory and experiment Synergy and complementarity to direct searches Huge experimental progress (B-factories, Tevatron, LHC, Belle II, . ) Motivation to study flavour CP violation Needed to explain matter-antimatter asymmetry (Sakharov conditions) CKM phase is the only established source of CP violation in the SM But too small to explain size of baryon asymmetry T. Huber Precision flavour physics 4 Huge experimental progress (B-factories, Tevatron, LHC, Belle II, . ) Motivation to study flavour CP violation Needed to explain matter-antimatter asymmetry (Sakharov conditions) CKM phase is the only established source of CP violation in the SM But too small to explain size of baryon asymmetry Indirect search for new physics Look for virtual effects of new phenomena Mostly looked for in rare processes Requires precision in theory and experiment Synergy and complementarity to direct searches T. Huber Precision flavour physics 4 Motivation to study flavour CP violation Needed to explain matter-antimatter asymmetry (Sakharov conditions) CKM phase is the only established source of CP violation in the SM But too small to explain size of baryon asymmetry Indirect search for new physics Look for virtual effects of new phenomena Mostly looked for in rare processes Requires precision in theory and experiment Synergy and complementarity to direct searches Huge experimental progress (B-factories, Tevatron, LHC, Belle II, . ) T. Huber Precision flavour physics 4 Problem: confinement of quarks into hadrons Computation of hadronic matrix elements highly non-trivial QCD effects could overshadow the interesting fundamental dynamics Need to get control over QCD effects Sophisticated tools available Effective field theories (HQET, SCET,.. ) Heavy-Quark expansion Factorization Perturbative calculations: Loops, . Non-pert. techniques: Lattice, Sum rules, . Applications also in Higgs, Collider, DM, . Motivation to study flavour SM parameters Precise knowledge of masses and mixing parameters needed in all branches of particle physics T. Huber Precision flavour physics 5 Problem: confinement of quarks into hadrons Computation of hadronic matrix elements highly non-trivial QCD effects could overshadow the interesting fundamental dynamics Need to get control over QCD effects Sophisticated tools available Effective field theories (HQET, SCET,.. ) Heavy-Quark expansion Factorization Perturbative calculations: Loops, . Non-pert. techniques: Lattice, Sum rules, . Applications also in Higgs, Collider, DM, . Motivation to study flavour SM parameters Precise knowledge of masses and mixing parameters needed in all branches of particle physics T. Huber Precision flavour physics 5 Motivation to study flavour SM parameters Precise knowledge of masses and mixing parameters needed in all branches of particle physics Problem: confinement of quarks into hadrons Computation of hadronic matrix elements highly non-trivial QCD effects could overshadow the interesting fundamental dynamics Need to get control over QCD effects Sophisticated tools available Effective field theories (HQET, SCET,.. ) Heavy-Quark expansion Factorization Perturbative calculations: Loops, . Non-pert. techniques: Lattice, Sum rules, . Applications also in Higgs, Collider, DM, . T. Huber Precision flavour physics 5 Effective theory for B decays π− u¯ d π− W − u¯ b u b d u 0 Qi 0 B− π −→ B− π u¯ u¯ MW , MZ , mt, mH mb: integrate out heavy gauge bosons, t-quark, Higgs Effective Weak Hamiltonian: [Buras,Buchalla,Lautenbacher’96; Chetyrkin,Misiak,Münz’98] " 10 # 4GF X p p X Heff = √ λp C1Q + C2Q + CkQk + h.c. 2 1 2 p=u,c k=3 p ¯ µ a a ¯ µ a P a Q1 = (dLγ T pL)(¯pLγµT bL) Q4 = (dLγ T bL) q(¯qγµT q) p ¯ µ ¯ µ ν ρ P Q2 = (dLγ pL)(¯pLγµbL) Q5 = (dLγ γ γ bL) q(¯qγµγν γρq) ¯ µ P ¯ µ ν ρ a P a Q3 = (dLγ bL) q(¯qγµq) Q6 = (dLγ γ γ T bL) q(¯qγµγν γρT q) e g Q = m s¯ σ F µν b Q = s m s¯ σ Gµν b 7 16π2 b L µν R 8 16π2 b L µν R µ ¯ µ ¯ ∗ Q9 = (¯sLγ bL)(`γµ`) Q10 = (¯sLγ bL)(`γµγ5`) λp = VpbVpd T. Huber Precision flavour physics 6 Effective theory for B decays Generic structure of amplitude for B decays X A(B¯ → f) = λCKM × C × hf|O|B¯iQCD+QED i i Interplay between Wilson coefficients C , known to NNLL in SM, values at scale µ ∼ mb [Bobeth,Misiak,Urban’99;Misiak,Steinhauser’04,Gorbahn,Haisch’04;Gorbahn,Haisch,Misiak’05;Czakon,Haisch,Misiak’06] C1 = −0.25 |C3,5,6| < 0.01 C7 = −0.30 C9 = 4.06 C2 = 1.01 C4 = −0.08 C8 = −0.15 C10 = −4.29 CKM factors λCKM . Hierarchy of CKM elements, weak phase Hadronic matrix elements hf|O|B¯i. Can contain strong phases. Interplay offers rich and interesting phenomenology for B decays Plethora of data, numerous observables Test of CKM mechanism and indirect search for New Physics BUT: Challenging QCD dynamics in hadronic matrix elements. Effects from many different scales !! T. Huber Precision flavour physics 7 Inclusive B decays, generalities Main tool for inclusive decays: Heavy Quark Expansion [Khoze,Shifman,Voloshin,Bigi,Uraltsev,Vainshtein,Blok,Chay,Georgi,Grinstein,Luke,. ’80s and ’90s] Z 1 X 4 (4) ˆ 2 Γ(Bq → X) = (2π) δ (pBq − pX )|hX|Heff |Bqi| 2mBq X PS Use optical theorem Z 1 4 Γ(Bq → X) = hBq|Tˆ |Bqi with Tˆ = Im i d xTˆ Hˆeff (x)Hˆeff (0) 2mBq Expand non-local double insertion of effective Hamiltonian in local operators ˜ hOD=5i ˜ hOD=6i Γ = Γ0hOD=3i + Γ2 2 + Γ3 3 + ... mb mb 2 hOD=6i hOD=7i hOD=8i +16π Γ3 3 + Γ4 4 + Γ5 5 + ... mb mb mb Expand each term in perturbative series α α 2 Γ = Γ(0) + s Γ(1) + s Γ(2) + ... i i 4π i 4π i T. Huber Precision flavour physics 8 HQE expansion parameters 2 Γ0: Decay of a free quark, known to O(αs) Γ1: Vanishes due to Heavy Quark Symmetry Two terms in Γ2 2 ¯ 2 Kinetic energy µπ: 2MB µπ = −hB(v)|bv(iD) bv|B(v)i 2 ¯ µ ν Chromomagnetic moment µG: 2MB µG = −ihB(v)|bvσµν (iD )(iD )bv|B(v)i Both known to O(αs) [Becher,Boos,Lunghi’07;Alberti,Ewerth,Gambino,Nandi’13’14;Mannel,Pivovarov,Rosenthal’15] Two more terms in Γ3 3 ¯ µ Darwin term ρD: 2MH ρD = −hB(v)|bv(iDµ)(ivD)(iD )bv|B(v)i 3 ¯ µ ν Spin-orbit term ρLS : 2MH ρLS = −ihB(v)|bvσµν (iD )(ivD)(iD )bv|B(v)i Recently, ρD became available at O(αs) [Mannel,Pivovarov’19] T. Huber Precision flavour physics 9 Higher orders in HQE and inclusive B → Xc`ν¯` b ¯b b ¯b c c l l ν¯ ν¯ ρD at O(αs) [Mannel,Pivovarov’19] 2 2 2 µπ µG aDρD + aLS ρLS Γ(B → Xc`ν¯`) = Γ0|Vcb| a0(1 + 2 ) + a2 2 + 3 + ... 2mb 2mb 2mb α One finds a = −57.159(1 − s 6.564) = −57.159(1 − 0.10) D 4π Number of parameters grows factorially at higher orders in 1/m Partial reduction by reparametrisation invariance [Mannel,Vos’18;Fael,Mannel,Vos’19] T. Huber Precision flavour physics 10 Semi-leptonic decays Non-leptonic decays Exclusive B decays, generalities µ − µ Leptonic decays h0|uγ¯ γ5b|B (p)i = if B p T. Huber Precision flavour physics 11 Non-leptonic decays Exclusive B decays, generalities µ − µ Leptonic decays h0|uγ¯ γ5b|B (p)i = if B p Semi-leptonic decays T. Huber Precision flavour physics 11 Exclusive B decays, generalities µ − µ Leptonic decays h0|uγ¯ γ5b|B (p)i = if B p Semi-leptonic decays Non-leptonic decays T. Huber Precision flavour physics 11 (∗) Exclusive B → D `ν¯` decays Decay rates in terms of form factors (w = vB · vD(∗) ) [Neubert’91’94] ¯ ∗ 2 2 dΓ(B → D ` ν¯) GF |Vcb| 2 3 p 2 2 = (m − m ∗ ) m ∗ w − 1 (w + 1) dw 48π3 B D D 2 2 4w mB − 2w mB mD∗ + mD∗ 2 × 1 + 2 |F(w)| w + 1 (mB − mD∗ ) dΓ(B¯ → D ` ν¯) G2 |V |2 = F cb (m + m )2 m3 (w2 − 1)3/2|V (w)|2 dw 48π3 B D D 1 Form factor parametrisations CLN: In terms of an intercept and a slope [Caprini,Lellouch,Neubert’97] BGL: More general, based on dispersion relations, analyticity, and crossing symmetry [Boyd,Grinstein,Lebed’94’95’97] T. Huber Precision flavour physics 12 Inclusive vs.