Studies of b quark decays using experiment plus lattice QCD Matthew - PowerPoint PPT Presentation

Studies of b quark decays using experiment plus lattice QCD Matthew Wingate DAMTP, University of Cambridge Particle Physics Seminar, University of Birmingham, 7 February 2018

Outline • Quark flavour & Lattice QCD • DiRAC facility • Example: |V cb | from B → D* l ν 2

Quark Flavour & Lattice QCD

Motivation • Precision predictions & measurements of quark flavour interactions • Is the Standard Model description of EWSB complete? • If not, quark flavour measurements constrain models of new physics • Experimental measurements of hadron decays: increasing precision, new modes • Precision QCD calculations required in order to make inferences about quark interactions 4

Quark flavour physics CKM matrix   V ud V us V ub = CKM Fitter V cd V cs V cb   V td V ts V tb  1 − λ 2 / 2 A λ 3 ( ρ − i η )  λ  + O ( λ 4 ) 1 − λ 2 / 2 A λ 2 − λ  A λ 3 (1 − ρ − i η ) − A λ 2 1 e + K → ⇡`⌫ B → ⇡`⌫ W + ν e B ( s ) → D ( ∗ ) ( s ) `⌫ D → ⇡`⌫ D → K `⌫ B 0 B 0 ( s ) − ¯ B c → J/ `⌫ d ′ ( s ) u tree 5

CKM matrix from Higgs couplings � u � i � Q i u i d i RH SU(2) singlets LH SU(2) doublets L = d � i R R L Interact with gauge bosons in covariant derivative ¯ R + ¯ Q i D Q i u i D u i d i D d i L i / R i / R i / L quark = L + ¯ R J µ, + u � i L γ µ d � i Gives rise to weak current weak = ¯ L The coupling to the Higgs field is not apparently diagonal in generation � � √ � ij L � d j La � ab � † b u j d ¯ u ¯ Q i R + � ij Q i L quark , φ = 2 R + h . c . − Fields may be transformed to mass basis � � � d ¯ m i d i L d i R + m i u i L u i � � L quark , φ | vev = u ¯ R + h . c . − i Showing the weak current allows mixing between generations J µ, + L γ µ V ij CKM d j u i weak = ¯ L 6

CKM matrix from Higgs couplings � u � i � Q i u i d i RH SU(2) singlets LH SU(2) doublets L = d � i R R L Interact with gauge bosons in covariant derivative ¯ R + ¯ Q i D Q i u i D u i d i D d i L i / R i / R i / L quark = L + ¯ R J µ, + u � i L γ µ d � i Gives rise to weak current weak = ¯ L The coupling to the Higgs field is not apparently diagonal in generation � � √ � ij L � d j La � ab � † b u j d ¯ u ¯ Q i R + � ij Q i L quark , φ = 2 R + h . c . − Fields may be transformed to mass basis � � � d ¯ m i d i L d i R + m i u i L u i � � L quark , φ | vev = u ¯ R + h . c . − i Showing the weak current allows mixing between generations J µ, + L γ µ V ij CKM d j u i weak = ¯ L 6

CKM matrix from Higgs couplings � u � i � Q i u i d i RH SU(2) singlets LH SU(2) doublets L = d � i R R L Interact with gauge bosons in covariant derivative ¯ R + ¯ Q i D Q i u i D u i d i D d i L i / R i / R i / L quark = L + ¯ R J µ, + u � i L γ µ d � i Gives rise to weak current weak = ¯ L The coupling to the Higgs field is not apparently diagonal in generation � � √ � ij L � d j La � ab � † b u j d ¯ u ¯ Q i R + � ij Q i L quark , φ = 2 R + h . c . − Fields may be transformed to mass basis � � � d ¯ m i d i L d i R + m i u i L u i � � L quark , φ | vev = u ¯ R + h . c . − i Showing the weak current allows mixing between generations J µ, + L γ µ V ij CKM d j u i weak = ¯ L 6

CKM matrix from Higgs couplings � u � i � Q i u i d i RH SU(2) singlets LH SU(2) doublets L = d � i R R L Interact with gauge bosons in covariant derivative ¯ R + ¯ Q i D Q i u i D u i d i D d i L i / R i / R i / L quark = L + ¯ R J µ, + u � i L γ µ d � i Gives rise to weak current weak = ¯ L The coupling to the Higgs field is not apparently diagonal in generation � � √ � ij L � d j La � ab � † b u j d ¯ u ¯ Q i R + � ij Q i L quark , φ = 2 R + h . c . − Fields may be transformed to mass basis � � � d ¯ m i d i L d i R + m i u i L u i � � L quark , φ | vev = u ¯ R + h . c . − i Showing the weak current allows mixing between generations J µ, + L γ µ V ij CKM d j u i weak = ¯ L 6

CKM matrix from Higgs couplings � u � i � Q i u i d i RH SU(2) singlets LH SU(2) doublets L = d � i R R L Interact with gauge bosons in covariant derivative ¯ R + ¯ Q i D Q i u i D u i d i D d i L i / R i / R i / L quark = L + ¯ R J µ, + u � i L γ µ d � i Gives rise to weak current weak = ¯ L The coupling to the Higgs field is not apparently diagonal in generation � � √ � ij L � d j La � ab � † b u j d ¯ u ¯ Q i R + � ij Q i L quark , φ = 2 R + h . c . − Fields may be transformed to mass basis � � � d ¯ m i d i L d i R + m i u i L u i � � L quark , φ | vev = u ¯ R + h . c . − i Showing the weak current allows mixing between generations J µ, + L γ µ V ij CKM d j u i weak = ¯ L 6

Experiment Models Role of Lattice QCD 7 Illustration from I. Shipsey, Nature 427, 591 (2004)

Lattice QCD Experiment Models Role of Lattice QCD 7 Illustration from I. Shipsey, Nature 427, 591 (2004)

Lattice QCD • Use methods of effective field theory and renormalization to turn a quantum physics problem into a statistical physics problem • Quarks propagating through strongly interacting QCD glue + sea of quark-antiquark bubbles • Numerically evaluate path integrals using Monte Carlo methods: importance sampling & correlation functions • Numerical challenge: solving M x = b where M is big and has a diverging condition number as am q ➙ 0 (vanishing lattice spacing × light quark mass) 8

Lattice QCD in a nutshell QFT : Imaginary-time path integral ⟨ J ( z ′ ) J ( z ) ⟩ = 1 � [ d ψ ][ d ¯ ψ ][ dU ] J ( z ′ ) J ( z ) e − S E Z SFT : Sum over all microstates ⟨ J ( z ′ ) J ( z ) ⟩ = 1 � J ( z ′ ) J ( z ) e − β H � Z Tr Use the same numerical methods! Monte Carlo Calculation : Find and use field “configurations” which dominate the integral/sum 9

Lattice QCD in a nutshell Gluonic expectation values 1 � ψ ][ dU ] Θ [ U ] e − S g [ U ] − ¯ [ d ψ ][ d ¯ ψ Q [ U ] ψ ⟨ Θ ⟩ = Z 1 � [ dU ] Θ [ U ] det Q [ U ] e − S g [ U ] = Z Fermionic expectation values � � [ dU ] δ ζ Γ δ ζ Q − 1 [ U ] ζ det Q [ U ] e − S g [ U ] δζ e − ¯ ⟨ ¯ � ψ Γ ψ ⟩ = δ ¯ � � ζ , ¯ ζ → 0 10

Lattice QCD in a nutshell Gluonic expectation values 1 � ψ ][ dU ] Θ [ U ] e − S g [ U ] − ¯ [ d ψ ][ d ¯ ψ Q [ U ] ψ ⟨ Θ ⟩ = Z 1 � [ dU ] Θ [ U ] det Q [ U ] e − S g [ U ] = Z Fermionic expectation values Probability weight � � [ dU ] δ ζ Γ δ ζ Q − 1 [ U ] ζ det Q [ U ] e − S g [ U ] δζ e − ¯ ⟨ ¯ � ψ Γ ψ ⟩ = δ ¯ � � ζ , ¯ ζ → 0 10

Lattice QCD in a nutshell Gluonic expectation values 1 � ψ ][ dU ] Θ [ U ] e − S g [ U ] − ¯ [ d ψ ][ d ¯ ψ Q [ U ] ψ ⟨ Θ ⟩ = Z 1 � [ dU ] Θ [ U ] det Q [ U ] e − S g [ U ] = Z Fermionic expectation values Probability weight � � [ dU ] δ ζ Γ δ ζ Q − 1 [ U ] ζ det Q [ U ] e − S g [ U ] δζ e − ¯ ⟨ ¯ � ψ Γ ψ ⟩ = δ ¯ � � ζ , ¯ ζ → 0 Determinant in probability weight difficult 1) Requires nonlocal updating; 2) Matrix becomes singular 10

Lattice QCD in a nutshell Gluonic expectation values 1 � ψ ][ dU ] Θ [ U ] e − S g [ U ] − ¯ [ d ψ ][ d ¯ ψ Q [ U ] ψ ⟨ Θ ⟩ = Z 1 � [ dU ] Θ [ U ] det Q [ U ] e − S g [ U ] = Z Fermionic expectation values Probability weight � � [ dU ] δ ζ Γ δ ζ Q − 1 [ U ] ζ det Q [ U ] e − S g [ U ] δζ e − ¯ ⟨ ¯ � ψ Γ ψ ⟩ = δ ¯ � � ζ , ¯ ζ → 0 Determinant in probability weight difficult 1) Requires nonlocal updating; 2) Matrix becomes singular Partial quenching = different mass for valence than for sea Q − 1 det Q 10

Lattice QCD h Φ π ( z ) V µ ( y ) Φ B ( x ) i = 1 Z Z Z ψ ][ dU ] Φ π ( z ) V µ ( y ) Φ B ( x ) e − S [ ψ , ¯ [ d ψ ][ d ¯ ψ ,U ] Z • Imaginary time formulation: path integrands real, non-negative • Discrete lattice points: regulates field theory • Sharply peaked path integrand: permits importance sampling Systematic error Controllable limit Theory Chiral pert. th. L � 1 /m π Lattice volume Brute force a � 1 / Λ QCD Lattice spacing Symanzik EFT Chiral pert. th. m π � m ρ , 4 π f π Light quark mass Brute force m Q � 1 /a NRQCD, HQET Heavy quark mass m Q < 1 /a Extra-fine, extra-improvement m Q ≈ 1 /a Fermilab

Meson mass splittings CTH Davies, [HPQCD Collaboration website] 12

Decay constants CTH Davies, [HPQCD Collaboration website] 13

Rare b decays Flavour changing neutral decays W t b s s b W W ν t γ , Z ℓ ℓ penguin box B → K ∗ ` + ` − B s → �` + ` − Horgan et al., (HPQCD) arXiv:1310.3722, arXiv:1310.3887 14

LQCD & DiRAC

UKQCD consortium 24 faculty at 8 UK institutions • Membership/Leadership in several • international collaborations (e.g. HPQCD, RBC-UKQCD, HadSpec, QCDSF, FastSum) Image credit: CIA World Factbook Broad range of physics: quark • flavour, hadron spectrum, hot/ dense QCD; BSM theories of EWSB, dark matter Widespread impact: LHC, BES-III, • Belle, JLab, J-PARC, FAIR, RHIC, NA62 16