B Physics: Theoretical Aspects Anirban Kundu

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1 B Physics: Theoretical Aspects Anirban Kundu Calcutta University, Kolkata, India

2 Why B Physics? CP violation. That s why we are here Test the CP violation mechanism of the SM Investigation of the third quark family Desperately need some new source of CPV Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.1/34

3 Why B Physics? CP violation. That s why we are here Test the CP violation mechanism of the SM Investigation of the third quark family Desperately need some new source of CPV Indirect signals of new physics, complementary to LHC: Is there already such a signal? Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.1/34

4 B physics: Experiments Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.2/34

5 B physics: Experiments ARGUS and CLEO: first B results LEP groups: ALEPH, DELPHI, L3, OPAL Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.2/34

6 B physics: Experiments ARGUS and CLEO: first B results LEP groups: ALEPH, DELPHI, L3, OPAL Tevatron experiments: CDF, D0: B s results BaBar and Belle: e + e asymmetric B-factories lumi 1200 fb 1, will go upto 2000 fb 1 First precision B physics Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.2/34

7 B physics: Experiments ARGUS and CLEO: first B results LEP groups: ALEPH, DELPHI, L3, OPAL Tevatron experiments: CDF, D0: B s results BaBar and Belle: e + e asymmetric B-factories lumi 1200 fb 1, will go upto 2000 fb 1 First precision B physics LHC-B (upcoming): B s, B c, Λ b SFF (proposed): Ultimate precision B physics Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.2/34

8 Standard Model L gauge CC = g ū iγ µ 1 γ 5 1 ij d 2 2 jw µ + h.c. Off-diagonal Yukawas, not stationary states u = U L u, d = D L d Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.3/34

9 Standard Model L gauge CC = g ū iγ µ 1 γ 5 1 ij d 2 2 jw µ + h.c. Off-diagonal Yukawas, not stationary states u = U L u, d = D L d L mass CC = g ū i γ µ 1 γ 5 V ij d j W µ + h.c. 2 2 V U L D L, V V = V V = 1 Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.3/34

10 Standard Model The CKM matrix V controls the CC interaction strength Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.4/34

11 Standard Model The CKM matrix V controls the CC interaction strength U L U L = D L D L = 1, so no FCNC, GIM is okay Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.4/34

12 Standard Model The CKM matrix V controls the CC interaction strength U L U L = D L D L = 1, so no FCNC, GIM is okay The coupling must be complex for CP violation Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.4/34

13 Standard Model The CKM matrix V controls the CC interaction strength U L U L = D L D L = 1, so no FCNC, GIM is okay The coupling must be complex for CP violation N(N 1)/2 real angles and (N 1)(N 2)/2 complex phases in N-gen CKM Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.4/34

14 Standard Model The CKM matrix V controls the CC interaction strength U L U L = D L D L = 1, so no FCNC, GIM is okay The coupling must be complex for CP violation N(N 1)/2 real angles and (N 1)(N 2)/2 complex phases in N-gen CKM At least 3 gens needed for CP violation! Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.4/34

15 The CKM matrix The major goal of B factories is to precisely measure the CKM elements Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.5/34

16 The CKM matrix The major goal of B factories is to precisely measure the CKM elements V ud V us V ub V = V cd V cs V cb V td V ts V tb Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.5/34

17 The CKM matrix The major goal of B factories is to precisely measure the CKM elements λ2 λ Aλ 3 (ρ iη) V = λ λ2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 Wolfenstein parametrisation λ = ± , A = 0.83 ± 0.02, ρ(1 1 2 λ2 ) = ± 0.028, η(1 1 2 λ2 ) = ± Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.5/34

18 The CKM matrix V V = V V = 1 gives V ud V ub + V cd V cb + V td V tb = 0 and five other such relations. They are triangles in the complex plane known as Unitarity Triangles Jarlskog invariant J = I(V ip V iqv jq V jp) Area of all UTs are same: A = 2J Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.6/34

19 The CKM matrix Construction: Scale by Aλ 3. The real arm between (0,0) and (1,0) The tip will be at (ρ, η) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.7/34

20 The CKM matrix Construction: Scale by Aλ 3. The real arm between (0,0) and (1,0) The tip will be at (ρ, η) (ρ,η) α V ud V ub V cd V cb V td V tb V cd V cb γ β (0,0) (1,0) V td = V td exp( iβ), V ub = V ub exp( iγ) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.7/34

21 Digression: Neutral B mixing b W d d u,c,t W u,c,t b Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.8/34

22 Digression: Neutral B mixing i dψ(t) dt H = ( B 0 (t) = Hψ(t), ψ(t) = B 0 (t) ( M i Γ M 2 12 i Γ ) 2 12 M12 i 2 Γ 12 M i Γ 2 ) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.9/34

23 Digression: Neutral B mixing i dψ(t) dt H = ( B 0 (t) = Hψ(t), ψ(t) = B 0 (t) ( M i Γ M 2 12 i Γ ) 2 12 M12 i 2 Γ 12 M i Γ 2 ) B H,L = pb 0 + ( )qb 0 M = 2 M 12, Γ = 2R(M 12Γ 12) M 12 M Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.9/34

24 Digression: Neutral B mixing i dψ(t) dt H = ( B 0 (t) = Hψ(t), ψ(t) = B 0 (t) ( M i Γ M 2 12 i Γ ) 2 12 M12 i 2 Γ 12 M i Γ 2 ) B H,L = pb 0 + ( )qb 0 M = 2 M 12, Γ = 2R(M 12Γ 12) M 12 M q p = exp(2iφ M), φ M = β for B d, β s for B s Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.9/34

25 Direct CP violation A d CP (B ± f ± ) = Γ(B+ f + ) Γ(B f ) Γ(B + f + ) + Γ(B f ) Needs two different amplitudes, with different weak and strong phases A d CP (B ± f ± ) = 2A 1 A 2 sin δ sin φ A A A 1 A 2 cos δ cos φ How to obtain A 1, A 2, and δ? Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.10/34

26 CP violation in mixing-decay int. Consider a CP eigenstate f: A CP (t, f) = Γ(B0 (t) f) Γ(B 0 (t) f) Γ(B 0 (t) f) + Γ(B 0 (t) f) = A d CP cos Mt + A m CP sin Mt A d CP = 1 ξ f ξ f 2, Am CP = 2Iξ f 1 + ξ f 2, ξ f = q p A(B 0 f) A(B 0 f) No strong-phase pollution, clean mode Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.11/34

27 Operator product expansion The effective weak Hamiltonian at low energy has the generic form H eff = G F 2 For example, in β-decay i V (i) C i (µ)o i H β eff = G F 2 cos θ C [ūγ µ (1 γ 5 )d] [ēγ µ (1 γ 5 )ν e ] Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.12/34

28 Operator product expansion H eff is a series of effective vertices and effective coupling constants evaluated at the low scale m b by integrating out the heavy degrees of freedom and running the Wilson coefficients down from m W to µ b c b c W d u d u Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.13/34

29 Operator product expansion Current-current: O 1,2 = ( cγ V A b) 8,1 ( sγ V A c) 8,1 QCD penguin: O 3,4 = ( sγ V A b) 1,8 q t,b ( qγv A q) 1,8 O 5,6 = ( sγ V A b) 1,8 q t,b ( qγv +A q) 1,8 Electroweak penguin: O 7,8 = 3 2 ( sγv A b) 1,8 q t,b e q( qγ V +A q) 1,8 O 9,10 = 3 2 ( sγv A b) 1,8 q t,b e q( qγ V A q) 1,8 Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.14/34

30 Operator product expansion Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.15/34

31 Operator product expansion How to evaluate the matrix elements of the operators between initial B and final state mesons? Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.16/34

32 Operator product expansion How to evaluate the matrix elements of the operators between initial B and final state mesons? There are several methods: Naive and QCD improved factorisation, Perturbative QCD approach, Soft collinear effective theory,... but these are all models (with some theoretical justification) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.16/34

33 Operator product expansion How to evaluate the matrix elements of the operators between initial B and final state mesons? There are several methods: Naive and QCD improved factorisation, Perturbative QCD approach, Soft collinear effective theory,... but these are all models (with some theoretical justification) The theoretical error is of the order of 10% and must be reduced to enter the era of precision B physics Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.16/34

34 First measurements V td in B 0 B 0 box; if no weak phase in decay, should measure β _ 0 0 B B f B J/ψK S : First clean measurement of β Tree-level and leading penguin diagrams have same phase: theoretically clean Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.17/34

35 Fact 1: The triangle is a triangle BaBar hep-ex/ Belle J/ψ K 0 PRL 98 (2007) Belle ψ(2s) K S arxiv: ALEPH PLB 492, (2000) OPAL EPJ C5, (1998) CDF PRD 61, (2000) Average HFAG sin(2β) sin(2φ 1 ) H F A G H F A G LP 2007 PRELIMINARY 0.71 ± 0.03 ± ± 0.03 ± ± 0.09 ± ± ± ± 0.03 Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.18/34

36 Fact 1: The triangle is a triangle 1.5 excluded area has CL > 0.95 γ 1 sin2β excluded at CL > 0.95 m s & m d η ε K γ α β α m d V ub -0.5 α -1 CKM f i t t e r Summer ρ γ ε K sol. w/ cos2β < 0 (excl. at CL > 0.95) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.19/34

37 The first triumph Large CP violation unlike ɛ K is there in the B system Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.20/34

38 The first triumph Large CP violation unlike ɛ K is there in the B system The CKM picture may not be complete, but it is definitely the dominant one. New Physics effects must be subdominant in B J/ψK S CP asymmetry Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.20/34

39 The first triumph Large CP violation unlike ɛ K is there in the B system The CKM picture may not be complete, but it is definitely the dominant one. New Physics effects must be subdominant in B J/ψK S CP asymmetry Next step: Measure the same angle from other processes b s ss (penguin) [B φk S ] Check if the measurements agree Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.20/34

40 Is the penguin a strange animal? b ccs π 0 π 0 K π 0 η K 0 S ω K S K S K + K - K 0 f ρ 0 K K φ K 0 0 K 0 S S K S K S sin(2β eff ) sin(2φ e 1ff ) HFAG LP 2007 HFAG LP 2007 LP HFAG 2007 World Average 0.68 ± 0.03 BaBar 0.21 ± 0.26 ± 0.11 Belle 0.50 ± 0.21 ± 0.06 Average 0.39 ± 0.17 BaBar 0.58 ± 0.10 ± 0.03 Belle 0.64 ± 0.10 ± 0.04 Average 0.61 ± 0.07 BaBar 0.71 ± 0.24 ± 0.04 Belle 0.30 ± 0.32 ± 0.08 Average 0.58 ± 0.20 BaBar 0.40 ± 0.23 ± 0.03 Belle 0.33 ± 0.35 ± 0.08 Average 0.38 ± 0.19 BaBar ± 0.09 ± 0.08 Average BaBar ± 0.02 Belle 0.11 ± 0.46 ± 0.07 Average 0.48 ± 0.24 BaBar 0.90 ± 0.07 Belle 0.18 ± 0.23 ± 0.11 Average 0.85 ± 0.07 BaBar ± 0.71 ± 0.08 Belle ± 0.49 ± 0.09 Average ± 0.41 BaBar 0.76 ± Belle 0.68 ± 0.15 ± Average 0.73 ± 0.10 LP HFAG 2007 HFAG LP 2007 HFAG HFAGLP 2007 HFAG LP 2007 LP 2007 LP HFAG 2007 HFAG LP 2007 H F A G H F A G LP 2007 PRELIMINARY Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.21/34

41 B s physics B s oscillates faster V ts 2 / V td 2 40 Rapid oscillation, experimentally challenging Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.22/34

42 B s physics B s oscillates faster V ts 2 / V td 2 40 Rapid oscillation, experimentally challenging M s = (17.77 ± 0.10 ± 0.07) ps 1 (CDF) Γ s = (0.17 ± 0.09 ± 0.02) ps 1 (D0) = ( ± 0.006) ps 1 (CDF) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.22/34

43 B s physics B s oscillates faster V ts 2 / V td 2 40 Rapid oscillation, experimentally challenging M s = (17.77 ± 0.10 ± 0.07) ps 1 (CDF) Γ s = (0.17 ± 0.09 ± 0.02) ps 1 (D0) = ( ± 0.006) ps 1 (CDF) Still large errors. Agrees with SM but enough room for NP. Follow at LHC-b Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.22/34

44 B s physics Parametrise the NP contribution as M s = M s SM (1 + κ s exp(iσ s )) φ s = φ s SM + arg (1 + κ s exp(iσ s )) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.23/34

45 B s agenda: Measurement of φ s φ s = arg(v tsv tb ) D0 : φ s = (45 ± ) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.24/34

46 B s agenda: Measurement of φ s φ s = arg(v tsv tb ) D0 : φ s = (45 ± ) Should be close to zero in SM ( 2λ 2 η 2 ) B s J/ψφ: Golden channel to measure φ s Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.24/34

47 B s agenda: Measurement of φ s φ s = arg(v tsv tb ) D0 : φ s = (45 ± ) Should be close to zero in SM ( 2λ 2 η 2 ) B s J/ψφ: Golden channel to measure φ s With 0.5 fb 1 by the end of 2009, σ(φ s ) 2.6, further improvement by 2010 with 2 fb 1 Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.24/34

48 B s agenda: Measurement of γ γ = (88 ± 16) [UTfit] Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.25/34

49 B s agenda: Measurement of γ γ = (88 ± 16) [UTfit] If box phase is known from B s J/ψφ, b u decays measure γ B s D s ± K [σ(γ) 5 by 2013 with 10 fb 1 ] Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.25/34

50 B s agenda: Measurement of γ γ = (88 ± 16) [UTfit] If box phase is known from B s J/ψφ, b u decays measure γ B s D ± s K [σ(γ) 5 by 2013 with 10 fb 1 ] A(B s D + s K ) V ub V cs = λ 3 exp(iγ) A( B s D + s K ) V usv cb = λ 3 Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.25/34

51 B s agenda: Measurement of γ γ = (88 ± 16) [UTfit] If box phase is known from B s J/ψφ, b u decays measure γ B s D ± s K [σ(γ) 5 by 2013 with 10 fb 1 ] A(B s D + s K ) V ub V cs = λ 3 exp(iγ) A( B s D + s K ) V usv cb = λ 3 B s K + K : penguin topologies important, unlike B d π + π can also be useful with enough statistics Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.25/34

52 B s agenda: Measurement of Γ s Γ s = Γ L Γ H > 0 in the SM Γ s /Γ s = Theory (SM): Γ s /Γ s = ± Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.26/34

53 B s agenda: Measurement of Γ s Γ s = Γ L Γ H > 0 in the SM Γ s /Γ s = Theory (SM): Γ s /Γ s = ± NP: reduces Γ s if no new absorptive amplitude (Grossman) Not true for models like RPV SUSY or Leptoquarks (Dighe, AK, Nandi) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.26/34

54 B s agenda: Measurement of Γ s Γ s = Γ L Γ H > 0 in the SM Γ s /Γ s = Theory (SM): Γ s /Γ s = ± NP: reduces Γ s if no new absorptive amplitude (Grossman) Not true for models like RPV SUSY or Leptoquarks (Dighe, AK, Nandi) LHC-b can measure Γ s from modes like B s J/ψφ Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.26/34

55 B s agenda: Measurement of Γ s Γ s = Γ L Γ H > 0 in the SM Γ s /Γ s = Theory (SM): Γ s /Γ s = ± NP: reduces Γ s if no new absorptive amplitude (Grossman) Not true for models like RPV SUSY or Leptoquarks (Dighe, AK, Nandi) LHC-b can measure Γ s from modes like B s J/ψφ Ambiguity in Γ s can be resolved with simultaneous tagged and untagged measurements of B s D s K (Nandi, Nierste) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.26/34

56 B s agenda: Rare modes Unambiguous signal for NP! Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.27/34

57 B s agenda: Rare modes Unambiguous signal for NP! B s µ + µ : observable signal in SUSY with high tan β Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.27/34

58 B s agenda: Rare modes Unambiguous signal for NP! B s µ + µ : observable signal in SUSY with high tan β B s φφ: Possible NP in b s penguins, use amplitude analysis Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.27/34

59 Why NP? What NP? New source of CP violation needed to explain baryogenesis Also, other standard puzzles like fine-tuning unification quantum gravity dark matter dark energy,... Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.28/34

60 Why NP? What NP? Minimal Flavour Violation No new phases, all FC transitions controlled by CKM NP enters only through Wilson coeff.s (minimal UED, 2HDM, SUGRA with small tan β and no new source of FCNC, GMSB, Little Higgs with T-parity,...) Universal UT for MFV models: very small room for NP to appear in B physics (sin 2β = 0.735(732) ± 049, η = 0.360(354) ± 0.031(027), ρ = 0.174(187) ± 0.068(059)) [UUT (SM)] Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.29/34

61 Why NP? What NP? Non-MFV 1: New operators but no new phases (MSSM with large tan β) Non-MFV 2: New phases but no new operators (Non-universal squark masses) Non-MFV 3: New phases, operators, FCNC (RPV SUSY, Z ) Non-MFV 4: CKM unitarity does not hold (4 gen) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.30/34

62 Diagnostic pattern Model B d unitarity Time-dep. CPV Rare decay Other msugra (low tan β) msugra mixing b sl + l B s µ + µ (large tan β) KK graviton b sl + l Bulk fermions mixing B d φk S b sl + l B s mixing in warped ED D 0 D 0 mixing UED b sl + l K πν ν b sγ (From D. Hitlin, talk at WHEPP-10, IMSc, Jan. 2008) Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.31/34

63 Future Entering the era of precision B physics... complementary to main LHC experiments Better precision expected on γ, M s, Γ s, and possible observation of rare modes at LHC-b Direct and indirect measurements can pin down the nature and parameters of any possible NP Theory errors need to be controlled. Lattice? And, ultimately, the super flavour factory... Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.32/34

64 The super flavour factory Integrated luminosity of fb 1 (compare with 2000 fb 1 for BaBar+Belle) : the ultimate precision machine Complementary to LHC-b Errors on UT angles can be reduced by an order of magnitude Very rare modes can be observed e.g., pure leptonic decays Can also look for LFV in τ decays Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.33/34

65 THANK YOU! Anirban Kundu B-Physics IIT-Guwahati, Feb. 23, 2008 p.34/34

Electroweak Theory: 5

Electroweak Theory: 5 Introduction QED The Fermi theory The standard model Precision tests CP violation; K and B systems Higgs physics Prospectus STIAS (January, 2011) Paul Langacker (IAS) 162 References