Going beyond the Standard Model with Flavour

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1 Going beyond the Standard Model with Flavour Anirban Kundu University of Calcutta January 19, 2019 Institute of Physics

2 Introduction to flavour physics

3 Although you have heard / will hear a lot about BSM, Standard Model is doing extremely well L SM = L gauge + L Higgs + L fermion and all sectors checked (not at same precision level though) No wonder. It has 19 free parameters With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. John von Neumann

4 Although you have heard / will hear a lot about BSM, Standard Model is doing extremely well L SM = L gauge + L Higgs + L fermion and all sectors checked (not at same precision level though) No wonder. It has 19 free parameters 13 in the flavour sector: 9 fermion masses + 4 CKM elements With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. John von Neumann

5 Although you have heard / will hear a lot about BSM, Standard Model is doing extremely well L SM = L gauge + L Higgs + L fermion and all sectors checked (not at same precision level though) No wonder. It has 19 free parameters 13 in the flavour sector: 9 fermion masses + 4 CKM elements With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. John von Neumann

6 The first question in flavour physics: Who ordered that?

7 Flavour physics has built up the SM 1 First generation of flavour physics (pre-1970) Strange particles, parity violation, eightfold way and Ω K 0 K 0 oscillation, tiny CP violation in K decay Cabibbo hypothesis, GIM mechanism 2 Second generation of flavour physics ( ) Kobayashi-Maskawa hypothesis J/ψ and Υ production Observation of B 0 B 0 oscillation

8 Flavour physics has built up the SM 1 First generation of flavour physics (pre-1970) Strange particles, parity violation, eightfold way and Ω K 0 K 0 oscillation, tiny CP violation in K decay Cabibbo hypothesis, GIM mechanism 2 Second generation of flavour physics ( ) Kobayashi-Maskawa hypothesis J/ψ and Υ production Observation of B 0 B 0 oscillation 3 Third generation of flavour physics ( present) e + e B factories, large CP violation in B system Top discovery Observation of B s B s and D 0 D 0 oscillation Rare B decays, Start of precision flavour physics

9 Flavour physics has built up the SM 1 First generation of flavour physics (pre-1970) Strange particles, parity violation, eightfold way and Ω K 0 K 0 oscillation, tiny CP violation in K decay Cabibbo hypothesis, GIM mechanism 2 Second generation of flavour physics ( ) Kobayashi-Maskawa hypothesis J/ψ and Υ production Observation of B 0 B 0 oscillation 3 Third generation of flavour physics ( present) e + e B factories, large CP violation in B system Top discovery Observation of B s B s and D 0 D 0 oscillation Rare B decays, Start of precision flavour physics 4 Fourth generation of flavour physics (Belle-II, LHCb upgrade) Precision flavour era. Very rare B decays Lepton flavour/universality violation, rare charm and τ decays Looking for NP at a level competitive to future colliders

10 Flavour physics has built up the SM 1 First generation of flavour physics (pre-1970) Strange particles, parity violation, eightfold way and Ω K 0 K 0 oscillation, tiny CP violation in K decay Cabibbo hypothesis, GIM mechanism 2 Second generation of flavour physics ( ) Kobayashi-Maskawa hypothesis J/ψ and Υ production Observation of B 0 B 0 oscillation 3 Third generation of flavour physics ( present) e + e B factories, large CP violation in B system Top discovery Observation of B s B s and D 0 D 0 oscillation Rare B decays, Start of precision flavour physics 4 Fourth generation of flavour physics (Belle-II, LHCb upgrade) Precision flavour era. Very rare B decays Lepton flavour/universality violation, rare charm and τ decays Looking for NP at a level competitive to future colliders

11 B-factories: past, present, and future : e + e, 429 fb 1, B B pairs Belle@KEK : e + e, over 1 ab 1, B B pairs LHCb : 6.8 fb 1 till 2017 (3.6 fb 1 at 13 TeV) 7 TeV: σ(pp b bx ) = (89.6 ± 6.4 ± 15.5) µb scales linearly with s ATLAS and CMS also have dedicated flavour physics programme

12 B-factories: past, present, and future : e + e, 429 fb 1, B B pairs Belle@KEK : e + e, over 1 ab 1, B B pairs LHCb : 6.8 fb 1 till 2017 (3.6 fb 1 at 13 TeV) 7 TeV: σ(pp b bx ) = (89.6 ± 6.4 ± 15.5) µb scales linearly with s ATLAS and CMS also have dedicated flavour physics programme LHCb: Upgrade I: L int > 50 fb 1, cm 2 s 1 Phase II with HL-LHC: L int > 300 fb 1, cm 2 s 1 Belle-II: L int = 50 ab 1 in 5 years, can go up even higher

13 B-factories: past, present, and future : e + e, 429 fb 1, B B pairs Belle@KEK : e + e, over 1 ab 1, B B pairs LHCb : 6.8 fb 1 till 2017 (3.6 fb 1 at 13 TeV) 7 TeV: σ(pp b bx ) = (89.6 ± 6.4 ± 15.5) µb scales linearly with s ATLAS and CMS also have dedicated flavour physics programme LHCb: Upgrade I: L int > 50 fb 1, cm 2 s 1 Phase II with HL-LHC: L int > 300 fb 1, cm 2 s 1 Belle-II: L int = 50 ab 1 in 5 years, can go up even higher

14 Why is flavour physics important? Better understanding of SM for N gen > 1 Window to flavour dynamics (e.g. B 0 B 0 mixing, b sγ, Z b b, B s µµ) Better understanding of low-energy QCD Form factors, Resummation of higher-order effects, Relative importance of subleading topologies

15 Why is flavour physics important? Better understanding of SM for N gen > 1 Window to flavour dynamics (e.g. B 0 B 0 mixing, b sγ, Z b b, B s µµ) Better understanding of low-energy QCD Form factors, Resummation of higher-order effects, Relative importance of subleading topologies CP violation studies New source of CP violation needed for n b /n γ

16 Why is flavour physics important? Better understanding of SM for N gen > 1 Window to flavour dynamics (e.g. B 0 B 0 mixing, b sγ, Z b b, B s µµ) Better understanding of low-energy QCD Form factors, Resummation of higher-order effects, Relative importance of subleading topologies CP violation studies New source of CP violation needed for n b /n γ Indirect window to New Physics Only way to look for BSM if Λ > O(1) TeV Only probe to flavour structure even if it is not

17 Why is flavour physics important? Better understanding of SM for N gen > 1 Window to flavour dynamics (e.g. B 0 B 0 mixing, b sγ, Z b b, B s µµ) Better understanding of low-energy QCD Form factors, Resummation of higher-order effects, Relative importance of subleading topologies CP violation studies New source of CP violation needed for n b /n γ Indirect window to New Physics Only way to look for BSM if Λ > O(1) TeV Only probe to flavour structure even if it is not

18 Need a basis transformation for quarks Mass and Yukawa matrices are diagonalised by same transformation GIM to ban tree-level FCNC L CC wk = g 2 ū j(u ji D ik)γ µ P L d k W + µ + h.c. = g 2 V jk ū jγ µ P L d k W + µ + h.c. V U D is the CKM matrix. Three real angles and one CP-violating phase. U U = D D = 1 GIM

19 Need a basis transformation for quarks Mass and Yukawa matrices are diagonalised by same transformation GIM to ban tree-level FCNC L CC wk = g 2 ū j(u ji D ik)γ µ P L d k W + µ + h.c. = g 2 V jk ū jγ µ P L d k W + µ + h.c. V U D is the CKM matrix. Three real angles and one CP-violating phase. U U = D D = 1 GIM

20 V = = V ud V us V ub V cd V cs V cb V td V ts V tb λ2 λ Aλ 3 (ρ iη) λ λ2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 V td = V td exp( iβ), V ub = V ub exp( iγ) Wolfenstein λ = , A = , ρ(1 1 2 λ2 ) = , η(1 1 }{{} 2 λ2 ) }{{} ρ η =

21 V = = V ud V us V ub V cd V cs V cb V td V ts V tb λ2 λ Aλ 3 (ρ iη) λ λ2 Aλ 2 + O(λ 4 ) Aλ 3 (1 ρ iη) Aλ 2 1 V td = V td exp( iβ), V ub = V ub exp( iγ) Wolfenstein λ = , A = , ρ(1 1 2 λ2 ) = , η(1 1 }{{} 2 λ2 ) }{{} ρ η =

22 V ud V ub + V cdv cb + V tdv tb = 1 Nonzero area indicates CP violation All UTs must have same area Falls short by about a billion

23 V ud V ub + V cdv cb + V tdv tb = 1 Nonzero area indicates CP violation All UTs must have same area Falls short by about a billion

24 α β direct β indirect 23.9 ± 1.2 β average γ

26 How can B Physics unravel BSM?

27 If NP is at < 1 TeV: within direct reach of LHC@8 TeV, ruled out a few TeV: within reach of LHC@13 TeV, data analysis coming up > a few TeV: beyond LHC. Maybe Belle-II Indirect detection Flav. structure < 1 TeV a few TeV > a few TeV Anarchy huge O(1) X O(1) X small ( < O(1)) Small Sizable O(1) X small tiny misalignment (O(0.1)) (O( )) Alignment small tiny out of reach (MFV) (O(0.1)) (O(0.01)) < O(0.01)

28 If NP is at < 1 TeV: within direct reach of LHC@8 TeV, ruled out a few TeV: within reach of LHC@13 TeV, data analysis coming up > a few TeV: beyond LHC. Maybe Belle-II Indirect detection Flav. structure < 1 TeV a few TeV > a few TeV Anarchy huge O(1) X O(1) X small ( < O(1)) Small Sizable O(1) X small tiny misalignment (O(0.1)) (O( )) Alignment small tiny out of reach (MFV) (O(0.1)) (O(0.01)) < O(0.01)

B 0 B 0 and B s B s mixing have been measured very precisely M d = 0.5065 ± 0.0019 ps 1 M s = 17.757 ± 0.021 ps 1 Γ s /Γ s = 0.132 ± 0.008 τ s /τ d = 0.993 ± 0.

29 B 0 B 0 and B s B s mixing have been measured very precisely M d = ± ps 1 M s = ± ps 1 Γ s /Γ s = ± τ s /τ d = ± Major uncertainties in M come from decay constants and bag factors G 2 F M 16π 2 V tqv tb 2 MW 2 S 0(x t )η B B B fb 2 M B Γ s has 15%, mostly from 1/m b and scale

30 ( Mq i H = 2 Γ q Mq 12 M 12 q i 2 Γ12 q i 2 Γ12 q M q i 2 Γ q ) M 12 q M 12 q,sm Re q + iim q = q exp(2iφ q,np )

31 B s plot does not include DØ dimuon

32 Caution!!! Need a better control over nuisance parameters Quark masses and CKM elements Form factors, decay constants Lattice people doing a commendable job uncertainty associated with LCD amplitudes Subleading Λ/m corrections Also, higher orders in α s, but they can be summed in most cases renormalization scale (µ) dependence

33 A few interesting anomalies [Also, talk by G. Mohanty]

34 R(D ( ) ) = BR(B D( ) τν) BR(B D ( ) lν) 2.3σ for R(D), 3.0σ for R(D ), 3.78σ combined with corr.

36 While we are talking about b cτν R J/ψ = BR(B c J/ψ τν) BR(B c J/ψ lν) = 0.71 ± 0.17 ± 0.18 (exp), ± (SM) And the neutral current b sl + l R K(K ) = BR(B K(K )µ + µ ) BR(B K(K )e + e )

37 While we are talking about b cτν R J/ψ = BR(B c J/ψ τν) BR(B c J/ψ lν) = 0.71 ± 0.17 ± 0.18 (exp), ± (SM) And the neutral current b sl + l R K(K ) = BR(B K(K )µ + µ ) BR(B K(K )e + e ) e or µ? B s φµ + µ is also interesting

38 While we are talking about b cτν R J/ψ = BR(B c J/ψ τν) BR(B c J/ψ lν) = 0.71 ± 0.17 ± 0.18 (exp), ± (SM) And the neutral current b sl + l R K(K ) = BR(B K(K )µ + µ ) BR(B K(K )e + e ) e or µ? B s φµ + µ is also interesting

39 Is there some pattern?

40 But B s /B d µµ is consistent with the SM (Only theory errors are from f B/Bs and CKM. NLO EW, NNLO QCD, soft photon, large Γ s effects taken into account) while B K µµ observable P 5 shows a deviation

41 LHCb: two bins deviating by 2.8σ and 3.0σ Belle confirms with larger uncertainty CMS and ATLAS: Consistent with both LHCb/Belle and SM, large uncertainties

42 Effective theory approach H eff = (CKM) i C i O i Main source of uncertainty: FF in M H eff B Ratios are relatively insensitive Example: b sµ + µ H SM eff = 4G F 2 V tb V ts C i (µ)o i (µ) with the relevant operators e O 7 = 16π 2 m b ( sσ µν P R b) F µν, C 7 = O 9 = O 10 = e 2 i 16π 2 ( sγµ P L b) ( µγ µ µ), C 9 = e 2 16π 2 ( sγµ P L b) ( µγ µ γ 5 µ), C 10 = 4.103

43 Effective theory approach H eff = (CKM) i C i O i Main source of uncertainty: FF in M H eff B Ratios are relatively insensitive Example: b sµ + µ H SM eff = 4G F 2 V tb V ts C i (µ)o i (µ) with the relevant operators e O 7 = 16π 2 m b ( sσ µν P R b) F µν, C 7 = O 9 = O 10 = e 2 i 16π 2 ( sγµ P L b) ( µγ µ µ), C 9 = e 2 16π 2 ( sγµ P L b) ( µγ µ γ 5 µ), C 10 = 4.103

45 Top-down: UV complete theory Get C i at high scale with proper matching Run down to m b Check consistency with data Bottom-up: Fit data with set of chosen operators Get the corresponding C i

46 How reliable are the form factors? B K, D : Only two FF, f 0 and f 1, determined over the entire q 2 -range from lattice B K, D : Four FF, V, A 0, A 1, A 2, lattice not yet complete, HQET is helpful, higher-order corrections can be estimated There can be more FF with BSM operators (like tensor) Are there other pitfalls? D is detected as Dπ, take finite decay width into consideration Reduces tension to 2.2σ [Chavez-Saab and Toledo, ] For B K ( ), no estimate for charmonium-dominated bins, have to be removed

47 How reliable are the form factors? B K, D : Only two FF, f 0 and f 1, determined over the entire q 2 -range from lattice B K, D : Four FF, V, A 0, A 1, A 2, lattice not yet complete, HQET is helpful, higher-order corrections can be estimated There can be more FF with BSM operators (like tensor) Are there other pitfalls? D is detected as Dπ, take finite decay width into consideration Reduces tension to 2.2σ [Chavez-Saab and Toledo, ] For B K ( ), no estimate for charmonium-dominated bins, have to be removed

48 Tension for CC with l = τ, comparable with SM tree ( 15% enhancement in amplitude) Tension for NC with l = µ, comparable with SM loop only. Destructive interference needed

49 Tension for CC with l = τ, comparable with SM tree ( 15% enhancement in amplitude) Tension for NC with l = µ, comparable with SM loop only. Destructive interference needed Consider a new operator involving τ. Rotate the leptonic (τ, µ) basis to (τ, µ ) [Glashow, Guadagnoli, Lane] τ = τ cos θ + µ sin θ, ν τ = ν τ cos θ + ν µ sin θ If the mixing angle θ is small, sin 2 θ suppression makes the BSM tree comparable with SM loop

50 Tension for CC with l = τ, comparable with SM tree ( 15% enhancement in amplitude) Tension for NC with l = µ, comparable with SM loop only. Destructive interference needed Consider a new operator involving τ. Rotate the leptonic (τ, µ) basis to (τ, µ ) [Glashow, Guadagnoli, Lane] τ = τ cos θ + µ sin θ, ν τ = ν τ cos θ + ν µ sin θ If the mixing angle θ is small, sin 2 θ suppression makes the BSM tree comparable with SM loop

51 A simultaneous solution? [Choudhury, AK, Mandal, SInha, PRL 2017, NPB 2018] O I = 3 A 1 ( Q 2L γ µ L 3L ) 3 ( L 3L γ µ Q 3L ) 3 2 A 2 ( Q 2L γ µ L 3L ) 1 ( L 3L γ µ Q 3L ) 1 Only 3rd gen leptons, but can rotate to get muons Can give a good fit to R(D), R(D ), R K, R K, R J/ψ, BR(B s φµµ), BR(B s µµ) and within limits for b s+ invisible and B K ( ) µτ Much improved χ 2 compared to the SM ( 8 O exp χ 2 i O th ) 2 i = ( i=1 O exp) 2 ( ) i + O th 2 i χ 2 /d.o.f. = 1.5 (this model), 6.1 (SM), with A 1 = 0.028/TeV 2, A 2 = 2.90/TeV 2, sin θ = 0.018, C9 NP = C10 NP = 0.61

52 For these models C9 NP = C10 NP : only LH currents B s τ + τ gets sizable contribution from C 10, not C 9 R K and R K need at least one of C 9 and C 10 to be significant This is ruled out by B s τ + τ (as well as by M s ) We need to break C 0 = C 10 introduce RH currents O II = 3 A 1 [ (Q 2L, Q 3L ) 3 (L 3L, L 3L ) (Q 2L, L 3L ) 3 (L 3L, Q 3L ) 3 ] + 2 A 5 (Q 2L, Q 3L ) 1 {τ R, τ R } = 3 A 1 4 (c, b) (τ, ν τ ) + 3 A 1 4 (s, b)(τ, τ) + A 5 (s, b) {τ, τ} + 3 A 1 4 (s, t) (ν τ, τ) + A 5 (c, t){τ, τ} + 3 A 1 4 (c, t) (ν τ, ν τ ) with {x, y} x R γ µ y R, (x, y) x L γ µ y L x, y

53 For these models C9 NP = C10 NP : only LH currents B s τ + τ gets sizable contribution from C 10, not C 9 R K and R K need at least one of C 9 and C 10 to be significant This is ruled out by B s τ + τ (as well as by M s ) We need to break C 0 = C 10 introduce RH currents O II = 3 A 1 [ (Q 2L, Q 3L ) 3 (L 3L, L 3L ) (Q 2L, L 3L ) 3 (L 3L, Q 3L ) 3 ] + 2 A 5 (Q 2L, Q 3L ) 1 {τ R, τ R } = 3 A 1 4 (c, b) (τ, ν τ ) + 3 A 1 4 (s, b)(τ, τ) + A 5 (s, b) {τ, τ} + 3 A 1 4 (s, t) (ν τ, τ) + A 5 (c, t){τ, τ} + 3 A 1 4 (c, t) (ν τ, ν τ ) with {x, y} x R γ µ y R, (x, y) x L γ µ y L x, y

54 Can also play the same game with O III = 3 A 1 (Q 2L, Q 3L ) 3 (L 3L, L 3L ) 3 + A 1 (Q 2L, Q 3L ) 1 (L 3L, L 3L ) A 5 (Q 2L, Q 3L ) 1 {τ R, τ R } = A 1 (c, b) (τ, ν τ ) + A 1 (s, b) (τ, τ) + A 5 (s, b) {τ, τ} + A 1 (s, t) (ν τ, τ) + A 1 (c, t)(ν τ, ν τ ) + A 5 (c, t) {τ, τ} Best fit points Model II Model III sinθ A 1 in TeV A 5 in TeV

55 [An ongoing analysis taking all 160 observables into account shows a slightly different fit for these models. Also, Model I seems to be allowed. (Biswas, Calcuttawala, Patra, Priv. Comm.]

56 Something futuristic: b s + invisibles at Belle-II [Calcuttawala, AK, Nandi, Patra 2016]

57 SM: b sν ν, only penguin and box Not always related to b sl + l : 1 Leptons can be R with no neutrino counterpart 2 ɛ ab La L γ µ Q b L : b ν, t l 3 The invisibles can be something different!

58 SM: b sν ν, only penguin and box Not always related to b sl + l : 1 Leptons can be R with no neutrino counterpart 2 ɛ ab La L γ µ Q b L : b ν, t l 3 The invisibles can be something different! Observables: BR, dγ/dq 2, F T (q2 ) (neutrinos), F L (q2 ) (light scalars)

59 SM: b sν ν, only penguin and box Not always related to b sl + l : 1 Leptons can be R with no neutrino counterpart 2 ɛ ab La L γ µ Q b L : b ν, t l 3 The invisibles can be something different! Observables: BR, dγ/dq 2, F T (q2 ) (neutrinos), F L (q2 ) (light scalars)

60 H eff = 4G F 2 V tb V tsc SM [ OSM + C 1O V1 + C 2O V2 ], O SM = O V1 = ( s L γ µ b L ) ( ν il γ µ ν il ), O V2 = ( s R γ µ b R ) ( ν il γ µ ν il ). Br(B K(K )ν ν) < 1.6(2.7) 10 5 Detection efficiencies are small (Belle, )

61 B K ν ν (50 and 2 ab 1 ) F T, B X s ν ν (50 ab 1 )

62 It can also be light invisible scalars (DM?) L b sss = C S1 m b s L b R S 2 + C S2 m b bl s R S 2 + H.c. (1) Higgs portal DM S = 0, hss coupling small to evade LHC limits

63 B K and B K for m S = 0.5 (1.8) GeV, L int = 50 ab 1

64 To conclude: The CKM paradigm works quite well. BSM CPV needed to explain the baryon asymmetry, but it has to be subleading at least in the B sector (also in K and probably D) Flavour physics is the only tool to probe BSM if the scale is beyond the direct reach of LHC There are some intriguing anomalies. The pattern is not yet clear but LFU violation is indicated The third generation may be the window to BSM. Watch out for LHCb and Belle-II for new results, confirmatory tests, and possible surprises!

65 To conclude: The CKM paradigm works quite well. BSM CPV needed to explain the baryon asymmetry, but it has to be subleading at least in the B sector (also in K and probably D) Flavour physics is the only tool to probe BSM if the scale is beyond the direct reach of LHC There are some intriguing anomalies. The pattern is not yet clear but LFU violation is indicated The third generation may be the window to BSM. Watch out for LHCb and Belle-II for new results, confirmatory tests, and possible surprises! Thank you!

66 To conclude: The CKM paradigm works quite well. BSM CPV needed to explain the baryon asymmetry, but it has to be subleading at least in the B sector (also in K and probably D) Flavour physics is the only tool to probe BSM if the scale is beyond the direct reach of LHC There are some intriguing anomalies. The pattern is not yet clear but LFU violation is indicated The third generation may be the window to BSM. Watch out for LHCb and Belle-II for new results, confirmatory tests, and possible surprises! Thank you!

CKM : Status and Prospects

CKM : Status and Prospects Anirban Kundu University of Calcutta February 20, 2014 IIT Guwahati, EWSB2014 Plan The CKM matrix V ud, V cd, V cs, V us V tb, V cb, V ub Combinations UT angles: α, β, γ, β s BSM hints? Summary: No spectacular