Flavor Physics: the Next Decade(S) Zoltan Ligeti (Ligeti@Berkeley.Edu)

Flavor Physics: the next decade(s) Zoltan Ligeti ([email protected])

Aug 10–21 2020, Online & World-wide Disclaimers

If available, I prefer giving summer school lectures on the blackboard • – More fun for you, and also for me

– Sketching a plot on the blackboard, we automatically focus on what matters

– Time spent updating many of the plots was not useful, but I still tried

Do interrupt any time with any questions or comments! I really mean it! • (Let’s try to make this as interactive as possible, but I may not notice raised hands in zoom)

Z L – p.2/1 Outline

Continue from where we stopped yesterday... • Testing the SM • ... K πνν¯, many B decays sensitive to a variety of BSM scenarios → Hints of lepton universality violation • ( ) + ( ) ... In B K ∗ ` `−, in B D ∗ τν¯ → → Other future directions • ... Higgs, top, new physics ﬂavor

Conclusions •

Z L – p.2/2 Yesterday: testing the SM with K+ → π+νν¯

50 years of searches (more than for Higgs), sensitive to (100 TeV) • O

+ + +4.0 11 NA62 @ ICHEP: (K π νν¯) = (11.0 3.5) 10− — at the SM level • B → − × KOTO, 2019: 4 events in K π0νν¯ search; @ ICHEP: 4 3 w/ 1.05 0.28 BG • L → → ± Z L – p.2/3 B mesons: what’s special about them?

Many interesting processes with clean theoretical interpretations: • – Top quark loops not too strongly suppressed – Large CP violating effects possible, some with clean interpretation – Some of the hadronic physics understood model independently( m Λ ) b QCD Experimentally feasible to study: • – Υ(4S) resonance is clean source of B mesons – Long B meson lifetime (If V were as large as V , no B factories built, these lectures would not take place, etc.) | cb| | us| – Timescale of oscillation and decay comparable: ∆m/Γ 0.77 (and ∆Γ Γ) '

Z L – p.2/4 a  a CP violation    a   a   CPV in interference between decay and mixing

Can get theoretically clean information in some 0 A B fCP • cases when B0 and B0 decay to same ﬁnal state q/p A Mass eigenstates: B = p B0 q B0 B0 | H,Li | i ∓ | i

Time-dependent CP asymmetry:

• 0 0 Γ[B (t) fCP ] Γ[B (t) fCP ] af = → − → CP Γ[B0(t) f ] + Γ[B0(t) f ] → CP → CP If amplitudes with one weak phase dominate, hadronic physics drops out: • a = ( 1) sin(phase difference between decay paths) sin(∆m t) fCP ± arg[(q/p)(A/A)]

Measure phases in the Lagrangian with small theoretical uncertainties •

Z L – p.2/5 Υ(4S) → B0B0: quantum entanglement

B0B0 pair created in a p-wave (L = 1) evolve coherently and undergo oscillations • Two identical bosons must be in a symmetric state — if one decays as a B0 (B0), then at the same time the other B must be B0 (B0)

EPR effect used for precision physics: •

Measure B decays and ∆z

First decay ends quantum correlation and determines ﬂavor of other B at t = t • 1 Z L – p.2/6 pp → b¯b or Z → b¯b: no quantum correlation

B0 with sufﬁcient boost to study CPV at Tevatron & LHC (+ Belle data on rates) • s

gg, qq¯ b¯b: measure ﬂavor of a b hadron, and ﬂavor of B0 as a function of time • → s 0 Need excellent time resolution, and fully reconstructed Bs to know its boost

Z L – p.2/7 CP violation in B → ψKS by the naked eye

CP violation is an (1) effect: sin 2β = 0.698 0.017

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Γ[B0(t) ψK] Γ[B0(t) ψK] af = → − → = sin2 β sin(∆m t) CP Γ[B0(t) ψK] + Γ[B0(t) ψK] → → CP violation in K decays is small because of small CKM elements, not because • CP violation is generically small — it is (1) in some B decays O

Z L – p.2/8 a a  CP violation   a   a    The B-factory money plot

1.5 excluded at CL > 0.95 Spectacular progress in last 20 years excluded area has CL > 0.95 • γ The CKM mechanism dominates 1.0 CP ∆md & ∆ms • violation & ﬂavor changing processes sin 2β 0.5 ∆md The implications of the consistency of εK α γ β

• η 0.0 measurements are often overstated α

Vub α Larger allowed region if there is NP •0.5 •

•1.0 γ εK CKM f i t t e r sol. w/ cos 2β < 0 Summer 19 (excl. at CL > 0.95) •1.5 •1.0 •0.5 0.0 0.5 1.0 1.5 2.0 ρ

Z L – p.2/9 The B-factory money plot

0.7 ∆m & ∆m CKM Spectacular progress in last 20 years γ d s f i t t e r 0.6 ∆m ε • d K Summer 19 0.5 sin 2β sol. w/ cos 2β < 0 The CKM mechanism dominates CP (excl. at CL > 0.95) 0.4 excluded area has CL > 0.95 > areaexcludedhas CL • η violation & ﬂavor changing processes 0.3 α α 0.2

Vub The implications of the consistency of 0.1 γ β • α measurements are often overstated 0.0 0.7•0.4 •0.2 0.0 0.2 0.4 0.6 0.8 1.0 ρ CKM f i t t e r 0.6 γ(α) Larger allowed region if there is NP Summer 19 • 0.5 Compare tree-level (lower plot) and 0.4 excluded area has CL > 0.95 > areaexcludedhas CL η • 0.3 loop-dominated measurements α 0.2

Vub 0.1 LHCb: constraints in the Bs sector γ β 0.0 • •0.4 •0.2 0.0 0.2 0.4 0.6 0.8 1.0 (2nd–3rd gen.) caught up with Bd ρ

(20%) NP contributions to most loop-level processes (FCNC) are still allowed • O Z L – p.2/9

Testing quark ﬂavor — take II

Assume that NP is negligible in tree-level processes, arbitrary in FCNCs (loops) • Consider tree-level + meson mixing: • General parametrization of many models by adding two real parameters to SM: C C 2iσ 0 0 0 0 SM: SM NP: NP he =ANP(B B )/ASM(B B ) 2 2 → → mW Λ

What is the scale Λ? How different is the CNP coupling from CSM?

Is h = (1) allowed? If not, the CKM mechanism dominates • O To answer, redo CKM ﬁt: tree-dominated unchanged, loop-mediated modiﬁed

(Importance of these constraints known since the 70s, conservative picture of future progress)

Z L – p.2/10 NP in B mixing: status and prospects

SM is the dominant contribution: NP < (0.25 SM) NP < (0.08 SM) • ∼ × ⇒ ∼ × Nowp•value LHCb 50/fb + Belle II 50/p•valueab 0.20 0.30 excluded area has CL > 0.95 CKM excluded area has CL > 0.95 CKM f i t t e r f i t t e r Summer 19 Prospects NP 0.25 2 2 Cij 4.5 TeV 0.15 Scale: h | | ' V V 2 Λ 0.20 • ti∗ tj s | | s 0.10 0.15 h h 2.3 103 TeV × 0.10 Λ 20 TeV (tree + CKM) 0.05 ⇒ ∼ 0.05 (2 TeV (loop + CKM) 0.00 0.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 0.05 0.10 0.15 0.20 0.25 0.30

hd hd Similar to LHC mg˜ reach (q) SM 2iσq [color: 2σ, dotted: 3σ] M12 = M12 (1+hqe ) [2006.04824] BSM sensitivity would continue to increase until much larger data sets • (LHCb will collect 300/fb after second upgrade in LS4, initial plans for a possible Belle II upgrade)

Complementary to high-p searches • T Z L – p.2/11 Hints of tensions with SM Hints of tensions with SM

“Who ordered that?”

The current B “anomalies”

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Lepton non-universality would be clear evidence for NP ©

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+ + 1) R and R (B Xµ µ−)/(B Xe e−) 20% correction to SM loop K K∗ → → ∼

ν 2) R(D) and R(D∗) (B Xτν¯)/(B X(e, µ)¯ν) 20% correction to SM tree → →

∼ ¢¡¤£ < 1 ( ) < 0 Scales: RK( ) few 10 TeV, R(D ∗ ) few 10 TeV Would bound NP scale! ∗ ∼ × ∼ × + Theor. less clean: 3) P 0 angular distribution (B K∗µ µ−) 5 → • + Theor. less clean: 4) B φµ µ− rate s → Can ﬁt 1), 3), 4) with one operator: C(NP)/C(SM) 0.2 , O = (¯sγ P b)(¯µγαµ) 9,µ 9,µ ∼ − 9,µ α L Viable BSM models... leptoquarks? No clear connection to DM & hierarchy puzzle • (Is the hierarchy problem or the ﬂavor problem more pressing for Nature?)

What are smallest deviations from SM, which can be unambiguously established? • Z L – p.2/12 Aside: highest impact LHCb papers

LHCb top-cited 5 papers [as of 8/8/2020] • (besides detector and its performance)

– Hints of lepton universality violation – in neutral & charged current decays

– Pentaquark discovery

None of these were anticipated • when LHCb was built!

(ATLAS, CMS: Higgs discovery & properties)

Z L – p.2/13 RK and RK∗: theoretically cleanest

( ) + B K ∗ µ µ− LHCb: R ( ) = → < 1 both ratios 2.5σ from lepton universality K ∗ B K( )e+e ∼ • → ∗ −

2.6σ 2.2σ 2.5σ

+ Theorists’ fits quote 3 – 5σ (sometimes including P 0 and/or B φµ µ−) • 5 s → Modifying one Wilson coefficient in (due to NP?) gives good fit: δ C 1 • Heff 9,µ ∼ − Z L – p.2/14 0 ∗ + − Aside: the P5 anomaly in B → K µ µ

“Optimized observables” [1202.4266 + long history] • (some assumptions about what’s optimal)

Global ﬁts: best solution: NP reduces C9µ

[Altmannshofer, Straub; Descotes-Genon, Matias, Virto; Jager, Martin Camalich; Bobet, Hiller, van Dyk; many more]

Difﬁcult for lattice QCD, large recoil

What is the calculation which detremines how far −→ below the J/ψ this comparison can be trusted? NP, ﬂuctuation, SM theory? Tests: other observables, q2 dependence, B and Λ decays, other ﬁnal states • s b Connected to many other processes: Is the cc¯ loop tractable perturbatively at • small q2? Can one calculate form factors (ratios) reliably at small q2 ? Impacts: semileptonic & nonleptonic, interpreting CP viol., etc.

Z L – p.2/15 Some concerns... maybe?

Key players: 4 • µν O7 = mb sσ¯ µνeF PRb

3 2 µ O9 = e (¯sγµPLb)(`γ¯ `)

2 µ 2 O10 = e (¯sγµPLb)(`γ¯ γ5`)

Best ﬁt: modify C9,µ 1 + b ccs¯ (cc¯ ` `−) contributes → → 0 0 5 10 15 20 [See also B DDK¯ analysis, LHCb @ ICHEP] → Questioned: validity of perturbative methods for cc¯ contribution

• 3 (B ψX ) 4 10− B → s ∼ × ↓ + 2 4 (ψ ` `−) 6 10− their product: 2 10− B → ∼ × ∼ × Much bigger than the short distance contribution

+ Not understood why so different than e e− hadrons [No affect on lepton universality] • → Z L – p.2/16 The B → D(∗)τ ν¯ decay rates

Γ(B Xτν¯) BABAR, Belle, LHCb: R(X)= → Γ(B X(e/µ)¯ν) • → 3.1σ from SM predictions — robust due to heavy quark symmetry + lattice QCD (only D so far)

more than statistics: R(D∗) with τ ν3π [1708.08856] → more than statistics: B J/ψ τν¯ [1711.05623] c →

Imply NP at a fairly low scale (leptoquarks, W 0, etc.), likely visible at ATLAS / CMS • Some of the models Fierz (mostly) to the same (SM) operator: distributions, τ polarization = SM

Tree level: three ways to insert mediator: (bν)(cτ), (bτ)(cν), (bc)(τν) • Tree level: overlap with ATLAS & CMS searches for ˜b, leptoquark, H±

Models built to ﬁt these anomalies have impacted many ATLAS & CMS searches • Z L – p.2/17 Exciting future

LHCb: R ( ) sensitivity with existing Run 1–2 data can still improve a lot • K ∗ + LHCb and Belle II: increase pp b¯b and e e− BB data sets by factor 50 • → → ∼ LHCb: • Belle II( 50/ab, at SM level): δR(D) 0.005 (2%) ∼ δR(D∗) 0.010 (3%) ∼

Measurements will improve a lot! (Even if central values change, plenty of room for establishing deviations from SM)

Competition, complementarity, cross-checks between LHCb and Belle II •

Z L – p.2/18 Lepton universality → lepton ﬂavor violation

quark sector lepton sector New charged current interactions New lepton-nonuniversal interactions generically introduce new FCNCs generically introduce LFV

Hope: new physics at LHC, couples to Hope: some of the hints for lepton quarks somehow (production, decays) non-univerality survive

However, no NP effect seen yet in However, no lepton ﬂavor violation ﬂavor-changing neutral currents seen yet in meson or lepton decays

Puzzle: How does NP “know” about Puzzle: Same for leptons question for the rotation between the quark mass whatever mediates the BSM interac- and weak interaction eigenstates tion

Solution: Some symmetry of NP, min- Solution: Same, maybe... Want data imal ﬂavor violation, natural in GMSB on many processes to give clues

Z L – p.2/19 E.g., leptoquark ﬂavor structures

( ) Leptoquarks are some of the most often discussed models for R ( ) and R(D ∗ ) • K ∗ A-priori no reason for the leptoquark couplings to be (approx.) ﬂavor conserving

+ + Need this to explain b s` `− data Need to worry about all b q` `− couplings → → 1 2

  λde λdµ λdτ   λ =  λse λsµ λsτ  λbe λbµ λbτ

(24 TeV)2 implies: 0.7 < Re(λ λ∗ λ λ∗ ) < 1.5 RK se be sµ bµ 2 • ∼ − M ∼ ( ) ( ) Search for LFV in B K ∗ µ±e∓, B K ∗ µ±τ ∓, etc., • → → similarly in D and K decays, and LFV in purely leptonic processes

Leptoquarks — almost by deﬁnition — connect quark and lepton ﬂavor • Z L – p.2/20 A possible pattern of couplings

  ρd κ ρd ρd rows = quarks Let’s assume: λ =  ρ κ ρ ρ  [de Medeiros Varzielas, Hiller, 1503.01084]   columns = leptons • κ 1 1 Allow for extra suppression of lighter quark couplings, e.g., ρ 2, ρ 3 or 4 ∼ d ∼ Can be arranged using ﬂavor symmetries (Froggatt-Nielsen mechanism, 0.2, Cabibbo angle) ∼ Predictions: •

For ﬁrst generation couplings, kaon decays give the strongest bounds at present • Mu2e and COMET will surpass these

Z L – p.2/21 Richness of directions √ Aside: at ﬁxed energy, 1/ L is about the best

It is often said that what’s excluded at • 300/fb, cannot be discovered at 3000/fb ... so why keep going?

– Holds for many heavy particle searches – Exception: light or weakly coupled particles, often with large backgrounds (e.g., charged Higgs) – HL-LHC highlights: reﬁne H couplings, SM particle properties, ﬂavor observables

(uncert. 1/√ ) — not Z0, q,˜ g˜ searches! ∼ L Statistics 10 can make 1.5σ 5σ, even without analysis improvements × → ∼ • (No one knows how many measurements are 1.5σ from SM expectation... which also improve)

Z L – p.2/22 Some key measurements, done much better

) 2 0 0.01s ∆χ = 1 1

(B HFLAV CL

SL LHCb 0 (*) CKM 2018 − B(s) → D(s)µX A 1 0.8 GLW Theory × 10 ADS 0 GGSZ World average 0.6 Combined

0.4 •0.01 DØ 68.3% D0 D0 0 (*) muons B(s) → D(s)µX 0.2 D0 •0.02 average 95.5% HFLAV B factory 0 average 0 50 100 150 Summer 2017 γ [°] •0.02 •0.01 0 0.01 0.020 ASL(B ) CP violation in Bs ψφ Measurements of γ crucial, → ASL: important, indep. now consistent with SM of DØ anomaly LHCb is now most precise

Uncertainty of predictions current experimental errors( seek lot more data) • ⇒ Breadth crucial, often have to combine many measurements and theory • (“The interesting messages are not simple, the simple messages are not interesting”)

Z L – p.2/23 B → µ+µ−: interesting well beyond HL-LHC

+ 10 B µ µ− in SM, 10− : LHCb expects 10% (300/fb), CMS expects 15% (3/ab) d → • 2 SM uncertainty (2%) f CKM [Bobeth, FPCP’15] and may be further reduced ' ⊕ Bq ⊕ − ×10 9 ATLAS, CMS, LHCb - Summer 2020

) 0.6 9 − Preliminary ATLAS 0.5 2011 - 2016 data CMS ) (10

− LHCb µ 0.4 + Combined µ 0.3 →

0 B

( 0.2 Β SM 0.1 × −9 0 10 1 2 3 4 5 Β 0 → µ+µ− −9 (Bs ) (10 ) + Theoretically cleanest V I know, use isospin: (B `ν¯)/ (B µ µ−) • | ub| B u → B d → A decay with mass-scale sensitivity (dim.-6 operator) that competes w/ K πνν¯ • → Z L – p.2/24 D – D mixing and CP violation

CP violation in D decays: • 3 LHCb, Nov. 2011: ∆ACP A + A + = (8.2 2.4) 10− ≡ K K− − π π− − ± × 3 LHCb, Mar. 2019: ∆ACP = (1.82 0.33) 10− - (a stretch in the SM, imho) − ± × I think we still don’t know how big an effect could (not) be accommodated in SM •

Mixing generated by down quarks • or in SUSY by up-type squarks SM Value of ∆m? Not even 3σ yet • • no mixing Connections to FCNC top decays • •

SUSY: interplay of D & K bounds: alignment, universality, heavy squarks? • Z L – p.2/25 The LHC is a top factory: top ﬂavor physics

l FCNC top decays not yet strongly constrained b • ν t cZ, cγ, cH, uZ, uγ, uH W → t 12 SM predictions: < 10− < 4 l Best current bound: few 10− [ATLAS, CMS] t ∼ × Z l Sensitivity will improve 2 orders of magnitude • ∼ u, c

Indirect constraints: t b tight bounds from B decays • L ↔ L ⇒ – Strong bounds on operators with left-handed ﬁelds – Right-handed operators could give rise to LHC signals

If top FCNC is seen, LHC & B factories will both probe the NP responsible for it • Z L – p.2/26 The LHC is a Higgs factory

Rich physics: many production and decay channels (fermion couplings crucial) •

Higgs ﬂavor param’s: 3rd gen: κ , κ , κ ; 2nd gen: κ , κ ; do κ , κ vanish? • t b τ c µ t,c τµ Thoroughly test Higgs paradigm seek much higher precision • ⇒ Z L – p.2/27 Higgs ﬂavor prospects

Higgs couplings to gauge bosons, τ, t, (b) have • been constrained with some precision, (10%) O + ICHEP 2020: Evidence for H µ µ− • → Reducing uncertainties is a key long-term goal •

Future precision of ﬂavor-diagonal couplings [Heinemann & Nir, 1905.00382]

Z L – p.2/28 Dark matter, with ﬂavor: • Final remarks Very broad program

Recall, most cited Belle paper is discovery of X(3872), for BaBar the D (2317) • s∗0 γ from CP asymmetries in tree-level decays •

CP asymmetries, e.g., SB ψKS , SBs ψφ, SB K π0γ • → → → S

Differences of CP asymmetries, e.g., SψK SφK , SBs ψφ SBs φφ • S − S → − → + + B µ µ−, search for B µ µ−, other rare / forbidden decays • s → d → ( ) + ( ) Rare decays, e.g., B K ∗ ` `−, B φγ, B K ∗ νν¯ • → s → → Search for charged lepton ﬂavor violation, e.g., τ µγ, τ 3µ • → → Search for CP violation in D0 D0 mixing, semileptonic decays, etc. • − Improvements in many measurements • Any of these measurements could establish new physics • Z L – p.2/29 More “exotic” searches

Better tests of (exact or approximate) conservation laws • Exhaustive list of dark / hidden sector searches • 0 + + + + LFV meson decays, e.g., M µ−e , B h µ−e , etc. • → → Invisible modes, even baryonic, B N +invis. [+mesons] [1907.10612, 1810.00880, 1708.01259] • → Hidden valley inspired scenarios, e.g., multiple displaced vertices, even with `+` • − Exotic Higgs decays, e.g., high multiplicity, displaced vertices( H XX abab) • → → Search for “quirks” (non-straight “tracks”) at LHCb using many velo layers • I do not know how many CP violating quantities have been measured... • neither how many new hadronic states discovered by BABAR, Belle, LHCb ...

Z L – p.2/30 What are the largest useful data sets?

No one has seriously studied it! (Recall, Sanda, 2003: the question is not 1035 or 1036...) • Which measurements will remain far from being limited by theory uncertainties? • – γ, theory limit only from higher order electroweak – B µµ, B µν and other leptonic decays (lattice QCD, [double] ratios) s,d → → – CP violation in D mixing (ﬁrm up theory) d,s – ASL (work on exp. syst. issues) – CLFV, EDM, etc.

In some decay modes, even in 2035 we’ll have: (exp. bound) SM > 103 + + ∼ • E.g., B e e−, τ τ − — can build models... (I hope to be proven wrong!) → My guess: until 100 (Belle II & LHCb Phase 2), sensitivity to NP would improve • × FCC-ee in tera-Z phase could be the ultimate B factory! • Z L – p.2/31 Some conclusions

Flavor physics probes scales 1 TeV; sensitivity limited by statistics, not theory • New physics could show up any time measurements improve ⇒ In FCNCs, NP/SM > 20% still allowed; any discovery upper bound on NP scale • ∼ ⇒ Precision tests of SM will improve in the next decade by 10–104 • Few tensions with SM; some of these (or others) could soon become decisive • Discovering lepton universality violation would focus even more attention on LFV • Many interesting theoretical questions relevant for optimal experimental sensitivity • Flavor measurements will tell us a lot, whether NP is discovered or not: • FLAVOR Evidence for BSM? yes no yes complementary information distinguish models ATLAS & CMS no points to where to look next sensitive to highest scales

Z L – p.2/32 Extra slides Theory challenges / opportunities

New methods & ideas: recall that the best α and γ measurements are in modes • proposed in light of Belle & BABAR data (i.e., not in the BABAR Physics Book)

– Better SM upper bounds on S S , S S , and S 0 S η0KS − ψKS φKS − ψKS π KS − ψKS – And similarly in Bs decays, and for sin 2β(s) itself – How big can CP violation be in D0 – D0 mixing (and in D decays) in the SM?

– Better understanding of semileptonic form factors; bound on 0 in SM? SKSπ γ – Many lattice QCD calculations (operators within and beyond SM) – Inclusive & exclusive semileptonic decays – Factorization at subleading order (different approaches), charm loops – Can direct CP asymmetries in nonleptonic modes be understood enough to – make them “discovery modes”? [SU(3), the heavy quark limit, etc.] We know how to make progress on some + discover new frameworks / methods? • Z L – p.2/i Dark sectors: broad set of searches

+ Started with bump hunting in B K∗µ µ− → • Nearly an order of magnitude improvement due to dedicated LHCb analysis ¯ In axion portal models, scalar couples as (mψ/fa) ψγ5ψ a (mt coupling in loops)

Freytsis, Ligeti, Thaler LHCb, m(a) = 600 MeV4 f

( [0911.5355] [1508.04094] B(χ → hadrons) = 0 LHCb χ )tan 2 Bound on fa Bound on f tan Β !Large tan Β" χ → a 1400B( hadrons) = 0.99 100 700

1 2 30 TeV β )=1 TeV [PeV], h

( 2 1200 20 TeV 80 560 m 10 TeV "

TeV 60 420 5 TeV !

1000 m Β

0.5 2

3 TeV ( h [PeV], 1 40 280 tan 2 TeV )=10 TeV β " a 2

800 f

GeV 1 TeV 20

! 140 )tan H χ 600 ( m

f 0 0 1000 2000 3000 4000 0 200 400 600 800 1000 1200 1400 + − 400 m(µ µ ) [MeV] 1 TeV mmH ± !(GeV)GeV" [LHCb, 1508.04094]50 TeV H 2 TeV 30 TeV 3 TeV FIG. 2: The shaded regions of f tan2 β are excluded in the 200 5 TeV a 20 TeV 10 TeV Many other current / future LHCb dark photonlarge searches tan β limit. To indicate[Ilten the et al., region 1603.08926, of validity 1509.06765] of the large tan β approximation, the dashed (dotted) curve shows • 0 the bound for tan β =3(tanβ =1). 0 1 2 3 4 5 6 Z L – p.2/ii tan Β b sa amplitude in Eq. (12) changes signs, indicated by → FIG. 1: Bounds on fa as a function of tan β and mH for n =1 the dashed curve in Fig. 1, along which the bound dis- 2 2 in Eq. (8), for ma mB.Foreachdisplayedvalueoffa there appears. Higher order corrections will affect where this are two contour lines,≪ and the region between them is allowed cancellation takes place, but away from a very narrow re- for fa below the shown value. The bound disappears along gion near this dashed curve, the derived bound is robust. the dashed curve, and gets generically weaker for larger tan β. The region tan β < 1 is constrained by the top Yukawa coupling becoming increasingly nonpertubative; this region is included in Figs. 1 and 3, nevertheless, to provide that LHCb should be able to carry out a precise mea- a clearer illustration of the parametric dependence of the surement [40]. Interestingly, since the B Ka signal is bounds. essentially a delta function in q2, the bound→ in Eq. (15) As one goes to large values of tan β,theX1 piece can be improved as experimental statistics increase by of Eq. (12) dominates, and sin(2β)/2=1/ tan β + considering smaller and smaller bin sizes, without being (1/ tan3 β). In this limit, the constraint takes a par- limited by theoretical uncertainties in form factors [41] ticularlyO simple form that only depends on the combi- (or by nonperturbative contributions [42]). The bound 2 nation fa tan β, as shown in Fig. 2. Except in the re- on f will increase compared to the results we obtain in a gion close to mH 550 GeV, the bound is better than the next section, simply by scaling with the bound on 2 ∼ fa tan β > few 10 TeV. 1/ Br(B Ka). These B∼ Ka× bounds are complementary to those → → + recently set by BaBar [30] in Υ(nS) γ a γ µ µ−: ! → → V. INTERPRETATION 2 fa > (1.4TeV) sin β . (16) ∼ × We now derive the bounds on f using the calculated For example, for mH 400 GeV, the Υ bound dominates a ≃ B Ka branching ratio in Eq. (14) and the experimen- for tan β > 5, while B Ka dominates for tan β < 5. → tal→ bound in Eq. (15). We start with the axion portal The bounds∼ in Figs. 1 and 2 apply for a generic∼ axion + scenario with Br(a µ µ−) 100% and where sin θ is portal model where mH and tan β are free parameters. → ∼ defined in terms of fa by Eq. (8). We will then look at One would like some sense of what the expected values the bound on more general scenarios, including the light of mH and tan β might be in a realistic model. Ref. [8] Higgs scenario in the NMSSM. considered a specific scenario based on the PQ-symmetric For the axion portal, Fig. 1 shows the constraints on fa NMSSM [31]. In that model small tan β is preferred, as a function of the charged Higgs boson mass mH and since large tan β requires fine-tuning the Higgs potential. tan β.Forconcreteness,wetaken = 1; other values of n In addition, mH is no longer a free parameter and is correspond to a trivial scaling of fa.Inthemassrange approximately related to the mass of the lightest CP- in Eq. (1), the dependence on ma is negligible for setting even scalar s0 via abound.Theboundonfa is in the multi-TeV range for 2 low values of tan β and weakens as tan β increases. At 2 2 2 ms0 fa mH mW + 2 . (17) each value of tan β, there is a value of mH for which the ≃ sin 2β vEW " # New particles, e.g., supersymmetry

Any new particle that couples to quarks or leptons new ﬂavor parameters • ⇒ The LHC will measure: masses, production rates, decay modes (some), etc. Details of interactions of new particles with quarks and leptons will be important

New physics ﬂavor structure can be: new physics mass scale: • – Minimally ﬂavor violating (mimic the SM) can be “light” – Related but not identical to the SM – Unrelated to the SM, or even completely anarchic ↑↓ must be heavy Some aspects will be understood from ATLAS & CMS data (masses, decays, etc.)

New sources of CP violation: squark & slepton couplings, ﬂavor diagonal pro- • + cesses (e, n EDM), neutral currents; may enhance FCNCs( B ` `−, µ eγ) (s) → →

Z L – p.2/iii Example: SUSY in K0 – K0 mixing

SUSY 2 2 2 (∆mK) 1 TeV ∆m ˜ h i 104 12 Re (Kd) (Kd ) (oversimpliﬁed) exp 2 L 12 R 12 • (∆mK) ∼ m˜ m˜ d KL(R): mixing in gluino couplings to left-(right-)handed down quarks and squarks

Constraint from : replace 104 Re (Kd) (Kd ) with 106 Im (Kd) (Kd ) • K L 12 R 12 ∼ L 12 R 12 (44 CPV phases: CKM +3 ﬂavor diagonal+ 40 in mixing of fermion-sfermion-gaugino couplings)

Classes of models to suppress each terms (structures imposed to satisfy bounds) • (i) Heavy squarks: m˜ 1 TeV (e.g., split SUSY) (ii) Universality: ∆m2 m˜ 2 (e.g., gauge mediation) Q,˜ D˜ (iii) Alignment: (Kd ) 1 (e.g., horizontal symmetry) | L,R 12| All models incorporate some of the above — known since the ’70s • Z L – p.2/iv The MSSM parameters and ﬂavor

Superpotential: [Haber, hep-ph/9709450] • P u ¯ d ¯ ` ¯ W = i,j Yij Hu QLiULj + YijHd QLiDLj + YijHd LLiELj + µHuHd ˜ ˜ ˜ Soft SUSY breaking terms: (S = Q˜L, D¯ L, U¯ L, L˜L, E¯L) • u d ` = A H Q˜ U˜¯ + A H Q˜ D˜¯ + A H L˜ E˜¯ + BH H Lsoft − ij u Li Lj ij d Li Lj ij d Li Lj u d X 2 1 (m )ij SiS¯j M1B˜B˜ + M2W˜ W˜ + M3g˜g˜ − S − 2 scalars 3 Y f Yukawa and 3 Af matrices — 6 (9 real + 9 imaginary) parameters × 5 m2 hermitian sfermion mass-squared matrices — 5 (6 real + 3 imag.) param’s S × 2 Gauge and Higgs sectors: g1,2,3, θQCD,M1,2,3, m , µ, B — 11 real + 5 imag. hu,d

Parameters:( 95 + 74) (15 + 30) from U(3)5 U(1) U(1) U(1) U(1) − × PQ × R → B × L

44 CPV phases: CKM +3 in M1,M2, µ (set µB∗,M3 real) + 40 in mixing matrices • 44 CPV phases: of fermion-sfermion-gaugino couplings (+80 real param’s)

Z L – p.2/v History of surprises: CP violation

Cronin & Fitch, Nobel Prize, 1980 ⇒ 3 generations, Kobayashi & Maskawa, Nobel Prize, 2008 ⇒ Near misses: CP violation

“At that stage the search was terminated by administration of the Lab.” [Okun, hep-ph/0112031]