Theoretical Overview of B Physics personal perspectives Xin-Qiang - - PowerPoint PPT Presentation

SLIDE 1

Theoretical Overview of B Physics → personal perspectives ← Xin-Qiang Li

Central China Normal University

Talk given at HFCPV-2018, Zhengzhou, 2018/10/26

SLIDE 2

Outline

Introduction Theoretical tools for B physics B − ¯ B mixings: ∆Ms,d, ∆Γs,d, as,d

fs

Bs,d → µ+µ−: powerful model killing Semi-leptonic decays: |Vub|, |Vcb| and R(D(∗)) Exclusive b → sℓ+ℓ− decays: several anomalies Non-leptonic decays: higher-order pert. corrs Conclusion

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SLIDE 3

Why B physics:

◮ What is B physics: properties, productions and decays of vari-

• us hadrons containing at least one bottom quark;

Bu,d,s,c mesons, Λb baryon ◮ Why study B physics: three main motivations;

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SLIDE 4

Dedicated B-physics experiments:

◮ Past: first observation of B → Xsγ by CLEO in 1994; continued by Tevatron @

Fermilab and the two B-factories: BaBar @ SLAC and Belle @ KEK with many key measurements; [A. J. Bevan et al., “The Physics of the B Factories,” 1406.6311]

◮ Current: dedicated LHCb (also ATLAS and CMS) @ LHC with many exciting

results; [I. Bediaga et al., “Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era,” arXiv:1808.08865]

◮ Future: besides LHCb @ LHC, also Belle II @ SuperKEKB expected to start

data taking in 2018, designed to find NP beyond the SM of particle physics; [https://confluence.desy.de/display/BI/B2TiP+WebHome; 1808.10567]

as

sl ±3.0 × 10

4

±10.0 × 10

4

±33.0 × 10

4

[ ]

±0.35 ±1.5 ±1.5 ±5.4 s [mrad] ±22 ±4 ±14 ±49

A

±1.0 × 10

5

±35.0 × 10

5

±4.3 × 10

5

±28.0 × 10

5 Current HL-LHC 2025

LHCb

LHCb ATLAS/CMS Belle II

RK [%]

±0.70 ±3.6 ±2.2 ±10.0

R(D * ) [%]

±0.20 ±0.50 ±0.72 ±2.6

(B0

+

) (B0

s +

) [%]

±21 ±10 ±34 ±90

Current HL-LHC 2025

LHCb

LHCb ATLAS/CMS Belle II

4 / 35

SLIDE 5

Theoretical tasks for B physics:

◮ Main task: try to improve the theory predictions to match the more

and more precise exp. data;

◮ Many dynamical frameworks developed:

HQET, SCET, NRQCD, QCDF, pQCD, · · · ֒ → based on QCD, and separate pert. from non-

• pert. strong interaction effects ↔ factorization theorem;

◮ For the non-pert.

• bjects: mostly from Lattice QCD and LCSR,

· · · ;

[for reviews see: http://flag.unibe.ch/, and https://hflav.web.cern.ch/]

160 175 190 205 220 235 250 = + + = + = MeV

ETM 09D ETM 11A ALPHA 11 ETM 12B ALPHA 12A ETM 13B, 13C ALPHA 13 ALPHA 14 FLAG average for = HPQCD 09 FNAL/MILC 11 HPQCD 12 / 11A HPQCD 12 RBC/UKQCD 13A (stat. err. only) RBC/UKQCD 14A RBC/UKQCD 142 RBC/UKQCD 141 FLAG average for = + HPQCD 13 ETM 13E FLAG average for = + +

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SLIDE 6

Current status of B physics:

◮ The CKM mechanism of flavor & CP violation well established! ֒

→ 2008 Nobel Prize for Kobayashi and Maskawa;

◮ Information on UT from tree- and loop-level processes well consistent!

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SLIDE 7

Current status of B physics:

◮ Remember: O(20%) NP contributions to most FCNC processes still

allowed by the current data;

◮ Several intriguing tensions/anomalies do observed in flavour physics,

might be any BSM signals?

Br(B->pi^0 pi^0) A_CP(B->pi K)

Z.Ligeti,1606.02756

† all of them not yet conclu- sive: theo. uncertainties

• r exp. fluctuations?

† except for theo. cleanest modes, more cross-checks needed; † exp. measurements of re- lated observables needed; † indep. theory and lattice calculations needed;

7 / 35

SLIDE 8

How to describe B-hadron weak decays:

◮ At the quark level: B-hadron weak decays mediated by weak charged-current Jµ

cc coupled to W ±; Lcc = − g2 √ 2 Jµ

cc W † µ + h.c.,

Jµ

cc = (¯

uL, ¯ cL, ¯ tL) γµ VCKM   dL sL bL  

֒ → VCKM: describes flavor violation, and very predictive, especially for CPV! ◮ In the real world: no free quarks due to confinement; quarks always confined inside hadrons through soft-gluon exchanges; ֒ → In B physics, simple weak decays overshadowed by complex strong interactions!

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SLIDE 9

Typical features for B-hadron weak decays:

◮ A typical multi-scale problem and scales are highly hierarchical;

EW interaction scale ≫

• ext. mom’a in B rest frame

≫ QCD-bound state effects mW ∼ 80.4 GeV ≫ mb ∼ 4.8 GeV ≫ ΛQCD ∼ 1 GeV

◮ Starting point Leff:

integrate out heavy d.o.f. (mW,Z,t ≫ mb), physics above (below) µ ∼ mb contained in Ci (Oi);

[A. J. Buras, 1102.5650]

◮ Ci: RG-improved pert. calculable;

matching at µ0 and running to µb; NNLL accuracy available!

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SLIDE 10

Hadronic matrix elements for B-hadron weak decays:

◮ How to evaluate f|Oi|B: 0|Oi|B, π|Oi|B, ππ|Oi|B, ¯

B|Oi|B, · · · ;

◮ M1M2|Oi|B: not yet possible in lattice QCD; expressed in terms of (few)

universal non-pert. hadronic quantities with pert. calculable coefficients;

• dynamical approaches based on factorization theorems:

PQCD, QCDF, SCET, · · · ;

[Keum, Li, Sanda, L¨

u, Yang ’00; Beneke, Buchalla, Neubert, Sachrajda, ’00; Bauer, Flemming, Pirjol, Stewart, ’01]

• (approximate) symmetries of QCD: Isospin, U-Spin, V-Spin, and flavor

SU(3) symmetries, · · · ;

[Zeppenfeld, ’81;

London, Gronau, Rosner, Chiang, Cheng et al.]

10 / 35

SLIDE 11

B − ¯ B mixings:

◮ Motivation: strongly suppressed in SM; highly sensitive to BSM effects; ֒ →

Λ ≥ 103 TeV

◮ ∆Ms,d . = 2|Ms,d

12 |: calculated from box diagrams with internal virtual par- ticles; main uncertainty from Bag parameters Bq|Oi| ¯ Bq ∝ f2

BqB(i) Bq;

∆MSM

d

= (0.53+0.03

−0.04) ps−1

∆MHFAG

d

= (0.5065 ± 0.0019) ps−1 ∆MSM

s

= (18.1+1.1

−1.2) ps−1

∆MHFAG

s

= (17.757 ± 0.021) ps−1

[Kirk,

Lenz and Rauh, 1711.02100;

• T. Rauh, talk given at CKM2018]

11 / 35

SLIDE 12

B − ¯ B mixings:

◮ ∆Γs,d . = 2|Γs,d

12 | cos φs,d 12 : arise from absorptive part of box diagrams, dom- inated by tree-level b → c¯ cs(d) transitions; [Artuso/Borissov/Lenz, 1511.09466] Γs

12 = Λ3

m3

b

• Γs,(0)

3

+ αs 4π Γs,(1)

3

+ αs 4π 2 Γs,(2)

3

+ ...

• + Λ4

m4

b

• Γs,(0)

4

+ ...

• + ... [H. M. Asatrian et al, 1709.02160]

b s s b c c

Quark Expansion (HQE)

◮ as,d

fs

. =

• Γs,d

12

Ms,d

12

• sin φs,d

12 : motivated by 2013 D0 dimuon charge asymmetry!

• 0.4
• 0.2
• 0.0

0.2 0.4

φ c¯

cs s [rad] 0.06 0.08 0.10 0.12 0.14

∆Γs[ps−1] ATLAS 19.2 fb−1 D0 8 fb−1 CMS 19.7 fb−1 CDF 9.6 fb−1 Combined LHCb 3 fb−1

SM

68% CL contours (∆ log L = 1.15)

HFLAV

PDG 2018

) (B

SL

A

• 0.02
• 0.01

0.01 0.02

)

s

(B

SL

A

• 0.02
• 0.01

0.01 HFLAV

PDG 2018

B factory average LHCb

X µ

(*) (s)

D →

(s)

B

D

X µ

(*) (s)

D →

(s)

B

D

muons

D

average

10 × Theory World average

= 1

2

χ ∆

12 / 35

SLIDE 13

B − ¯ B mixing:

◮ ∆Ms,d vs ∆Γs,d: state-of-the-art comparison; [Kirk, Lenz and

Rauh, 1711.02100; T. Rauh, talk given at CKM2018]

◮ SM predictions and exp. averages consistent with each other! ֒ → Large NP effect in Bs,d mixings now closed!

13 / 35

SLIDE 14

Bs,d → µ+µ−:

◮ Facts about Bs,d → µ+µ−: highly suppressed within the SM;

• helicity suppressed, by a factor of (mµ/mB)2;
• FCNC process, forbidden at tree-level, proceed
• nly via loop diagrams;
• CKM suppressed by |VtbV ∗

ts|2;

֒ →

very sensitive to NP, especially from OS(P );

◮ Theory status: CA now to NNLO QCD + NLO EW; enhanced EM correction

included; [Bobeth et al., 1311.0903; Beneke, Bobeth and Szafron, 1708.09152] Heff = − GF α √ 2πs2

W

• VtbV ∗

tq A,S,P

• i
• Ci Oi + C′

i O′ i

• + h.c.
• OA = (¯

qγµPLb) (¯ ℓγµγ5ℓ) , OS(P ) = mb(¯ qPRb) [¯ ℓ(γ5)ℓ] B(Bs → µ+µ−) = (3.57 ± 0.17) × 10−9, B(Bd → µ+µ−) = (1.06 ± 0.09) × 10−10

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SLIDE 15

Bs,d → µ+µ−:

◮ CMS + LHCb and LHCb updated results: [1411.4413, 1703.05747]

B(Bs → µ+µ−) = (3.0 ± 0.6+0.3

−0.2) · 10−9 (7.8σ);

B(Bd → µ+µ−) = (3.9+1.6

−1.4) ·

10−10 (3.0σ);

)

−

µ

+

µ →

s

BF(B

2 4 6 8

9 −

10 ×

)

−

µ

+

µ → BF(B

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

9 −

10 ×

6 8 . 2 7 % 9 5 . 4 5 % 9 9 . 7 3 % 9 9 . 9 9 %

SM LHCb

◮ Powerful in model killing: good consistency between SM and exp. data; [D. Straub, 1205.6094]

15 / 35

SLIDE 16

Bs,d → µ+µ−:

◮ Time-dependent observables: due to sizeable ∆Γs; [De Bruyn et

al., 1204.1737; Fleischer et al., 1703.10160; 1709.04735]

◮ With the updated LHC: these observables provide new d.o.f.

for NP searches;

[Fleischer, Jaarsma, Tetlalmatzi-Xolocotzi, 1703.10160; 1709.04735]

16 / 35

SLIDE 17

|Vub| and |Vcb| problem:

◮ Importance of |Vxb|: play a key role in determining the apex of UT;

• |Vub| or |Vub/Vcb| constraints

drectly the UT;

• b → s induced FCNC processes ∝

|VtbV ∗

ts|2 ≃ |Vcb|2

1 + O(λ2)

• ;
• ǫK ≃ x|Vcb|2 + · · · ;

֒ → More precise determination of

|Vxb| is of utmost importance!

◮ Incl. vs excl. methods: [Nandi, Gambino, Tackmann, talks at CKM 2016]

• Inclusive |Vcb|:

OPE/HQE, dominated by theory uncertainties, especially by correlations of theoretical parameters;

• Inclusive |Vub|: OPE/HQE, limited knowledge of leading and subleading SFs;
• Exclusive |Vxb|: how precise can the form factors be calculated by LQCD or LCSR;

17 / 35

SLIDE 18

|Vub| and |Vcb| problem:

◮ Status of global fit for |Vxb|: [Gambino, Silva, Bona, talks at CKM2018] ◮ Results for CKM2018: [Silva, Bona, talks at CKM2018]

|Vcb|incl. = (42.2 ± 0.4 ± 0.6) · 10−3, |Vub|incl. = (4.44 ± 0.17 ± 0.31) · 10−3 |Vcb|excl. = (41.2 ± 0.6 ± 0.9 ± 0.2) · 10−3, |Vub|excl. = (3.72 ± 0.09 ± 0.22) · 10−3 ֒ → |Vxb| tension significantly reduced, especially for |Vcb|! ֒ → global fit favours |Vub|excl. & |Vcb|incl.!

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SLIDE 19

R(D) and R(D∗) anomalies:

◮ B → D(∗)τ ¯ ν decays: tree-level processes;massive τ makes them sensitive

to tree-level NP like RH currents, charged Higgs, leptoquarks, · · · ;

◮ Current status: R(D(∗)) = Br(B→D(∗)τντ )

Br(B→D(∗)ℓνℓ) ; [BaBar, 1205.5442, 1303.0571;

Belle, 1507.03233, 1607.07923, 1612.00529; LHCb, 1506.08614, 1708.08856]

0.2 0.3 0.4 0.5 0.6

R(D)

0.2 0.25 0.3 0.35 0.4 0.45 0.5

R(D*)

BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, PRD94,072007(2016) Belle, PRL118,211801(2017) LHCb, PRL120,171802(2018) Average Average of SM predictions

= 1.0 contours

2

χ ∆

0.003 ± R(D) = 0.299 0.005 ± R(D*) = 0.258 ) = 74%

2

χ P( σ 4 σ 2

HFLAV

Summer 2018

⊲ R(D)SM = 0.299 ± 0.003 2.3σ [0.407 ± 0.039 ± 0.024] ⊲ R(D∗)SM = 0.258 ± 0.005 3.0σ [0.306 ± 0.013 ± 0.007] ֒ → combined ∼ 3.78σ deviation!

◮ Theo.: more precise lattice calculations for B → D(∗) FFs at non-zero recoil! ◮ Exp.: AD(∗)

λ

, RD∗

L , Λb → Λcτ ¯

ν, Bs → D(∗)

s

τ ¯ ν, Bc → J/Ψ(ηc)τ ¯ ν, B → Xcτ ¯ ν;

19 / 35

SLIDE 20

R(D) and R(D∗) anomalies:

◮ Importance of other observables: [Celis, Jung, Li, Pich, 1612.07757] ◮ Bc-lifetime constraint: [Li/Yang/Zhang, 1605.09308; Hu/Li/Yang, 1810.04939]

LSMEFT = L(4)

SM + 1

Λ2

• i

Ci(Λ)Qi, Q(3)

lq

= (¯ lγµτ Il)(¯ qγµτ Iq), Q(1)

lequ = (¯

lje)εjk(¯ qku) Qledq = (¯ lje)( ¯ dqj), Q(3)

lequ = (¯

ljσµνe)εjk(¯ qkσµνu) ֒ → V − A and/or tensor Lorentz structure needed!

20 / 35

SLIDE 21

R(D) and R(D∗) anomalies:

◮ The observed tension is model independent: exclusive already

• ver-saturates inclusive;

[M. Freytsis, Z. Ligeti, J. Ruderman, 1506.08896]

⊲ The data on R(D) and R(D∗) imply:

Br( ¯ B → D∗τ ¯ ν) + Br( ¯ B → Dτ ¯ ν) = (2.78 ± 0.25)%

⊲ Including the four lightest orbitally excited D meson states:

Br( ¯ B → D(∗)τ ¯ ν) + Br( ¯ B → D∗∗τ ¯ ν) ∼ 3%

⊲ From inclusive=exclusive:

Br(b → Xcτ ¯ ν) = (2.35 ± 0.23)% (LEP)

◮ R(Xc) constraint: [Kamali/Rashed/Datta,1801.08259; Lai/Li/Li/Yang, w.i.p.]

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.15 0.20 0.25 0.30 0.35 gL R(Xc)

• 0.2
• 0.1

0.0 0.1 0.2 0.3 0.4 0.5 0.15 0.20 0.25 0.30 gT R(Xc)

21 / 35

SLIDE 22

R(D) and R(D∗) anomalies:

◮ Another hint of LFUV: around 1.7σ above SM; [LHCb, 1711.05623;

Cohen/Lamm/Lebed, 1807.02730; Wang/Zhu, 1808.10830] R(J/ψ) = Br(Bc → J/ψτντ) Br(Bc → J/ψℓνℓ) = 0.71 ± 0.17 ± 0.18 vs 0.20 ∼ 0.39 (theo.)

◮ Future prospects with Belle-II and LHCb very promising![Albrecht

et al., 1709.10308; I. Bediaga et al., 1808.08865]

3 23 50 300 Integrated Luminosity [fb−1] 0.001 0.01 0.1 Absolute σR(X)

LHCb X = D∗, τ − → µ−¯ νµντ X = D∗, τ − → π−π+π−ντ X = J/ψ, τ − → µ−¯ νµντ

R(D) R(D*)

0.3 0.35 0.4 0.45 0.24 0.26 0.28 0.3 0.32 0.34

LHCb Belle II Future WA SM prediction

SM σ 1 σ 3 σ 5 σ 7 σ 9

• 1

8fb

• 1

22fb

• 1

50fb

• 1

5ab

• 1

50ab

◮ Maybe the first tantalizing hint for BSM? Let’s stay tuned!

22 / 35

SLIDE 23

Exclusive b → sℓ+ℓ− decays:

◮ Heff for b → sℓ+ℓ−: [Bobeth, Gambino, Gorbahn, Haisch, hep-ph/0312090]

Hb→s

eff

= − 4GF √ 2 VtbV ∗

ts

• i
• CiOi + C′

iO′ i

• ,

O(′)

7

= e 16π2 ¯ mb

• ¯

sσµνPR(L)b

• Fµν

O(′)

9

= e2 16π2

• ¯

sγµPL(R)b ¯ ℓγµℓ

• O(′)

10 =

e2 16π2

• ¯

sγµPL(R)b ¯ ℓγµγ5ℓ

• ◮ Amplitudes for exclusive decays: [Descotes-Genon, talk at FPCP 2016;

Bobeth, Chrzaszcz, Dyk, and Virto, arXiv:1707.07305]

B M ℓ+ ℓ− O7,7′ B M ℓ+ ℓ− O9,10,9′,10′... B M ℓ+ ℓ− Oi

c ¯ c

A(ℓ) L,R

λ

= N (ℓ)

λ

• (C(ℓ)

9 ∓C(ℓ) 10 )Fλ(q2)+ 2mbMB

q2

• C(ℓ)

7 FT λ (q2)−16π2 MB

mb Hλ(q2)

• 23 / 35

SLIDE 24

Exclusive b → sℓ+ℓ− decays:

◮ Hadronic matrix elements of Oi: [Beneke/Feldmann/Seidel, 0106067,

0412400; Grinstein/Pirjol, hep-ph/0404250; Beylich/Buchalla/Feldmann, 1101.5118]

†

Large recoil (low-q2)

• very low-q2 (≤ 1 GeV2)

dominated by O7;

• low-q2

([1, 6] GeV2) dominated by O9,10;

• QCDF or SCET, LCSR;

†

Small recoil (high-q2)

• dominated by O9,10; - local OPE + HQET;

◮ Key issues: how large of power corrs from b → sc¯

c → sℓ+ℓ− for q2 ≤ 6 GeV2 and from fact. FF terms?

[Descotes-Genon et al., 1510.04239]

24 / 35

SLIDE 25

Exclusive b → sℓ+ℓ− decays:

◮ Parametrisation of Hλ(q2): [Khodjamirian et al., 1006.4945; Bobeth et

al., 1707.07305;] AL,R

λ

= Nλ

• (C9 ∓ C10)Fλ(q2) + 2mbMB

q2

• C7FT

λ (q2) − 16π2 MB

mb Hλ(q2)

• Hλ(z) =

1 − z z∗

J/ψ

z − zJ/ψ 1 − z z∗

ψ(2S)

z − zψ(2S) ˆ Hλ(z), ˆ Hλ(z) =

• K
• k=0

α(λ)

k

zk Fλ(z) z(q2) ≡

• t+ − q2 − √t+ − t0
• t+ − q2 + √t+ − t0

◮ Based on analyticity + data and valid for −7 ≤ q2 ≤ m2

ψ(2S):

[Bobeth et al.,

1707.07305; Chrzaszcz et al., 1805.06378; Mauri et al., 1805.06401]

NP 9

C Re

3 − 2 − 1 − 1

NP 10

C Re

1.5 − 1 − 0.5 − 0.5 1 1.5 2 2.5

99% CL

LHCb Run2 ]

• 1

LHCb Upgrade [50 fb ]

• 1

LHCb Phase 2 [300 fb ]

• 1

BelleII [50 ab

25 / 35

SLIDE 26

Exclusive b → sℓ+ℓ− decays:

◮ Observed anomalies: [Dettori, Langenbruch, talks at Moriond 2018]

]

4

c /

2

[GeV

2

q

5 10 15

5

' P

1 − 0.5 − 0.5 1 (1S) ψ / J (2S) ψ

LHCb data Belle data ATLAS data CMS data SM from DHMV SM from ASZB

]

4

c /

2

[GeV

2

q

5 10 15 20

K

R

0.5 1 1.5 2 SM

LHCb LHCb

LHCb BaBar Belle

PRL 113, 151601 (2014) 1 2 3 4 5 6

q2 [GeV2/c4]

0.0 0.2 0.4 0.6 0.8 1.0

RK∗0 LHCb

LHCb BIP CDHMV EOS flav.io JC

]

4

c /

2

[GeV

2

q

5 10 15

]

4

c

• 2

GeV

• 8

[10

2

q )/d µ µ φ →

s

B dB(

1 2 3 4 5 6 7 8 9

LHCb

SM pred. Data

◮ Comments: 1, P ′

5 stat. fluctuation unlikely; 2, precise evaluation of QED effect in

R(∗)

K

very necessary; 3, cross-checks about hadronic nuisance parameters needed;

26 / 35

SLIDE 27

Exclusive b → sℓ+ℓ− decays:

◮ Global fits to b → sℓ+ℓ− data: [Danny van Dyk, talk at CKM2018] ◮ Conclusion: while different in the treatment of local and non-local hadronic contri-

butions, all groups agree on a negative shift to C9 by −1.1...−1.76 ≃ −25...40%

• f the SM value, although other contributions are also possible.

27 / 35

SLIDE 28

Exclusive b → sℓ+ℓ− decays:

◮ New global fits: [Capdevila et al., 1704.05340; D. Straub, talk at CKM2018] ◮ New directions for model builders: [G. Isodro, talk at CKM2018]

28 / 35

SLIDE 29

Non-leptonic B decays:

◮ To leading power in the heavy-quark expansion, M1M2|Oi| ¯

B obeys the follow- ing factorization formula:

[Beneke, Buchalla, Neubert, Sachrajda, ’99-’04]

M1M2|Oi| ¯ B ≃ m2

B F BM1 +

(0) fM2

• du T I

i (u) φM2(u) + (M1 ↔ M2)

+ fB fM1 fM2

• dωdvdu T II

i

(ω, v, u) φB(ω) φM1(v) φM2(u) + O(1/mb)

O

i(µ)

+ O(1/M )

W

i(µ)

C µ ∼ m >

b

π + π- B

i=1...10

π + B π-

Ci(µ)

i,j=1...10

π- B

Oj

fact(µ)

T (µ)

ij I j fact(µ)

Q T (µ)

ij II

+ µ m b < + O(1/m )

b π+

◮ Systematic framework to all orders in αs, but limited accuracy by 1/mb corrs.

29 / 35

SLIDE 30

Non-leptonic B decays:

◮ Status of the hard kernels T I,II: [Bell/Beneke/Huber/Li, from ’09]

◮ Missing NNLO pieces: 2-loop tree with insertion of penguin operators Q3−6;

2-loop penguin with insertion of penguin operators Q3−6; work in progress!

30 / 35

SLIDE 31

Non-leptonic B decays:

◮ How to deal with power corrections of order O(1/mb); ◮ New insights from collider-physics applications like collinear anomaly/rapidity di-

vergence? [Becher/Neubert ’10; Becher/Bell ’11; Chiu/Jain/Neill/Rothstein ’12]

֒ → our next task: how to evaluate the power corrections?

31 / 35

SLIDE 32

Non-leptonic B decays:

◮ Tree-dominated decays: Brs [×10−6] [Beneke, Huber, Li ’09]

◮ Theory II: small λB and form-factor hypothesis are more favoured; ◮ Colour-allowed modes well described, but colour-suppressed modes less;

32 / 35

SLIDE 33

Non-leptonic B decays:

◮ Penguin-dominated decays: ACP [×10−2] [Bell, Beneke, Huber, Li ’15]

◮ “NLO” and “NNLO”: including only pert. calculable SD contribution; ◮ “NNLO+LD”: power-suppressed spectator and annihilation terms included back; ◮ For πK, NNLO change minor, since the total penguin ˆ

αc

4 = ac 4 + rπ χac 6 + βc 3;

◮ NNLO correction does not help resolving the observed πK CP asymmetry puzzle;

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SLIDE 34

Non-leptonic B decays:

◮ Brs and ratios: 10−3 (b → c¯

ud), 10−4 (b → c¯ us)

[Huber, Kr¨

ankl, Li ’16]

◮ For ¯

Bd decays, NNLO Brs higher than the data; for Λb decays, NNLO Brs smaller than the data; ֒ → non-negligible power corrections with natural size ∼ 10−15%?

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SLIDE 35

Conclusion and outlook

◮ High-luminosity frontier is very complementary to high-energy fron-

tier, especially for NP searches;

◮ Great progress achieved in both theo. and exp. sides for B physics,

and also a very promising future (LHCb and Belle II, · · · );

◮ CKM mechanism of flavor and CP violation well established. How-

ever, 20% NP effects in most FCNC processes often possible;

◮ Several deviations observed at 2 ∼ 4σ in b → cτ ¯

ν and b → sµµ decays, implications of LFUV? Lets stay tuned!

◮ QCDF at leading power and at NNLO in QCD established and almost

• complete. Any further breakthroughs welcome;

Thank You for Your Attention!

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