·The State of Rare B Decay Anomalies
Wolfgang Altmannshofer
waltmann@ucsc.edu

Beyond the BSM
The 4th Kavli IPMU-Durham IPPP-KEK-KIAS workshop
Ikaho, Japan, October 1-4, 2018
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 2018

1 / 30

The State of Flavor Anomalies 2014

adapted from
Zoltan Ligeti
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 20182 / 30

The State of Flavor Anomalies 2016

adapted fromZoltan Ligeti
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay AnomaliesOct 1, 20183 / 30

The State of Flavor Anomalies 2018

adapted from
Zoltan Ligeti
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 20184 / 30

The State of Flavor Anomalies 2018

adapted from
Zoltan Ligeti
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 20184 / 30New Physics in Rare B Decays
sbts

G

Wolfgang Altmannshofer (UCSC)µ−=γµWsbbµ++µ−

The State of Rare B Decay Anomalies+NPµ+µ−

Oct 1, 2018

5 / 30New Physics in Rare B Decayssbts

Gµ−=γµW++NPµ−Anomalies in rare B decays would establish
a scale of new physics
Wolfgang Altmannshofer (UCSC)

sbbµ+

The State of Rare B Decay AnomaliesΛNP ∼ pµ+µ−4πv∼ O(10TeV)|Vtb Vts∗ |Oct 1, 2018

5 / 30LHC is a “b-factory”

more than ∼ 1012 b quarks produced in the LHCb detector so far⇒ unique sensitivity to many rare b decays
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 2018

6 / 30Many Accessible b → s Decay Modes

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 20187 / 30Branching Ratios I

several b → sµµ branching ratios seem to besystematically smaller compared to SM predictions

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 20188 / 30Branching Ratios II

several b → sµµ branching ratios seem to besystematically smaller compared to SM predictions

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 2018

9 / 30Branching Ratios III

several b → sµµ branching ratios seem to besystematically smaller compared to SM predictions

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201810 / 30

Angular Distributions I
AFB (B → K ∗ µµ) agrees reasonably well with SM predictions

ABSZ = WA, Straub 1411.3161 + Bharucha, Straub, Zwicky 1503.05534

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201811 / 30

Angular Distributions II
P50 (B → K ∗ µµ) is off by ∼ 2.5σ in a couple of bins

ASZB = WA, Straub 1411.3161 + Bharucha, Straub, Zwicky 1503.05534
DHMV = Descotes-Genon, Hofer, Matias, Virto 1510.04239

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201812 / 30

Lepton Flavor Universality Tests I

RK =BR(B → K µµ)22= 0.745+0.090−0.074 ± 0.036 for 1 < q /GeV < 6BR(B → Kee)

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201813 / 30

Lepton Flavor Universality Tests IIBR(B → K ∗ µµ)
RK ∗ ==BR(B → K ∗ ee)(Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

220.66+0.11−0.07 ± 0.03 for 0.045 < q /GeV < 1.1
2
20.69+0.11−0.07 ± 0.05 for 1.1 < q /GeV < 6

Oct 1, 201814 / 30

What Could It Be?
branchingratiosWolfgang Altmannshofer (UCSC)

angularobservables

The State of Rare B Decay Anomalies

LFU
ratiosOct 1, 201815 / 30

What Could It Be?

statisticalfluctuations?

Wolfgang Altmannshofer (UCSC)

branchingratiosangularobservables

LFU
ratios√√√The State of Rare B Decay Anomalies

Oct 1, 201815 / 30

What Could It Be?

statisticalfluctuations?
parametric
uncertainties?

Wolfgang Altmannshofer (UCSC)

branchingratiosangularobservables

LFU
ratios

√

√

√

××

√

The State of Rare B Decay Anomalies

Oct 1, 201815 / 30

What Could It Be?

statisticalfluctuations?
parametric
uncertainties?
underestimatedhadronic effects?

Wolfgang Altmannshofer (UCSC)

branchingratiosangularobservables

LFU
ratios

√

√

√

×
√

×

√√

The State of Rare B Decay Anomalies

×

Oct 1, 201815 / 30

What Could It Be?

statisticalfluctuations?
parametricuncertainties?
underestimatedhadronic effects?

branchingratios

angularobservables

LFUratios√√√×√×√√√√×√

New Physics?

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201815 / 30

Standard Model Predictions for RK and RK ∗RK (∗) = 1

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201816 / 30

Standard Model Predictions for RK and RK ∗RK (∗) = 1 + Omµ2
q2!  2 ΛQCDαemme2
× 1+O+ O (αs ) + O
logmbπmµ2

phase space(tiny effect)

Wolfgang Altmannshofer (UCSC)

hadronic corrections(tiny effect)

The State of Rare B Decay Anomalies

QED corrections(soft and collinear
photon emission)Oct 1, 201816 / 30

Standard Model Predictions for RK and RK ∗RK (∗) = 1 + O

mµ2
q2! 
 2 
ΛQCD
αem
me
2
× 1+O+ O (αs ) + O
logmb
π
mµ2

phase space(tiny effect)

QED corrections(soft and collinear
photon emission)

hadronic corrections(tiny effect)

Bordone, Isidori, Pattori 1605.07633[1,6]RK= 1.00 ± 0.01 ,[1.1,6]RK ∗= 1.00 ± 0.01 ,[0.045,1.1]

RK ∗= 0.91 ± 0.03

I QED corrections seem well modeled by Monte Carlo (Photos)
I additional corrections at low q 2 from B → K ∗ η(→ eeγ)
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201816 / 30

Model Independent New Physics Analysis
e2 X 4GF
b→sHeff
Ci Oi + Ci0 Oi0= − √ Vtb Vts∗
216π2imagnetic dipole operators

semileptonic operators

bR(L)

bL(R)

scalar operators
bR(L)

ℓL(R)

(′)

(′)

(′)

CS,P

C9,10C7sL(R)

sL(R)

(0)

C7 (s̄σµν PR(L) b)F µν,ℓR(L)

sL(R)

ℓL(R)

(0)

C9 (s̄γν PL(R) b)(µ̄γ ν µ),ℓL(R)(0)

CS (s̄PR(L) b)(µ̄PL(R) µ)(0)

C10 (s̄γν PL(R) b)(µ̄γ ν γ5 µ)neglecting tensor operators and additional scalar operators (secretly dimension 8)

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201817 / 30

Complementary Sensitivity

C7 , C70

C9 , C900C10 , C10CS , CS0

B → (Xs , K ∗ )γF

Bs → φγF

B → (Xs , K , K ∗ ) µ+ µ−

FFF?

Bs → φ µ+ µ−

FFF?

Λb → Λ µ+ µ−

FFF?

FF

Bs → µ+ µ−

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201818 / 30

Global Fit(Without LFU Data)
Strong preference for new
physics in form ofC9NP (s̄γµ PL b)(µ̄γ ` `)ReC9NP ∼ −25%C9SM

WA, Niehoff, Stangl, Straub 1703.09189(+ many others ...)

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201819 / 30

Global Fit(Without LFU Data)
Strong preference for newphysics in form ofC9NP (s̄γµ PL b)(µ̄γ ` `)ReC9NP ∼ −25%C9SM¯ µ PL `)CLNP (s̄γµ PL b)(`γ
ReCLNP ∼ −15%C9SM
WA, Niehoff, Stangl, Straub 1703.09189(+ many others ...)

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

works almost equally well

Oct 1, 201819 / 30

Fits of LFU Data
the LFU observables arefully compatible with theother anomalies
Best description of allanomalies by:
new physics in final stateswith muons
C9µ (s̄γµ PL b)(µ̄γ µ µ)

WA, Stangl, Straub 1704.05435(+ many others ...)

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies(RK (∗) by themselves could
also be explained byµe
C10, C9e , or C10)
Oct 1, 201820 / 30

Implications for the New Physics Scale4π(s̄γν PL b)(µ̄γ ν µ)
Λ2NP

ΛNP ' 120 TeV × (C9NP )−1/21(s̄γν PL b)(µ̄γ ν µ)
Λ2NP

ΛNP ' 35 TeV × (C9NP )−1/2

1MFV tree
Λ2NP1Vtb Vts∗ (s̄γν PL b)(µ̄γ ν µ)
Λ2NP

ΛNP ' 7 TeV × (C9NP )−1/21Λ2NP1generic loop
Λ2NP

11(s̄γν PL b)(µ̄γ ν µ)
Λ2NP 16π 2

ΛNP ' 3 TeV × (C9NP )−1/2

1
Λ2NP

1
MFV loop
Λ2NP

1
1Vtb Vts∗ (s̄γν PL b)(µ̄γ ν µ)
Λ2NP 16π 2

ΛNP ' 0.6 TeV × (C9NP )−1/2

1unitarity boundΛ2NP
1
generic tree
Λ2NP

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 2018

1Λ1
Λ2N

1
Λ2N21 / 30

My Favorite ModelZ 0 based on gauging Lµ − Lτwith effective flavor violating couplings to quarks
WA, Gori, Pospelov, Yavin 1403.1269; WA, Yavin 1508.07009

bL∗ hφi2g ′YQb YQs
22mQµ+hφiZ′
Q

sL

hφig′

µ−

Q: heavy vectorlike fermions with mass ∼ 1 − 10 TeV
φ: scalar that breaks Lµ − Lτ

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201822 / 30

My Favorite ModelZ 0 based on gauging Lµ − Lτwith effective flavor violating couplings to quarks
WA, Gori, Pospelov, Yavin 1403.1269; WA, Yavin 1508.07009

bL∗ hφi2g ′YQb YQs
22mQµ+hφiZ′
QsLhφig′

predicted Lepton
Universality Violation!

µ−Q: heavy vectorlike fermions with mass ∼ 1 − 10 TeV
φ: scalar that breaks Lµ − Lτ

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201822 / 30

Viable Z 0 Parameter Space
C9NP = -1.1

Most important
constraints fromΝ

tridentsZ®2Μ Z'Bs − B̄s oscillation
frequencyg'Bs mixing1

neutrino tridents
0.1

νµ N → νµ Nµµ
direct searches
0.01
10mZ ' HGeVL
102

Wolfgang Altmannshofer (UCSC)

CMS 1808.03684
103

The State of Rare B Decay Anomalies

Z → 2µZ 0 → 4µOct 1, 201823 / 30

The low q 2 Bin in RK ∗WA, Stangl, Straub 1704.05435

B → K ∗ `+ `− decays at low q 2 are dominated by the(lepton flavor universal) photon pole B → K ∗ γ→ Effect of (heavy) new physics in RK ∗ gets diluted at low q 2 .
This behavior is not seen in the data.
Hint for new light degrees of freedom?
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201824 / 30

A Light Resonance at the Di-Muon Threshold?
Example: Dark photon∗ with mA0 ∼ 2mµ

B → K ∗ A0
A0 → e+ e−(∗ a dark photon that forsome reason has alarge flavor violatingb → s coupling)

WA, Baker, Gori, Harnik, Pospelov, Stamou, Thamm 1711.07494
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201825 / 30

Smoking Gun Signature
Resonance in the di-electron spectrum in B → K ∗ e+ e−right around q 2 ∼ 4mµ2

WA, Baker, Gori, Harnik, Pospelov, Stamou, Thamm 1711.07494
Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201826 / 30

·b

Future Prospects

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201827 / 30

Cross Check of Electron Efficiencies

LFU

1.4OKL

1.3

E

With run 2 data several
10,000 φ → `` decays fromD ± → π ± φ, D 0 → π + π − φ,
Ds± → π ± φ, ...

GHΦ®eeL HkeVL

LHCb should accumulate
enough statistics to measure
LFU in φ → `` decays(q 2 ∼ 1 GeV2 ).

±5%

1.5

Nov

1.2

osibirs

kWA, Baker, Gori, Harnik, Pospelov,Stamou, Thamm 1711.07494

1.1
1.0

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay AnomaliesGHΦ®ΜΜL HkeVL
1.2

1.4

1.6

Oct 1, 201828 / 30

RK and RK ∗I LHCb and Belle II canpush uncertainties down
to few percent
I (also ATLAS and CMS
might be able to saysomething)
I with sufficient statistics,
LFU of angular distrib.
can be tested

I LHCb can cross check in many other modes:
Rφ ,Wolfgang Altmannshofer (UCSC)

RΛ ,RΛ∗ ,RK ππ ,The State of Rare B Decay Anomalies...
Oct 1, 201829 / 30

Summary

I Over the last few years, several anomalies
appeared in rare B decay data.
I The LFU ratios RK (∗) are theoretically clean
probes of new sources of flavor violation.
I With more data from LHCb and Belle II(+ATLAS and CMS) it should be possible tounderstand if current discrepancies are signsof new physics.

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 201830 / 30

·Back Up

Wolfgang Altmannshofer (UCSC)The State of Rare B Decay Anomalies

Oct 1, 2018/ back-up

The B → K ∗ µ+ µ− Angular Decay Distribution

1d(Γ + Γ̄)
dq 2=d 4 (Γ + Γ̄)=~dq 2 d Ω3(1 − FL ) sin2 θK ∗ + FL cos2 θK ∗4
1+ (1 − FL ) sin2 θK ∗ cos 2θ` − FL cos2 θK ∗ cos 2θ`4+ S3 sin2 θK ∗ sin2 θ` cos 2φ + S4 sin 2θK ∗ sin 2θ` cos φ+ S5 sin 2θK ∗ sin θ` cos φ
4AFB sin2 θK ∗ cos θ` + S7 sin 2θK ∗ sin θ` sin φ3+ S8 sin 2θK ∗ sin 2θ` sin φ + S9 sin2 θK ∗ sin2 θ` sin 2φ+P50 = p
Wolfgang Altmannshofer (UCSC)

S5FL (1 − FL )The State of Rare B Decay Anomalies

Oct 1, 2018

1 / back-up