Flavour Physics

Tim GershonUniversity of Warwick

4 April 2014

Outline

● Lecture 4– B physics

● time-dependent CP violation● the B factories BaBar and Belle● measurements of UT angles β and α● the LHCb experiment (B physics at hadron machines) ● searches for new physics in

– Bs oscillations

– rare B decays

– Future flavour physics

Some theory papers

● Ellis, Gaillard, Nanopoulos & Rudaz, NPB 131, 285 (1977)

● Bander, Silverman & Soni, PRL 43, 242 (1979)– CP violation may be large in the B system

● Carter & Sanda, PRD 23, 1567 (1981)– time-dependence in e+e- → Υ(4S) → B0B0

● Bigi & Sanda, NPB 193, 85 (1981)

– B0 → J/ψ KS and other possible decay modes

Categories of CP violation● Consider decay of

neutral particle to a CP eigenstate

CP=qp

AA

∣qp∣≠1

∣AA

∣≠1

ℑ qp

AA ≠0

CP violation in mixingCP violation in mixing

CP violation in interference CP violation in interference between mixing and decaybetween mixing and decay

CP violation in decay (direct CPV)CP violation in decay (direct CPV)

Neutral B mixing parameters

● Recall: q/p = – (Δm – ½iΔΓ)/2(M12

– ½iΓ12

)

(Δm)2 – ¼(ΔΓ)2 = 4(|M12

|2 + ¼|Γ12

|2) ΔmΔΓ = 4Re(M12

Γ12

*)

● In the neutral B system Δm >> ΔΓ

Δm ~ 2|M12

| ΔΓ ~ 2Re(M12

Γ12

*)/|M12

| q/p ~ –|M12

|/M12

● |M12

| from mixing diagram

⇒ q/p ~ e-2iβ (in the usual phase convention)

Evolution with time

● Consider a B meson which is known to be B0 at time t=0

● At later time t:B0

(phys)(Δt) =

e-iMte-Γt/2 cos(ΔmΔt/2) B0 + i (q/p) e-iMte-Γt/2 sin(ΔmΔt/2) B0

● SimilarlyB0

(phys)(Δt) =

(p/q) i e-iMte-Γt/2 sin(ΔmΔt/2) B0 + e-iMte-Γt/2 cos(ΔmΔt/2) B0

amplitudes

7

Time-Dependent CP Violation in the B0–B0 System–

● For a B meson known to be 1) B0 or 2) B0 at time t=0, that at later time t decays to the CP eigenstate f

CP :

Bphys0 f CP t ∝ e− t 1−S sin mt −C cosmt

Bphys0 f CP t ∝ e− t 1S sin mt −C cosmt

–

S =2 ℑCP

1∣CP2 ∣

C =1−∣CP

2 ∣1∣CP

2 ∣CP =

qp

AA

For B0 → J/ψ KS, S = sin(2β), C=0

qp

NPB 193 (1981) 85

here assume ΔΓ negligible – will see full expressions later

The golden mode – B0 → J/ψ KS

● Dominated by b→ccs tree diagram– subleading b→scc penguin has (predominantly) the

same weak phase● |A| = |A| ⇒ no direct CP violation

● C = 0 & S = –ηCP

sin(2β)

● Reasonable branching fraction & experimentally clean signature

Problem● How can we measure decay time in e+e- →

Υ(4S) → B0B0?

● The answer: (P.Oddone)

asymmetric-energy B factory

● Key points– Υ(4S) → B0B0 produces coherent pairs– B mesons are moving in lab frame

Asymmetric B factory principle

KEKB energies

Asymmetric B Factories

PEPII at SLAC9.0 GeV e- on 3.1 GeV e+

KEKB at KEK8.0 GeV e- on 3.5 GeV e+

B factories – world record luminosities

~ 433/fb on Υ(4S) ~ 711/fb on Υ(4S)

µ / KL detection 14/15 lyr. RPC+Fe

Central Drift Chamber small cell +He/C2H6

CsI(Tl) 16X0

Aerogel Cherenkov cnt. n=1.015~1.030

Si vtx. det.- 3 lyr. DSSD- 4 lyr. since summer 2003

TOF counter

SC solenoid 1.5T

8 GeV e−

3.5 GeV e+

Belle Detector

DIRC (PID)144 quartz bars

11000 PMs

1.5 T solenoid

EMC6580 CsI(Tl) crystals

Drift Chamber40 stereo layers

Instrumented Flux Returniron / RPCs (muon / neutral hadrons)

2/6 replaced by LST in 2004Rest of replacement in 2006

Silicon Vertex Tracker5 layers, double sided strips

e+ (3.1 GeV)

e- (9 GeV)

BaBar Detector

PRL 108 (2012) 171802

BABAR

Results for the golden mode

PRD 79 (2009) 072009

BELLE

Compilation of results

Another taste of things to come (not yet world leading

for this measurement)

Constraint from β measurement

β = (21.5 ± 0.8)°

Measurement of α● Time-dependent CP violation in modes dominated by

b → uud tree diagrams probes α (or π–(β+γ))

– C = 0 & S = +ηCP

sin(2α)

● b → duu penguin transitions contribute to same final states ⇒ “penguin pollution”

– C ≠ 0 ⇔ direct CP violation can occur

– S ≠ +ηCP

sin(2α)

● Two approaches (optimal approach combines both)

– try to use modes with small penguin contribution– correct for penguin effect (isospin analysis)

B0 → π+π- -- Experimental Situation

Large penguin effectLarge direct CP violation

Isospin analysis● Use triangle construction to find

difference (θ) between “αeff

” and α● Requires measurement of rates and

asymmetries of B+→π+π0 & B0→π0π0

B0 → ρ+ρ– -- Experimental Situation

Small penguin effectSmall direct CP violation

Measurement of α

α = (85.4 +4.0–3.8

)°

THES

E SO

LUTIO

NS

RU

LED O

UT B

Y OB

SER

VATION

OF D

IREC

T CP VIO

LATION

IN B0

→π+

π-

Consistency of measurements with the KM mechanism

Different statistical approaches

... same answer

Where we are now ... and what's coming next

● Measurements of the CKM matrix elements and properties of the Unitarity Triangle are consistent with the Standard Model

– Nobel Prize for Kobayashi and Maskawa in 2008● Constraints for (beyond standard) model builders

– Minimal Flavour Violation?● Several hints (~3σ) for new physics

– Plenty of room still for discoveries– Some sectors relatively unexplored

● Need next generation of flavour physics experiments

26

Constraints on NP from mixing

● All measurements of Δm & ΔΓ consistent with SM

– K0, D0, Bd

0 and Bs

0

● This means |ANP

| < |ASM

| where

● Express NP as perturbation to the SM Lagrangian

– couplings ci and scale Λ > m

W

● For example, SM like (left-handed) operators

arXiv:1002.0900

27

New Physics Flavour Problem

● Limits on NP scale at least 100 TeV for generic couplings– model-independent argument, also for rare decays

● But we need NP at the TeV scale to solve the hierarchy problem (and to provide DM candidate, etc.)

● So we need NP flavour-changing couplings to be small● Why?

– minimal flavour violation?● perfect alignment of flavour violation in NP and SM

– some other approximate symmetry?– flavour structure tells us about physics at very high scales

● There are still important observables that are not yet well-tested

NPB 645 (2002) 155

Searches for New Physics● Massive, beyond SM, particles may contribute to B

decay processes in loop diagrams

– same true for kaon, charm & charged lepton physics– strong constraints in NP model building (flavour problem)

● Particularly interesting (not yet well tested) are b → s– B

s mixing

– b → sg (eg. time-dependence in B0 →φKS, etc.)

– b → sγ (eg. rates and moments, TDCPV in B0 → KSπ0γ)

– b → sl+l– (eg. FB asymmetry in B → K*l+l–)– b → sνν (also s → dνν)

29

Like-sign dimuon asymmetry

D0 experimentPhys.Rev. D89 (2014) 012002

3.6σ

● Semileptonic decays are flavour-specific● B mesons are produced in BB pairs● Like-sign leptons arise if one of BB pair mixes before decaying● If no CP violation in mixing N(++) = N(––)

● Inclusive measurement ↔ contributions from both Bd0 and B

s0

– relative contributions from production rates, mixing probabilities & SL decay rates

–

–

30

Flavour physics at hadron colliders

31

Geometry

● In high energy collisions, bb pairs produced predominantly in forward or backward directions

● LHCb is a forward spectrometer

The LHCb DetectorJINST 3 (2008) S08005

–

32

VELO

Material imaged used beam gas collisions

33

RICH

34

LHCb integrated luminosity

Instantaneous luminosity (2012) ~ 4 1032/cm2/sLHCb design luminosity: 2 1032/cm2/s

35

Note “luminosity levelling”

36

What does ∫Ldt = 1/fb mean?

● Measured cross-section, in LHCb acceptanceσ(pp→bbX) = (75.3 ± 5.4 ± 13.0) μb

PLB 694 (2010) 209● So, number of bb pairs produced in 1/fb (2011 sample)

1015 x 75.3 10–6 ~ 1011

● Compare to combined data sample of e+e– “B factories” BaBar and Belle of ~ 109 BB pairs

for any channel where the (trigger, reconstruction, stripping, offline) efficiency is not too small, LHCb has world's largest data sample

● p.s.: for charm, σ(pp→ccX) = (6.10 ± 0.93) mbLHCb-CONF-2010-013

–

–

–

–

37

The all important triggerChallenge is

● to efficiently select most interesting B decays

● while maintaining manageable data rates

Main backgrounds● “minimum bias” inelastic

pp scattering● other charm and beauty

decays

Handles● high p

T signals (muons)

● displaced vertices

JINST 8 (2013) P04022

38

The other Unitarity Triangles

● High statistics available at LHCb will allow sensitivity to smaller CP violating effects

– CP violating phase in Bs oscillations (O(λ4))

● Bs oscillations (Δm

s) measured 2006 (CDF)

– CP violating phase in D0 oscillations (O(λ5))● D0 oscillations (x

D = Δm

D/Γ

D & y

D = 2ΔΓ

D/Γ

D) measured 2007

(BaBar, Belle, later CDF)

● Observations of CP violation in both K0 and B0 systems won Nobel prizes!

39

Time-dependent CP Violation Formalism

● Generic (but shown for Bs) decays to CP eigenstates

40

Time-dependent CP Violation Formalism

● Generic (but shown for Bs) decays to CP eigenstates

ACPdir

2 A

2 ACP

mix

2=1

CP violating asymmetries CP conserving parameter

ACPdir

= CCP =1−∣CP∣

2

1∣CP∣2 A =

2 ℜCP

1∣CP∣2 ACP

mix= SCP =

2 ℑCP

1∣CP∣2

41

Time-dependent CP Violation Formalism

● Generic (but shown for Bs) decays to CP eigenstates

● Untagged analyses still sensitive to some interesting physics

42

Time-dependent CP Violation Formalism

● Generic (but shown for Bs) decays to CP eigenstates

● In some channels, expect no direct CP violation● and/or no CP violation in mixing

0

0

0

43

Time-dependent CP Violation Formalism

● Generic (but shown for Bs) decays to CP eigenstates

● In some channels, expect no direct CP violation

● Bd case: ΔΓ negligible

1 0

1 0

44

Time-dependent CP Violation Formalism

● Generic (but shown for Bs) decays to CP eigenstates

● In some channels, expect no direct CP violation

● Bd case: ΔΓ negligible

● D0 case: both x = Δm/Γ and y=ΔΓ/2Γ small

1

1

1

1

yΓt

yΓt

xΓt

xΓt

45

Φs = –2β

s

● Most attractive channelB

s

0→J/ψφ

● VV final statethree helicity amplitudes

→ mixture of CP-even and CP-odd

disentangled using angular & time-dependent distributions→ additional sensitivity

many correlated variables

→ complicated analysis

● LHCb also uses Bs→J/ψf

0 (f

0→π+π–)

– CP eigenstate; simpler analysis

– fewer events; requires input from J/ψφ analysis (Γs, ΔΓ

s)

46

Bs→J/ψφ formalism

± signs differ for B

s and B

s

–

Bs→J/ψφ (→μ+μ–K+K–) is golden channel to study B

s oscillations ...

... but not a pure CP eigenstate

47

Current Bs→J/ψφ world average

… significant improvement possible from data in hand at LHCb & ATLAS (&CMS)

48

B→K*μ+μ–

● b→sl+l– processes also governed by FCNCs– rates and asymmetries of many exclusive processes

sensitive to NP

● Queen among them is Bd→K*0μ+μ–

– superb laboratory for NP tests– experimentally clean signature– many kinematic variables … – … with clean theoretical predictions (at least at low q2)

49

Operator Product Expansion

Build an effective theory for b physics– take the weak part of the SM– integrate out the heavy fields (W,Z,t)– (like a modern version of Fermi theory for weak

interactions)

Wilson coefficients● encode information on the weak scale● are calculable and known in the SM (at least to leading order)● are affected by new physics

For K*μμ we care about C7 (also affects b→sγ), C

9 and C

10

50

Effective operators

Four-fermion operators (except Q

7γ & Q

8g) – dimension 6

51

Theory of B→K*μ+μ–

● Given for inclusive b→sμ+μ– for simplicity

– physics of exclusive modes ≈ same but equations are more complicated (involving form factors, etc.)

● Differential decay distribution

This term gives a forward-backward asymmetry

Forward-backward asymmetry in B→K*μ+μ–

Zero crossing-pointq2

0 = (4.9 ± 0.9) GeV2/c4

(consistent with SM)

JHEP 08 (2013) 131

Another angular observable in B→K*μ+μ–

Possible discrepancy with SM PRL 111 (2013) 191801

54

Bs→μ+μ–

Killer app. for new physics discovery

● Very small in the SM● Huge NP enhancement possible

(tan β = ratio of Higgs vevs)

● Clean experimental signature

● Was considered one of the hottest channels for early NP discovery at LHC (B

d→μ+μ– also interesting ...)

BR(B s→μ+μ

−)SM

= (3.3±0.3)×10− 9 BR(B s→μ+μ

−)MSSM

∝ tan6β/M A0

4

55

B(s)

0→μ+μ–

Searches over 30 years

56

B(s)

0→μ+μ– – analysis ingredients ● Produce a very large sample of B mesons● Trigger efficiently on dimuon signatures● Reject background

– excellent vertex resolution (identify displaced vertex)– excellent mass resolution (identify B peak)

● also essential to resolve B0 from Bs0 decays

– powerful muon identification (reject background from B decays with misidentified pions)

– typical to combine various discriminating variables into a multivariate classifier● e.g. Boosted Decision Trees algorithm

57

B(s)

0→μ+μ–

latest results from CMS & LHCbLHCb PRL 111 (2013) 101805CMS PRL 111 (2013) 101804

Events weighted by S/(S+B) Only events with BDT > 0.7

4.0σ4.3σ

58

B(s)

0→μ+μ– – combined results

B(Bs0→μ+μ−) = (2.9±0.7) × 10 9−

The Future of Flavour Physics

● charged lepton sector– proposals for improved measurements of many

processes (often using new facilities built for other purposes)● kaon system

– search for K → πνν [the holy grail] continues● charm system

– BESIII @ BEPC has taken over from CLEO-c– charm also studied at LHCb and B factories

● B system– Belle2 will be online 2016 / LHCb upgrade 2019

Peter Križan, Ljubljana

e- 2.6 A

e+ 3.6 A

To obtain x40 higher luminosity

Colliding bunches

Damping ring

Low emittance gun

Positron source

New beam pipe& bellows

Belle II

New IR

TiN-coated beam pipe with antechambers

Redesign the lattices of HER & LER to squeeze the emittance

Add / modify RF systems for higher beam current

New positron target / capture section

New superconducting /permanent final focusing quads near the IP

Low emittance electrons to inject

Low emittance positrons to inject

Replace short dipoles with longer ones (LER)

KEKB to SuperKEKB

Peter Križan, Ljubljana

Belle II Detector

electrons (7GeV)

positrons (4GeV)

KL and muon detector:Resistive Plate Counter (barrel outer layers)Scintillator + WLSF + MPPC (end-caps , inner 2 barrel layers)

Particle Identification Time-of-Propagation counter (barrel)Prox. focusing Aerogel RICH (fwd)

Central Drift ChamberHe(50%):C2H6(50%), small cells, long lever arm, fast electronics

EM Calorimeter:CsI(Tl), waveform sampling (barrel)Pure CsI + waveform sampling (end-caps)

Vertex Detector2 layers DEPFET + 4 layers DSSD

Beryllium beam pipe2cm diameter

62

LHC upgrade and the all important trigger

Already running here

higher luminosity → need to cut harder at L0 to keep rate at 1 MHz

→ lower efficiency

●readout detector at 40 MHz●implement trigger fully in software → efficiency gains●run at L

inst up to 2 1033/cm2/s

Lim

itatio

n is

her

e

63

LHCb detector upgrade

Technical decisions all made! TDRs getting approved

Summary

● CKM mechanism accurately describes quark mixing and CP violation within the Standard Model

● Flavour physics is, and will remain, an essential tool to search for and diagnose new physics

● Not covered– Grand Unification– Baryon asymmetry of the Universe

References and background reading

● Heavy Flavour Averaging Group (HFAG)– http://www.slac.stanford.edu/xorg/hfag/

● CKMfitter– http://ckmfitter.in2p3.fr/

● UTFit– http://www.utfit.org/

● Documentation available from above web sites

References and background reading

● Reviews in the Particle Data Group (PDG)'s Review of Particle Physics– Quark Model [C.Amsler, T.DeGrand & B.Krusche]

– Rare Kaon Decays [L.Littenberg & G.Valencia]

– CP Violation in Meson Decays [D.Kirkby & Y.Nir]

– CKM quark mixing matrix [A.Ceccucci, Z.Ligeti & Y.Sakai]

– Determination of Vcb and V

ub [R.Kowalewski & T.Mannel]

– Vud

, Vus

, the Cabibbo Angle and CKM Unitarity [E.Blucher

& W.J.Marciano]

References and background reading

● Most introductory particle physics books contain some background on flavour physics– eg. Perkins, Martin & Shaw

● Feynman lectures has an interesting chapter on lifetimes in the neutral kaon system

● More detailed books on quark flavour physics– CP violation, I.I.Bigi and A.I.Sanda (CUP)– CP violation, G.C.Branco, L.Lavoura & J.P.Silva (OUP)