CKM angle g measurement

at LHCb

Susan Haines

University of Cambridge

on behalf of

the LHCb collaboration

LHCP 2018

Susan Haines 2

CKM angle g

▪ Least well measured Unitarity Triangle angle

▪ Can measure at tree level with 𝐵 → 𝐷𝑋 decays

▪ Exploit weak phase difference g between 𝑏 → 𝑢 and 𝑏 → 𝑐 transitions

▪ Theoretically clean but room for NP JHEP 01 (2014) 051 PRD 92 033002 (2015)

Susan Haines 3

▪ At LHCb, perform

▪ time-integrated measurements

𝐵− → 𝐷(∗)𝐾(∗)−, 𝐵0 → 𝐷𝐾∗0, 𝐵0 → 𝐷𝐾+𝜋−, 𝐵− → 𝐷𝐾−𝜋+𝜋−

▪ GLW analysis (𝐷 → 𝐶𝑃 eigenstate)

▪ ADS analysis (𝐷 → flavour specific)

▪ GGSZ analysis (𝐷 → multibody)

▪ Dalitz analysis (𝐵 → multibody)

▪ time-dependent measurements

𝐵𝑠0 → 𝐷𝑠

∓𝐾±, 𝐵0 → 𝐷∓𝜋±

▪ combination of LHCb g measurements

PLB 557 198 (2003)

PLB 253 483 (1991) PLB 265 172 (1991)

PRL 78 3257 (1997) PRD 63 036005 (2001)

PRD 68 054018 (2003) PRD 70 072003 (2004)

PRD 79 051301(R) (2009) PRD 80 092002 (2009)

PRD 37 3186 (1988) ZPC 54 653 (1992) NPB 671 459 (2003)

Susan Haines 4

The LHCb experiment

▪ Designed for study of particles containing 𝑏 or 𝑐

▪ High precision tracking and vertexing

▪ Momentum resolution 0.5 − 1.0 %

▪ Impact parameter resolution (15 + 29 / 𝑝𝑇) 𝜇m

▪ RICH detectors for hadron PID (𝐾 − 𝜋 separation)

JINST 3 S08005 (2008)

2 < 𝜂 < 5

▪ Determine g using 𝐷 decay to three-body self-conjugate 𝐾𝑆

0𝜋+𝜋− or 𝐾𝑆0𝐾+𝐾− final state

▪ One solution for g in [0, p]

▪ Requires knowledge of resonant structure of 𝐷 → 𝐾𝑆

0ℎ+ℎ− decay across phase space

▪ Observables: 𝑥± = 𝑟𝐵cos(𝛿𝐵 ± 𝛾), 𝑦± = 𝑟𝐵sin(𝛿𝐵 ± 𝛾)

PRELIMINARY

RUN 2PRELIMINARY

RUN 2

Susan Haines 5

GGSZ analysis of𝑩−→ 𝑫𝑲−, 𝑫 → 𝑲𝑺𝟎𝒉+𝒉−

𝐴𝐵+ ∝ ҧ𝐴𝑓 + 𝑟𝐵𝑒𝑖(𝛿𝐵+𝛾)𝐴𝑓

𝐴𝐵− ∝ 𝐴𝑓 + 𝑟𝐵𝑒)𝑖(𝛿𝐵−𝛾 ҧ𝐴𝑓

𝐵−𝐵+

LHCb-PAPER-2018-017

In preparation

▪ Model-independent method: bin 𝐷 decay phase

space according to 𝐷0 − ഥ𝐷0 strong phase

difference

▪ Yield in bin 𝑖

▪ (𝑐𝑖 , 𝑠𝑖) strong phase difference measurements from

CLEO-c

Susan Haines 6

LHCb-PAPER-2018-017

In preparation

PRD 82 112006 (2010)

𝑁±𝑖+ = ℎ𝐵+ 𝐹∓𝑖 + 𝑥+

2 + 𝑦+2 𝐹±𝑖 + 2 𝐹𝑖𝐹−𝑖 𝑥+𝑐±𝑖 − 𝑦+𝑠±𝑖

𝑁±𝑖− = ℎ𝐵− 𝐹±𝑖 + 𝑥−

2 + 𝑦−2 𝐹∓𝑖 + 2 𝐹𝑖𝐹−𝑖 𝑥−𝑐±𝑖 + 𝑦−𝑠±𝑖

2𝑁 bins (𝑖 ∈ [−𝑁,𝑁], 𝑖 ≠ 0)

𝑖 > 0 for 𝑚−2 > 𝑚+

2

▪ Results with Run 2 data (2 fb-1 at 𝑠 = 13 TeV):

Susan Haines 7

Statistical

uncertainties

only

LHCb-PAPER-2018-017

In preparation

PRELIMINARY

2 fb-1 at 𝑠 = 13 TeV

PRELIMINARY

𝑥− = (9.0 ± 1.7 ± 0.7 ± 0.4) × 10−2

𝑦− = (2.1 ± 2.2 ± 0.5 ± 1.1) × 10−2

𝑥+ = (−7.7 ± 1.9 ± 0.7 ± 0.4) × 10−2

𝑦+ = (−1.0 ± 1.9 ± 0.4 ± 0.9) × 10−2

First observation

of 𝐶𝑃 violation in

𝐵−→ 𝐷𝐾−,𝐷 → 𝐾𝑆

0ℎ+ℎ−

▪ Combine with Run 1 results (3 fb-1 at 𝑠 = 7,8TeV) to give constraint on g:

Susan Haines 8

GGSZ, PRELIMINARY

𝛾 = 80−9+10 °

LHCb-PAPER-2018-017

In preparation

GGSZ

PRELIMINARY

GGSZ

PRELIMINARY

JHEP 10 (2014) 097

▪ Phase difference of (2𝛽 + 𝛾) between direct 𝐵0

decay and decay after oscillation

▪ Measure decay-time-dependent 𝐶𝑃 asymmetries using decay rates as function of tagged 𝐵0/ ത𝐵0

decay time

▪ Fix 𝐶𝑓 = −𝐶 ҧ𝑓 = 1 in fit; constrain Δ𝑚 and Γ

Susan Haines 9

Time-dependent analysis of 𝑩𝟎 → 𝑫∓𝝅±arXiv:1805.03448

Γ𝐵0→𝑓(𝑡) ∝ 𝑒−Γ𝑡[1 + 𝐶𝑓 cos Δ𝑚𝑡 − 𝑆𝑓 sin Δ𝑚𝑡 ]

Γ𝐵0→ ҧ𝑓(𝑡) ∝ 𝑒−Γ𝑡[1 + 𝐶 ҧ𝑓 cos Δ𝑚𝑡 − 𝑆 ҧ𝑓 sin Δ𝑚𝑡 ]

HFLAVEPJ C 76 412 (2016)

Assume

𝑞/𝑝 = 1and ΔΓ = 0

𝐶𝑓 =1 − 𝑟𝐷𝜋

2

1 + 𝑟𝐷𝜋2 = −𝐶 ҧ𝑓 𝑆𝑓 = −

]2𝑟𝐷𝜋sin[𝛿 − 2𝛽 + 𝛾

1 + 𝑟𝐷𝜋2 𝑆 ҧ𝑓 =

]2𝑟𝐷𝜋sin[𝛿 + 2𝛽 + 𝛾

1 + 𝑟𝐷𝜋2

▪ Analysis with 3 fb-1 at 𝑠 = 7,8 TeV

Susan Haines 10

arXiv:1805.03448

𝑆𝑓 = 0.058 ± 0.020 ± 0.011

𝑆 ҧ𝑓 = 0.038 ± 0.020 ± 0.007

𝛾 ∈ [5,86]° ∪ [185,266]°

𝑁𝑠𝑖𝑔 = 479000 ± 700

▪ First measurements at

hadron collider

▪ Agree with, and more precise

than, previous measurementsPRD 73 111101(R) (2006) PRD 73 092003 (2006)

Susan Haines 11

Combination of LHCb measurements▪ Combine tree-level LHCb g measurements:

▪ Frequentist approach

▪ Auxiliary inputs from HFLAV, CLEO and LHCb

LHCb-CONF-2018-002

Susan Haines 12

▪ Most precise determination of g from a single

experiment

▪ World average: 𝛾 = 73.5−5.1+4.2 °

▪

LHCb-CONF-2018-002

PRELIMINARY

𝛾 = 74.0−5.8+5.0 °

HFLAV

Susan Haines 13

Future g decay modes:

𝑩(𝒔)𝟎 → ഥ𝑫(∗)𝟎𝝓 and 𝑩(𝒔)

𝟎 → ഥ𝑫𝟎𝑲+𝑲−

▪ Possible future measurements of

▪ g with 𝐵𝑠0 → 𝐷𝜙

▪ g (and 𝜙𝑠) with time-dependent Dalitz plot analysis of

𝐵𝑠0 → 𝐷𝐶𝑃𝐾

+𝐾−

▪ NEW branching fraction measurements and limits

with 3 fb-1 at 𝑠 = 7,8 TeV

PRD 85 114015 (2012)

LHCb-PAPER-2018-014

LHCb-PAPER-2018-015

In preparationNEW

Susan Haines 14

PRELIMINARY

PRELIMINARY

ℬ 𝐵𝑠0 → ഥ𝐷0𝜙 = (3.0 ± 0.3 ± 0.3 ± 0.2) × 10−5

ℬ 𝐵𝑠0 → ഥ𝐷∗0𝜙 = (3.8 ± 0.5 ± 0.3 ± 0.2) × 10−5

ℬ 𝐵0 → ഥ𝐷0𝜙 < 2.0 × 10−6 (@ 90% 𝐶. 𝐿. )

FIRST OBSERVATION

MOST PRECISE

BEST LIMIT

ℬ 𝐵0 → ഥ𝐷0𝐾+𝐾− = (6.1 ± 0.4 ± 0.3 ± 0.3) × 10−5

MOST PRECISE

ℬ 𝐵𝑠0 → ഥ𝐷0𝐾+𝐾− = (5.7 ± 0.5 ± 0.5 ± 0.5) × 10−5

FIRST OBSERVATION

LHCb-PAPER-2018-014

LHCb-PAPER-2018-015

In preparationNEW

PRELIMINARY

Susan Haines 15

▪ Combination of LHCb results gives most precise

determination of g from a single experiment

▪ Covered most recent results and updated

combination here

▪ Coming soon:

▪ studies of new decay modes

▪ further updates including Run 2 data set

Conclusions and prospects

PRELIMINARY

𝛾 = 74.0−5.8+5.0 °

Susan Haines 16

Backup:

GGSZ analysis of 𝑩−→ 𝑫𝑲−, 𝑫 → 𝑲𝑺𝟎𝒉+𝒉−

LHCb-PAPER-2018-017

In preparation

𝐵−𝐵+

PRELIMINARY PRELIMINARY

𝐾𝑆0 without

VELO (Si

vertex tracker)

daughter hits

𝐾𝑆0 with VELO

(Si vertex

tracker)

daughter hits

𝐵− → 𝐷ℎ−,𝐷 → 𝐾𝑆

0𝜋+𝜋−

PRELIMINARYPRELIMINARY

PRELIMINARY PRELIMINARY

Susan Haines 17

LHCb-PAPER-2018-017

In preparation

𝐵−𝐵+

PRELIMINARY PRELIMINARY

𝐾𝑆0 without

VELO (Si

vertex tracker)

daughter hits

𝐾𝑆0 with VELO

(Si vertex tracker)

daughter hits

𝐵− → 𝐷ℎ−,𝐷 → 𝐾𝑆

0𝐾+𝐾−

PRELIMINARY PRELIMINARY

PRELIMINARY PRELIMINARY

Susan Haines 18

Backup:

Time-dependent analysis of 𝑩𝟎 → 𝑫∓𝝅±

arXiv:1805.03448

Susan Haines 19

Backup:

Combination of LHCb measurements

LHCb-CONF-2018-002

Susan Haines 20

Backup:

𝑩(𝒔)𝟎 → ഥ𝑫(∗)𝟎𝝓 and 𝑩(𝒔)

𝟎 → ഥ𝑫𝟎𝑲+𝑲−

𝐵0 → ഥ𝐷0𝐾+𝐾−

PRELIMINARY

𝐵𝑠0 → ഥ𝐷0𝐾+𝐾−

PRELIMINARY

LHCb-PAPER-2018-014

LHCb-PAPER-2018-015

In preparationNEW