Réunion annuelle du “Groupement de recherche” (GDR) - QCD 2016

Hadron Spectroscopy in Lattice QCD Gabriela Bailas LPC - Clermont Ferrand

Outline

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Outline •

Introduction

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Outline •

Introduction

•

Hadron Spectroscopy •

Masses

•

Decay Constants

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Outline •

Introduction

•

Hadron Spectroscopy

•

•

Masses

•

Decay Constants

Results

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Outline •

Introduction

•

Hadron Spectroscopy •

Masses

•

Decay Constants

•

Results

•

Conclusion and Perspectives

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Introduction

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Introduction Hadron spectroscopy: charmonium mesons

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Introduction Hadron spectroscopy: charmonium mesons

Lattice QCD - only way to use full QCD and do nonperturbative calculation

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Introduction Hadron spectroscopy: charmonium mesons

Lattice QCD - only way to use full QCD and do nonperturbative calculation

Ground state: pseudoscalar and vectorial cases

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Spectroscopy

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Spectroscopy Why? Study the masses and decay constants of mesons

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Spectroscopy Why? Study the masses and decay constants of mesons How? Using two-point correlation functions

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Spectroscopy Why? Study the masses and decay constants of mesons How? Using two-point correlation functions C(t) =

t!1 † h⌦|O1 (t)O2 (0)|⌦i !

ZO1 O2

ZO1 O2 [e

mt

]

1 † = h⌦|O1 (0)|M i hM |O2 (0)|⌦i 2m O1

O2 : interpolating fields

m : meson mass |M i : ground state meson mass |⌦i : vacuum state GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Masses

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Masses Pseudoscalar Mass

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Masses Pseudoscalar Mass †

C(t) = h⌦|O(t)O (0)|⌦i ZOO

mP

! ZOO [e

mP t

]

1 2 = | h⌦|O(0)|MP i | 2mP

By a fit we extract:

ZOO

t!1

O † : creation operator |MP i : ground state pseudoscalar mass mp : pseudoscalar mass

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Pseudoscalar Meson

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Pseudoscalar Meson Decay constant definition

< ⌦|A|MP >=fP mP

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Pseudoscalar Meson Decay constant definition So

< ⌦|A|MP >=fP mP

O1 = A O2 = P

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Pseudoscalar Meson Decay constant definition So

O1 = A O2 = P

< ⌦|A|MP >=fP mP †

C(t) =< ⌦|A(t)P (0)|⌦ >

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

t!1

!

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Decay Constants Pseudoscalar Meson Decay constant definition So

O1 = A O2 = P

< ⌦|A|MP >=fP mP †

C(t) =< ⌦|A(t)P (0)|⌦ > †

< ⌦|A(0)|MP > < MP |P |⌦ > e | {z }| {z } fP m P

p

2mP

p

t!1

!

mP t

ZP P

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Pseudoscalar Meson Decay constant definition So

O1 = A O2 = P

< ⌦|A|MP >=fP mP †

C(t) =< ⌦|A(t)P (0)|⌦ > 2mP ZAP †

< ⌦|A(0)|MP > < MP |P |⌦ > e | {z }| {z } fP m P

p

2mP

p

t!1

!

mP t

ZP P

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Pseudoscalar Meson Decay constant definition So

O1 = A O2 = P

< ⌦|A|MP >=fP mP †

C(t) =< ⌦|A(t)P (0)|⌦ > 2mP ZAP †

< ⌦|A(0)|MP > < MP |P |⌦ > e | {z }| {z } fP m P

Decay constant:

p

2mP

p

f P mP = Z A

t!1

!

mP t

ZP P

p

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

ZAP 2mP ZP P 6

Decay Constants

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Vector Meson

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Vector Meson Decay constant definition

< ⌦|V0 |MV >=fV mV

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Vector Meson Decay constant definition

< ⌦|V0 |MV >=fV mV

So O = V

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Vector Meson Decay constant definition So O = V

< ⌦|V0 |MV >=fV mV

C(t) =


t!1

!

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Decay Constants Vector Meson Decay constant definition So O = V

< ⌦|V0 |MV >=fV mV

C(t) =
| e | {z }

>

t!1

!

mV t

ZV

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Decay Constants Vector Meson Decay constant definition So O = V

< ⌦|V0 |MV >=fV mV

C(t) =
| e | {z }

>

t!1

!

mV t

ZV

Decay constant:

f V mV = Z V

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

p

ZV 7

Results (masses)

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Results (masses)

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Results (masses) Effective Mass Plateau

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Results (masses) Effective Mass Plateau

LL 0.9857 +/- 0.0004 LS 0.9850 +/- 0.0004 SL 0.9851 +/- 0.0004 SS 0.9858 +/- 0.0005

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Results (decay constants) Pseudoscalar

Vectorial

LL

0.1209 +/- 0.0005 GeV

0.1983 +/- 0.0004 GeV

LS

0.0003 +/- 0.0005 GeV

0.0582 +/- 0.0004 GeV

SL

0.0004 +/- 0.0005 GeV

0.0308 +/- 0.0004 GeV

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Conclusion and Perspectives

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Conclusion and Perspectives Lattice QCD provides the study of hadrons properties

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Conclusion and Perspectives Lattice QCD provides the study of hadrons properties We have calculated mass and decay constants of charmonium states, using pseudoscalar and vectorial mesons

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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Conclusion and Perspectives Lattice QCD provides the study of hadrons properties We have calculated mass and decay constants of charmonium states, using pseudoscalar and vectorial mesons Next step: Consider excited states

GDR QCD 2016 - Gabriela Bailas (LPC - Clermont Ferrand)

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