Isoscalar scattering and the /f 0 (500) resonance Ral Briceo - - PowerPoint PPT Presentation

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isoscalar scattering and the f 0 500 resonance
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Isoscalar scattering and the /f 0 (500) resonance Ral Briceo - - PowerPoint PPT Presentation

Apr 03, 2024 436 likes •788 views

Isoscalar scattering and the /f 0 (500) resonance Ral Briceo rbriceno@jlab.org [ with Jozef Dudek, Robert Edwards & David Wilson] HadSpec Collaboration Lattice 2016 Southampton, UK July, 2016 Motivation

slide-1
SLIDE 1

Isoscalar ππ scattering and the σ/f0(500) resonance

Raúl Briceño

rbriceno@jlab.org

[ with Jozef Dudek, Robert Edwards & David Wilson]

Lattice 2016 Southampton, UK July, 2016

HadSpec Collaboration

slide-2
SLIDE 2

Motivation

K

π π

¯ b

d

u

d d

¯ u

¯ d ¯ d

π π

u

d

¯ u

¯ d ¯ d

π π

u

d

¯ u

¯ d

d

d

d

u

u

n n

d d

u

d

u

d d d

n n

π π

f0(500)/σ f0(500)/σ

scattering/spectroscopy precision tests of SM long range nuclear forces

Sample of previous lattice efforts: Alford & Jaffe (2000) Prelovsek, et al. (2010) Fu (2013) Wakayama, et al. (2015) Howarth & Giedt, (2015)

  • Z. Bai et al. (RBC, UKQCD) (2015)
slide-3
SLIDE 3

The experimental situation

summary of various experiments

slide-4
SLIDE 4

Eσ = 449(22

16) MeV

Γσ = 550(24) MeV

“f0(500)/σ”

The experimental situation

Peláez (2015)

slide-5
SLIDE 5

bound state threshold

Im[s]

Infinite volume

s = E2

cm

first Riemann sheet

Re[s]

branch cut - where scattering takes place

Finite vs. infinite volume spectrum

slide-6
SLIDE 6

s = E2

cm

Im[s] Re[s]

second Riemann sheet

Infinite volume

narrow resonance broad resonance

Re[s]

Finite vs. infinite volume spectrum

sR = (ER − i

2ΓR)2

slide-7
SLIDE 7

Finite vs. infinite volume spectrum

finite volume eigenstates

finite volume

“only a discrete number of modes can exist in a finite volume”

no continuum of states: no cuts no sheet structure no resonances no asymptotic states: no scattering

slide-8
SLIDE 8

Lüscher formalism

spectrum satisfy:

scattering amplitude

an exact mapping

finite volume spectrum

det[F −1(EL, L) + M(EL)] = 0

L

EL = finite volume spectrum L = finite volume F = known function

M = scattering amplitude

slide-9
SLIDE 9

Lüscher formalism

Lüscher (1986, 1991) [elastic scalar bosons] Rummukainen & Gottlieb (1995) [moving elastic scalar bosons] Kim, Sachrajda, & Sharpe/Christ, Kim & Yamazaki (2005) [QFT derivation] Bernard, Lage, Meissner & Rusetsky (2008) [Nπ systems] RB, Davoudi, Luu & Savage (2013) [generic spinning systems] Feng, Li, & Liu (2004) [inelastic scalar bosons] Hansen & Sharpe / RB & Davoudi (2012) [moving inelastic scalar bosons] RB (2014) / RB & Hansen (2015) [moving inelastic spinning particles] spectrum satisfy: det[F −1(EL, L) + M(EL)] = 0

slide-10
SLIDE 10

Extracting the spectrum

Two-point correlation functions:

Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 2009)]

e.g. π[000]π[110]

mπ = 236 MeV

C2pt.

ab (t, P) ⌘ h0|Ob(t, P)O† a(0, P)|0i =

X

n

Zb,nZ†

a,ne−Ent

  • 0.004

0.004 0.008 0.012 0.016 4 8 12 16 20 24 28 32 36

  • 0.002

0.002 4 8 12 16 20 24

eE0tC(t, 0)

slide-11
SLIDE 11

Extracting the spectrum

Two-point correlation functions:

Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 2009)]

e.g. π[000]π[110]

mπ = 236 MeV

C2pt.

ab (t, P) ⌘ h0|Ob(t, P)O† a(0, P)|0i =

X

n

Zb,nZ†

a,ne−Ent

  • 0.002

0.002 4 8 12 16 20 24

(d) (b) (a) (c) (c) close up

slide-12
SLIDE 12

all

ηη KK

ππ

mm

¯ ψΓψ

KK|thr. ηη|thr.

…

Extracting the spectrum

Two-point correlation functions:

‘Diagonalize’ correlation function variationally Use a large basis of operators with the same quantum numbers

e.g.

Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 2009)]

C2pt.

ab (t, P) ⌘ h0|Ob(t, P)O† a(0, P)|0i =

X

n

Zb,nZ†

a,ne−Ent

atEcm

0.1

0.15 0.20 0.25

ηη

KK ππ

¯ ψΓψ

~ d = ~ PL 2⇡ = [110] mπ = 391 MeV L/as = 24

slide-13
SLIDE 13

all

ηη KK

ππ

mm

¯ ψΓψ

KK|thr. ηη|thr.

…

Extracting the spectrum

Two-point correlation functions:

‘Diagonalize’ correlation function variationally Use a large basis of operators with the same quantum numbers

e.g.

Evaluate all Wick contraction - [distillation - Peardon, et al. (Hadron Spectrum, 2009)]

C2pt.

ab (t, P) ⌘ h0|Ob(t, P)O† a(0, P)|0i =

X

n

Zb,nZ†

a,ne−Ent

atEcm

0.1

0.15 0.20 0.25

ηη

KK ππ

¯ ψΓψ

~ d = ~ PL 2⇡ = [110] mπ = 391 MeV L/as = 24

correct spectrum

slide-14
SLIDE 14

Finite volume spectra

mπ=236 MeV mπ=391 MeV

40

slide-15
SLIDE 15

Finite volume spectra

600 700 800 900 1000 1100 16 20 24 16 20 24 16 20 24 16 20 24 16 20 24 500 600 700 800 900 1000 24 32 40 24 32 40 24 32 40 24 32 40 24 32 40 mπ=391 MeV mπ=236 MeV

det[F −1(EL, L) + M(EL)] = 0

Spectrum satisfies: Use a various parametrizations One channel, ignoring partial wave mixing: cot δ0(Ecm) + cot φ(P, L) = 0 e.g. [unitarity]

M−1 = K−1 + I, Im(I) = −ρ K = g2 s0 − s + c

40

slide-16
SLIDE 16
  • 1
  • 0.5

0.5 1

  • 0.06
  • 0.03

0.03 0.06 0.09 0.12

Scattering amplitude vs mπ

HadSpec Collaboration

slide-17
SLIDE 17
  • 1
  • 0.5

0.5 1

  • 0.06
  • 0.03

0.03 0.06 0.09 0.12

Scattering amplitude vs mπ

[scattering lengths]-1

HadSpec Collaboration

slide-18
SLIDE 18
  • 1
  • 0.5

0.5 1

  • 0.06
  • 0.03

0.03 0.06 0.09 0.12

Scattering amplitude vs mπ

[bound state]

HadSpec Collaboration

slide-19
SLIDE 19

30 60 90 120 150 180 0.01 0.03 0.05 0.07 0.09 0.11 0.13

Scattering amplitude vs mπ

HadSpec Collaboration

slide-20
SLIDE 20

30 60 90 120 150 180 0.01 0.03 0.05 0.07 0.09 0.11 0.13

Scattering amplitude vs mπ

[no narrow resonance]

HadSpec Collaboration

slide-21
SLIDE 21
  • 300
  • 200
  • 100

300 500 700 900 200 400 600 800 150 200 250 300 350 400

The σ/f0(500) vs mπ

s0 = (Eσ − i

2Γσ)2,

g2

σππ = lim s→s0(s0 − s) t(s)

−Im√s0 = 1 2Γσ/MeV

slide-22
SLIDE 22
  • 300
  • 200
  • 100

300 500 700 900 200 400 600 800 150 200 250 300 350 400

The σ/f0(500) vs mπ

s0 = (Eσ − i

2Γσ)2,

g2

σππ = lim s→s0(s0 − s) t(s)

−Im√s0 = 1 2Γσ/MeV

slide-23
SLIDE 23

The σ/f0(500) vs mπ

s0 = (Eσ − i

2Γσ)2,

g2

σππ = lim s→s0(s0 − s) t(s)

200 400 600 800 150 200 250 300 350 400

  • 300
  • 200
  • 100

300 500 700 900

−Im√s0 = 1 2Γσ/MeV

slide-24
SLIDE 24
  • 300
  • 200
  • 100

300 500 700 900

The σ/f0(500) vs mπ

s0 = (Eσ − i

2Γσ)2,

g2

σππ = lim s→s0(s0 − s) t(s)

400 500 600 700 800 900 1000 1100 1200 Re sσ

1/2 (MeV)
  • 500
  • 400
  • 300
  • 200
  • 100

Im sσ

1/2 (MeV)

PDG estimate 1996-2010 poles in RPP 2010 poles in RPP 1996

Historical perspective

  • J. R. Peláez (2015)

Review of Particle Physics (RPP)

−Im√s0 = 1 2Γσ/MeV

slide-25
SLIDE 25

The σ/f0(500) vs mπ

s0 = (Eσ − i

2Γσ)2,

g2

σππ = lim s→s0(s0 − s) t(s)

  • 300
  • 200
  • 100

300 500 700 900

UχPT - Nebreda & Peláez (2015)

mπ~350 MeV

slide-26
SLIDE 26

The σ/f0(500) vs mπ

s0 = (Eσ − i

2Γσ)2,

g2

σππ = lim s→s0(s0 − s) t(s)

200 400 600 800 150 200 250 300 350 400

UχPT - Nebreda & Peláez (2015)

slide-27
SLIDE 27

ππ-KK / f0(980) dispersive analysis chiral extrapolation Elastic form factors of composite particles

Outlook

slide-28
SLIDE 28

ππ-KK / f0(980) dispersive analysis chiral extrapolation Elastic form factors of composite particles

Outlook

  • 300
  • 200
  • 100

300 500 700 900

slide-29
SLIDE 29

ππ-KK / f0(980) dispersive analysis chiral extrapolation, more quark masses(?) Elastic form factors of composite particles

Outlook

δ1/

E?

⇡⇡/MeV

Ecm/MeV

mπ = 140 MeV

Bolton, RB & Wilson Phys.Lett. B757 (2016) 50-56.

slide-30
SLIDE 30

ππ-KK / f0(980) dispersive analysis chiral extrapolation, more quark masses(?) Elastic form factors of composite particles

Outlook

2.0 2.1 2.3 2.2 2.4 2.5 2.0 2.1 2.3 2.2 2.4 2.5 2.0 50 100 4.0 6.0

RB, Hansen - Phys.Rev. D94 (2016) no.1, 013008. RB, Hansen - Phys.Rev. D92 (2015) no.7, 074509. RB, Hansen, Walker-Loud - Phys.Rev. D91 (2015) no.3, 034501. Bernard, D. Hoja, U. G. Meissner, and A. Rusetsky (2012)

formalism understood:

RB, Dudek, Edwards, Thomas, Shultz, Wilson - Phys.Rev. D93 (2016) 114508. RB, Dudek, Edwards, Thomas, Shultz, Wilson - Phys.Rev.Lett. 115 (2015) 242001

first implementation: πγ*-to-ππ/πγ*-to-ρ

slide-31
SLIDE 31

Take-home message

  • 1
  • 0.5

0.5 1

  • 0.06
  • 0.03

0.03 0.06 0.09 0.12

Dudek Edwards Wilson

30 60 90 120 150 180 0.01 0.03 0.05 0.07 0.09 0.11 0.13

  • 300
  • 200
  • 100

300 500 700 900 200 400 600 800 150 200 250 300 350 400

arXiv:1607.05900 [hep-ph]

HadSpec Collaboration

slide-32
SLIDE 32

HadSpec talks

Resonance in coupled channels- David Wilson, Monday 10:30 Searches for charmed tetraquarks- Gavin Cheung, Monday 13:55 Radiative transitions in charmonium - Cian O'Hara, Monday 17:25 Optimised operators and distillation - Antoni Woss, Tuesday 14:40 a0 resonance in πη, KK - Jozef Dudek, Tuesday 15:50 Charmed meson spectroscopy - David Tims, Thursday 14:20 Dπ, Dη and DsK scattering - Graham Moir, Thursday 15:00 DK scattering - Christopher Thomas, Thursday 15:20 Charmed-bottom mesons - Nilmani Mathur, Friday 15:40

slide-33
SLIDE 33

30 60 90 120 150 180 0.01 0.03 0.05 0.07 0.09 0.11 0.13

Scattering amplitude vs mπ

[Levinson’s theorem]

HadSpec Collaboration