bottom and charm hadron spectroscopy from lattice QCD - Parallel... · bottom and charm hadron spectroscopy from lattice QCD m uˇm d

bottom and charm hadronspectroscopy from lattice QCD

mu ≈ md < ms ∼ ΛQCD < mc <1

a< mb

[email protected]

bottom baryons in context

Y

B

I

ΞΞb

−

Ξb−

Σbo

Ξob

bo

+Σ

oΞ

p

Λ

−Ξ

−Σ

n

Σο

Ω

ΣΛ

Σ

Ξ

Ω

Ξ

b−

b−

bo

b+

bbo

bb−

bb−

bb

Σ

Ξ

Σ’

bΩ

Ξ

bbb

b

bb

Σ−

b

Σ

−

’b

o*

+*

o*−*

−*

−*

−*

−*

Ξ

o*

++∆

−∆

Ω−

Σ+

Ξo

o

+∆

o∆

Ξb

Σ b−*

bb

Ω

Ξ

Ω

spin 1/2 spin 3/2

Mass differences between these multiplets, eg. m(Σ∗)−m(Σ), vanish as mb →∞.

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c

2 ] Meinel,Detmold,Lin,Wingate LAT2009

( Preliminary. Systematic errors unavailable. )

Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV

/c2 ] Lewis,Woloshyn PRD,2009

Λb Ξb Σb Ξ' b Ωb Σ*b Ξ*

b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]

experimentLewis,Woloshyn PRD,2009Burch,Hagan,Lang,Limmer,Schafer PRD,2009Detmold,Lin,Wingate NPB,2009Lin,Cohen,Mathur,Orginos PRD,2009

CDF

D0

ALSO:Na (and Gottlieb) PhD thesis, 2008contains valuable data for mass differencesof b and bb baryons.They see a curious systematic dependence:O5 for Λb,Ξb versus Oµ for Σb,Ξ

′b,Ωb.

MDLW also have preliminary results for bband b baryons (see LAT2009 proceedings).

4. Results and discussion 91

(absolute masses) in Sec. 1.3.2, and here in the figure we show mass differences obtained by simply

subtracting the original data. We also show the four independent mass differences in Fig. 4.7.

Figure 4.6: The mass differences of Jp = 12

+singly bottom baryons. In the legend, “full” indicates

the full QCD data point fit result, and “quad” indicates the simultaneous quadratic fit result.

In general, the error bars are compatible with that of the singly charmed baryons, except on some

occasions of the medium-coarse lattice with the full QCD data point fit.

The pattern of the result in Fig. 4.6 is similar with that of the singly charmed baryons. The

mass differences of !b ! "b, !!b ! #b, $b ! #b, and $b ! !!

b, which consist of the same operator,

agree with the experimental data and the Lewis and Woloshyn’s result. There are the constant shift

about 60 " 100 MeV in the other mass differences of baryons that consist of the different operator

combinations. For the fine lattice especially we can observe the pattern more clearly.

Lastly, we show the doubly charmed and bottom baryons in Fig. 4.8. We display our fine and

coarse lattice results with ! = 2.1 and 2.5 lattice results of Lewis et al. [3] for the doubly charmed

baryons, and Lewis and Woloshyn [5] for the doubly bottom baryons. We note that Lewis and

Woloshyn’s paper [5] contains a dynamical sea quark flavor simulation result. We set the scale of

This is figure 4.6 of Heechang Na’s thesis (2008).

Fine lattice results produce systematically large splittings of (Λb,Ξb) versus (Σb,Ξ′b,Ωb)

relative to other lattice results and experiment.

The thesis suggests a possible cause: “we cannot separate Jp = 12

+ and 32

+ states usingthe spin projection operators” for Oµ. See the thesis for a thorough discussion.

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0

ALSO:Na (and Gottlieb) PhD thesis, 2008contains valuable data for mass differencesof b and bb baryons.

AUTHORS : GAUGE ACTIONLW : IwasakiNG : one-loop Symanzik

BHLLS : one-loop Lüscher-WeiszDLW : Iwasaki

LCMO : SymanzikMDLW : Iwasaki

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : u,d,s ACTIONLW : nonpert-tuned cloverNG : improved staggered

BHLLS : chirally improvedDLW : domain wall

LCMO : sea = impr. staggered: valence = domain wall

MDLW : domain wall

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : b ACTIONLW : NRQCD incl O(1/M 3)NG : Fermilab

BHLLS : staticDLW : static

LCMO : staticMDLW : NRQCD

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : LATTICE SPACINGLW : 0.104 fmNG : 0.15, 0.12, 0.09 fm

BHLLS : 0.11, 0.16 fmDLW : 0.114 fm

LCMO : 0.124 fmMDLW : 0.11 fm

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : LATTICE VOLUMELW : (2.1 fm)3

NG : (2.4 fm)3

BHLLS : (1.35 fm)3, (2.5 fm)3

DLW : (2.7 fm)3

LCMO : (2.5 fm)3

MDLW : (2.7 fm)3

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : PION MASSLW : 4; minimum∼600 MeVNG : 2 or 3; min∼290 MeV

BHLLS : 461 MeV and 525 MeVDLW : 3 sea + 6 valence;

: minimum∼275 MeVLCMO : 4; minimum∼290 MeVMDLW : 331 MeV

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : s MASSLW : 2; interpolate to physicalNG : ∼physical

BHLLS : s quark is absentDLW : O(10%) > physical

LCMO : ∼physicalMDLW : O(10%) > physical

Ω*bbb

14.3

14.4

14.5m

ass

[ G

eV/c



Ξbb Ωbb Ξ*bb Ω*

bb

10.1

10.2

10.3

mas

s [

GeV



b Ω*b

5.4

5.6

5.8

6

6.2

mas

s [

GeV

/c2 ]


CDF

D0


AUTHORS : b MASSLW : 3; interpolate to physicalNG : 1; ∼physical

BHLLS : ∞DLW : ∞

LCMO : ∞MDLW : 1; physical

charmed baryons in context

I

Y

CΣ Λ

−

pn

Σο

−Ξ

Ξo

Ωco

Ξc+

Σc++Σc

o

Ωcc+

Ξcc++

Ξcc+

Λ+c

Σ+

Ξco

cΞo Ξc

+

Σc+

Ω

Σ

cc

Σ

o

o*

Σ

++*

c

−

+*

o

++*

c

ΞΞ

+∆

o∆

Ω

+

c++∆

Σ

Ξ

−∆

−

c

Ωccc

−

c’

Σ

++*

Ξc

’

Ξ

+*

+*

o*

cc

o*

Ξ

Ω

cc

Σ

+

spin 1/2 spin 3/2

á

á á

áá

á áá

á á

áá

á

á

á á

áá

á áá

á á

áá

á

ç

ç

ç

ç ç

ç

ç

ç

ç

ç

ç ç

ç

ç

ç

ç

õ õ

õ

õ

õ

õ õ

õ

õ

õ

ó

ó ó

ó

ó

ó

áá

áá

çç

çç

õõ

óó

Liu et al. 1Liu et al. 1Liu et al. 2Liu et al. 2Na et al.Ha~0.12 fmLNa et al.Ha~0.12 fmLFlynn et al.Flynn et al.

Mathur et al.Mathur et al.Chiu et al.Chiu et al.

Lc Xc Sc Xc' Wc Xcc Wcc

2000

2500

3000

3500

4000

MeV

This is figure 14 of Liu,Lin,Orginos,Walker-Loud arxiv:0909.3294.

LLOW use Symanzik gauge, staggered sea, domain wall valence, Fermilab charm,a = 0.125 fm, volume = (2.4 fm)3, mπ ≥ 290 MeV.

NG study many mass differences, including Ξ∗cc and Ω∗cc.

Flynn+, Mathur+, and Chiu+ are quenched results, including spin 3/2.

(direct)(from splittings)

bottom mesons in context

I

Y

B

_

B

Ko

π+πο

ηc

η

’η

−π

K+

*

−+

ο

ρρ

ρ ω

φ

KKo +

B−

*

*_

Bs

B+

o

B+

Bo

B+

_

s

−*K o_

K*

s

J/ψ

**

Bo

oK

B

B*o

B*−

K

_

−

_

s*B

pseudoscalars vectors

As mb →∞, heavy quark symmetry⇒ m(B−) = m(B∗−), m(B0) = m(B∗0), m(Bs) = m(B∗s ).

These doublets are named 1S. Excited doublets are named 1P−, 1P+, 1D−,1D+,. . . 2S,. . . .

Status of the static-strange (∼ Bs) spectrum for Nf = 2 in 2007

0 0.03 0.06 0.09 0.12 0.15 0.18Lattice spacing a

400

600

800

1000∆E

2S-1S1P

--1S

1P+-1S

D--1S

D+-1S

MeV

ETM

UKQCD

BGR

TrinLat

This is figure 21 of Koponen Phys.Rev.D78:074509,2008.

Warning: Do not attempt continuum extrapolations with different actions.

spectrum of static-light mesons with Nf = 2

S P- P+ D± D+ F± S P- P+ D± D+ F±static with u,d static with s

500

1000

1500m

ass r

elat

ive

to 1

S [

MeV

/c2 ]

Burch,Hagan,Lang,Limmer,Schafer PRD 2009Jansen,Michael,Shindler,Wagner JHEP 2008Michael,Shindler,Wagner arxiv:1004.4235

JMSW use tree-level Symanzik gauge, two twisted mass light quarks, static “b”,a = 0.0855 fm, volume = (2.05 fm)3, mπ ≥ 300 MeV.

MSW is similar but a = 0.051, 0.064, 0.080 fm and a partially-quenched s quark.

(Black ovals are onlyto guide the eye ingrouping relevant data.)

spectrum of bottom mesons

B B* B0 B1 B' 1 B2 Bs B*s Bs0 Bs1 B' s1Bs2 Bc B*c Bc05200

5400

5600

5800

6000

6200

6400

6600

6800m

ass [

MeV

/c2 ]

experimentKoponen PRD 2008Lewis,Woloshyn PRD 2009Jansen,Michael,Shindler,Wagner JHEP 2008Gregory et al. (HPQCD) LAT2009Michael,Shindler,Wagner arxiv:1004.4235

HPQCD: tune parameters to Υ, ηc, pion and kaon.

charmed mesons in context

D−

D

_

I

C

Y

o +K

π−

η’

η

cη

οπ+π

−+

ο

ρρ

ρ ω

φ

KKo +

*

oD

K

s−

Ds*

_

−

−*K

o*D

o_

K*o

D

_

D

K

J/ψ

**

o

*s+

D

*+

sD+

D

−*D

+

D

o

−K

pseudoscalars vectors

1600

1800

2000

2200

2400

2600

2800

Mas

s(M

eV)

Ds(0−) D∗s0(0

+) Ds1(1+) Ds1(1+) D∗s(1

−?)

Ds(1969)

Ds1(2460)Ds1(2536)

D∗s0(2317)

D∗s(2112)

ss

s

s

This is figure 5 of Dong,Alexandru,Draper,Liu,Li,Streuer,Zhang LAT2009.

Iwasaki gauge, domain wall sea, overlap valence,a = 0.08 fm, volume = (2.7 fm)3, mπ = 331 MeV.

References mentioned on the preceeding pages

Mathur,Lewis,Woloshyn Phys.Rev.D66:014502,2002Flynn,Mescia,Tariq JHEP0307:066,2003Chiu,Hsieh Nucl.Phys.A755:471,2005Foley,O’Cais,Peardon,Ryan (TrinLat) Phys.Rev.D75:094503,2007Koponen Phys.Rev.D78:074509,2008Burch,Chakrabarti,Hagen,Maurer,Schafer,Lang,Limmer (BGR) LAT2007 arxiv:0709.3708Lewis,Woloshyn Phys.Rev.D79:014502,2009Na PhD thesis August 2008. Available from proquest.umi.com.Jansen,Michael,Shindler,Wagner (ETMC) LAT2008 arxiv:0808.2121Burch,Hagan,Lang,Limmer,Schafer Phys.Rev.D79:014504,2009Jansen,Michael,Shindler,Wagner JHEP0812:058,2008Na,Gottlieb LAT2008 arxiv:0812.1235Detmold,Lin,Wingate Nucl.Phys.B818:17,2009Lin,Cohen,Mathur,Orginos Phys.Rev.D80:054027,2009Liu,Lin,Orginos,Walker-Loud arxiv:0909.3294Meinel,Detmold,Lin,Wingate LAT2009 arxiv:0909.3837Dong,Alexandru,Draper,Liu,Li,Steuer,Zhang LAT2009 arxiv:0911.0868Gregory,Davies,Follana,Gamiz,Kendall,Lepage,Na,Shigemitsu,Wong LAT2009 arxiv:0911.2133

Michael,Shindler,Wagner arxiv:1004.4235

http://arxiv.org/abs/hep-ph/0203253

http://arxiv.org/abs/hep-lat/0307025



http://arxiv.org/abs/0708.2807



http://www.slac.stanford.edu/spires/find/hep/www?r=AAT-3337539












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bottom and charm hadron spectroscopy from lattice QCD - Parallel... · bottom and charm hadron spectroscopy from lattice QCD m uˇm d