Studying hadron excitations with lattice QCD hadron excitations with lattice QCD Mike Peardon School...
Transcript of Studying hadron excitations with lattice QCD hadron excitations with lattice QCD Mike Peardon School...
Studying hadron excitations with latticeQCD
Mike PeardonSchool of Mathematics, Trinity College Dublin, Ireland
ECT? Trento 14th January 2014
Overview
• Motivation and challenges• Excited hadrons• Scattering and resonances
• Progress and new directions• Framework for measurements - distillation• Light mesons• Charmonium• Scattering
• Summary and outlook
Hadrons beyond the quark model
• QCD allows for states beyond the simple mesons andbaryons, including those with intrinsic gluonic excitationssuch as hybrids and glueballs.
• The “charmonium renaissance” found many newresonance above the open-charm threshold, some arerather narrow.• X(3872) — 1++ resonance close to DD∗ threshold and verynarrow (Γ < 3MeV)
• Z+(4430) – charged state so cannot be cc
• Where are the gluonic excitations? A few hybrid mesonand glueball candidates. Very little consensus.
• SigniVcant experimental activity — new data will becoming soon...
The GlueX experiment at JLab
• 12 GeV upgrade toCEBAF ring
• New experimental hall:Hall D
• New experiment: GlueX
• Aim: photoproduce mesons, in particular hybrids• Expected to start operation this year?
Panda@FAIR, GSI
• Extensive new construction atGSI Darmstadt
• Expected to start operation201x?
PANDA: Anti-Proton ANnihilationat DArmstadt• Anti-proton beam from FAIRon Vxed-target.
• Physics goals includecharmonium and searches forhybrids and glueballs.
Can Lattice QCD study these states?
• Lattice calculations of glueballs and hybrids have beencarried out since 1980s. Focus was ground-states.
• Most experimental candidates for non-QM states arehigh-lying resonances, “hidden inside” a simpler QMspectrum. In QCD, states mix.
• For lattice calculations to be relevant, need:• Precision data on highly-excited states, including reliablespin resolution.
• scattering information, including data above inelasticthresholds
• to study QCD with quarks
• Most of these demands require new ideas and methods toemerge
Excitations and the variational method
• Suppose for a particular set of quantum numbers, we candeVne a basis of interpolating Velds φa for a = 1 . . .N
Variational method
If we can measure Cab(t) = 〈0|φa(t)φ†b(0)|0〉 for all a, b and
solve generalised eigenvalue problem:
C(t) v = λC(t0) v
then
limt−t0→∞
λk = e−Ekt
• v contains overlaps of operators onto states 〈0|φa|k〉• For this to be practical, we need: a ‘good’ basis set thatresembles the states of interest
Scattering
Scattering matrix elements not directly accessible from Eu-clidean QFT [Maiani-Testa theorem]
• Scattering matrix elements:asymptotic |in〉, |out〉 states.〈out |eiHt| in〉 → 〈out |e−Ht| in〉
• Euclidean metric: project ontoground-state
In
States
Out
States
• Lüscher’s formalism: information on elastic scatteringinferred from volume dependence of spectrum
• Requires precise data, resolution of two-hadron andexcited states.
Hadrons in a Vnite box: scattering• On a Vnite lattice with periodic b.c., hadrons have quantisedmomenta; p = 2π
L
{nx, ny, nz
}• Two hadrons with total P = 0 have a discrete spectrum• These states can have same quantum numbers as those created byqΓq operators and QCD can mix these
• This leads to shifts in thespectrum in Vnite volume
• This is the same physics thatmakes resonances in anexperiment
• Lüscher’s method - relateelastic scattering to energyshifts
Toy model
H =
(m gg 4π
L
)
6 8 10 12 14 16 18 20
mL
0
0.5
1
1.5
2
E/m
g/m=0.1
g/m=0.2
New measurement framework — distillation
• Better creation operators are smeared• In lattice calculation, don’t have direct access to quarkVelds, so using complicated operators tricky
• Observation: good smearing operators reduce eUectivedegrees of freedom on a time slice by many orders ofmagnitude.
• Re-deVne smearing as projection operator into low-rankvector space of smooth quark Velds. This enables eUectivecalculations of many otherwise inaccessible correlationfunctions
�(x, y) =
NV∑k=1
vk(x) v∗k(y)
• Problem — expensive, with steep dependence on volume
Spin on the lattice
• Lattice states classiVed by quantumletter, R ∈ {A1,A2, E, T1, T2}.
• Start with continuum: ψΓDiDj . . . ψ andsubduce O(3) irreps→ Oh
• Example:Φij = ψ
(γiDj + γjDi − 2
3δijγ · D)ψ
• Lattice: substitute D→ Dlatt
• Now have a reducible representation:
ΦT2 = {Φ12,Φ23,Φ31} & ΦE ={
1√2(Φ11−Φ22),
1√6(Φ11+Φ22−2Φ33)
}• Look for signature of continuum symmetry:
〈0|ΦT2|2++(T2)〉 = 〈0|ΦE|2++(E)〉Remnants of continuum spin can be found on the lattice. Buildoperators in continuum and measure overlaps to Vnd patterns
Isoscalar/isovector light meson spectrum
500
1000
1500
2000
2500
3000
Caveat: mπ ≈ 400MeV [Dudek et.al Phys.Rev.D88 094505]
Excitation spectrum of charmonium
DDDD
DsDsDsDs
0-+0-+ 1--1-- 2-+2-+ 2--2-- 3--3-- 4-+4-+ 4--4-- 0++0++ 1+-1+- 1++1++ 2++2++ 3+-3+- 3++3++ 4++4++ 1-+1-+ 0+-0+- 2+-2+-0
500
1000
1500M
-M
Ηc
HMeV
L
• Quark model: 1S, 1P, 2S, 1D, 2P, 1F, 2D, . . . all seen.• Not all Vt quark model: spin-exotic (and non-exotic)hybrids seen
[Liu et.al. arXiv:1204.5425]
Gluonic excitations in charmonium?
DDDD
DsDsDsDs
0-+0-+ 1--1-- 2-+2-+ 1-+1-+ 0++0++ 1+-1+- 1++1++ 2++2++ 3+-3+- 0+-0+- 2+-2+-0
500
1000
1500M
-M
Ηc
HMeV
L
• See states created by operators that excite intrinsic gluons• two- and three-derivatives create states in the open-charmregion.
[Liu et.al. arXiv:1204.5425]
I = 2 π − π phase shift
0.10
0.15
0.20
0.25
0.30
0.35
0.40
• Lüscher’s method: Vrstdetermine energy shiftsas volume changes
• Data forL = 16as, 20as, 24as
• Small energy shifts areresolved
• Measured δ0 and δ2 (δ4 is very small)• I = 2 a useful Vrst test - simplest Wick contractions
Dudek et.al. [Phys.Rev.D83:071504,2011, arXiv:1203.6041]
I = 2 π − π phase shift
-50
-40
-30
-20
-10
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Dudek et.al. [Phys.Rev.D83:071504,2011, arXiv:1203.6041]
I = 1 π − π phase shift (near the ρ)
0
20
40
60
80
100
120
140
160
180
800 850 900 950 1000 1050
Dudek et.al. [arXiv:1212.0830]
I = 3/2, Dπ in a Vnite volume
0.40
0.45
0.50
0.55
aE t
A1+ P = (0,0,0)
[2,0,0][-2,0,0]
[1,1,1][-1,-1,-1]
[1,1,0][-1,-1,0]
[1,0,0][-1,0,0]
[0,0,0][0,0,0]
D πP P
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Inelastic
0.40
0.45
0.50
0.55
aE
t
A1 P = (1,0,0)
[1,0,0][0,0,0]
[0,0,0][-1,0,0]
[1,1,0][0,-1,0]
[0,1,0][-1,-1,0][2,0,0][-1,0,0]
[1,1,1][0,-1,-1]
[0,1,1][-1,-1,-1]
[1,0,0][-2,0,0]
P PD π
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Inelastic
0.40
0.45
0.50
0.55
aE
t
A 1 P = (1,1,0)
[2,0,0][-1,-1,0]
[1,1,0][-2,0,0][1,0,1][0,-1,-1]
[0,0,1][-1,-1,-1]
[0,0,0][-1,-1,0][1,1,0][0,0,0]
[1,1,1][0,0,-1]
[1,0,0][0,-1,0]
P PD π
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Inelastic
0.40
0.45
0.50
0.55
aE
t
A1 P = (1,1,1)[2,0,0][-1,-1,-1]
[1,1,1][-2,0,0]
[0,0,0][-1,-1,-1]
[1,0,0][0,-1,-1]
[1,1,0][0,0,-1]
[1,1,1][0,0,0]
P PD π
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Inelastic
I = 3/2, Dπ scattering phase shift
PRELIMINARY
60
50
40
30
20
10
00.40 0.41 0.42 0.43 0.44 0.45 0.46
_
_
_
_
_
_
δ0(
deg)
a tEcm
P = (0,0,0)P = (1,0,0)P = (1,1,0)P = (1,1,1)
Summary
• To study states beyond the quark model (hybrids,tetraquarks, glueballs) on the lattice requires precisiondeterminations of excitation spectra
• New framework show this can be achieved, but is stillexpensive.
• Precision data on excitations in charmonium and lightmeson spectra.
• Studying elastic scattering using Lüscher formalism isworking well.
• Approaching the physical point — more thresholds open• Next challenge — what to do above inelastic thresholds?