The Upsilon spectrum and m_b from full lattice QCD

A.Gray; C. T. H. Davies; E. Gulez; G. P. Lepage; I. Allison; J. Shigemitsu; M. Wingate

REVIEW

The Upsilon spectrum and m_b from full lattice QCD

A.Gray, I. Allison, C. T. H. Davies, E. Gulez, G. P. Lepage, J. Shigemitsu, M. Wingate

High Energy Physics - Lattice · Submitted 13 Jul 2005 · 54 references

Pith's verdict: First bottomonium spectrum and bottom mass from 2+1-flavor lattice QCD; the scale-consistency argument is the real result, and the m_b error bar is the part to argue about.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 10 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-lat/0507013 (version 2)

Pith IDBW2Q3EFA, Pith's permanent record of this paper and its review

CitationA.Gray, C. T. H. Davies, E. Gulez, G. P. Lepage, I. Allison, J. Shigemitsu, M. Wingate. "The Upsilon spectrum and m_b from full lattice QCD." arXiv:hep-lat/0507013 (2005). https://pith.science/paper/BW2Q3EFA

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The thing to know: this is the first Upsilon spectrum and the first bottom mass from lattice QCD with 2+1 flavors of sea quarks, and the internal-consistency argument is what matters. The ratio of lattice spacings from 1P-1S and 2S-1S is 1.09 in quenched and 0.98-1.02 with 2+1 flavors (Tables IX, X, Fig. 3). That is the signature you would want if missing sea quarks were the source of the old scale ambiguity, and it is the strongest result here. The same bare bottom mass then reproduces the B_s mass at the 4% level, which is the kind of cross-sector check quenched work could never make cleanly. Credit where due: the systematic budget in Tables II and III is itemized per ensemble rather than waved at, and the cross-checks with n=4 and a plaquette-based u0 (Fig. 1, Table VII) are the right ones to run. The body is also more candid than the abstract; the classifier found no stated limitations, but section VI says plainly that the pole mass cannot be obtained accurately because alpha_V(0.6/a) is about 0.75, and that a two-loop self-energy is in progress. On the stress-test concern about mu = 2/a: it lands, but less hard than stated. Fig. 10 compares the perturbative shift Z_m M_b^0 - E_0 against the nonperturbative (M_Upsilon - E_sim)/2 across three lattice spacings while the shift varies by a factor of two, and they agree. That is real evidence the one-loop coefficients and BLM scales are roughly right, and it is the check the reader did not credit. What Fig. 10 does not test is the -4/3 - 2log(mu/M_b^0) piece, and the paper does pick mu = 2/a by hand. A mu-scan would cost little and settle it; worth asking for. The other soft spot is the hyperfine number. The 61(14) MeV depends on rescaling by the sixth power of the ratio of used to corrected u0L, with the corrected value from private communication [8]. That moves the fine and super-coarse points by roughly 6%, comparable to the quoted discretisation error. The prediction is plausible and consistent with the charmonium ratio, but it is the least secure number in the abstract. Who should read it: anyone doing lattice B physics, and anyone who needs a defensible m_b. The 4.4(3) GeV will be quoted; the error bar will be argued about until the two-loop matching appears. Send it to referees. This is a real result with an honest error budget, and the referees should push on the mu-dependence and the u0L rescaling rather than on the framework.

Referee report

Significance

If the results hold, this is the first determination of the bottom quark mass from full lattice QCD and the first demonstration that the lattice-spacing ambiguity which plagued quenched B physics is resolved once 2+1 flavors of light sea quarks are included. The paper is unusually explicit about its own systematics: Tables II and III tabulate estimated errors per ensemble, Fig. 1 and Table VII test the sensitivity to the NRQCD stability parameter and to the tadpole-improvement choice, and Fig. 10 compares the perturbative mass shift Z_m M_b^0 − E_0 with the nonperturbative (M_Υ − E_sim)/2 across three lattice spacings as that shift varies by a factor of two. The falsifiable predictions (Υ−η_b, Υ′−η_b′, h_b−χ̄_b, and the leptonic-width ratio) are a genuine strength, as is the internal consistency check that the same bare b mass reproduces the B_s mass to about 4%. The paper is also candid in the body about what is not yet under control: the one-loop matching, the unknown radiative coefficient c_4, and the strong a^2 dependence of the wavefunction at the origin.

Major objections (4)

[§VI.B, Eq. (18) and Table XV] The headline m_b^MSbar(m_b^MSbar) = 4.4(3) GeV rests on a one-loop conversion in which the scale is chosen by hand. The manuscript states that the first-order coefficient in Eq. (18) is made small (0.06 to 0.16) only by setting μ = 2/a, and that the scale aμ* at which the coefficient vanishes is 1.9–2.4; it then says explicitly 'We simplify the analysis here by setting μ = 2/a'. The quoted ±0.3 GeV is described as an estimate of unknown α_V^2(2/a) terms, not a computed bound. Fig. 10 is a real and valuable check, but it validates the shift Z_m M_b^0 − E_0 against (M_Υ − E_sim)/2; it does not test the −4/3 − 2 log(μ/M_b^0) piece of the MSbar conversion, which is precisely where the μ choice enters. I would ask the authors to add a short paragraph or small figure showing m_b^MSbar(m_b^MSbar) as a function of μ over a reasonable range (say 1/a to 4/a) at fixed lattice spacing, so that the residual μ-dependence can be read off and compared with the quoted error. If that dependence is comfortably inside 0.3 GeV, the error estimate is vindicated; if not, the error should be enlarged or the central value qualified. The authors' candour about the missing two-loop calculation is commendable and should be preserved; the request is for one additional diagnostic, not a new calculation.
[§VII.A, Eq. (19) and Fig. 15] The continuum value of the ground-state hyperfine splitting, 61(4)(12)(6) MeV, is obtained from a three-point fit in a^2 with the coefficient Λ ≈ 640 MeV determined by the fit itself, after a post-hoc rescaling of the fine and super-coarse points by (u_0L^{used}/u_0L^{correct})^6, which shifts those points by roughly 6% and 3% respectively. Because the splitting scales as u_0^{-6}, this correction is not a small perturbation on the fit, and the 12 MeV discretisation error is an estimate from a constrained fit rather than a measured spread. I would ask for the fit to be shown explicitly (points, curve, and χ^2), together with the value obtained if the super-coarse ensemble is dropped and the value obtained if an a^4 term is allowed. The spread among those three numbers is the honest discretisation error, and it should be quoted as such. This matters because the hyperfine splitting is one of the paper's named predictions and because the same a^2-fit machinery is used for the leptonic-width ratio in §VIII.
[§VIII, Eqs. (24)–(25) and Fig. 18] The leptonic-width ratio 0.48(5) is obtained from an a^2 extrapolation with Λ ≈ 900 MeV, i.e. a stronger a-dependence than the hyperfine splitting, and the super-coarse point sits well off the two finer points. In addition, the 4% relativistic correction that is applied to the continuum leading-order result is computed on a single ensemble (the coarse 0.01/0.05 set) and then applied universally. The manuscript should state what the continuum value becomes if the super-coarse ensemble is excluded from the fit, and whether the size of the relativistic correction was checked on a second ensemble or lattice spacing. If the correction is genuinely a v^2 effect it should scale mildly, but the reader cannot verify that from the present text. As with the hyperfine splitting, the quoted 10% error should be traceable to a stated spread rather than to a single constrained fit.
[§IV–§V, Tables VIII–X and Figs. 4–7] The physical results r_0 = 0.469(7) fm, r_1 = 0.321(5) fm, and the spectrum comparison of Fig. 7 are quoted from the finest ensemble rather than from a continuum extrapolation. Given the estimated a^2 errors of 0.4% on the fine lattices this is defensible, and the agreement of the two lattice-spacing determinations across three a values is itself a scaling check. But the manuscript should say so explicitly: one sentence stating that no continuum extrapolation is performed for these quantities, that the fine-lattice value is taken as the best estimate, and that the residual a^2 error is folded into the quoted uncertainty. Without that sentence the reader is left to infer the procedure from the tables.

Minor objections (10)

[Abstract] The abstract quotes m_b^MSbar(m_b^MSbar) = 4.4(3) GeV without noting that this is a one-loop matching result; the body is explicit about this in §VI.B. One qualifying clause in the abstract would bring it into line with the paper's own candour.
[Abstract and §I] The phrase 'for the first time' attached to u, d and s vacuum polarisation is correct as stated but could be misread as claiming the first unquenched Υ calculation; earlier n_f = 2 results are discussed in §VII. 'First with 2+1 flavors' would be unambiguous.
[§VI.A, Eq. (12)] The construction M_b^0(a) = aM_{b,sim}^0 × M_{Υ,expt}/(aM_{Υ,latt}) is transparent and the cancellation of lattice-spacing and tuning errors is a genuine feature, not a circularity; the text explains this. A single added sentence stating that M_b^0(a) is a running mass defined at scale ~1/a, and that its decrease with decreasing a in Table XV is the expected running, would preempt a misreading.
[§VI and §VII, valence s quark mass] The B_s mass in Fig. 11 uses am_s = 0.04 (coarse) and 0.031 (fine) for the valence quark, which differs from the sea value of 0.05 on the coarse ensembles in Table I. This is explained in §VII but should also be flagged where the B_s result first appears in §VI, since a reader comparing Table I with Fig. 11 will otherwise be confused.
[Eq. (1) and Eq. (6)] The symbol n denotes both the NRQCD stability parameter in Eq. (1) and Eq. (3) and, implicitly, the exponent count n_exp in Eq. (6). A distinct symbol for one of them would help.
[§II.B, Eq. (5)] The smearing parameter a_0 = 1.0 in lattice units is used on all three ensembles, so the physical smearing radius differs by roughly a factor of two between the super-coarse and fine sets. Since Ψ(0) in §VIII is extracted from the local (delta-function) amplitude, this should not matter in principle, but a sentence confirming that the fitted local amplitudes are stable against the choice of a_0 would close the loop.
[Table VII] The u_0 = 4√plaq energies are shifted by about 0.18 in aE(1S) relative to the u_0L values, which is large compared with the splittings being compared. The caption should state explicitly that only the splittings, not the absolute energies, are being compared between the two halves of the table.
[§VII.B, Eq. (22)] The combination M(χ_b2) − 3M(χ_b1) + 2M(χ_b0) gives −31(7) MeV on the lattice against −46(3) MeV experimentally, a roughly 2σ tension. The text notes it, but this is the one place in the P-wave analysis where the unquenched result does not obviously agree, and it deserves a sentence in the conclusions alongside the successes.
[Fig. 19] The quenched 1D−1S and 2m_{B_s}−m_Υ entries are taken from earlier work with adjustments and are described in the text as 'indicative only' (refs. [52], [53]). They should be marked as such on the figure itself, not only in the caption.
[References] Reference [37] contains a stray comma ('C, Morningstar'). Reference [45] is a conference-talk URL and is correctly described as preliminary where used; that description should be repeated at the point of the 0.517(10) comparison in §VIII.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

With light and strange quark vacuum polarization included, two independent splittings in the Upsilon spectrum finally agree on a single lattice spacing, and the same bare bottom mass reproduces both the Upsilon and the B_s meson.

The reading

Lattice QCD has a long-standing embarrassment: different quantities used to fix the lattice spacing give different answers, so predictions cannot be made unambiguously. This paper argues that the fault lies with the sea-quark content of the simulation, not with the method. Using gluon configurations that include vacuum polarization from up, down and strange quarks, the authors compute the Upsilon spectrum with nonrelativistic bottom quarks and find that the orbital $1P-1S$ and radial $2S-1S$ splittings give the same lattice spacing, whereas the quenched approximation gives answers differing by about 9 percent. If that is right, the parameters of QCD can be fixed consistently for the first time, and the payoff is a bottom quark mass from full lattice QCD, $m_b^{MSbar}(m_b^{MSbar}) = 4.4(3)$ GeV, together with physical values for the heavy-quark potential scales $r_0 = 0.469(7)$ fm and $r_1 = 0.321(5)$ fm.

What carries the argument

The load-bearing device is a consistency test rather than a single number: two spin-independent splittings in the same meson family, one orbital and one radial, are each matched to experiment to give an inverse lattice spacing, and the ratio of the two answers is examined as a function of sea quark mass and lattice spacing. The bottom quarks are handled by lattice nonrelativistic QCD through next-to-leading order in $v^2$, with the relativistic, radiative and discretisation corrections estimated term by term and tabulated, so that the reader can see which uncertainty dominates at each lattice spacing. The same bare bottom mass then feeds the heavy-light sector, where the $B_s$ mass is extracted from a dispersion relation, making the Upsilon and B sectors a joint test rather than two separate calculations.

Extended reading notes

Core claim

The central claim is that a simulation with realistic sea quarks restores internal consistency to the bottomonium spectrum. On the coarse 2+1-flavor ensembles the ratio of the inverse lattice spacing from $2S-1S$ to that from $1P-1S$ is $0.984(20)(34)$; on the fine ensembles it is $1.021(23)(13)$; on quenched ensembles the same ratio is about $1.09$. Since the lattice spacing should be unique, the quenched disagreement was a symptom of missing quark vacuum polarization, and its disappearance is the paper's evidence that the 2+1-flavor configurations are close enough to the real world to fix QCD's parameters. The authors then show that the bare bottom mass tuned to reproduce the Upsilon mass also reproduces the $B_s$ mass to within the quoted errors, and convert the bare mass to the $MSbar$ scheme at one loop, obtaining $m_b^{MSbar}(m_b^{MSbar}) = 4.4(3)$ GeV. Along the way they quote predictions for states not yet measured: $M_ ext{Upsilon} - M_{eta_b} = 61(14)$ MeV, $M_{ ext{Upsilon}'} - M_{eta_b'} = 30(19)$ MeV, and a splitting between the $h_b$ and the spin average of the $chi_b$ states below 6 MeV.

Load-bearing premise

The step from the bare lattice bottom mass to the quoted $MSbar$ value rests on one-loop perturbative matching evaluated at a scale $mu = 2/a$ chosen by hand to make the first-order coefficient small, with the quoted error being an estimate of the uncomputed next-order terms rather than a calculated bound.

Editorial extensions

If this is right

The lattice spacing can be fixed from the Upsilon $2S-1S$ splitting without the ambiguity that plagued quenched calculations, so dimensionful predictions from these ensembles become well defined.
A bottom quark mass in the $MSbar$ scheme, $4.4(3)$ GeV, follows from one-loop matching of the bare lattice mass, removing the roughly 30 percent spread between bottom masses used in separate quenched Upsilon and B analyses.
The $B_s$ mass comes out about 4 percent high, within one standard deviation, when the bottom mass is fixed from the Upsilon, which is the check that the same parameters describe both sectors.
The heavy-quark potential scales come out as $r_0 = 0.469(7)$ fm and $r_1 = 0.321(5)$ fm, giving other lattice calculations a common ruler tied to an experimentally measured splitting.
The predicted $eta_b$ mass of 9.399(14) GeV and the near-degeneracy of the $h_b$ with the $chi_b$ spin average are concrete targets for experiment.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the consistency of the two splittings really is driven by sea-quark content rather than by the improved gluon action or the improved operators, then other quantities that disagreed in the quenched approximation, such as the charmonium spectrum and heavy-light decay constants, should show the same repair on these ensembles.
The prediction that the $h_b$ lies within 6 MeV of the $chi_b$ spin average is a sharp test that does not depend on the overall scale, so a future measurement of the $h_b$ mass would probe the spin-dependent part of the nonrelativistic action almost independently of the tuning.
Because the quoted $4.4(3)$ GeV error is an estimate of uncomputed higher-order matching terms rather than a derived bound, the same ensembles combined with a two-loop self-energy calculation would convert this result from a plausible central value into a controlled one.
The pattern here, where a long-standing discrepancy between two scale determinations dissolves once the sea-quark content is realistic, suggests that other reported tensions between lattice observables should first be checked against sea-quark content before being attributed to the discretisation or the effective theory.

Original abstract

We show results for the Upsilon spectrum calculated in lattice QCD including for the first time vacuum polarization effects for light u and d quarks as well as s quarks. We use gluon field configurations generated by the MILC collaboration. The calculations compare the results for a variety of u and d quark masses, as well as making a comparison to quenched results (in which quark vacuum polarisation is ignored) and results with only u and d quarks. The b quarks in the Upsilon are treated in lattice Nonrelativistic QCD through NLO in an expansion in the velocity of the b quark. We concentrate on accurate results for orbital and radial splittings where we see clear agreement with experiment once u, d and s quark vacuum polarisation effects are included. This now allows a consistent determination of the parameters of QCD. We demonstrate this consistency through the agreement of the Upsilon and B spectrum using the same lattice bare b quark mass. A one-loop matching to continuum QCD gives a value for the b quark mass in full lattice QCD for the first time. We obtain m_b^{\bar{MS}}(m_b^{\bar{MS}}) = 4.4(3) GeV. We are able to give physical results for the heavy quark potential parameters, r_0 = 0.469(7) fm and r_1 = 0.321(5) fm. Results for the fine structure in the spectrum and the Upsilon leptonic width are also presented. We predict the Upsilon - eta_b splitting to be 61(14) MeV, the Upsilon^{\prime} - eta_b^{\prime} splitting as 30(19) MeV and the splitting between the h_b and the spin-average of the chi_b states to be less than 6 MeV. Improvements to these calculations that will be made in the near future are discussed.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 9,642 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.90 · states limitation 0.57 · human participants 0.01 · controlled comparison 0.83 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We show results for the Upsilon spectrum calculated in lattice QCD including for the first time vacuum polarization effects for light u and d quarks as well as s quarks. We use gluon field configurations generated by the MILC collaboration. The calculations compare the results for a variety of u and d quark masses, as well as making a comparison to quenched results (in which quark vacuum polarisation is ignored) and results with only u and d quarks. The b quarks in the Upsilon are treated in lattice Nonrelativistic QCD through NLO in an expansion in the velocity of the b quark. We concentrate on accurate results for orbital and radial splittings where we see clear agreement with experiment once u, d and s quark vacuum polarisation effects are included. This now allows a consistent determination of the parameters of QCD. We demonstrate this consistency through the agreement of the Upsilon and B spectrum using the same lattice bare b quark mass. A one-loop matching to continuum QCD gives a value for the b quark mass in full lattice QCD for the first time. We obtain m_b^{\bar{MS}}(m_b^{\bar{MS}}) = 4.4(3) GeV. We are able to give physical results for the heavy quark potential parameters, r_0 = 0.469(7) fm and r_1 = 0.321(5) fm. Results for the fine structure in the spectrum and the Upsilon leptonic width are also presented. We predict the Upsilon - eta_b splitting to be 61(14) MeV, the Upsilon^{\prime} - eta_b^{\prime} splitting as 30(19) MeV and the splitting between the h_b and the spin-average of the chi_b states to be less than 6 MeV. Improvements to these calculations that will be made in the near future are discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show results for the Upsilon spectrum calculated in lattice QCD including for the first time vacuum polarization effects for light u and d quarks as well as s quarks.	contribution 0.99	0.96	0.17	asserted 1.00
s1	We use gluon field configurations generated by the MILC collaboration.	method 1.00	0.34	0.01	asserted 1.00
s2	The calculations compare the results for a variety of u and d quark masses, as well as making a comparison to quenched results (in which quark vacuum polarisation is ignored) and results with only u and d quarks.	method 0.86	0.89	0.05	asserted 0.96
s3	The b quarks in the Upsilon are treated in lattice Nonrelativistic QCD through NLO in an expansion in the velocity of the b quark.	method 1.00	0.79	0.04	asserted 1.00
s4	We concentrate on accurate results for orbital and radial splittings where we see clear agreement with experiment once u, d and s quark vacuum polarisation effects are included.	result 0.90	0.96	0.41	asserted 1.00
s5	This now allows a consistent determination of the parameters of QCD.	interpretation 0.98	0.52	0.26	asserted 0.92
s6	We demonstrate this consistency through the agreement of the Upsilon and B spectrum using the same lattice bare b quark mass.	result 0.64	0.94	0.15	asserted 1.00
s7	A one-loop matching to continuum QCD gives a value for the b quark mass in full lattice QCD for the first time.	contribution 0.62	0.94	0.19	asserted 1.00
s8	We obtain m_b^{\bar{MS}}(m_b^{\bar{MS}}) = 4.4(3) GeV.	result 1.00	0.97	0.30	asserted 1.00
s9	We are able to give physical results for the heavy quark potential parameters, r_0 = 0.469(7) fm and r_1 = 0.321(5) fm.	result 1.00	0.96	0.08	asserted 1.00
s10	Results for the fine structure in the spectrum and the Upsilon leptonic width are also presented.	result 0.76	0.91	0.03	asserted 0.99
s11	We predict the Upsilon - eta_b splitting to be 61(14) MeV, the Upsilon^{\prime} - eta_b^{\prime} splitting as 30(19) MeV and the splitting between the h_b and the spin-average of the chi_b states to be less than 6 MeV.	result 1.00	0.94	0.08	asserted 0.93
s12	Improvements to these calculations that will be made in the near future are discussed.	future work 1.00	0.24	0.02	asserted 0.55

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Dependence of Υ energy splittings on change in

**Figure 2.** FIG. 2: Υ energies in lattice units as a function of number

**Figure 3.** FIG. 3: The ratio of lattice spacing values obtained from the

**Figure 6.** FIG. 6: Spin-independent splittings in the Υ spectrum as a

**Figure 8.** FIG. 8: The value of the Υ mass in physical units plotted

**Figure 10.** FIG. 10: The perturbative estimate of the shift between mass

**Figure 11.** FIG. 11: The value of the

**Figure 13.** FIG. 13: The ratio of the splitting between the Υ

**Figure 14.** FIG. 14: The ground-state hyperfine splitting in the Υ system

**Figure 15.** FIG. 15: Hyperfine splittings in the Υ and

**Figure 16.** plots the lattice results for the ground state P-wave splittings, each relative to the spin average. We use the 2S−1S lattice spacing values to convert to physical units. The plot shows the coarse and fine unquenched and fine quenched results only since the results on the super-coarse ensemble have error bars which are too large to be useful, although they are consistent with the others. The Figure shows that the size of the quenched P-wave splittings are smaller than experiment. The results on the coarse 2+1 flavor configurations look consistent with -60 -40 -20 0 20 40 60 MeV…

**Figure 17.** FIG. 17: The ratio of leptonic width times mass squared for

**Figure 18.** FIG. 18: The dependence on

**Figure 19.** FIG. 19: The ratio of lattice results to experiment for var

Showing 15 of the paper's 19 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-lat/0507013 by the authors.

References

Works cited (54)

[8]

C. Aubin et al , Phys. Rev. D 70, 094505 (2004), hep-lat/0402030

View on Pith Pith review arXiv 2004
[1]

Fermilab, HPQCD, MILC, UKQCD collaborations, C. T. H. Davies et al , Phys. Rev. Lett. 92, 022001 (2004), hep-lat/0304004

View on Pith Pith review arXiv 2004
[2]

HPQCD, MILC, UKQCD collaborations, C. Aubin et al , Phys. Rev. D 70, 031504 (2004), hep-lat/0405022

View on Pith Pith review arXiv 2004
[3]

MILC collaboration, C. Aubin et al , hep-lat/0407028

View on Pith Pith review arXiv
[4]

Fermilab, HPQCD collaborations, I. Allison, C. T. H. Davies, A. Gray, A.S. Kronfeld, P. B. Mackenzie, J. N. Simone, Phys. Rev. Lett. 94, 172001 (2005), hep-lat/0411027

View on Pith Pith review arXiv 2005
[5]

Fermilab, MILC collaborations, C. Aubin et al , hep-ph/0408306

View on Pith Pith review arXiv
[6]

C. W. Bernard et al , Phys. Rev. D 64, 054506 (2001), hep-lat/0104002

View on Pith Pith review arXiv 2001
[7]

(where r2F (r) = 1 .00) of 0.321(5)fm. This is also shown as a function of light quark mass in Figure 5 and also agrees with the preliminary value from [7]. This vari- able in fact shows a very ﬂat curve as a function of light quark mass when the scale is set by the Υ 2 S − 1S split- ting, i.e. the light quark vacuum polarisation eﬀects are very similar i...

View on Pith
[9]

MILC collaboration, private communication

View on Pith
[10]

The action was ﬁrst given in: G. P. Lepage, Phys. Rev. D59, 074502 (1999), hep-lat/9809157. See the follow- ing for studies of its performance: K. Orginos, D. Tou- ssaint, R. L. Sugar, Phys. Rev. D 60, 054503 (1999), hep-lat/9903032; MILC collaboration, C. Bernard et al , Phys. Rev. D 61, 111502 (2000), hep-lat/9912018

View on Pith Pith review arXiv 1999
[11]

M. Alford, W. Dimm, G. P. Lepage, G. Hockney and P. B. Mackenzie, Phys. Lett. B 361 (1995) 87, hep-lat/9507010

View on Pith Pith review arXiv 1995
[12]

M.Nobes, hep-lat/0501009

View on Pith Pith review arXiv
[13]

B. A. Thacker and G. P. Lepage, Phys. Rev. D 43 (1991) 196

View on Pith 1991
[14]

G. P. Lepage et al , Phys. Rev. D 46, 4052 (1992), hep-lat/9205007

View on Pith Pith review arXiv 1992
[15]

C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lep- age, A. Lidsey, J. Shigemitsu, J. Sloan, Phys. Rev. D 50, 6963 (1994), hep-lat/9406017

View on Pith Pith review arXiv 1994
[16]

C. Morningstar, Phys. Rev. D 50 (1994) 5902, hep-lat/9406002

View on Pith Pith review arXiv 1994
[17]

G. P. Lepage and P. Mackenzie, Phys. Rev. D 48 (1993) 2250

View on Pith 1993
[18]

The value of u0 does aﬀect the value of the ground state energy as is clear from comparing Tables V and VII. The dependence on u0 can be seen in perturbation theory or in a mean ﬁeld approach [13] which gives a reasonably good quantitative description of the results

View on Pith
[19]

M. Nobes, private communication

View on Pith
[20]

C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. Lidsey, J. Shigemitsu and J. H. Sloan, Phys. Lett. B 345 (1995) 42, hep-ph/9408328

View on Pith Pith review arXiv 1995
[21]

C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. Lid- sey, P. McCallum, J. Shigemitsu, J. H. Sloan, Phys. Rev. D58, 054505 (1998), hep-lat/9802024

View on Pith Pith review arXiv 1998
[22]

S. Groote and J. Shigemitsu, Phys. Rev. D 62, 014508 (2000), hep-lat/0001021

View on Pith Pith review arXiv 2000
[23]

G. P. Lepage et al , Nucl. Phys. B (Proc. Suppl. 106) (2002)12, hep-lat/0110175

View on Pith Pith review arXiv 2002
[24]

S. Eidelman et al , Phys. Lett. B 592 (2004) 1

View on Pith 2004
[25]

C. T. H. Davies, K. Hornbostel, G. P. Lepage, P.McCallum, J. Shigemitsu, J. H. Sloan, Phys. Rev. D 56 (1997) 2755

View on Pith 1997
[26]

N. Eicker et al , Phys. Rev. D 57, 4080 (1998), hep-lat/9709002

View on Pith Pith review arXiv 1998
[27]

CP-PACS collaboration, T. Manke et al , Phys. Rev D 62, 114508 (2000), hep-lat/0005022

View on Pith Pith review arXiv 2000
[28]

UKQCD collaboration, L. Marcantonio, P. Boyle, C. T. H. Davies, J. Hein, J. Shigemitsu, Nucl. Phys. B (Proc. Suppl.94), 363 (2001), hep-lat/0011053

View on Pith Pith review arXiv 2001
[29]

R. Sommer, Nucl. Phys. B 411 (1994) 839, hep-lat/9310022

View on Pith Pith review arXiv 1994
[30]

CLEO collaboration, G. Bonvicini et al , Phys. Rev. D70:32001 (2004), hep-ex/0404021

View on Pith Pith review arXiv 2004
[31]

M. Alford, T. R. Klassen and G. P. Lepage, Nucl. Phys. B496 (1997) 377, hep-lat/9611010

View on Pith Pith review arXiv 1997
[32]

Y. Kayaba et al , Nucl. Phys. B (Proc. Suppl.) 140 (2005) 479, hep-lat/0409086

View on Pith Pith review arXiv 2005
[33]

J. Shigemitsu et al , Proceedings of LAT04, Nucl. Phys. B(Proc. Suppl. 140) (2005) 464, hep-lat/0408019

View on Pith Pith review arXiv 2005
[34]

C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lep- age, A. Lidsey, C. J. Morningstar, J. Shigemitsu, J. Sloan, Phys. Rev. Lett. 73 (1994) 2654, hep-lat/9404012

View on Pith Pith review arXiv 1994
[35]

E. Gulez, J. Shigemitsu and M. Wingate, Phys. Rev. D69:074501 (2004), hep-lat/0312017

View on Pith Pith review arXiv 2004
[36]

Q. Mason et al , Phys. Rev. Lett. (in press), hep-lat/0503005; Q. Mason and H. Trottier, in prepa- ration

View on Pith Pith review arXiv
[37]

S. J. Brodsky, G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 28 (1983) 228

View on Pith 1983
[38]

C, Morningstar, private communication from the calcu- lation of [15] , using a slightly diﬀerent NRQCD action and an unimproved gluon action

View on Pith
[39]

NRQCD collaboration, K. Hornbostel, Nucl. Phys. B (Proc. Suppl. 73) (1999) 339, hep-lat/9809177

View on Pith Pith review arXiv 1999
[40]

K. Melnikov and T. van Ritbergen, Phys. Lett. B 482 (2000) 99, hep-ph/9912391

View on Pith Pith review arXiv 2000
[41]

A. Ali Khan et al , Phys. Rev. D 62:054505 (2000), hep-lat/9912034

View on Pith Pith review arXiv 2000
[42]

Belle collaboration, S.-K. Choi et al , Phys. Rev. Lett. 89:102001 (2002)

View on Pith 2002
[43]

HPQCD collaboration, in preparation

View on Pith
[44]

H. Trottier, Phys. Rev. D 55 (1997) 6844, hep-lat/9611026; T. Manke et al , Phys. Lett. B 468 (1997) 308, hep-lat/9706003; N. H. Shakespeare and H. D. Trottier, Phys. Rev. D 58:034502 (1998), hep-lat/9802038

View on Pith Pith review arXiv 1997
[45]

C. Davies, Springer Lecture notes in Physics, Eds Gaus- terer, Lang, 1998, hep-ph/9710394

View on Pith Pith review arXiv 1998
[46]

Jean Duboscq, CLEO, talk at the HEP2005 Europhysics conference, Lisbon, July 2005, www.lip.pt/events/2005/hep2005/talks/session5.html

View on Pith 2005
[47]

See, for example, D. H. Perkins, Introduction to High En- ergy Physics , 3rd Ed. (Addison-Wesley, Reading, MA)

View on Pith
[48]

G. von Hippel, PhD thesis, University of Cambridge, 2003; R. Horgan, private communication

View on Pith 2003
[49]

C. J. Morningstar and J. Shigemitsu, Phys. Rev. D 57 (1998) 6741, hep-lat/9712016

View on Pith Pith review arXiv 1998
[50]

J. Erler, Phys. Rev. D 59:054008 (1999), hep-ph/9803453

View on Pith Pith review arXiv 1999
[51]

B. D. Jones and R. M. Woloshyn, Phys. Rev. D60:014502(1999), hep-lat/9812008

View on Pith Pith review arXiv 1999
[52]

E. Eichten and C. Quigg, Phys. Rev. D 52 (1995) 1726, hep-ph/9503356

View on Pith Pith review arXiv 1995
[53]

M. Campbell, MSc thesis, University of Glasgow, 1998. We use the average of the 1 1D2,T and 1 1D2,E (since these seem more reliable than the corresponding 1 3D2 results) and combine it with the 1 3S1 energy and a−1 25 value from [14]

View on Pith 1998
[54]

J. Hein et al , Phys. Rev. D 62:074503 (2000), hep-ph/0003130. We take results for unimproved glue at β=6.2 and combine with results from [20], after adjust- ment to use the lattice spacing from the Υ 2 S − 1S split- ting consistently, including for the s quark mass. This can only be done to a limited extent because the original cal- culations used a diﬀe...

View on Pith Pith review arXiv 2000

Forward citations

Cited by 37 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The $\Upsilon$ and $\Upsilon^{\prime}$ Leptonic Widths, $a_{\mu}^b$ and $m_b$ from full lattice QCD
hep-lat 2014-08 conditional novelty 7.0 of 10

Full lattice QCD with radiatively improved NRQCD bottom quarks yields Γ(Υ→e+e−) = 1.19(11) keV and Γ(Υ'→e+e−) = 0.69(9) keV, plus m_b(m_b, nf=5) = 4.196(23) GeV and a_μ^b = 0.271(37)×10^-10.
High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
hep-lat 2008-05 accept novelty 7.0 of 10

Lattice QCD combined with four-loop perturbation theory gives m_c(3 GeV) = 0.986(10) GeV and alpha_MS(M_Z) = 0.1174(12), matching independent continuum determinations.
Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
hep-lat 2006-10 accept novelty 7.0 of 10

A new staggered-quark lattice action (HISQ) reduces taste-exchange errors about tenfold versus ASQTAD and removes tree-level a^2 and (am)^4 errors, yielding a psi-eta_c splitting of 111(5) MeV.
The QCD transition temperature: results with physical masses in the continuum limit
hep-lat 2006-09 accept novelty 7.0 of 10

With physical up, down and strange quark masses and a continuum extrapolation over three lattice spacings, the chiral susceptibility peak gives a QCD crossover temperature of 151(3)(3) MeV, while strange-quark number ...
Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu}^c$
hep-lat 2020-05 accept novelty 6.0 of 10

Lattice QCD plus quenched QED gives f_J/psi = 0.4104(17) GeV, m_c(3 GeV) = 0.9841(51) GeV and a_mu^c = 14.638(47)e-10, with the connected charmonium hyperfine splitting exceeding experiment by 7.3(1.2) MeV, read as th...

Show 32 more citing papers

Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD
hep-lat 2018-10 conditional novelty 6.0 of 10

A lattice QCD calculation finds evidence that a ud cbar bbar tetraquark is bound by 15 to 61 MeV below the Dbar B* threshold, with mass about 7154 MeV.
B-meson decay constants: a more complete picture from full lattice QCD
hep-lat 2015-03 accept novelty 6.0 of 10

Lattice QCD gives f_B*/f_B = 0.941(26), f_B*_s/f_B_s = 0.953(23) and f_B*_c/f_B_c = 0.988(27), so the vector decay constant sits below the pseudoscalar one for b-light mesons and approaches it as the lighter quark get...
Lattice NRQCD study of S- and P-wave bottomonium states in a thermal medium with $N_f=2+1$ light flavors
hep-lat 2014-09 conditional novelty 6.0 of 10

Using a new Bayesian spectral reconstruction on Nf=2+1 lattice NRQCD correlators, the chi_b1 bottomonium ground state is found to survive up to T=249 MeV, contrary to maximum-entropy-based claims of melting near Tc.
B-meson decay constants from improved lattice NRQCD and physical u, d, s and c sea quarks
hep-lat 2013-02 accept novelty 6.0 of 10

Lattice QCD with physical light quark masses gives f_B = 0.186(4) GeV, f_Bs = 0.224(5) GeV and f_Bs/f_B = 1.205(7), removing the chiral extrapolation from these hadronic inputs.
Precision tests of the J/{\psi} from full lattice QCD: mass, leptonic width and radiative decay rate to {\eta}_c
hep-lat 2012-08 conditional novelty 6.0 of 10

Full lattice QCD with 2+1 sea quarks reproduces the J/psi-eta_c hyperfine splitting and the J/psi leptonic width to a few percent, and predicts the radiative decay rate to eta_c.
Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD
hep-lat 2012-07 accept novelty 6.0 of 10

Full lattice QCD with relativistic heavy quarks gives f_Bc = 0.427(6) GeV, m_Bc = 6.285(10) GeV and f_eta_b = 0.667(6) GeV, with the B_c decay constant well below potential-model values.
Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy
hep-lat 2012-06 conditional novelty 6.0 of 10

Tuning a three-parameter relativistic heavy-quark lattice action against B_s and B_s* masses reproduces the low-lying bottomonium spectrum to roughly 0.5 percent, validating the method for future B-meson matrix elemen...
B_s->D_s/B->D Semileptonic Form-Factor Ratios and Their Application to BR(B^0_s->\mu^+\mu^-)
hep-lat 2012-02 conditional novelty 6.0 of 10

First lattice-QCD determination of the B_s to D_s over B to D scalar form-factor ratio gives 1.046(44)(15), consistent with U-spin symmetry and roughly four sigma below the QCD sum-rule estimate of 1.24(8).
The chiral and deconfinement aspects of the QCD transition
hep-lat 2011-11 accept novelty 6.0 of 10

Continuum-extrapolated lattice QCD gives a chiral crossover temperature of 154 +/- 9 MeV at physical quark masses, defined by the peak of the chiral susceptibility under O(4) scaling.
Precise B, B_s and B_c meson spectroscopy from full lattice QCD
hep-lat 2010-10 accept novelty 6.0 of 10

Full lattice QCD with 2+1 sea flavors and NRQCD bottom quarks yields m_B = 5.291(18) GeV, m_Bs = 5.363(11) GeV, and m_Bc = 6.280(10) GeV, in agreement with experiment.
Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings
hep-lat 2010-07 accept novelty 6.0 of 10

Including order-v^6 spin-dependent terms in lattice NRQCD and using ratios that cancel radiative corrections yields a 1S bottomonium hyperfine splitting of 60.3 ± 5.5 ± 5.0 ± 2.1 MeV.
High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
hep-lat 2010-04 accept novelty 6.0 of 10

Moments of pseudoscalar heavy-quark correlators on lattice QCD give m_c(3 GeV) = 0.986(6) GeV, m_b(10 GeV) = 3.617(25) GeV and alpha_MS(M_Z) = 0.1183(7), with an independent nonperturbative m_b/m_c cross-check agreein...
Precise determination of the lattice spacing in full lattice QCD
hep-lat 2009-10 accept novelty 6.0 of 10

Combining three methods on MILC ensembles gives a continuum scale r1 = 0.3133(23)(3) fm, plus a new eta_s-based recipe for setting the lattice spacing and strange-quark mass.
The B -> pi l nu semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|
hep-lat 2008-11 conditional novelty 6.0 of 10

A combined lattice-QCD and BABAR analysis yields |Vub| = 3.38 ± 0.36 × 10⁻³ using a model-independent z-expansion fit, the first such determination to include a continuum extrapolation.
Unquenched determination of the kaon parameter B_K from improved staggered fermions
hep-lat 2006-03 conditional novelty 6.0 of 10

A first unquenched lattice QCD computation of B_K with improved staggered fermions gives \hat B_K = 0.83 ± 0.18, dominated by perturbative matching uncertainty.
B Meson Semileptonic Form Factors from Unquenched Lattice QCD
hep-lat 2006-01 conditional novelty 6.0 of 10

Unquenched lattice QCD gives the B to pion form factors f+ and f0, and combined with HFAG branching fractions yields |Vub| = 3.55(25)(50) x 10^-3 once an erratum corrects a normalization bug in the f_perp analysis.
The determination of potential scales in 2+1 flavor QCD
hep-lat 2024-12 conditional novelty 5.0 of 10

A new lattice QCD determination of the hadronic scales r0 = 0.4729(75) fm and r1 = 0.3127(40) fm in 2+1 flavor QCD, together with r0 Λ_MSbar^(3) = 0.820(28).
New methods for B meson decay constants and form factors from lattice NRQCD
hep-lat 2017-11 accept novelty 5.0 of 10

One-loop matching coefficients for NRQCD-HISQ pseudoscalar and scalar currents are computed, giving f_B = 0.196(6) GeV and f_Bs = 0.236(7) GeV from a route independent of the temporal axial current.
Lattice QCD inputs to the CKM unitarity triangle analysis
hep-ph 2009-10 conditional novelty 5.0 of 10

Averaging 2+1 flavor lattice QCD matrix elements and fitting the CKM unitarity triangle yields a 2-3 sigma tension, interpretable as new physics in neutral kaon mixing.
The QCD transition temperature: results with physical masses in the continuum limit II.
hep-lat 2009-03 accept novelty 5.0 of 10

Using finer lattices and physical quark masses, the Wuppertal-Budapest collaboration confirms a QCD crossover temperature near 150 to 155 MeV and reports an unresolved 20 to 35 MeV discrepancy with the hotQCD collaboration.
A Unified Study of Hidden-Charm and Hidden-Bottom Mesons
hep-ph 2026-07 conditional novelty 4.0 of 10

A common screened-potential and QCD sum-rule framework yields consistent spectra, E1/M1 widths, Regge slopes, decay constants and finite-spectrum thermal indicators for c¯c and b¯b mesons.
Bottomonium spectrum revisited
hep-ph 2016-01 conditional novelty 4.0 of 10

A nonrelativistic constituent quark model reproduces the known bottomonium spectrum and predicts masses and decay widths for unobserved states such as the eta_b(3S), h_b(3P), and the D-wave levels.
|V_cd| from D Meson Leptonic Decays
hep-lat 2012-06 accept novelty 4.0 of 10

Lattice QCD gives f_D = 208.3(3.4) MeV, which combined with CLEO-c data yields |V_cd| = 0.223(10)(4), a third independent determination agreeing with semileptonic and neutrino results.
Quarkonium mass splittings in three-flavor lattice QCD
hep-lat 2009-12 conditional novelty 4.0 of 10

Fermilab-method lattice QCD reproduces most charmonium and bottomonium mass splittings once tuning and discretization errors are included, with the charmonium 2S-1S splitting a conspicuous exception.
MILC results for light pseudoscalars
hep-ph 2009-10 conditional novelty 4.0 of 10

Lattice QCD data at three lattice spacings, fit with SU(2) and SU(3) chiral perturbation theory including NNLO logarithms, yield preliminary values for pion and kaon decay constants, light quark masses, Gasser-Leutwyl...
Update: Accurate Determinations of alpha_s from Realistic Lattice QCD
hep-lat 2008-07 conditional novelty 4.0 of 10

The strong coupling is determined to 0.7 percent, alpha_MSbar(M_Z, nf=5) = 0.1183(8), by fitting 22 short-distance Wilson-loop quantities computed on 12 MILC lattice ensembles spanning six lattice spacings.
FLAG Review 2021
hep-lat 2021-11 accept novelty 3.0 of 10

The Flavour Lattice Averaging Group reviews lattice-QCD results published before 30 April 2021 and issues colour-coded, correlation-aware averages for quark masses, decay constants, form factors, mixing parameters, al...
Exotics: Heavy Pentaquarks and Tetraquarks
hep-ph 2017-06 accept novelty 3.0 of 10

A comprehensive review of the charmonium- and bottomonium-like exotics and the two LHCb pentaquarks, covering the experimental evidence state by state and the four competing theoretical explanations for them.
The QCD equation of state from the lattice
hep-lat 2012-07 accept novelty 3.0 of 10

Lattice QCD simulations now give a controlled, near-continuum equation of state for hot quark matter at physical quark masses, with residual systematic errors concentrated in the staggered-fermion rooting question and...
FLAG Review 2024
hep-lat 2024-11 accept novelty 2.0 of 10

The FLAG 2024 review provides updated averages of lattice QCD determinations for quark masses, decay constants, form factors, mixing parameters, and nucleon matrix elements.
Quarkonia in the Quark Gluon Plasma
hep-ph 2013-02 conditional novelty 2.0 of 10

Quarkonium melting in the quark-gluon plasma is governed by a complex-valued heavy-quark potential whose imaginary part produces in-medium widths of 20 to 100 MeV, blurring the sharp dissociation temperatures of the o...
The phase diagram of quantum chromodynamics
hep-ph 2009-08 accept novelty 2.0 of 10

Lattice QCD places the zero-density confinement transition at roughly 151 to 175 MeV and finds it to be an analytic crossover, while the nonzero-density critical point remains unlocated.

How the literature uses it

49 arXiv papers cite this in 90 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 36 sentences without a confident label

Builds on it 1 paper

Here we improve on the calculations in [ref] which used results from MILC super-coarse, coarse and fine ensembles and compared ensembles with and without sea quarks.

Precise determination of the lattice spacing in full lattice QCD · $m_Υ^'-m_Υ$ · 0.86

Uses its method or tool 9 papers

We therefore initialise $N_smear$ NRQCD $b$ propagators by setting [equation] and evolve with [equation] We use an improved lattice NRQCD Hamiltonian [ref] : [equation] [equation]

Precision $B_c$ and $B_s$ mass calculations · Heavy-light 2-point functions · 1.00
Here, improved non-relativistic QCD (NRQCD) [ref] is employed instead, following closely the methods used in the calculation of the bottomonium spectrum on the MILC gauge configurations in [ref] (these configurations use an improved staggered fermion action for the sea quarks and a one-loop Symanzik-improved gluon action).

The bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions · Introduction · 0.96
For the heavy quark fields, $ψ(𝐱,t)$, we use the NRQCD action of [ref] , which is improved through $O(1/M_0^2)$ and $O(a^2)$ and includes the leading relativistic $O(1/M_0^3)$ correction.

Matching lattice and continuum axial-vector and vector currents with NRQCD and HISQ quarks · Heavy Quark Action · 0.99

Uses its data or values 13 papers

In our analysis we use simulation values for $r_1/a$, from the static-quark potential, to determine ratios of scales from different configuration sets, and simulation values for the $Υ^'$–$Υ$ mass difference to set the overall scale [ref] .

Update: Accurate Determinations of alpha_s from Realistic Lattice QCD · Conclusions · 0.95
The reader is referred to [ref] and [ref] for the details.

The bottomonium spectrum from lattice QCD with 2+1 flavors of domain wall fermions · Radial/orbital splittings and the lattice spacing · 0.92
The absolute scale from the $Υ$ $2S$-$1S$ splitting was determined on most of our ensembles by the HPQCD Collaboration [ref] .

Quarkonium mass splittings in three-flavor lattice QCD · Configuration details · 0.96

Compares with it 11 papers

Our result is $1.5σ$ from our previous analysis [ref] using only the $Υ$ $2S-1S$ splitting on fewer ensembles and combined with less accurate $r_1/a$ values.

Precise determination of the lattice spacing in full lattice QCD · Conclusions · 0.90
[ref] (pre-dating the discovery of the $1$) and Meinel [ref] are consistent with all of the measured values and the PDG averages; Dowdall .

Hyperfine splitting and the experimental candidates for \eta_b(2S) · Lattice QCD · 0.88
Our calculation improves on a previous determination of $m_b(m_b) = 4.4(3)$ GeV from unquenched lattice QCD simulations using NRQCD valence b quarks [ref] .

The b quark mass from lattice nonrelativistic QCD · Introduction · 0.94

Cites it as background 10 papers

Currently most high-precision lattice work on $b$ physics relies upon nonrelativistic effective field theories, like NRQCD [ref] .

High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD · Introduction · 0.89
The bottomonium spectrum was calculated using improved lattice NRQCD of order $v^4$ on the MILC gauge field ensembles in [ref] .

Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings · Introduction · 0.81
Many phenomenological researches on $η_b$ have been done by some groups [ref] .

Study on the radiative decays of $\Upsilon(nS)\to \eta_b+\gamma$ · introduction · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [8]

C. Aubin et al , Phys. Rev. D 70, 094505 (2004), hep-lat/0402030

View on Pith Pith review arXiv 2004

[2] [1]

Fermilab, HPQCD, MILC, UKQCD collaborations, C. T. H. Davies et al , Phys. Rev. Lett. 92, 022001 (2004), hep-lat/0304004

View on Pith Pith review arXiv 2004

[3] [2]

HPQCD, MILC, UKQCD collaborations, C. Aubin et al , Phys. Rev. D 70, 031504 (2004), hep-lat/0405022

View on Pith Pith review arXiv 2004

[4] [3]

MILC collaboration, C. Aubin et al , hep-lat/0407028

View on Pith Pith review arXiv

[5] [4]

Fermilab, HPQCD collaborations, I. Allison, C. T. H. Davies, A. Gray, A.S. Kronfeld, P. B. Mackenzie, J. N. Simone, Phys. Rev. Lett. 94, 172001 (2005), hep-lat/0411027

View on Pith Pith review arXiv 2005

[6] [5]

Fermilab, MILC collaborations, C. Aubin et al , hep-ph/0408306

View on Pith Pith review arXiv

[7] [6]

C. W. Bernard et al , Phys. Rev. D 64, 054506 (2001), hep-lat/0104002

View on Pith Pith review arXiv 2001

[8] [7]

(where r2F (r) = 1 .00) of 0.321(5)fm. This is also shown as a function of light quark mass in Figure 5 and also agrees with the preliminary value from [7]. This vari- able in fact shows a very ﬂat curve as a function of light quark mass when the scale is set by the Υ 2 S − 1S split- ting, i.e. the light quark vacuum polarisation eﬀects are very similar i...

View on Pith

[9] [9]

MILC collaboration, private communication

View on Pith

[10] [10]

The action was ﬁrst given in: G. P. Lepage, Phys. Rev. D59, 074502 (1999), hep-lat/9809157. See the follow- ing for studies of its performance: K. Orginos, D. Tou- ssaint, R. L. Sugar, Phys. Rev. D 60, 054503 (1999), hep-lat/9903032; MILC collaboration, C. Bernard et al , Phys. Rev. D 61, 111502 (2000), hep-lat/9912018

View on Pith Pith review arXiv 1999

[11] [11]

M. Alford, W. Dimm, G. P. Lepage, G. Hockney and P. B. Mackenzie, Phys. Lett. B 361 (1995) 87, hep-lat/9507010

View on Pith Pith review arXiv 1995

[12] [12]

M.Nobes, hep-lat/0501009

View on Pith Pith review arXiv

[13] [13]

B. A. Thacker and G. P. Lepage, Phys. Rev. D 43 (1991) 196

View on Pith 1991

[14] [14]

G. P. Lepage et al , Phys. Rev. D 46, 4052 (1992), hep-lat/9205007

View on Pith Pith review arXiv 1992

[15] [15]

C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lep- age, A. Lidsey, J. Shigemitsu, J. Sloan, Phys. Rev. D 50, 6963 (1994), hep-lat/9406017

View on Pith Pith review arXiv 1994

[16] [16]

C. Morningstar, Phys. Rev. D 50 (1994) 5902, hep-lat/9406002

View on Pith Pith review arXiv 1994

[17] [17]

G. P. Lepage and P. Mackenzie, Phys. Rev. D 48 (1993) 2250

View on Pith 1993

[18] [18]

The value of u0 does aﬀect the value of the ground state energy as is clear from comparing Tables V and VII. The dependence on u0 can be seen in perturbation theory or in a mean ﬁeld approach [13] which gives a reasonably good quantitative description of the results

View on Pith

[19] [19]

M. Nobes, private communication

View on Pith

[20] [20]

C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. Lidsey, J. Shigemitsu and J. H. Sloan, Phys. Lett. B 345 (1995) 42, hep-ph/9408328

View on Pith Pith review arXiv 1995

[21] [21]

C. T. H. Davies, K. Hornbostel, G. P. Lepage, A. Lid- sey, P. McCallum, J. Shigemitsu, J. H. Sloan, Phys. Rev. D58, 054505 (1998), hep-lat/9802024

View on Pith Pith review arXiv 1998

[22] [22]

S. Groote and J. Shigemitsu, Phys. Rev. D 62, 014508 (2000), hep-lat/0001021

View on Pith Pith review arXiv 2000

[23] [23]

G. P. Lepage et al , Nucl. Phys. B (Proc. Suppl. 106) (2002)12, hep-lat/0110175

View on Pith Pith review arXiv 2002

[24] [24]

S. Eidelman et al , Phys. Lett. B 592 (2004) 1

View on Pith 2004

[25] [25]

C. T. H. Davies, K. Hornbostel, G. P. Lepage, P.McCallum, J. Shigemitsu, J. H. Sloan, Phys. Rev. D 56 (1997) 2755

View on Pith 1997

[26] [26]

N. Eicker et al , Phys. Rev. D 57, 4080 (1998), hep-lat/9709002

View on Pith Pith review arXiv 1998

[27] [27]

CP-PACS collaboration, T. Manke et al , Phys. Rev D 62, 114508 (2000), hep-lat/0005022

View on Pith Pith review arXiv 2000

[28] [28]

UKQCD collaboration, L. Marcantonio, P. Boyle, C. T. H. Davies, J. Hein, J. Shigemitsu, Nucl. Phys. B (Proc. Suppl.94), 363 (2001), hep-lat/0011053

View on Pith Pith review arXiv 2001

[29] [29]

R. Sommer, Nucl. Phys. B 411 (1994) 839, hep-lat/9310022

View on Pith Pith review arXiv 1994

[30] [30]

CLEO collaboration, G. Bonvicini et al , Phys. Rev. D70:32001 (2004), hep-ex/0404021

View on Pith Pith review arXiv 2004

[31] [31]

M. Alford, T. R. Klassen and G. P. Lepage, Nucl. Phys. B496 (1997) 377, hep-lat/9611010

View on Pith Pith review arXiv 1997

[32] [32]

Y. Kayaba et al , Nucl. Phys. B (Proc. Suppl.) 140 (2005) 479, hep-lat/0409086

View on Pith Pith review arXiv 2005

[33] [33]

J. Shigemitsu et al , Proceedings of LAT04, Nucl. Phys. B(Proc. Suppl. 140) (2005) 464, hep-lat/0408019

View on Pith Pith review arXiv 2005

[34] [34]

C. T. H. Davies, K. Hornbostel, A. Langnau, G. P. Lep- age, A. Lidsey, C. J. Morningstar, J. Shigemitsu, J. Sloan, Phys. Rev. Lett. 73 (1994) 2654, hep-lat/9404012

View on Pith Pith review arXiv 1994

[35] [35]

E. Gulez, J. Shigemitsu and M. Wingate, Phys. Rev. D69:074501 (2004), hep-lat/0312017

View on Pith Pith review arXiv 2004

[36] [36]

Q. Mason et al , Phys. Rev. Lett. (in press), hep-lat/0503005; Q. Mason and H. Trottier, in prepa- ration

View on Pith Pith review arXiv

[37] [37]

S. J. Brodsky, G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 28 (1983) 228

View on Pith 1983

[38] [38]

C, Morningstar, private communication from the calcu- lation of [15] , using a slightly diﬀerent NRQCD action and an unimproved gluon action

View on Pith

[39] [39]

NRQCD collaboration, K. Hornbostel, Nucl. Phys. B (Proc. Suppl. 73) (1999) 339, hep-lat/9809177

View on Pith Pith review arXiv 1999

[40] [40]

K. Melnikov and T. van Ritbergen, Phys. Lett. B 482 (2000) 99, hep-ph/9912391

View on Pith Pith review arXiv 2000

[41] [41]

A. Ali Khan et al , Phys. Rev. D 62:054505 (2000), hep-lat/9912034

View on Pith Pith review arXiv 2000

[42] [42]

Belle collaboration, S.-K. Choi et al , Phys. Rev. Lett. 89:102001 (2002)

View on Pith 2002

[43] [43]

HPQCD collaboration, in preparation

View on Pith

[44] [44]

H. Trottier, Phys. Rev. D 55 (1997) 6844, hep-lat/9611026; T. Manke et al , Phys. Lett. B 468 (1997) 308, hep-lat/9706003; N. H. Shakespeare and H. D. Trottier, Phys. Rev. D 58:034502 (1998), hep-lat/9802038

View on Pith Pith review arXiv 1997

[45] [45]

C. Davies, Springer Lecture notes in Physics, Eds Gaus- terer, Lang, 1998, hep-ph/9710394

View on Pith Pith review arXiv 1998

[46] [46]

Jean Duboscq, CLEO, talk at the HEP2005 Europhysics conference, Lisbon, July 2005, www.lip.pt/events/2005/hep2005/talks/session5.html

View on Pith 2005

[47] [47]

See, for example, D. H. Perkins, Introduction to High En- ergy Physics , 3rd Ed. (Addison-Wesley, Reading, MA)

View on Pith

[48] [48]

G. von Hippel, PhD thesis, University of Cambridge, 2003; R. Horgan, private communication

View on Pith 2003

[49] [49]

C. J. Morningstar and J. Shigemitsu, Phys. Rev. D 57 (1998) 6741, hep-lat/9712016

View on Pith Pith review arXiv 1998

[50] [50]

J. Erler, Phys. Rev. D 59:054008 (1999), hep-ph/9803453

View on Pith Pith review arXiv 1999

[51] [51]

B. D. Jones and R. M. Woloshyn, Phys. Rev. D60:014502(1999), hep-lat/9812008

View on Pith Pith review arXiv 1999

[52] [52]

E. Eichten and C. Quigg, Phys. Rev. D 52 (1995) 1726, hep-ph/9503356

View on Pith Pith review arXiv 1995

[53] [53]

M. Campbell, MSc thesis, University of Glasgow, 1998. We use the average of the 1 1D2,T and 1 1D2,E (since these seem more reliable than the corresponding 1 3D2 results) and combine it with the 1 3S1 energy and a−1 25 value from [14]

View on Pith 1998

[54] [54]

J. Hein et al , Phys. Rev. D 62:074503 (2000), hep-ph/0003130. We take results for unimproved glue at β=6.2 and combine with results from [20], after adjust- ment to use the lattice spacing from the Υ 2 S − 1S split- ting consistently, including for the s quark mass. This can only be done to a limited extent because the original cal- culations used a diﬀe...

View on Pith Pith review arXiv 2000