scholarly journals Quark–hadron duality: Pinched kernel approach

2016 ◽  
Vol 31 (27) ◽  
pp. 1630026 ◽  
Author(s):  
C. A. Dominguez ◽  
L. A. Hernandez ◽  
K. Schilcher ◽  
H. Spiesberger
Keyword(s):  
Perturbative Qcd ◽  
Sum Rules ◽  
Axial Vector ◽  
Finite Energy ◽  
Aleph Collaboration ◽  
Spectral Functions ◽  
Vector Channel ◽  
Kernel Approach ◽  
Model Independent ◽  
Hadron Duality

Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark–hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to s = 10 GeV2 by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using e[Formula: see text] e[Formula: see text] annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.

scholarly journals Tests of quark–hadron duality in τ-decays

2016 ◽  
Vol 31 (31) ◽  
pp. 1630036 ◽  
Author(s):  
C. A. Dominguez ◽  
L. A. Hernandez ◽  
K. Schilcher ◽  
H. Spiesberger
Keyword(s):  
Sum Rules ◽  
Axial Vector ◽  
Gluon Condensate ◽  
Finite Energy ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Spectral Functions ◽  
Linear Integration ◽  
Experimental Errors ◽  
Hadron Duality

An exhaustive number of QCD finite energy sum rules for [Formula: see text]-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension d = 2 condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions d = 6 and d = 8, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark–hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic [Formula: see text]-decay in the kinematic region above s [Formula: see text] 2.2 GeV2 for these kernels.

scholarly journals Finite energy chiral sum rules and τ spectral functions

1998 ◽  
Vol 58 (9) ◽  
Author(s):  
M. Davier ◽  
A. Höcker ◽  
L. Girlanda ◽  
J. Stern
Keyword(s):  
Sum Rules ◽  
Finite Energy ◽  
Spectral Functions

Quark mass determinations in QCD

2014 ◽  
Vol 29 (28) ◽  
pp. 1430031 ◽  
Author(s):  
C. A. Dominguez
Keyword(s):  
Heavy Quark ◽  
Light Quark ◽  
Finite Energy ◽  
Experimental Information ◽  
Bottom Quarks ◽  
Spectral Functions ◽  
Quark Masses ◽  
Quark Sector ◽  
Vector Channel ◽  
Systematic Uncertainties

Recent progress on QCD sum rule determinations of the light and heavy quark masses is reported. In the light quark sector a major breakthrough has been made recently in connection with the historical systematic uncertainties due to a lack of experimental information on the pseudoscalar resonance spectral functions. It is now possible to suppress this contribution to the 1% level by using suitable integration kernels in Finite Energy QCD sum rules. This allows to determine the up-, down-, and strange-quark masses with an unprecedented precision of some 8–10%. In the heavy quark sector, the availability of experimental data in the vector channel, and the use of suitable multipurpose integration kernels allows to increase the accuracy of the charm- and bottom-quarks masses to the 1% level.

scholarly journals Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
César Ayala ◽  
Gorazd Cvetič ◽  
Diego Teca
Keyword(s):  
Perturbation Theory ◽  
Perturbative Qcd ◽  
Sum Rules ◽  
Finite Energy ◽  
Operator Product ◽  
Decay Data ◽  
Fixed Order ◽  
Principal Value ◽  
Adler Function

AbstractWe present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $$\tau $$ τ -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the $${\overline{\mathrm{MS}}}$$ MS ¯ coupling is $$\alpha _s(m_{\tau }^2) = 0.3116 \pm 0.0073$$ α s ( m τ 2 ) = 0.3116 ± 0.0073 [$$\alpha _s(M_Z^2)=0.1176 \pm 0.0010$$ α s ( M Z 2 ) = 0.1176 ± 0.0010 ] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $$\alpha _s(m_{\tau }^2) = 0.3194 \pm 0.0167$$ α s ( m τ 2 ) = 0.3194 ± 0.0167 [$$\alpha _s(M_Z^2)=0.1186 \pm 0.0021$$ α s ( M Z 2 ) = 0.1186 ± 0.0021 ].

scholarly journals Note on finite temperature sum rules for vector and axial-vector spectral functions

2002 ◽  
Vol 530 (1-4) ◽  
pp. 88-92 ◽  
Author(s):  
E. Marco ◽  
R. Hofmann ◽  
W. Weise
Keyword(s):  
Finite Temperature ◽  
Sum Rules ◽  
Axial Vector ◽  
Spectral Functions ◽  
Temperature Sum

scholarly journals XYZ-SU3 breakings from Laplace sum rules at higher orders

2018 ◽  
Vol 33 (16) ◽  
pp. 1850082 ◽  
Author(s):  
R. Albuquerque ◽  
S. Narison ◽  
D. Rabetiarivony ◽  
G. Randriamanatrika
Keyword(s):  
Sum Rules ◽  
Chiral Limit ◽  
Axial Vector ◽  
Operator Product ◽  
Leading Order ◽  
Spectral Functions ◽  
Quark State ◽  
Future Data ◽  
The Masses ◽  
Spectral Sum Rules

We present new compact integrated expressions of SU3 breaking corrections to QCD spectral functions of heavy–light molecules and four-quark [Formula: see text]-like states at lowest order (LO) of perturbative (PT) QCD and up to [Formula: see text] condensates of the Operator Product Expansion (OPE). Including next-to-next-to-leading order (N2LO) PT corrections in the chiral limit and next-to-leading order (NLO) SU3 PT corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results for the [Formula: see text]-like masses and decay constants from QCD spectral sum rules (QSSR). Systematic errors are estimated from a geometric growth of the higher order PT corrections and from some partially known [Formula: see text] nonperturbative contributions. Our optimal results, based on stability criteria, are summarized in Tables 18–21 while the [Formula: see text] and [Formula: see text] channels are compared with some existing LO results in Table 22. One can note that, in most channels, the SU3 corrections on the meson masses are tiny: [Formula: see text] (respectively [Formula: see text]) for the [Formula: see text] (respectively [Formula: see text])-quark channel but can be large for the couplings ([Formula: see text]). Within the lowest dimension currents, most of the [Formula: see text] and [Formula: see text] states are below the physical thresholds while our predictions cannot discriminate a molecule from a four-quark state. A comparison with the masses of some experimental candidates indicates that the [Formula: see text] [Formula: see text] might have a large [Formula: see text] molecule component while an interpretation of the [Formula: see text] candidates as four-quark ground states is not supported by our findings. The [Formula: see text] [Formula: see text] and [Formula: see text] are compatible with the [Formula: see text], [Formula: see text] molecules and/or with the axial-vector [Formula: see text] four-quark ground state. Our results for the [Formula: see text], [Formula: see text] and for different beauty states can be tested in the future data. Finally, we revisit our previous estimates1 for the [Formula: see text] and [Formula: see text] and present new results for the [Formula: see text].

scholarly journals QUASILOCAL QUARK MODELS AS EFFECTIVE THEORY OF NON-PERTURBATIVE QCD

2005 ◽  
Vol 20 (08n09) ◽  
pp. 1850-1854 ◽  
Author(s):  
A. A. ANDRIANOV ◽  
V. A. ANDRIANOV
Keyword(s):  
Perturbative Qcd ◽  
Chiral Symmetry ◽  
Sum Rules ◽  
Axial Vector ◽  
Effective Theory ◽  
Operator Product ◽  
Decay Constants ◽  
Intermediate Energies ◽  
Quark Models ◽  
Meson States

We consider the Quasilocal Quark Model of NJL type (QNJLM) as an effective theory of non-perturbative QCD including scalar (S), pseudoscalar (P), vector (V) and axial-vector (A) four-fermion interaction with derivatives. In the presence of a strong attraction in the scalar channel the chiral symmetry is spontaneously broken and as a consequence the composite meson states are generated in all channels. With the help of Operator Product Expansion the appropriate set of Chiral Symmetry Restoration (CSR) Sum Rules in these channels are imposed as matching conditions to QCD at intermediate energies. The mass spectrum and some decay constants for ground and excited meson states are calculated.

scholarly journals QCD parameter correlations from heavy quarkonia

2018 ◽  
Vol 33 (10) ◽  
pp. 1850045 ◽  
Author(s):  
Stephan Narison
Keyword(s):  
Sum Rules ◽  
Axial Vector ◽  
Gluon Condensate ◽  
Sum Rule ◽  
Channel One ◽  
Vector Channel ◽  
Stability Point ◽  
Pseudo Scalar ◽  
First Time ◽  
Good Agreement

Correlations between the QCD coupling [Formula: see text], the gluon condensate [Formula: see text] and the [Formula: see text], [Formula: see text]-quark running masses [Formula: see text] in the [Formula: see text]-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium and bottomium ratios of Laplace sum rules (LSR) evaluated at the [Formula: see text]-subtraction stability point where perturbative (PT) @N2LO, N3LO and [Formula: see text] @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of [Formula: see text] from [Formula: see text] sum rule and also show the sensitivity of the sum rules on the choice of the [Formula: see text]-subtraction scale which does not permit a high-precision estimate of [Formula: see text]. We obtain from the (axial-)vector [respectively (pseudo)scalar] channels: [Formula: see text] [respectively [Formula: see text] GeV4, [Formula: see text] [respectively 1266(16)] MeV and [Formula: see text] MeV. Combined with our recent determinations from vector channel, one obtains the average: [Formula: see text] MeV and [Formula: see text] MeV. Adding the two above values of the gluon condensate to different previous estimates in Table 1, one obtains the 2018 sum rule average: [Formula: see text] GeV4. The mass-splittings [Formula: see text] give @N2LO: [Formula: see text] in good agreement with the world average.

scholarly journals Constraints on hadronic spectral functions from continuous families of finite energy sum rules

1998 ◽  
Vol 440 (3-4) ◽  
pp. 367-374 ◽  
Author(s):  
Kim Maltman
Keyword(s):  
Sum Rules ◽  
Finite Energy ◽  
Spectral Functions

scholarly journals QUARK MASSES IN QCD: A PROGRESS REPORT

2011 ◽  
Vol 26 (10) ◽  
pp. 691-710 ◽  
Author(s):  
C. A. DOMINGUEZ
Keyword(s):  
Heavy Quark ◽  
Light Quark ◽  
Finite Energy ◽  
Experimental Information ◽  
Spectral Functions ◽  
Quark Masses ◽  
Quark Sector ◽  
Vector Channel ◽  
Systematic Uncertainties ◽  
Improved Accuracy

Recent progress on QCD sum rule determinations of the light and heavy quark masses is reported. In the light quark sector a major breakthrough has been made recently in connection with the historical systematic uncertainties due to a lack of experimental information on the pseudoscalar resonance spectral functions. It is now possible to suppress this contribution to the 1% level by using suitable integration kernels in Finite Energy QCD sum rules. This allows one to determine the up-, down-, and strange-quark masses with an unprecedented precision of some 8–10%. Further reduction of this uncertainty will be possible with improved accuracy in the strong coupling, now the main source of error. In the heavy quark sector, the availability of experimental data in the vector channel, and the use of suitable multipurpose integration kernels allows one to increase the accuracy of the charm- and bottom-quarks masses to the 1% level.

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