Extraction of light quark masses from sum rule analyses of axial vector and vector current Ward identities

Bhattacharya, Tanmoy; Gupta, Rajan; Maltman, Kim

doi:10.1103/PhysRevD.57.5455

Extraction of light quark masses from sum rule analyses of axial vector and vector current Ward identities

Tanmoy Bhattacharya
(
- Los Alamos
)
,
Rajan Gupta
(
- Los Alamos
)
,
Kim Maltman
(
- York U., Canada and
- Adelaide U.
)

Mar, 1997

28 pages

Published in:

Phys.Rev.D 57 (1998) 5455-5467

e-Print:

hep-ph/9703455 [hep-ph]

DOI:

10.1103/PhysRevD.57.5455

Report number:

LA-UR-96-2698

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Abstract:

We re-examine the use of sum rules in the extraction of light quark masses and discuss a number of potential problems with existing analyses. The most important issue is that of the overall normalization of the hadronic spectral functions should not be fixed by assuming complete resonance dominance of the continuum threshold region as it can overestimate the resonance contributions to spectral integrals by factors as large as

\sim 5

. The second important uncertainty comes from the assumed location,

s_0

, of the onset of duality with perturbative QCD, as the extracted quark masses depend very sensitively on this parameter. The assumption of duality and the requirement of positivity of

\rho_5(s)

imposes very severe constraints on the shape of the relevant spectral function in the dual region, and leads to rigorous lower bounds for

m_u+m_d

as a function of

s_0

. In the extractions of

m_s

we find that the conventional choice of the value of

s_0

is not physical. For a more reasonable choice of

s_0

we are not able to find a solution that is stable with respect to variations of the Borel transform parameter. This problem can be overcome only if the hadronic spectral function is determined up to significantly larger values of

s

than is currently possible. Finally, we also estimate the error associated with the convergence of perturbative QCD expressions used in the sum rule analyses. Our conclusion is that, taking all of these issues into account, the resulting sum rule estimates for both

m_u+m_d

and

m_s

could easily have uncertainties as large as a factor of 2.

Note:

28 pages. Published version. Modified axis source for figures also included Report-no: LAUR-96-2698 Journal-ref: Phys.Rev. D57 (1998) 5455-5467 DOI: 10.1103/PhysRevD.57.5455

quark: mass
sum rule: finite energy
current: vector
current: axial-vector
spectral representation
Ward identity
perturbation theory: chiral
quantum chromodynamics: perturbation theory
two-point function
duality

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