Light quark masses beyond leading order

Journal Article · Sat Feb 01 00:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.892· OSTI ID:7235230

Donoghue, J F ^[1]; Wyler, D ^[2]

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1. Department of Physics and Astronomy, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
2. Institut fuer Theoretical Physik, Universitaet Zurich, CH8001 Zurich (Switzerland) Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (United States)

We describe the measurement of the light quark mass ratios when one calculates to second order in the quark masses. At this order there is an ambiguity in the meaning of the quark mass, which afflicts the past attempts to provide a model-independent measurement of the ratios. We argue that this is similar to the regularization-scheme dependence of coupling constants. We study the anomalous Ward identities and the effects of strong {ital CP} violation in an attempt to resolve the ambiguity. The ambiguity persists even with singlet fields, such as the {eta}{prime}, but can be resolved by observing the {theta} dependence of the theory. Since matrix elements of {ital F{tilde F}} are related to {partial derivative}{ital scrL}{sub QCD}/{partial derivative}{theta}, they are useful probes of quark masses. We give a procedure by which quark mass ratios can be measured in a model-independent way through the matrix elements {l angle}0{vert bar}{ital F{tilde F}}{vert bar}{pi}{sup 0}{r angle}, {l angle}0{vert bar}{ital F{tilde F}}{vert bar}{eta}{r angle}, and {l angle}0{vert bar}{ital F{tilde F}}{vert bar}3{pi}{r angle}, which in turn are observable in {ital V}{prime}{r arrow}{ital V}{pi}{sup 0} ({eta},3{pi}), with {ital V} being {psi} or {Upsilon}, when analyzed using a heavy-quark multipole expansion. Present data are not sufficient to complete this program, but we use available results to provide the value (({ital m}{sub {ital d}}{minus}{ital m}{sub {ital u}})/({ital m}{sub {ital d}}+{ital m}{sub {ital u}}))({ital m}{sub {ital s}}+{ital {cflx m}})/({ital m}{sub {ital s}}{minus}{ital {cflx m}})=0.5 9{plus minus}0.07{plus minus}0.08 (i.e., {ital m}{sub {ital u}}/{ital m}{sub {ital d}}=0.30{plus minus}0.05{plus minus}0.05), where the first error is experimental and the second is our estimate of the remaining theoretical model dependence.

• OSTI ID: 7235230
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 45:3; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUARKS
MASS
CHIRAL SYMMETRY
COUPLING CONSTANTS
CP INVARIANCE
MATRIX ELEMENTS
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
RENORMALIZATION
STANDARD MODEL
WARD IDENTITY
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
SYMMETRY
UNIFIED GAUGE MODELS
662230* - Quantum Chromodynamics- (1992-)
662120 - General Theory of Particles & Fields- Symmetry
Conservation Laws
Currents & Their Properties- (1992-)
662440 - Properties of Other Particles Including Hypothetical Particles- (1992-)