<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>Z</mml:mi></mml:math>corrections to forward-angle parity-violating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi><mml:mi>p</mml:mi></mml:math>scattering

Sibirtsev, A.; Blunden, P. G.; Melnitchouk, Wally; Thomas, A. W.

doi:10.1103/physrevd.82.013011

Cited by 76 publications

(135 citation statements)

References 30 publications

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“…This value for ✷ γZ is the one adopted in Ref. [2], and contributes almost half of the error in the theoretical estimate Q p W = 0.0713 (8). To progress in a systematic way beyond the approach of MS [3], and to determine the dependence on energy E, we present a new formulation of the box diagram contribution in which the dominant part of the correction is expressed in terms of empirical moments of structure functions.…”

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confidence: 99%

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New Formulation ofγZBox Corrections to the Weak Charge of the Proton

2011

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We present a new formulation of one of the major radiative corrections to the weak charge of the proton -that arising from the axial-vector hadron part of the γZ box diagram, ℜe ✷ A γZ . This formulation, based on dispersion relations, relates the γZ contributions to moments of the F γZ 3 interference structure function. It has a clear connection to the pioneering work of Marciano and Sirlin, and enables a systematic approach to improved numerical precision. Using currently available data, the total correction from all intermediate states is ℜe ✷ A γZ = 0.0044(4) at zero energy, which shifts the theoretical estimate of the proton weak charge from 0.0713(8) to 0.0705(8). The energy dependence of this result, which is vital for interpreting the Q weak experiment, is also determined.As modern parity-violating (PV) experiments press to ever improving levels of precision, they remain a vital complement to direct tests of the Standard Model at the high energy frontier. The classic example of this, involving precise measurements of parity violation in atoms, led to a remarkably accurate determination of sin 2 θ W . A complementary PV electron-proton scattering measurement underway by the Q weak Collaboration [1] at Jefferson Lab has the potential to increase the mass scale associated with new physics to 2 TeV or higher, provided that the critical radiative corrections are under control. In this Letter we present a new formulation of the important γZ radiative corrections which allows for their controlled, systematic evaluation.Including electroweak radiative corrections, the proton weak charge is defined, at zero electron energy E and zero momentum transfer, as [2]where sin 2 θ W (0) is the weak mixing angle at zero momentum, and the corrections ∆ρ, ∆ e and ∆ ′ e are given in [2] and references therein. The contributions ✷ W W and ✷ ZZ arise from the W W and ZZ box and crossed-box diagrams, and can be computed perturbatively. They are expected to be energy independent for electron scattering in the GeV range. By contrast, the γZ interference correction ✷ γZ (E) depends on physics at both short and long distance scales.In the classic work of Marciano and Sirlin (MS) [3], ✷ γZ (0) was evaluated in a quark model-inspired loop calculation using either a "perturbative" (p) or a "nonperturbative" (np) ansatz,where v e (M 2 Z ) = (1 − 4ŝ 2 ), andŝ 2 ≡ sin 2 θ W (M 2 Z ) = 0.23116 in the MS scheme [4].The perturbative ansatz [3]is the free quark model result, with m a hadronic mass scale, and shows the leading-log behavior. For the nonperturbative ansatz, B np = K m + L m is the sum of a long-distance part, L m , and a short-distance part, K m , withHere m is a mass scale representing the onset of asymptotic behavior at large loop momenta, and the factor (1 − α s (u)/π) is the lowest-order correction induced by the strong interactions. In Ref.[3] L m is taken to be the elastic nucleon (Born) contribution, which is evaluated to be 2.04 using the same dipole form factors for both the electromagnetic and axial-vector coupling. MS...

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“…The F γZ 1,2 contributions to ✷ γZ involve the vector hadron coupling of the Z, and were recently computed in Refs. [7][8][9][10].…”

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New Formulation ofγZBox Corrections to the Weak Charge of the Proton

2011

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“…To extend the W range, we use the parameterizations of Refs. [47,48] which fit proton structure functions in the diffraction region using forms recognizable as Pomeron and rho meson Regge trajectories. The former is isoscalar and the latter isovector, so we have a straightforward extension to the neutron case.…”

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Electromagnetic Self-Energy Contribution toMp−Mnand the Isovector Nucleon Magnetic Polarizability

2012

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We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham's formula is corrected and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find δM γ p−n = 1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with additional input from lattice QCD to constrain this polarizability as: βp−n = −0.87(85) × 10 −4 fm 3 .PACS numbers: 13.40. Dk, 13.40.Ks, 13.60.Fz, 14.20.Dh Given only electrostatic forces, one would predict that the proton is more massive than the neutron but the opposite actually occurs [1-3]:Before we knew of quarks and gluons there were many attempts to explain this contradiction, see Ref.[4] for a review. We now know there are two sources of isospin breaking in the standard model, the masses of the up and down quarks as well as the electromagnetic interactions between quarks governed by the charge operator. The effects of the mass difference between down and up quarks are larger and of the opposite sign than those of electromagnetic effects, see the reviews [5][6][7]. The net result of the quark mass difference and electromagnetic effects is well known, Eq. (1), but our ability to disentangle the contributions from these two sources remains poorly constrained. In contrast, lattice QCD calculations have matured significantly. There are now calculations performed with the light quark masses at or near their physical values [8][9][10][11][12], reproducing the ground state hadron spectrum within a few percent. These advances have allowed for calculations to begin including explicit isospin breaking effects from both the quark masses [13][14][15][16][17] and electromagnetism [15,[18][19][20][21]. While the lattice calculations of m d − m u effects are robust, the contributions from electromagnetism are less mature and suffer from larger systematics, due in large part to the disparity between the photon mass and a typical hadronic scale. Improved knowledge of m d − m u and its effects in nucleons will enhance the ability to use effective field theory to compute a variety of isospin-violating (charge asymmetric) effects in nuclear reactions [7,[22][23][24][25][26][27]].An application [28] of the Cottingham sum rule [29], which relates the electromagnetic self-energy of the nucleon to measured elastic and inelastic cross sections, gives the result δM γ p−n = 0.76 ± 0.30 MeV. Given the high present interest in the precise value of δM γ p−n and its many possible implications, it is worthwhile to revisit this result. Many high quality electron scattering experiments have been performed since 1975 and there have also been theoretical advances. The central aim of this work is to provide a modern, robust evaluation of δM γ p−n . We wil...

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“…It can also be expressed in terms of the weak vector couplings of the light quarks, Q p w = −2(2C 1u + C 1d ) which are again functions of the mixing angle. These expressions are modified beyond tree level by loop corrections [3], however after recent theoretical work on the troublesome Z box term [4][5][6][7][8], these are now sufficiently under control, and the standard model predictions for Q p w and for C 1u and C 1d are robust. The experimental observable is the parity-violating asymmetry, the difference over the sum of the elastic scattering cross section for electrons with positive and negative helicity,…”

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First result from Q_weak

Armstrong

2014

EPJ Web of Conferences

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Abstract.Initial results are presented from the recently-completed Q weak experiment at Jefferson Lab. The goal is a precise measurement of the proton's weak charge Q p w , to yield a test of the standard model and to search for evidence of new physics. The weak charge is extracted from the parity-violating asymmetry in elastic ep scattering at low momentum transfer, Q 2 = 0.025 GeV 2 . A 180 A longitudinally-polarized 1.16 GeV electron beam was scattered from a 35 cm long liquid hydrogen at small angles, 6 • < < 12 • . Scattered electrons were analyzed in a toroidal magnetic field and detected using an array of eight Cerenkov detectors arranged symmetrically about the beam axis. The initial result, from 4% of the complete data set, is Q p W = 0.064 ± 0.012, in excellent agreement with the standard model expectation. Full analysis of the data is expected to yield a value for the weak charge to about 5% precision.

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γZcorrections to forward-angle parity-violatingepscattering

Cited by 76 publications

References 30 publications

New Formulation ofγZBox Corrections to the Weak Charge of the Proton

New Formulation ofγZBox Corrections to the Weak Charge of the Proton

Electromagnetic Self-Energy Contribution toMp−Mnand the Isovector Nucleon Magnetic Polarizability

First result from Q_weak

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γZcorrections to forward-angle parity-violatingepscattering

Cited by 76 publications

References 30 publications

New Formulation ofγZBox Corrections to the Weak Charge of the Proton

New Formulation ofγZBox Corrections to the Weak Charge of the Proton

Electromagnetic Self-Energy Contribution toMp−Mnand the Isovector Nucleon Magnetic Polarizability

First result from Qweak

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Product

Resources

About

First result from Q_weak