scholarly journals Dispersion relations for hadronic light-by-light scattering and the muon g – 2

2018 ◽  
Vol 166 ◽  
pp. 00014 ◽  
Author(s):  
Massimiliano Procura ◽  
Gilberto Colangelo ◽  
Martin Hoferichter ◽  
Peter Stoffer
Keyword(s):  
Partial Wave ◽  
Form Factors ◽  
Pion Pole ◽  
Vector Form ◽  
Partial Wave Expansion ◽  
Left Hand ◽  
Pion Polarizability ◽  
Pion Loop ◽  
Crossing Symmetry ◽  
The One

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g – 2)μ come from hadronic effects, and in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory error. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g – 2)μ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain [see formula in PDF]. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to [see formula in PDF].

scholarly journals Dispersion relations for hadronic light-by-light and the muon g − 2

2020 ◽  
Vol 234 ◽  
pp. 01013
Author(s):  
Massimiliano Procura ◽  
Gilberto Colangelo ◽  
Martin Hoferichter ◽  
Peter Stoffer
Keyword(s):  
Partial Wave ◽  
Accurate Determination ◽  
Form Factors ◽  
Pion Pole ◽  
Vector Form ◽  
Partial Wave Expansion ◽  
Left Hand ◽  
Pion Loop ◽  
The One

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g−2)µ come from hadronic effects, namely hadronic vacuum polarization (HVP) and hadronic lightby-light (HLbL) contributions. Especially the latter is emerging as a potential roadblock for a more accurate determination of (g−2)µ. The main focus here is on a novel dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g−2)µ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain $ \alpha _\mu ^{\pi {\rm{ - box}}} = - 15.9(2) \times {10^{ - 11}} $. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to $ \alpha _\mu ^{\pi {\rm{ - box}}} + \alpha _{\mu ,J = 0}^{\pi \pi ,\pi {\rm{ - pole}}\,{\rm{LHC}}} = - 24(1) \times {10^{ - 11}} $.

scholarly journals A new angle on an old problem: helicity approach to neutron beta decay in the Standard Model

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Stefan Groote ◽  
Jürgen G. Körner ◽  
Blaženka Melić
Keyword(s):  
Axial Vector ◽  
Form Factors ◽  
Semileptonic Decays ◽  
The Other ◽  
Vector Form ◽  
Neutron Beta Decay ◽  
Heavy Baryons ◽  
The Standard Model ◽  
The One ◽  
Three Body

AbstractWe elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron $$\beta $$β decays on the other hand. For example, almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays $$B_1 \rightarrow B_2 + W_\mathrm{off-shell}$$B1→B2+Woff-shell and $$W_{\mathrm{off-shell}} \rightarrow \ell + \nu _\ell $$Woff-shell→ℓ+νℓ whereas neutron $$\beta $$β decays are analyzed as true three-body decays $$n \rightarrow p + e^- +{\bar{\nu }}_e$$n→p+e-+ν¯e. Within the cascade approach it is possible to define a set of seven angular observables for polarized neutron $$\beta $$β decays as well as the longitudinal, transverse and normal polarization of the decay electron. We determine the dependence of the observables on the usual vector and axial vector form factors. In order to be able to assess the importance of recoil corrections we expand the rate and the $$q^2$$q2 averages of the observables up to NLO and NNLO in the recoil parameter $$\delta =(M_n-M_p)/(M_n+M_p)= 0.689\cdot 10^{-3}$$δ=(Mn-Mp)/(Mn+Mp)=0.689·10-3. Remarkably, we find that the rate and three of the four parity conserving polarization observables that we analyze are protected from NLO recoil corrections when the second class current contributions are set to zero.

The State Policy towards the Homeless in Moldova between the ‘Left Hand’ and the ‘Right Hand’. The Case of Chișinău Shelter

Südosteuropa ◽  
2019 ◽  
Vol 67 (2) ◽  
pp. 175-195
Author(s):  
Petru Negură
Keyword(s):  
Homeless People ◽  
Severe Disabilities ◽  
The State ◽  
Small Scale ◽  
Left Hand ◽  
Right Hand ◽  
Binary Approach ◽  
The One ◽  
The Right ◽  
Depth Interviews

Abstract The Centre for the Homeless in Chișinău embodies on a small scale the recent evolution of state policies towards the homeless in Moldova (a post-Soviet state). This institution applies the binary approach of the state, namely the ‘left hand’ and the ‘right hand’, towards marginalised people. On the one hand, the institution provides accommodation, food, and primary social, legal assistance and medical care. On the other hand, the Shelter personnel impose a series of disciplinary constraints over the users. The Shelter also operates a differentiation of the users according to two categories: the ‘recoverable’ and those deemed ‘irrecoverable’ (persons with severe disabilities, people with addictions). The personnel representing the ‘left hand’ (or ‘soft-line’) regularly negotiate with the employees representing the ‘right hand’ (‘hard-line’) of the institution to promote a milder and a more humanistic approach towards the users. This article relies on multi-method research including descriptive statistical analysis with biographical records of 810 subjects, a thematic analysis of in-depth interviews with homeless people (N = 65), people at risk of homelessness (N = 5), professionals (N = 20) and one ethnography of the Shelter.

Duality and crossing symmetry of the narrow resonance model

1970 ◽  
Vol 48 (12) ◽  
pp. 1426-1429 ◽  
Author(s):  
K. Nakazawa
Keyword(s):  
Finite Energy ◽  
Complex Variables ◽  
Narrow Resonance ◽  
Veneziano Amplitude ◽  
Resonance Model ◽  
Sum Rule ◽  
Crossing Symmetry ◽  
The One

In the narrow resonance approximation, conditions of duality and crossing symmetry are derived using the finite energy sum rule for an amplitude which is completely determined as a function of two complex variables by its meromorphic part in one of these variables. As an example, the one term Veneziano amplitude is discussed.

scholarly journals Measurement of Strange Quark Contributions to the Vector Form Factors of the Proton atQ2=0.22  (GeV/c)2

2009 ◽  
Vol 102 (15) ◽  
Author(s):  
S. Baunack ◽  
K. Aulenbacher ◽  
D. Balaguer Ríos ◽  
L. Capozza ◽  
J. Diefenbach ◽  
...  
Keyword(s):  
Strange Quark ◽  
Form Factors ◽  
Vector Form

scholarly journals An analysis of the partial wave expansion of the dispersion energy for Ne2

1984 ◽  
Vol 110 (4) ◽  
pp. 369-374 ◽  
Author(s):  
G. Chałasiński ◽  
J.H. van Lenthe ◽  
Th.P. Groen
Keyword(s):  
Partial Wave ◽  
Dispersion Energy ◽  
Partial Wave Expansion ◽  
Wave Expansion
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