Next-to-Leading Order QCD Corrections to $\Delta F =2$ effective Hamiltonians

E. Franco; G. Martinelli; I. Scimemi; L. Silvestrini; M. Ciuchini; V. Lubicz

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Next-to-Leading Order QCD Corrections to $\Delta F =2$ effective Hamiltonians

M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, I. Scimemi, L. Silvestrini

High Energy Physics - Phenomenology · Submitted 20 Nov 1997

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The authors' main claim The most general QCD next-to-leading anomalous-dimension matrix of all possible four-fermion, dimension-six $\Delta F=2$ operators is computed.

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arXiv IDhep-ph/9711402 (version 1)

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CitationE. Franco, G. Martinelli, I. Scimemi, L. Silvestrini, M. Ciuchini, V. Lubicz. "Next-to-Leading Order QCD Corrections to $\Delta F =2$ effective Hamiltonians." arXiv:hep-ph/9711402 (1997). https://pith.science/paper/RVVADOFS

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.04 · mentions code or data availability 0.02.

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The most general QCD next-to-leading anomalous-dimension matrix of all possible four-fermion, dimension-six $\Delta F=2$ operators is computed. The results of this calculation can be used in many phenomenological applications, among which the most important are those related to theoretical predictions of $K^0-\bar{K}^0 $ and $B^0-\bar{B}^0$ mixing in several extension of the Standard Model (Supersymmetry, left-right symmetric, multi-Higgs models, etc.), to estimates of the $B^0_s$--$\bar B^0_s$ width difference, $\Delta \Gamma_{B_s}$, and to the calculation of the $O(1/m_b^3)$ corrections for inclusive b-hadron decay rates.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The most general QCD next-to-leading anomalous-dimension matrix of all possible four-fermion, dimension-six $\Delta F=2$ operators is computed.	contribution 0.77	0.95	0.75	asserted 1.00
s1	The results of this calculation can be used in many phenomenological applications, among which the most important are those related to theoretical predictions of $K^0-\bar{K}^0 $ and $B^0-\bar{B}^0$ mixing in several extension of the Standard Model (Supersymmetry, left-right symmetric, multi-Higgs models, etc.), to estimates of the $B^0_s$--$\bar B^0_s$ width difference, $\Delta \Gamma_{B_s}$, and to the calculation of the $O(1/m_b^3)$ corrections for inclusive b-hadron decay rates.	interpretation 0.94	0.46	0.20	asserted 0.73

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

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The paper

Original abstract

The most general QCD next-to-leading anomalous-dimension matrix of all possible four-fermion, dimension-six $\Delta F=2$ operators is computed. The results of this calculation can be used in many phenomenological applications, among which the most important are those related to theoretical predictions of $K^0-\bar{K}^0 $ and $B^0-\bar{B}^0$ mixing in several extension of the Standard Model (Supersymmetry, left-right symmetric, multi-Higgs models, etc.), to estimates of the $B^0_s$--$\bar B^0_s$ width difference, $\Delta \Gamma_{B_s}$, and to the calculation of the $O(1/m_b^3)$ corrections for inclusive b-hadron decay rates.

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How later papers used it

67 later papers cite it

Evidence: substantial. 63 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

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3 later papers by other authors are listed below: 3 used its method or tool.

Uses its method or tool 3 of 14 papers with this label

Obtained its matching factor in the MS scheme from this paper by replacing J_RI/MOM with another quantity.

B_K with two flavors of dynamical overlap fermions (2008) · 0.90 · paraphrased: the licence does not allow quoting
Converted its renormalization factor between the scale-invariant, MS, and RI/MOM schemes using one-loop renormalization group running formulae from this paper.

The neutral kaon mixing parameter B_K from unquenched mixed-action lattice QCD (2009) · 1.00 · paraphrased: the licence does not allow quoting
Applied this paper's next-to-leading-order anomalous dimension matrix at leading order to yield its Wilson coefficients.

Relating D0-anti-D0 Mixing and D0 -> l+l- with New Physics (2009) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

67 arXiv papers cite this in 104 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

The most general QCD-NLO Anomalous-Dimension Matrix of all four-fermion dimension six Delta F=2 operators is presented.

NLO corrections to Delta F=2 effective Hamiltonians and SUSY contribution to FCNC · 1.00

Papers citing it · 74 sentences without a confident label

Contests it 1 paper

In this manner we could also find the compatibility of the RI result in [ref] and our NDR result but the one loop matrices connecting these two schemes were clearly different from those given in [ref] .

Climbing NLO and NNLO Summits of Weak Decays: 1988-2023 · More Operators · contest 0.78

Uses its method or tool 14 papers

To follow the standard convention, the matching factor is converted to that in the $MS$ scheme using [equation] where $w_MS(μ^2)$ is obtained from ([ref]) by replacing $J_RI/MOM$ with [ref] [equation] We obtain $w_MS(μ^2)=0.7086$ at $μ=$2 GeV.

B_K with two flavors of dynamical overlap fermions · Nonperturbative matching · 0.90
The Wilson coefficients are evolved to the low scale $μ_low$ by solving their renormalization group equations [ref] .

A Supersymmetric Flavor Clockwork · Constraints from Meson Mixing · 0.98
We convert the renormalization factor $Z_B_K$ between the scale-invariant, $MS$, and RI/MOM schemes using the one-loop renormalization group running formulae with $n_f=3$ [ref] :

The neutral kaon mixing parameter B_K from unquenched mixed-action lattice QCD · Perturbative Running and Scheme Matching for $Z_B_K$ · 1.00

Uses its data or values 5 papers

Using the RGE factors in Ref. [ref] and the $B_LRi(μ)$ factors from lattice [ref] leads to P_LL = 0.7 , P_LR1=-5.0 , P_LR2=6.3 , with negligible differences between $B_s$ and $B_d$ cases.

Solving the flavour problem with hierarchical fermion wave functions · $ΔF=2$ operators · 0.99
In order to consider the new physics contributions, when we use the $ΔM^exp_q$ to bound the free parameters, we take the SM predictions to be $ΔM^SM_d= 0.555^+0.073_-0.046$ ps$^-1$ and $ΔM^SM_s=16.8^+2.6_-1.5$ ps$^-1$ [ref] , in which the next-to-leading order (NLO) QCD corrections [ref] and the uncertainties from various parameters, such as CKM matrix elements, decay constants, and top-quark mass, are taken into account.

$R_{K^{(*)}}$ anomaly in type-III 2HDM · Constraints from $ΔM_q$ · 0.98
where $S(m_t^2/m_W^2)≈2.30$ is the Inami-Lim function [ref] , $η̂_B≃0.84$ accounts for NLO QCD corrections [ref] , and $c(M)≈0.8$ includes the running from $M$ down to $m_B$ using the NLO anomalous dimension calculated in Refs. [ref] .

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Compares with it 2 papers

Our results agree with previous calculations in Refs [ref] .

Gauge-invariant renormalization of four-quark operators · Mixing matrices in the $$ scheme · 0.97
In our basis with operators $O_i=1,…,10^q$ and their respective evanescent operators $E_i=1,…,8^q$, they are given by[We recomputed them directly with vanishing external momenta and universal mass $m$ for all quark propagator denominators and checked agreement with Refs. [ref] .

HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model · Evanescent operators and anomalous dimension matrix in QCD · 0.95

Cites it as background 8 papers

As far as short-distance contributions encoded in the Wilson coefficients are concerned, they have been known for the SM operators already for 25 years at the NLO level [ref] and for the BSM operators two-loop anomalous dimensions have been known [ref] for almost two decades.

Master formula for $\varepsilon'/\varepsilon$ beyond the Standard Model · Introduction · 0.92
[ref] denote the full set of twenty linearly independent four-quark operators that can contribute, either directly or through operator mixing, to the weak $b→c u̅ d(s)$ transitions [ref] .

Probing new physics in class-I $B$-meson decays into heavy-light final states · Effective weak Hamiltonian · 0.85
In 1997 an Italian group consisting of six climbers [ref] , including three from the expedition of early 1990's calculated two-loop anomalous dimensions of a set of operators relevant at NLO for $ΔΓ_s,d$ in $B^0_s,d-B̅^0_s,d$ mixings and in particular for $ΔF=1$ and $ΔF=2$ non-leptonic decays and transitions in the extensions of the SM, like MSSM at large $tanβ$, multi-Higgs models and generally models that include in addition to left-handed currents also right-handed currents and scalar currents.

Climbing NLO and NNLO Summits of Weak Decays: 1988-2023 · More Operators · 0.80

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