{"arxiv_id":"hep-ph/0403286","incoming":{"papers":33,"sentences":48,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1612.09178","title":"Flavour Structure of GUTs and Uncertainties in Proton Lifetime Estimates","url":"/paper/1612.09178","section":"Introduction","sentence":"To this end, we first (in Section II) recapitulate the generic analytic observations made by Dorsner and Fileviez-Perez [ref] in the realm of the simplest $SU(5)$, flipped-$SU(5)$ and $SO(10)$ scenarios and complement them with an explicit numerical simulation of the relevant formulae revealing, e.g., an extra room for large cancellation effects in $SO(10)$ GUTs; we will show how these can in some cases boost the uncertainties beyond naive expectation.","intent_p":0.98,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":6,"sentences":6,"quotes":[{"arxiv_id":"2406.06861","title":"Exploring flavour space of an economical SU(5) GUT in future proton decay measurements","url":"/paper/2406.06861","section":"Proton decays","sentence":"Partial decay widths of some typical channels of proton decay into a lepton and a meson are given by [ref] [equation] Here $f_M$ is the phase space contribution ignoring charged lepton masses, [equation] $A_LD$ and $A_SD$ parametrising the long-distance and short-distance effect of the baryon-number-violating operators [ref] , accounting for renormalisation contribution of the QCD running from $m_t$ to the proton mass scale [equation] and that from the GUT scale down to $m_t$ [equation] respectively, where we considered the extra matter at a single intermediate scale $M_I$ and $Δa_i≡∑_Ia_i^I$.","intent_p":0.87,"contests_p":null},{"arxiv_id":"2401.16907","title":"Gauge and Scalar Boson Mediated Proton Decay in a Predictive SU(5) GUT Model","url":"/paper/2401.16907","section":"Proton decay via gauge bosons","sentence":"To evaluate relevant decay widths we resort to a formalism presented in Refs. [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"0809.1069","title":"Minimal SO(10) splits supersymmetry","url":"/paper/0809.1069","section":"Split SUSY case","sentence":"We derive them using the flavour structure dependence of the relevant $d=6$ operators spelled out in Ref. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2212.05291","title":"Probing Minimal Grand Unification through Gravitational Waves, Proton Decay, and Fermion Masses","url":"/paper/2212.05291","section":"Proton decay","sentence":"The expression of the lifetime of this process is then given by [ref] : [equation] where, $M_X$ is the mass of the superheavy gauge boson, and $A_SL$ and $A_SR$ are the short-range enhancement factors associated with the left-handed $𝒪^d=6_L( e^C, d)$ and right-handed $𝒪^d=6_R( d^C, e )$ operators, respectively.","intent_p":0.8,"contests_p":null},{"arxiv_id":"2403.04644","title":"Leptoquark-Mediated Two-Loop Neutrino Mass in Unified Theory","url":"/paper/2403.04644","section":"Gauge mediated proton decay","sentence":"The complete formula for the gauge mediated two-body proton decay widths are [ref] [equation] Here, $A_L=1.2$ denotes the long-range coefficient [ref] , while $A_SL(R)$ are the short-distance coefficients defined as [equation] Moreover, $m_p=938.33$ MeV, $m_π=134$ MeV, $m_η=548$ MeV, and $m_K=493.677$ MeV are the proton, pion, eta meson, and kaon mass, respectively.","intent_p":0.83,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1305.2850","title":"Unification scale vs. electroweak-triplet mass in the SU(5) + 24_F model at three loops","url":"/paper/1305.2850","section":"Introduction","sentence":"More precisely, assuming no cancellations in the flavour structure of the gauge-induced proton decay rates [ref] , the latest experimental data from the Super-Kamiokande observatory [ref] imply a conservative lower bound on the unification scale $M_G$ of about $10^15.5 GeV$.","intent_p":0.81,"contests_p":null},{"arxiv_id":"2406.06861","title":"Exploring flavour space of an economical SU(5) GUT in future proton decay measurements","url":"/paper/2406.06861","section":"Proton decays","sentence":"We use the best-fit values reported in the recent paper [ref] , i.e., [equation] The $c$ coefficients appearing in these formulas are [ref] [equation] where $α,β=1,2$.","intent_p":1.0,"contests_p":null},{"arxiv_id":"2303.11070","title":"$W$ Boson Mass and Grand Unification via the Type-$\\rm{I\\hspace{-.01em}I}$ Seesaw-like Mechanism","url":"/paper/2303.11070","section":"Proton decay and gauge unification","sentence":"The coefficients in Eq. [ref] are given by [ref] [equation] The $V$'s are the mixing matrices defined as [equation] where the matrices $U, E,$ and $D$ diagonalize the Yukawa couplings [equation] The $⟨π^0|(ud)_Lu_R|p⟩$ and $⟨π^0|(ud)_Ru_L|p⟩$ are the hadronic matrix elements computed in lattice QCD calculations and the numerical values are [ref] [equation] Note that we assume the correct mass relation between down-type quarks and charged leptons by introducing non-renormalizable operators.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1901.05867","title":"Unification, Proton Decay and Topological Defects in non-SUSY GUTs with Thresholds","url":"/paper/1901.05867","section":"Dimension-6 Proton decay operators","sentence":"In the physical basis, the relevant effective terms in the Lagrangian leading to $p→e^+π^0$ decay are expressed as [ref] : [equation] with their respective the Wilson coefficients ($𝒲𝒞_1,2$) : [equation] where, $|V_ud| = 0.9742$ is the CKM matrix element [ref] .","intent_p":0.85,"contests_p":null},{"arxiv_id":"2301.00809","title":"Fully Testable Axion Dark Matter within a Minimal $SU(5)$ GUT","url":"/paper/2301.00809","section":"Proton decay","sentence":"Finally, the c-coefficients of Eq. [ref] read [ref] [equation] where the unitary matrices $U_L/R$, $E_L/R$, $D_L/R$, and $N$ diagonalize the SM fermion mass matrices through the following transformations [equation]","intent_p":0.86,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":5,"sentences":5,"quotes":[{"arxiv_id":"2410.18743","title":"Fermion masses and mixing in SO(10) GUT with a universal two-zero texture","url":"/paper/2410.18743","section":"proton decay","sentence":"In non-SUSY $SO(10)$ GUTs, proton decay will be induced by integrating out the superheavy gauge fields $(3,2,-5/6),(3,2,5/6),(3,2,1/6),(3,2,-1/6)$, which are typically denoted as $X^μ,Y^μ,X^'μ,Y^'μ$, and resulting in the following four dimension-six operators [ref] : [equation] where $i,j,k$ ($α,β$) denotes colour (flavour) indices and $Λ_1≃√(2)M_(X,Y)/g_GUT, Λ_2≃√(2)M_(X^',Y^')/g_GUT$ are the UV completion scales of the GUT symmetry.","intent_p":0.8,"contests_p":null},{"arxiv_id":"2504.16022","title":"Non-Renormalizable SU(5) GUTs: Leptoquark-Induced Neutrino Masses","url":"/paper/2504.16022","section":"Introduction","sentence":"(For alternative approaches to the proton decay suppression of interest, see Refs. [ref] .)","intent_p":0.93,"contests_p":null},{"arxiv_id":"2203.07748","title":"Anatomy of scalar mediated proton decays in $SO(10)$ models","url":"/paper/2203.07748","section":"Background","sentence":"The latter has been extensively studied including the flavour effects [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1009.0509","title":"Probing Seesaw in an Adjoint SUSY SU(5) Model at LHC","url":"/paper/1009.0509","section":"Proton Decay","sentence":"The predicted decay width for the following channels are [ref] τ(p →π^+ ν̅) = 1.44×10^-31((M_G/GeV)^4/α_G^2) years , τ(p →K^+ ν̅) = 4.31×10^-30((M_G/GeV)^4/α_G^2) years .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2507.16605","title":"Unravelling the Scalar Sector of Grand Unification: Phenomenology & Implications","url":"/paper/2507.16605","section":"Background:chap1","sentence":"The latter has been extensively studied including the flavour effects [ref] .","intent_p":0.85,"contests_p":null}]}],"unlabelled_sentences":31},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-ph/0403286"}}