Standard Model and Related Topics
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摘要
The Review summarizes much of particle physics and cosmology.Using data from previous editions,plus 3,062 new measurements from 721 papers,we list,evaluate,and average measured properties of gauge bosons and the recently discovered Higgs boson,leptons,quarks,mesons,and baryons.We summarize searches for hypothetical particles such as supersymmetric particles,heavy bosons,axions,dark photons,etc.All the particle properties and search limits are listed in Summary Tables.We also give numerous tables,figures,formulae,and reviews of topics such as Higgs Boson Physics,Supersymmetry,Grand Unified Theories,Neutrino Mixing,Dark Energy,Dark Matter,Cosmology,Particle Detectors,Colliders,Probability and Statistics.Among the 117 reviews are many that are new or heavily revised,including new reviews on Pentaquarks and Inflation.
The Review summarizes much of particle physics and cosmology.Using data from previous editions,plus 3,062 new measurements from 721 papers,we list,evaluate,and average measured properties of gauge bosons and the recently discovered Higgs boson,leptons,quarks,mesons,and baryons.We summarize searches for hypothetical particles such as supersymmetric particles,heavy bosons,axions,dark photons,etc.All the particle properties and search limits are listed in Summary Tables.We also give numerous tables,figures,formulae,and reviews of topics such as Higgs Boson Physics,Supersymmetry,Grand Unified Theories,Neutrino Mixing,Dark Energy,Dark Matter,Cosmology,Particle Detectors,Colliders,Probability and Statistics.Among the 117 reviews are many that are new or heavily revised,including new reviews on Pentaquarks and Inflation.
The Review summarizes much of particle physics and cosmology.Using data from previous editions,plus 3,062 new measurements from 721 papers,we list,evaluate,and average measured properties of gauge bosons and the recently discovered Higgs boson,leptons,quarks,mesons,and baryons.We summarize searches for hypothetical particles such as supersymmetric particles,heavy bosons,axions,dark photons,etc.All the particle properties and search limits are listed in Summary Tables.We also give numerous tables,figures,formulae,and reviews of topics such as Higgs Boson Physics,Supersymmetry,Grand Unified Theories,Neutrino Mixing,Dark Energy,Dark Matter,Cosmology,Particle Detectors,Colliders,Probability and Statistics.Among the 117 reviews are many that are new or heavily revised,including new reviews on Pentaquarks and Inflation.
引文
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1 On leave from LPTHE,UMR 7589,CNHS,Paris,France
The situation is significantly worse near thresholds,e.g.the tt production threshold.An overview of some of the methods used in such cases is to be found for example in Ref.31.
There is an important caveat to this statement:at sufficiently high orders,perturbative series generally suffer from"renormalon"divergencesα_s~n n!(reviewed in Ref.23).This phenomenon is not usually visible with the limited number of perturbative terms available today.However it is closely connected with non-perturbative contributions and sets a limit on the possible precision of perturbative predictions.The cancellation of scale dependence will also ultimately be affected by this renormalon-induced breakdown of perturbation theory.
LO is generally taken to mean the lowest order at which a quantity is non-zero.This definition is nearly always unambiguous,the one major exception being for the case of the hadronic branching ratio of virtual photons,Z,τ,etc.,for which two conventions exist:LO can either mean the lowest order that contributes to the hadronic branching fraction,i.e.the term"1"in Eq.(9.7);or it can mean the lowest order at which the hadronic branching ratio becomes sensitive to the coupling,n=1 in Eq.(9.8),as is relevant when extracting the value of the coupling from a measurement of the branching ratio.Because of this ambiguity,we avoid use of the term"LO"in that context.
Processes with jets or photons in the final state have divergent cross sections unless one places cut on the jet or photon momentum.Accordingly they are discussed below in Section 9.2.3.2.
To be precise one should be aware of two causes of the divergence of perturbative series.That which interests us here is associated with the presence of a new large parameter(e.g.ratio of scales).It is distinct from the"renormalon"induced factorial divergences of perturbation theory that were discussed above.
Whether or not this happens depends on the quantity being resummed.A classic example involves jet rates in e~+e~-collisions as a function of a jet-resolution parameter y_(cut).The logarithms of 1/y_(cut)exponentiate for the k_t(Durham)jet algorithm[154],but not[155]for the JADE algorithm[156](both are discussed below in Sec.9.3.1.1).
The program ARIADNE[201]has also been widely used for simulating e~+e~-and DIS collisions.
A number of prescriptions also exist for setting the scale automatically,e.g.Refs.214-217,eliminating uncertainties from scale variation,though not from the truncation of the perturbative series itself.Recently,there have also been studies of how to estimate uncertainties from missing higher orders that go beyond scale variations[218,219,220].
The time evolution ofα_s combinations can be followed by consulting Refs.[330-332]as well as earlier editions of this Review.
In most practical cases,this procedure arrives at similar values as obtained from the'range averaging'method which we used in previous Reviews,while it avoids potential shortcomings and biases of the latter.
Note that for jet production at a hadron collider,only NLO predictions are available,while for the structure functions full NNLO was utilized.
The weighted average,treating all inputs as uncorrelated measurements with Gaussian uncertainties,results inα_s(M_Z~2)=0.11810±0.00078 with x~2/d.o.f.=3.7/5.Requiring x~2/d.o.f.to reach unity calls for an overall correlation factor of 0.28,which increases the overall uncertainty to±0.00114.
We note,however,that in many such studies,like those based on exclusive states of jet multiplicities,the relevant energy scale of the measurement is not uniquely defined.For instance,in studies of the ratio of 3-to 2-jet cross sections at the LHC,the relevant scale was taken to be the average of the transverse momenta of the two leading jets[381],but could alternatively have been chosen to be the transverse momentum of the 3~(rd)jet.
There is no generally accepted convention to write the quartic term.Our numerical coefficient simplifies Eq.(10.3a)below and the squared coupling preserves the relation between the number of external legs and the power counting of couplings at a given loop order.This structure also naturally emerges from physics beyond the SM,such as supersymmetry.
We emphasize that in the fits described in Sec.10.6 and Sec.10.7the values of the SM parameters are affected by all observables that depend on them.This is of no practical consequence forαand G_f,however,since they are very precisely known.
In the spirit of the Fermi theory,we incorporated the small propagator correction,3/5 m_μ~2/M_W~2,into△r(see below).This is also the convention adopted by the MuLan collaboration[11].While this breaks with historical consistency,the numerical difference was negligible in the past.
In practice,α(Mz)is directly evaluated in the ms scheme using the FORTRAN package GAPP[21],including the QED contributions of both leptons and quarks.The leptonic three-loop contribution in the on-shell scheme has been obtained in Ref.22.
Other authors[46]advocate to evaluate and quote m_c(μ=3 GeV)instead.We use m_c(μ=m_c)because in the global analysis it is convenient to nullify any explicitly m_c dependent logarithms.Note also that our uncertainty for m_c(and to a lesser degree for m_b)is larger than in Refs.46 and 47,for example.The reason is that we determine the continuum contribution for charm pair production using only resonance data and theoretical consistency across various sum rule moments,and then use any difference to the experimental continuum data as an additional uncertainty.We also include an uncertainty for the condensate terms which grows rapidly for higher moments in the sum rule analysis.
All explicit numbers quoted here and below include the two-and three-loop corrections described near the end of Sec.10.2.
We use here slightly different definitions(and to avoid confusion also a different notation)for the coefficients of these four-Fermi operators than we did in previous editions of this Review.The new couplings[80]are defined in the static limit,Q~2→0,with specific radiative corrections included,while others(more experiment specific ones)are assumed to be removed by the experimentalist.They are convenient in that their determinations from very different types of processes can be straightforwardly combined.
Note thatσ_(had)receives additional EW corrections that are not captured in the partial widths[163,153],but they only enter at twoloop order.
In what follows,we summarize the most important aspects of g_μ-2,and give some details on the evaluation in our fits.For more details see the dedicated contribution on"The Muon Anomalous Magnetic Moment"in this Review.There are some numerical differences,which are well understood and arise because internal consistency of the fits requires the calculation of all observables from analytical expressions and common inputs and fit parameters,so that an independent evaluation is necessary for this Section.Note,that in the spirit of a global analysis based on all available information we have chosen here to use an analysis[20]which considers the r decay data,as well.
Alternatively,one can use A_e=0.1481±0.0027,which is from LEP 1 alone and in excellent agreement with the SM,and obtain A_b=0.893±0.022 which is 1.9σlow.This illustrates that some of the discrepancy is related to the one in A_(LR).
1 In the case of neutrinos,it is possible that the electroweak symmetry breaking mechanism plays only a partial role in generating the observed neutrino masses,with additional contributions at a higher scale via the so called see-saw mechanism.
2Another solution to the naturalness problem is to lower the fundamental scale of quantum gravity,like for instance in models with large extra-dimensions,see Ref.[8].
3 Similarly at the Tevatron where the CDF and DO experiments have gathered approximately 10 fb-1 of data at 1.96 TeV,the predicted numbers of SM Higgs boson events produced per experiment are approximately 10,000 and 2,000 events in the gluon fusion and VH associated production,respectively.
4 In the combination performed by the ATLAS and CMS experiments the systematic uncertainties on these parameters are taken into account by allowing these parameters to vary in the fit.
5Complete classifications of D=8 operators have recently appeared in the literature,see Ref.[222].Still,in this review,the EFT Lagrangians will be truncated at the level of dimension-6 operators.
6There remains an accidental flat direction[227]in the fit of anomalous gauge boson couplings using LEP2 data on diboson production alone.This flat direction can be lifted when LHC Higgs data are considered[228].
7For a pedagogical introduction to models of partial compositeness,see Ref.[248].
8Observe that in the SM sections of this review,H denotes the SM Higgs,whereas in the sections about SUSY,or extensions of the SM with two Higgs doublets,H is used for the heaviest CP-even Higgs boson,since this is the standard notation in the literature,and the125 GeV SM-like light Higgs boson will be denoted by h.
9 Additional gauge interactions in the UMSSM contribute to this increase with a term of O{g′_1~2(Q_(φ2)~2 cos~2β+Q_(φ1)~2 sin~2β)).
10 For instance in the SO(5)/SO(4)composite models,when the top quark is embedded into a spinorial representation of SO(5),thenγ=0and when it is part of a 5,10 or 14 representation,α=0 as it can be inferred by looking at the structure of the H-dependent invariants built out of these representations[394].The coefficientγalso generically comes with an extra power of the top compositeness fractions.
1 For lattice QCD inputs,we use the averages from Ref.[14]whenever possible,unless the minireviews[10,15]choose other values.We only use unquenched lattice QCD results.Hereafter,the first error is statistical and the second is systematic,unless mentioned otherwise.
In our convention the electric charge is Q=T_3+F/2 and all our spinor fields are left-handed.
Equivalently,the SU(2)_L and U(1)_Y couplings are denoted as g=g_2 and g'=(3/5)~(1/2)g_1.One also usesα_s=α_3=(g_3~2/4π),α_(EM)=(e~2/4π)with e=g sinθ_W and sin~2θ_W=(g')~2/(g~2+(g')~2).
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The solution of[28]relies on the absence of the fundamental superpotential termμH_u H_d(orμ5_H5_H).This is ensured by a U(1)_R.The latter clashes with typical superpotentials for the GUT breaking sector.However,higher-dimensional or stringy GUTs,where the triplet Higgs is simply projected out,can be consistent with the U(1)_R symmetry.
See however[40].
The DR scheme is frequently used in a supersymmetric regularization[63].The renormalization transformation of the gauge coupling constants from MS to DR scheme is given in Ref.[64].For an alternative treatment using holomorphic gauge couplings and NSVZβ-functions see e.g.[65].
It is interesting to note that a ratio M_*/M_c~100,needed for gauge coupling unification to work in orbifold GUTs,is typically the maximum value for this ratio consistent with perturbativity[78].
Adding extra vector-like sets of fields,e.g.two fermions which only transform under U(1)and have charges Y and-Y,is considered to violate minimality.
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69.In the convention we use,the neutrino masses are not ordered in magnitude according to their index number:Δm_(31)~2<0 corresponds to m_3
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136.In Eq.(14.31)we have neglected the possible instability of neutrinos v_j.In most theoretical models with nonzero neutrino masses and neutrino mixing,the predicted half life-time of neutrinos with mass of 1 eV exceeds the age of the Universe,see,e.g.,S.T.Petcov,Yad.Fiz.25,641(1977),(E)ibid.,25(1977)1336[Sov.J.Nucl.Phys.25,340(1977),(E)ibid.,25,(1977),698],and Phys.Lett.B115,401(1982);W.Marciano and A.I.Sanda,Phys.Lett.B67,303(1977);P.Pal and L.Wolfenstein,Phys.Rev.D25,766(1982).
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143.S.Goswami et al.,Nucl.Phys.(Proc.Supp.)B143,121(2005).
144.These processes are important,however,for the supernova neutrinos see,e.g.,G.Raffelt,Proc.International School of Physics"Enrico Fermi",CLII Course"Neutrino Physics",23July-2 August 2002,Varenna,Italy[hep-ph/0208024]),and articles quoted therein.
145.We standardly assume that the weak interaction of the flavour neutrinos v_l and antineutrinos v_l is described by the Standard Model(for alternatives see,e.g.,Ref.26;M.M.Guzzo et al.,Phys.Lett.B260,154(1991);E.Roulet,Phys.Rev.D44,R935(1991)and Ref.86).
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148.The difference between the v_μand v_τindices of refraction arises at one-loop level and can be relevant for the v_μ-v_τoscillations in very dense media,like the core of supernovae,etc.;see F.J.Botella,C.S.Lim,and W.J.Marciano,Phys.Rev.D35,896(1987).
149.The relevant formulae for the oscillations between the v_e and a sterile neutrino v_s,v_e■v_s,can be obtained from those derived for the case of v_s,v_e■v_(μ(τ))oscillations by Refs.[65,147]replacing N_e with(N_e-1/2N_n),N_n being the neutron number density in matter.
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1 On leave from LPTHE,UMR 7589,CNHS,Paris,France
The situation is significantly worse near thresholds,e.g.the tt production threshold.An overview of some of the methods used in such cases is to be found for example in Ref.31.
There is an important caveat to this statement:at sufficiently high orders,perturbative series generally suffer from"renormalon"divergencesα_s~n n!(reviewed in Ref.23).This phenomenon is not usually visible with the limited number of perturbative terms available today.However it is closely connected with non-perturbative contributions and sets a limit on the possible precision of perturbative predictions.The cancellation of scale dependence will also ultimately be affected by this renormalon-induced breakdown of perturbation theory.
LO is generally taken to mean the lowest order at which a quantity is non-zero.This definition is nearly always unambiguous,the one major exception being for the case of the hadronic branching ratio of virtual photons,Z,τ,etc.,for which two conventions exist:LO can either mean the lowest order that contributes to the hadronic branching fraction,i.e.the term"1"in Eq.(9.7);or it can mean the lowest order at which the hadronic branching ratio becomes sensitive to the coupling,n=1 in Eq.(9.8),as is relevant when extracting the value of the coupling from a measurement of the branching ratio.Because of this ambiguity,we avoid use of the term"LO"in that context.
Processes with jets or photons in the final state have divergent cross sections unless one places cut on the jet or photon momentum.Accordingly they are discussed below in Section 9.2.3.2.
To be precise one should be aware of two causes of the divergence of perturbative series.That which interests us here is associated with the presence of a new large parameter(e.g.ratio of scales).It is distinct from the"renormalon"induced factorial divergences of perturbation theory that were discussed above.
Whether or not this happens depends on the quantity being resummed.A classic example involves jet rates in e~+e~-collisions as a function of a jet-resolution parameter y_(cut).The logarithms of 1/y_(cut)exponentiate for the k_t(Durham)jet algorithm[154],but not[155]for the JADE algorithm[156](both are discussed below in Sec.9.3.1.1).
The program ARIADNE[201]has also been widely used for simulating e~+e~-and DIS collisions.
A number of prescriptions also exist for setting the scale automatically,e.g.Refs.214-217,eliminating uncertainties from scale variation,though not from the truncation of the perturbative series itself.Recently,there have also been studies of how to estimate uncertainties from missing higher orders that go beyond scale variations[218,219,220].
The time evolution ofα_s combinations can be followed by consulting Refs.[330-332]as well as earlier editions of this Review.
In most practical cases,this procedure arrives at similar values as obtained from the'range averaging'method which we used in previous Reviews,while it avoids potential shortcomings and biases of the latter.
Note that for jet production at a hadron collider,only NLO predictions are available,while for the structure functions full NNLO was utilized.
The weighted average,treating all inputs as uncorrelated measurements with Gaussian uncertainties,results inα_s(M_Z~2)=0.11810±0.00078 with x~2/d.o.f.=3.7/5.Requiring x~2/d.o.f.to reach unity calls for an overall correlation factor of 0.28,which increases the overall uncertainty to±0.00114.
We note,however,that in many such studies,like those based on exclusive states of jet multiplicities,the relevant energy scale of the measurement is not uniquely defined.For instance,in studies of the ratio of 3-to 2-jet cross sections at the LHC,the relevant scale was taken to be the average of the transverse momenta of the two leading jets[381],but could alternatively have been chosen to be the transverse momentum of the 3~(rd)jet.
There is no generally accepted convention to write the quartic term.Our numerical coefficient simplifies Eq.(10.3a)below and the squared coupling preserves the relation between the number of external legs and the power counting of couplings at a given loop order.This structure also naturally emerges from physics beyond the SM,such as supersymmetry.
We emphasize that in the fits described in Sec.10.6 and Sec.10.7the values of the SM parameters are affected by all observables that depend on them.This is of no practical consequence forαand G_f,however,since they are very precisely known.
In the spirit of the Fermi theory,we incorporated the small propagator correction,3/5 m_μ~2/M_W~2,into△r(see below).This is also the convention adopted by the MuLan collaboration[11].While this breaks with historical consistency,the numerical difference was negligible in the past.
In practice,α(Mz)is directly evaluated in the ms scheme using the FORTRAN package GAPP[21],including the QED contributions of both leptons and quarks.The leptonic three-loop contribution in the on-shell scheme has been obtained in Ref.22.
Other authors[46]advocate to evaluate and quote m_c(μ=3 GeV)instead.We use m_c(μ=m_c)because in the global analysis it is convenient to nullify any explicitly m_c dependent logarithms.Note also that our uncertainty for m_c(and to a lesser degree for m_b)is larger than in Refs.46 and 47,for example.The reason is that we determine the continuum contribution for charm pair production using only resonance data and theoretical consistency across various sum rule moments,and then use any difference to the experimental continuum data as an additional uncertainty.We also include an uncertainty for the condensate terms which grows rapidly for higher moments in the sum rule analysis.
All explicit numbers quoted here and below include the two-and three-loop corrections described near the end of Sec.10.2.
We use here slightly different definitions(and to avoid confusion also a different notation)for the coefficients of these four-Fermi operators than we did in previous editions of this Review.The new couplings[80]are defined in the static limit,Q~2→0,with specific radiative corrections included,while others(more experiment specific ones)are assumed to be removed by the experimentalist.They are convenient in that their determinations from very different types of processes can be straightforwardly combined.
Note thatσ_(had)receives additional EW corrections that are not captured in the partial widths[163,153],but they only enter at twoloop order.
In what follows,we summarize the most important aspects of g_μ-2,and give some details on the evaluation in our fits.For more details see the dedicated contribution on"The Muon Anomalous Magnetic Moment"in this Review.There are some numerical differences,which are well understood and arise because internal consistency of the fits requires the calculation of all observables from analytical expressions and common inputs and fit parameters,so that an independent evaluation is necessary for this Section.Note,that in the spirit of a global analysis based on all available information we have chosen here to use an analysis[20]which considers the r decay data,as well.
Alternatively,one can use A_e=0.1481±0.0027,which is from LEP 1 alone and in excellent agreement with the SM,and obtain A_b=0.893±0.022 which is 1.9σlow.This illustrates that some of the discrepancy is related to the one in A_(LR).
1 In the case of neutrinos,it is possible that the electroweak symmetry breaking mechanism plays only a partial role in generating the observed neutrino masses,with additional contributions at a higher scale via the so called see-saw mechanism.
2Another solution to the naturalness problem is to lower the fundamental scale of quantum gravity,like for instance in models with large extra-dimensions,see Ref.[8].
3 Similarly at the Tevatron where the CDF and DO experiments have gathered approximately 10 fb-1 of data at 1.96 TeV,the predicted numbers of SM Higgs boson events produced per experiment are approximately 10,000 and 2,000 events in the gluon fusion and VH associated production,respectively.
4 In the combination performed by the ATLAS and CMS experiments the systematic uncertainties on these parameters are taken into account by allowing these parameters to vary in the fit.
5Complete classifications of D=8 operators have recently appeared in the literature,see Ref.[222].Still,in this review,the EFT Lagrangians will be truncated at the level of dimension-6 operators.
6There remains an accidental flat direction[227]in the fit of anomalous gauge boson couplings using LEP2 data on diboson production alone.This flat direction can be lifted when LHC Higgs data are considered[228].
7For a pedagogical introduction to models of partial compositeness,see Ref.[248].
8Observe that in the SM sections of this review,H denotes the SM Higgs,whereas in the sections about SUSY,or extensions of the SM with two Higgs doublets,H is used for the heaviest CP-even Higgs boson,since this is the standard notation in the literature,and the125 GeV SM-like light Higgs boson will be denoted by h.
9 Additional gauge interactions in the UMSSM contribute to this increase with a term of O{g′_1~2(Q_(φ2)~2 cos~2β+Q_(φ1)~2 sin~2β)).
10 For instance in the SO(5)/SO(4)composite models,when the top quark is embedded into a spinorial representation of SO(5),thenγ=0and when it is part of a 5,10 or 14 representation,α=0 as it can be inferred by looking at the structure of the H-dependent invariants built out of these representations[394].The coefficientγalso generically comes with an extra power of the top compositeness fractions.
1 For lattice QCD inputs,we use the averages from Ref.[14]whenever possible,unless the minireviews[10,15]choose other values.We only use unquenched lattice QCD results.Hereafter,the first error is statistical and the second is systematic,unless mentioned otherwise.
In our convention the electric charge is Q=T_3+F/2 and all our spinor fields are left-handed.
Equivalently,the SU(2)_L and U(1)_Y couplings are denoted as g=g_2 and g'=(3/5)~(1/2)g_1.One also usesα_s=α_3=(g_3~2/4π),α_(EM)=(e~2/4π)with e=g sinθ_W and sin~2θ_W=(g')~2/(g~2+(g')~2).
Useful references on group theory in the present context include[15]and refs.therein.
The solution of[28]relies on the absence of the fundamental superpotential termμH_u H_d(orμ5_H5_H).This is ensured by a U(1)_R.The latter clashes with typical superpotentials for the GUT breaking sector.However,higher-dimensional or stringy GUTs,where the triplet Higgs is simply projected out,can be consistent with the U(1)_R symmetry.
See however[40].
The DR scheme is frequently used in a supersymmetric regularization[63].The renormalization transformation of the gauge coupling constants from MS to DR scheme is given in Ref.[64].For an alternative treatment using holomorphic gauge couplings and NSVZβ-functions see e.g.[65].
It is interesting to note that a ratio M_*/M_c~100,needed for gauge coupling unification to work in orbifold GUTs,is typically the maximum value for this ratio consistent with perturbativity[78].
Adding extra vector-like sets of fields,e.g.two fermions which only transform under U(1)and have charges Y and-Y,is considered to violate minimality.
The value ofη~(CC)deduced from Ref.1 is found to be a factor of two too small;η~(CC)of Eq.(19.9)agrees with Refs.[2,3].