CMS实验在8和13 TeV质子-质子碰撞中搜索重共振到玻色子对的组合分析

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"在8和13 TeV质子-质子碰撞中搜索重共振衰变到WW，WZ，ZZ，WH和ZH玻色子对的组合分析" 这篇论文是CMS合作组在《物理信函B》上发表的，详细介绍了他们在大型强子对撞机（LHC）上进行的一系列实验。他们对质子-质子碰撞数据进行了统计分析，这些数据是在质心能量为8和13 TeV的情况下收集的，分别对应19.7和最高2.7 fb^-1的综合光度。研究的主要目标是寻找可能存在的重共振，这些共振可能会衰变成WW，WZ，ZZ，WH和ZH玻色子对。在这项工作中，研究团队首次将针对WW，WZ，WH和ZH的共振搜索进行了组合，这样可以提高检测信号的敏感性。他们考虑了多种理论模型来解释可能的结果，其中包括重矢量三重态和单重态模型，这些模型与复合希格斯模型的特性相吻合，预测了W'和Z'玻色子的存在，它们可以衰变为上述提到的玻色子对。此外，还探讨了含有重重力子的模型，这些重力子可能衰变为WW和ZZ对。通过对这些模型的比较和分析，研究人员设定了针对不同质量的W'和Z'单峰以及三重峰的限制。具体来说，在95%的置信水平下，他们设定了2.3 TeV质量的W'和Z'单峰以及2.4 TeV质量的三重峰的界限。此外，这项工作还提供了迄今为止对于扭曲的超维（k = 0.5）曲率标度下的窄本体引力子共振生产截面的最严格限制。论文的关键词包括CMS（紧凑型缪子线圈），物理学，双玻色子，共振，组合分析，这些标签反映了研究的核心内容和方法。通过这样的组合分析，科学家们能够更深入地理解基本粒子之间的相互作用，以及可能存在的超出标准模型的新物理现象。这不仅有助于验证现有理论，也为探索未知的物理领域提供了宝贵的线索。

The CMS Collaboration / Physics Letters B 774 (2017) 533–558 537

Table 3

Correlation

across analyses of systematic uncertainties in the signal prediction affecting the event yield in the signal region and the reconstructed diboson invariant mass

distribution. A“yes” signiﬁes 100% correlation, and “no” means uncorrelated.

Source Quantity 8 and 13 TeV e and μ HP and LP W-, Z-, and H-enriched

Lepton trigger yield no no yes yes

Lepton identiﬁcation yield no no yes yes

Lepton momentum scale yield, shape no no yes yes

Jet energy scale yield, shape no yes yes yes

Jet energy resolution yield, shape no yes yes yes

Jet mass scale yield no yes yes yes

Jet mass resolution yield no yes yes yes

b tagging yield no yes yes yes

W tagging

(HP/LP) yield no yes yes yes

Integrated luminosity yield no yes yes yes

Pileup yield no yes yes yes

PDF yield yes yes yes yes

and μ

scales yield yes yes yes yes

previously obtained in the same models as those considered in this

letter and a reinterpretation is not needed.

4. Combination procedure

We search for a peak on top of a falling background spectrum

by means of a ﬁt to the data. The likelihood function is con-

structed

using the diboson invariant mass distribution in data, the

background prediction, and the resonant line-shape, to assess the

presence of a potential diboson resonance. We deﬁne the likeli-

hood

function L as

L(data | μ s(θ) +b(θ)) = P (data | μ s(θ ) +b(θ )) p(

θ|θ), (1)

where “data” stands for the observed data; θ represents the full

ensemble of nuisance parameters; s(θ ) and b(θ ) are the expected

signal and background yields; μ is a scale factor for the signal

strength; P(data | μ s(θ) + b (θ )) is the product of Poisson prob-

abilities

over all bins of diboson invariant mass distributions in

all channels (or over all events for channels with unbinned dis-

tributions);

and p(

θ|θ) is the probability density function for all

nuisance parameters to measure a value

given its true value θ

[52]. After maximizing the likelihood function, the best-ﬁt value

of μ = σ

best-ﬁt

/σ

theory

corresponds therefore to the ratio of the

best-ﬁt signal cross section σ

best-ﬁt

to the predicted cross section

theory

, assuming that all branching fractions are as predicted by

the relevant signal models.

The treatment of the background in the maximum likelihood

ﬁt depends on the analysis channel. In the qqqq, qqbb, and 6q

analyses,

the parameters in the background function are left ﬂoat-

ing

in the ﬁt, such that the background prediction is obtained

simultaneously with μ, in each hypothesis [15]. In the remaining

analyses (νqq, qq, bb, νbb, ννbb), the background is esti-

mated

using sidebands in data, and the uncertainties related to

its parametrized distribution are treated as nuisance parameters

constrained through Gaussian probability density functions in the

ﬁt [14]. The likelihoods from all analysis channels are combined.

The asymptotic approximation [53] of the CL

criterion [54,55]

used to obtain limits on the signal scale factor μ that take into

account the ratio of the theoretical predictions for the production

cross sections at 8 and 13 TeV.

Systematic

uncertainties in the signal and background yields

are treated as nuisance parameters constrained through log-normal

probability density functions. All such parameters are proﬁled (re-

ﬁtted

as a function of the parameter of interest μ) in the maxi-

mization

of the likelihood function. When the likelihoods from dif-

ferent

analysis channels are combined, the correlation of system-

atic

effects across those channels is taken into account by treating

the uncertainties as fully correlated (associated with the same nui-

sance

parameter) or fully uncorrelated (associated with different

nuisance parameters). Table 3 summarizes which uncertainties are

treated as correlated among 8 and 13 TeV analyses, e and μ chan-

nels,

HP and LP categories, and mass categories enriched in W,

Z, and Higgs bosons in the combination. Additional categorization

within individual analyses is described in their corresponding pa-

pers.

The nuisance parameters treated as correlated between 8 and

13 TeV analyses are those related to the parton distribution func-

tions

(PDFs) and the choice of the factorization (μ

) and renormal-

ization

(μ

) scales used to estimate the signal cross sections. The

signal cross sections and their associated uncertainties are reevalu-

ated

for this combination at both 8 and 13 TeV, estimating thereby

their full impact on the expected signal yield rather than just the

impact on the signal acceptance. The PDF uncertainties are evalu-

ated

using the NNPDF 3.0 [56] PDFs. The uncertainty related to the

choice of μ

and μ

scales is evaluated following [57,58] by chang-

ing

the default choice of scales in six combinations of (μ

, μ

) by

factors of (0.5, 0.5), (0.5, 1), (1, 0.5), (2, 2), (2, 1), and (1, 2). The

experimental uncertainties are all treated as uncorrelated between

8 and 13 TeV analyses. The case where the most important uncer-

tainties

are treated as fully correlated among 8 and 13 TeV analyses

has been studied and found to have negligible impact on the re-

sults.

After the combined ﬁt, no nuisance parameter was found to

differ signiﬁcantly from its expectation and from the ﬁt result in

individual analyses.

5. Results

We evaluate the combined signiﬁcance of the 8 and 13 TeV

CMS

searches for all signal hypotheses. The ATLAS Collaboration

reported an excess in the all-jet VV → qqqqsearch, corresponding

to a local signiﬁcance of 3.4 standard deviations (s.d.) for a W



res-

onance

with a mass of 2TeV [21]. Similarly, the CMS experiment

reported a local deviation of 2.2 s.d. in the lepton+jet WH →νbb

for a W



resonance with a mass of 1.8 TeV [16]. The present

combination does not conﬁrm these small excesses (within the

context of the models considered), as the highest combined sig-

niﬁcance

in the mass range of the reported excesses is found to

be for a W



resonance at 1.8 TeV with a local signiﬁcance of 0.8

standard deviations.

In the following, we present for each channel 95% CL exclusion

limits on the signal strength μ in Eq. (1), expressed as the exclu-

sion

limit on the ratio σ

95%

/σ

theory

of the signal cross section to

the predicted cross section, assuming that all branching fractions

are as predicted by the relevant signal models.

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