CMS实验在13 TeV质子-质子碰撞中搜寻MSSM中性希格斯玻色子至μμ衰变

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"这篇物理论文是在质子-质子碰撞中搜索MSSM（最小超对称标准模型）中衰变为μ+μ-的中性非标准模型希格斯玻色子的研究。CMS实验在CERN大型强子对撞机上以13TeV的质心能量收集了35.9fb-1的综合光度数据，以此为基础进行分析。研究关注胶子融合过程和与bb夸克对关联产生的希格斯玻色子。没有发现与标准模型预测的显著差异。结果以95%置信水平为mhmod +和现象学MSSM场景中的tan⁡β参数设定了限制，这些限制与伪标量A玻色子的质量有关，范围从130至600 GeV。此外，对于质量在130至1000 GeV的中性标量玻色子，通过胶子融合或与b夸克相关的衰变到μ对的分支比与生产截面的乘积也设定了模型独立的限制。" 在本文中，研究人员探讨了超对称理论的一个关键方面，即MSSM，这是一个扩展的标准模型，其中包含希格斯玻色子的超对称伙伴。希格斯玻色子是粒子物理学标准模型的一部分，负责赋予其他基本粒子质量。MSSM预言了多种不同类型的希格斯玻色子，包括标量、标量和伪标量。在本实验中，重点是寻找那些可能衰变为μ+μ-对的中性非标准模型希格斯玻色子。实验采用了CMS探测器，它是一个高度复杂的设备，能够检测高能粒子碰撞产生的各种产物。在13TeV的质子-质子碰撞中，研究团队分析了大量数据，旨在揭示任何可能超出标准模型预期的信号。由于没有观察到显著的异常，他们能够对MSSM的某些参数设定上限，特别是tan⁡β与A玻色子质量的关系。 tan⁡β是MSSM中的一个重要参数，表示希格斯双线性耦合的比率，而A玻色子是MSSM中的一个标量粒子。在mhmod +和现象学MSSM场景中，这些限制提供了对超对称模型参数空间的洞察，有助于进一步缩小理论模型的可能范围。此外，研究还设定了模型独立的限制，这适用于任何通过胶子融合或与b夸克关联产生的中性玻色子，其衰变至μ+μ-对的分支比乘以其生成截面。这种限制方法允许对各种理论框架进行比较，而不依赖于特定的模型假设。这项工作加深了我们对希格斯玻色子可能性质的理解，并对超对称性提供了更严格的测试。通过对超出标准模型的希格斯玻色子衰变模式的探索，物理学家们继续寻找可能揭示新物理的线索，这对于理解宇宙的基本构造至关重要。

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6 The CMS Collaboration / Physics Letters B 798 (2019) 134992

–tanβ values. The function F

sig

used to parametrize the signal

mass shape [21]is deﬁned as:

sig

= w

+ w

. (1)

In Eq. (1), the terms F

, F

, and F

describe the mass shape of

the h, H, and A signals, respectively. Each term is a convolution

of a Breit–Wigner (BW) function to describe the resonance, with a

Gaussian function to account for the detector resolution. The two

parameters of the BW function, as well as the variance of each

Gaussian function, are free parameters of the ﬁt used to determine

the signal model, while the quantities w

, w

, and w

are the

numbers of expected events for each boson passing the event se-

lection.

For the m

–tanβ points for which the signal samples were

not generated, the parameters are interpolated from the nearby

generated points. In order to correct for differences of the order

of a fewGeV between the pythia prediction of m

with respect to

the value calculated by FeynHiggs in the m

mod+

or the value used

in the hMSSM, especially for m

 200 GeV, the invariant mass dis-

tribution

of the H boson is shifted by the corresponding amount.

For the model-independent analysis the signal shape is described

using one single resonance in Eq. (1).

The

analysis does not use background estimation from simula-

tion

due to the limited size of simulated events compared to data

in the region of interest, as well as due to the large theoretical un-

certainties

in the background description at high invariant masses.

Therefore, given the smooth dependence of the background shape

on the dimuon invariant mass, it is estimated from the data, by as-

suming

a functional form to describe its dependence as a function

of the reconstructed dimuon invariant mass, m

μμ

, and by ﬁtting it

to the observed distribution.

The

functional form used to describe the background shape is

deﬁned as:

bkg

= exp(λm

μμ

)

⎡

⎣

μμ

−m

)



(

1 − f )

μμ

⎤

⎦

(2)

The quantity exp(λm

μμ

) parametrizes the exponential part of the

mass distribution, and f represents the weight of the BW term

with respect to DY photon exchange, while N

and N

correspond

to the integral of each term in F

bkg

. The quantities λ and f are free

parameters of the ﬁt. The parameters 

and m

are separately

determined for the two event categories by ﬁtting the dimuon

mass distribution close to the Z boson mass. The ﬁt provides the

effective values of such quantities, which include detector and res-

olution

effects. Their values are then kept constant when using

bkg

in the ﬁnal ﬁt. The systematic uncertainty that stems from

the choice of the functional form in Eq. (2), which was used in

earlier searches [21], is assessed as described below.

linear combination of the functions describing the expected

signal and the background is then used to perform a binned maxi-

mum

likelihood ﬁt to the data, where the uncertainties are treated

as nuisance parameters:

ﬁt

= (1 − f

bkg

sig

+ f

bkg

. (3)

The ﬁt is performed for each m

and tan β hypothesis, as the yield

of the signal events and the shape of F

sig

depend on these quan-

tities.

The parameters that describe the signal are determined by

ﬁtting the simulated samples that pass the event selection with

Eq. (1), for each m

and tan β pair, as explained above. Subse-

quently

they are assigned as constant terms in F

ﬁt

. The quantity

bkg

is a free parameter in the ﬁt, and the fraction of signal events

is deﬁned as f

sig

= (1 − f

bkg

). The overall normalization is also a

free parameter and is proﬁled in the ﬁt.

For

each m

assumption, the function F

ﬁt

is used to ﬁt the data

over an m

μμ

range centered on m

. The range has to be large

enough to account for the signal width, including the experimental

resolution, and it is ±50 GeV for m

≤ 290 GeV, ±75 GeV for 290 <

≤ 390 GeV, and ±100 GeV for 390 < m

≤ 500 GeV. For values

of m

smaller than 165 GeV the lower bound of the mass window

is set to 115 GeV. For m

> 500 GeV, the entire range from 400

to 1200 GeV is used. The h boson is used to constrain the results

when its mass is included in the ﬁtted mass range.

The

uncertainty introduced by the choice of the analytical func-

tion

used to parametrize the background is estimated by using a

method similar to that used in Refs. [3,21,89]. The method is based

on the determination of the number of spurious signal events that

are introduced by the choice of the background function F

bkg

when the background is ﬁt by the function F

ﬁt

. The invariant

mass spectrum is ﬁtted by the function F

bkg

, chosen among var-

ious

functional forms: Eq. (2)or other similar expressions that

include a BW plus exponentials, and sum of exponentials. All these

functional forms adequately describe the background distribution

observed in data. The ﬁt is performed in the proper mass range

centered around the assumed value of m

, and the parameters of

bkg

are determined. Then, thousands of MC pseudo-experiments

are generated, each one containing the same number of events

as observed in the data, distributed according to the functional

form F

bkg

. For each pseudo-experiment, the invariant mass dis-

tribution

is then ﬁt with the function F

ﬁt

of Eq. (3), once using

bkg

, and then using a different function F

bkg

, given by Eq. (2). For

each pseudo-experiment, the spurious signal yield, expressed by

the number of events N

bias

and N

bias

, is determined. The quantity

bias

is on average consistent with zero within statistical ﬂuctua-

tions.

The quantity N

bias

represents the number of spurious signal

events that are found in the signal yield if the function F

bkg

is used

to describe the background, when the background itself is actually

distributed according to F

bkg

. The median of the distribution of

the difference N

bias

− N

bias

obtained from the pseudo-experiments

is deﬁned as the bias introduced by using the function F

bkg

, rel-

ative

to the tested mass m

. This procedure is repeated for each

function F

bkg

among the functional forms mentioned above, and

the largest bias is taken as the systematic uncertainty in the num-

ber

of signal events obtained from the maximum likelihood ﬁt, due

to the choice of Eq. (2)to parametrize the background distribution.

Choosing a different function F

bkg

, instead of Eq. (2), was shown

to lead to similar biases over the whole mass range. The num-

ber

of spurious signal events varies between a few units and a

few hundred depending on the mass of the signal and the event

category. Although the bias is due to the modeling of the back-

ground,

its impact on the result depends on the expected signal

strength and shape, both varying according to m

and tan β in the

model-dependent analysis, and according to the mass of a generic

resonance φ for the model-independent case. More details about

the effect of the bias on the ﬁnal results are discussed in Section 7.

example of ﬁts to the data with Eq. (3), for the model-

independent

case, is shown in Fig. 4. Two mass hypotheses, 400

and 980 GeV, are assumed for a single narrow-width resonance φ

decaying to two muons. The two event categories are combined

according to their sensitivity, S/(S + B), where S and B are the

number of events in the expected signal and observed background,

respectively. The uncertainties in the integrated luminosity, in the

signal eﬃciency, and in the background parametrization are taken

into account as nuisance parameters.

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