利用Bc→D(*)衰变测定|Vub|：竞争力提取与Lepton flavor universality测试

Open

Access

11 浏览量更新于2024-07-16 收藏 1.34MB PDF 举报

身份认证购VIP最低享 7 折!

领优惠券(最高得80元）

资源详情

资源推荐

JHEP02(2020)171

(a) (b) (c) (d)

Figure 1. Contributions to correlation function from left to right: (a) perturbative diagram, (b)

nonlocal quark condensate diagram, (c) an example of a quark-gluon condensate diagram, (d) an

example of a gluon condensate diagram.

with the model-dependent function [30]

f(ν) =

a−2

Γ(a − 2)

1−a

−λ/ν

, a − 3 =

4λ

(2.14)

or in the simpler version [28, 29], which we use in this paper

f(ν) = δ



ν −



. (2.15)

The ﬁrst two moments of the model function f(ν) are ﬁxed by the OPE as

∞

dν f(ν) = 1,

∞

dν ν f(ν) =

(2.16)

Here m

is the standard OPE parameter [31–33] connected with the average quark virtu-

ality, and is deﬁned as a ratio of quark and quark-gluon condensates

gh¯q(x)(σ·G)q(0)i ≈ m

h¯q(x)q(0)i. (2.17)

We have checked explicitly that the use of the more sophisticated function f(ν) given

in (2.14) does not change anything in the conclusion. Namely, numerically the non-local

quark condensates Π

(3)

= Π

h¯qqi

and the mixed quark-condensate Π

(5)

= Π

h¯qσ.Gqi

are con-

tributing just up to 1% to the result. The analytic expressions are given in appendix A.2

and A.3, respectively.

The gluon condensate contributions Π

(4)

= Π

hGGi

to B

→ D

(∗)

form factors are

calculated from diagrams in ﬁgure 1d. The procedure is well known and the expressions

are very lengthy and cumbersome and similar to those already published in the literature

for B

→ J/ψ, η

transitions [34] and will not be given explicitly here. Some subtleties of

the calculation are given in appendix A.3. Numerically the gluon condensate contributions

do not exceed O(1%) in determined window of Borel parameters, but somewhat stabilize

the sum rules at smaller values of these parameters.

We deduce that all non-perturbative parts are numerically negligible, and can be safely

neglected. The main contribution to the correlation function (2.11) comes from the per-

turbative parts, eqs. (A.3)–(A.5).

– 7 –

JHEP02(2020)171

Meson lattice [MeV] our value [MeV] s

eﬀ

[GeV

] M

[GeV

]

427±8 [36], 434±5 [37] 425±25 53–55 30–50

213±2 [38], 207±4 [39] 212±16 7–7.5 4–6

∗

278±23 [40], 224±9 [41] 258±40 6–8 6–8

Table 1. Decay constants of mesons with 3ptSR parameters.

To calculate the form factors in QCD sum rules, in which the correlation function is

written as a sum of perturbative and non-perturbative contributions as in eq. (2.11), the

perturbative part is calculated by the usual expansion in the coupling constant, while the

non-perturbative part is described by the manner of Wilson’s operator product expansion

as a sum of expectation values of operators of increasing dimension. Since it is known that

when using the Borel-transformed sum rules in calculating heavy meson decay constants

higher orders of perturbation series can contribute as much as 30–40%, depending on the

scheme (heavy-light decay constants are known to NNLO [35]), whereas the QCD 3-point

function is only known to LO, here we parametrize the 3-point function with the same

threshold parameters s

eﬀ

that, at LO in QCDSR reproduce the meson decay constants

obtained from the lattice QCD calculations, listed in table 1, whereas the 3ptSR Borel

mass parameters M

are taken in the region where the stability is achieved in the sense of

appearance of the so called Borel plateau. An approximate relation connecting the Borel

mass parameters of diﬀerent meson decay constants noticed by authors in [42]

≈

− m

(2.18)

where m

is mass of the meson, and m

is the mass of its heavier quark, is found to

hold here too, and, as will be shown later, in 3-point calculations as well. Note however,

that the uncertainties of decay constants arising in our calculation are connected with our

speciﬁc method of calculation, since the threshold parameters are actually ﬁxed so that

they reproduce the lattice values, along with their uncertainties. Venturing into the 3-point

calculation, as mentioned above, we use the same Borel thresholds paired with the decay

constants that are reproduced by them. It is important to notice that, when estimating

uncertainties in the parameters of the 3ptSR calculation we do not vary the decay constants

and thresholds independently, but rather we always use decay constants values together

with the corresponding thresholds ﬁxed by the decay constants calculation. The hope is

that all the higher order/higher dimension operator contributions are reproduced through

the threshold modiﬁcation in the 3-point calculation as well. Otherwise, for the b quark

we use the so called “potential subtracted” mass [43], which is coincidentally very close to

both the Υ(1S) scheme mass [44] and the kinetic scheme mass [45, 46], whereas the c-quark

the mass is then given by varying the ratio Z of the two masses given by the QCD lattice

calculation [47, 48], keeping in mind that we do not use the MS masses, and this ratio for

pole masses tends to be lower as higher order corrections are included — which is why we

choose to use a somewhat lower value of Z. The same method described above was already

– 8 –

剩余44页未读，继续阅读

weixin_38550812

粉丝: 3
资源: 894

利用Bc→D(*)衰变测定|Vub|：竞争力提取与Lepton flavor universality测试

x0=[1;1]; A=[2 3 ;1 4]; b=[6;5]; Aeq=[];beq=[]; VLB=[0;0]; VUB=[]; [x,fval]=fmincon('fun3',x0,A,b,Aeq,beq,VLB,VUB);

function［xstar，fxstar，flagOut，iter］=BranchBound1（A，b，c，Aeq，Beq，vlb，vub，opXin，optF，iter）

function［xstar，fxstar，flagOut，iter］=BranchBound1（A，b，c，Aeq，Beq，vlb，vub，optXin，optF，iter）

c=[-10,-9]; A=[6 5;10 20;1 0]; b=[60;150;8]; vlb=zeros(2,1); Aeq=[]; beq=[]; vub=[]; [x,fval]=linprog(c,A,b,Aeq,beq,vlb,vub);

function [xstar, fxstar, flagOut, iter] = BranchBound1(A, b, c, Aeq, Beq, vlb, vub, optXin, optF, iter)

［x，fit，status］=linprog（c，A，b，Aeq，Beq，vlb，vub，［］）；

ALTER TABLE vub_details.detail_raw_sy_univ ADD COLUMN major varchar(500) CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_ci not NULL DEFAULT null comment '专业' AFTER is_calc;

具体的建模代码呢

markdown修改图片大小

能否将这个代码中的所有点都绘制在一张图片上

min{max{qixi}}这种目标函数，要如何用linprog表示

Avatar_Utils-1.0.6-py3-none-any.whl.zip

“人力资源+大数据+薪酬报告+涨薪调薪”

2024-2030全球及中国聚硅氮烷行业研究及十五五规划分析报告 Sample-yb.pdf

用于目标检测的一个GUI程序界面.zip

使用笔记本电脑上的无线网卡，生成wifi热点，让设备连接_ShareVirtualWiFi.zip

基于springboot的名城小区物业管理系统设计与实现.docx

基于springboot校园资产管理设计与实现.docx

最新资源