Our main objective is to derive the decay rate for the semileptonic decays <math><mi>D</mi><mo>→</mo><mi>V</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math>, where <math><mi>V</mi></math> represents a vector particle. In these decays, the vector particle <math><mi>V</mi></math> decays into three pseudoscalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the <math><mi>D</mi><mo>→</mo><mi>ω</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math><mi>ω</mi></math> subsequently decays into <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of <math><mi>D</mi><mo>→</mo><mi>ω</mi></math> form factors. These measurements can be performed using data obtained from BESIII.

China

Yechun Yu

Han Zhang

Bai-Cian Ke

Yao Yu

Zhuang Xiong

Jia-Wei Zhang

Xue-Wen Chen

Five-body <math><mi>D</mi><mo>→</mo><mi>V</mi></math> semileptonic decays

In this paper, we study the quasi-two-body decays <math><mi>B</mi><mo>→</mo><mi>P</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>P</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> [with <math><mi>P</mi><mo>=</mo><mo>(</mo><mi>π</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>η</mi><mo>,</mo><msup><mi>η</mi><mo>′</mo></msup><mo>)</mo></math>] within framework of perturbative QCD (PQCD) factorization approach. With the help of <math><mi>π</mi><mo>−</mo><mi>π</mi></math> distribution amplitude and scalar form factor <math><msub><mi>F</mi><mrow><mi>π</mi><mi>π</mi></mrow></msub><mo>(</mo><msup><mi>ω</mi><mn>2</mn></msup><mo>)</mo></math>, we calculate the <math><mi>C</mi><mi>P</mi></math> averaged branching fraction and the <math><mi>C</mi><mi>P</mi></math> asymmetry for the quasi-two-body decays <math><mi>B</mi><mo>→</mo><mi>P</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>P</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. Taking the quasi-two-body decay <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> as an explicit example, we present the behavior of differential branching fraction and direct <math><mi>C</mi><mi>P</mi></math> violation versus the <math><mrow><mi>π</mi><mtext>−</mtext><mi>π</mi></mrow></math> invariant mass. The total branching fraction and direct <math><mi>C</mi><mi>P</mi></math> violation are <math><mi>B</mi><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mo>[</mo><mi>σ</mi><mo>→</mo><mo>]</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo><mo>=</mo><mo>(</mo><mn>1.78</mn><mo>±</mo><mn>0.41</mn><mo>±</mo><mn>0.51</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> and <math><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mo>[</mo><mi>σ</mi><mo>→</mo><mo>]</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo><mo>=</mo><mo>(</mo><mn>29.8</mn><mo>±</mo><mn>11.1</mn><mo>±</mo><mn>13.0</mn><mo>)</mo><mo>%</mo></math> respectively. Our results could be tested by further experiments.

Bo-Yan Cui

Xing-Gang Wu

Hai-Bing Fu

Ya-Hui Chen

Quasi-two-body decays <math><mi>B</mi><mo>→</mo><mi>P</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo><mo>→</mo><mi>P</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> in the perturbative QCD approach

In this paper, we present an improved calculation for the decay rate of the rare Z-boson decay into  $$J/\psi + J/\psi .$$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>.</mo> </mrow> </math>   This decay is dominated by the photon fragmentation mechanism, i.e., the transition  $$Z\rightarrow J/\psi + \gamma ^{*}$$  <math> <mrow> <mi>Z</mi> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <msup> <mi>γ</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> </mrow> </math>   followed by the fragmentation  $$\gamma ^{*}\rightarrow J/\psi .$$  <math> <mrow> <msup> <mi>γ</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>.</mo> </mrow> </math>   In our calculation, the amplitude of  $$\gamma ^{*}\rightarrow J/\psi $$  <math> <mrow> <msup> <mi>γ</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> </mrow> </math>   is extracted from the measured value of  $$\Gamma (J/\psi \rightarrow e^+ e^-),$$  <math> <mrow> <mi>Γ</mi> <mo>(</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>→</mo> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>)</mo> <mo>,</mo> </mrow> </math>   and the amplitude of  $$Z\rightarrow J/\psi + \gamma ^{*}$$  <math> <mrow> <mi>Z</mi> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <msup> <mi>γ</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> </mrow> </math>   is calculate through the light-cone approach. The higher-order QCD and relativistic corrections in the amplitude of  $$\gamma ^{*}\rightarrow J/\psi $$  <math> <mrow> <msup> <mi>γ</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> </mrow> </math>   and the large logarithms of  $$m_{_Z}^2/m_c^2$$  <math> <mrow> <msubsup> <mi>m</mi> <mrow> <msub> <mrow></mrow> <mi>Z</mi> </msub> </mrow> <mn>2</mn> </msubsup> <mo>/</mo> <msubsup> <mi>m</mi> <mi>c</mi> <mn>2</mn> </msubsup> </mrow> </math>   that appear in the amplitude of  $$Z\rightarrow J/\psi + \gamma ^{*}$$  <math> <mrow> <mi>Z</mi> <mo>→</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <msup> <mi>γ</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> </mrow> </math>   are resummed in our calculation. Besides, the non-fragmentation amplitude is calculated based on the NRQCD factorization, and the next-to-leading order QCD and relativistic corrections are included. The obtained branching fraction for this Z decay channel is  $$8.66 ^{+1.48} _{-0.69}\times 10^{-11}.$$  <math> <mrow> <mn>8</mn> <mo>.</mo> <msubsup> <mn>66</mn> <mrow> <mo>-</mo> <mn>0.69</mn> </mrow> <mrow> <mo>+</mo> <mn>1.48</mn> </mrow> </msubsup> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>11</mn> </mrow> </msup> <mo>.</mo> </mrow> </math>

Guang-Yu Wang

Xu-Chang Zheng

Jiang Yan

Improved analysis of double  $$J/\psi $$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> </mrow> </math>   production in Z-boson decay

We study the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4000</mn><mo>)</mo></math> exotic states in the decays of <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub></math> baryons through a molecular scenario. In the final state interaction, the <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msubsup></math> decays are followed by the <math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msubsup></math> to <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>p</mi></math> rescatterings via exchange of a <math><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></math> meson. We predict a branching fraction of <math><mo>(</mo><msubsup><mrow><mn>3.1</mn></mrow><mrow><mo>−</mo><mn>2.6</mn></mrow><mrow><mo>+</mo><mn>1.4</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> for <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>p</mi></math>, which can be measured in the <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo><mo>−</mo></mrow></msup><mi>p</mi></math> decay. This study proposes a new approach to test the molecular model, and guides future experimental searches for the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4000</mn><mo>)</mo></math>.

Dong-Ze He

Rui-Yu Zhou

Investigating (3985) and (4000) Exotic States in Decays

An analysis of the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>η</mi><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>γ</mi></math> decay by the BESIII collaboration claims the observation of an exotic state <math><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math> with <math><msup><mrow><mi>I</mi></mrow><mrow><mi>G</mi></mrow></msup><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mo>+</mo></mrow></msup></math>. To establish its C-parity partner <math><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo></math> in the picture of the <math><mi>K</mi><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math> molecular state, we propose that <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math> receives the main contributions from the final state interaction of <math><mi>K</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>(<math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msup></math>, <math><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mo>+</mo></mrow></msup></math>, <math><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math>, and <math><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math>). Specifically, K and <math><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> in <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>K</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> decays transform as <math><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math>, by exchanging a <math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1400</mn><mo>)</mo></math>. We predict <math><mi>B</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><mi>η</mi><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>6.3</mn></mrow><mrow><mo>−</mo><mn>3.5</mn></mrow><mrow><mo>+</mo><mn>12.6</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, and <math><mi>B</mi><mo>(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1855</mn><mo>)</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>6.5</mn></mrow><mrow><mo>−</mo><mn>4.6</mn></mrow><mrow><mo>+</mo><mn>6.6</mn></mrow></msubsup><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, which can be studied in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mi>η</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></math> decays.

Yi Teng

Qing-Shan Liu

Investigating the Exotic State in the Decays

In this paper, we investigate the possibility of testing the weakly interacting massive particle (WIMP) dark matter (DM) models by applying the simplest phenomenological model which introduces an interaction term between dark energy (DE) and WIMP DM, i.e., Q = 3γ DM Hρ DM. In general, the coupling strength γ DE is close to 0 as the interaction between DE and WIMP DM is very weak, thus the effect of γ DE on the evolution of Y associated with DM energy density can be safely neglected. Meanwhile, our numerical calculation also indicates that x  f  ≈ 20 is associated with DM freeze-out temperature, which is the same as the vanishing interaction scenario. As for DM relic density, it will be magnified by   <math> <mfrac> <mrow> <mn>2</mn> <mo>−</mo> <mn>3</mn> <msub> <mi>γ</mi> <mi>DM</mi> </msub> </mrow> <mn>2</mn> </mfrac> <msup> <mfenced> <mrow> <mn>2</mn> <mi>π</mi> <msub> <mi>g</mi> <mo>∗</mo> </msub> <msubsup> <mi>m</mi> <mi>DM</mi> <mn>3</mn> </msubsup> <mo>/</mo> <mfenced> <mrow> <mn>45</mn> <msub> <mi>s</mi> <mn>0</mn> </msub> <msubsup> <mi>x</mi> <mi>f</mi> <mn>3</mn> </msubsup> </mrow> </mfenced> </mrow> </mfenced> <msub> <mi>γ</mi> <mi>DM</mi> </msub> </msup> </math>  $$ \frac{2-3{\upgamma}_{\mathrm{DM}}}{2}{\left[2\pi {g}_{\ast }{m}_{\mathrm{DM}}^3/\left(45{s}_0{x}_f^3\right)\right]}^{\gamma_{\mathrm{DM}}} $$  times, which provides a new way to test WIMP DM models. As an example, we analyze the case in which WIMP DM is a scalar DM. (SGL+SNe+Hz) and (CMB+BAO+SNe) cosmological observations will give γ DM =   <math> <msubsup> <mn>0.134</mn> <mrow> <mo>−</mo> <mn>0.069</mn> </mrow> <mrow> <mo>+</mo> <mn>0.17</mn> </mrow> </msubsup> </math>  $$ {0.134}_{-0.069}^{+0.17} $$  and γ DM = −0.0008 ± 0.0016, respectively. After further considering the constraints from DM direct detection experiment, DM indirect detection experiment, and DM relic density, we find that the allowed parameter space of the scalar DM model will be completely excluded for the former cosmological observations, while it will increase for the latter ones. Those two cosmological observations lead to an almost paradoxical conclusion. Therefore, one could expect more stringent constraints on the WMIP DM models, with the accumulation of more accurate cosmological observations in the near future.

Wei Cheng

Yuan He

Jing-Wang Diao

Yu Pan

Jun Zeng

A new way to test the WIMP dark matter models

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of 
					 in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of 
					 is triggered by at least two electroweak singlet scalars.
				

Wei Chao

Wen-Feng Cui

Huai-Ke Guo

Jing Shu

Gravitational wave imprint of new symmetry breaking JS is Supported by the National Natural Science Foundation of China (11647601, 11690022, 11675243) and also Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100). Wei Chao is Supported by the National Natural Science Foundation of China (11775025)

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a numerical evaluation of the known exact Fredholm determinant expression. We also obtain the next order term for the Brownian initial condition. Although initially devised for short time, a resummation of the series allows to obtain also the long time large deviation function, found to agree with previous works using completely different techniques. Unexpected similarities with stationary large deviations of TASEP with periodic and open boundaries are discussed. Two additional applications are given. (i) Our method is generalized to study the linear statistics of the Airy point process, i.e. of the GUE edge eigenvalues. We obtain the generating function of the cumulants of the empirical measure to a high order. The second cumulant is found to match the result in the bulk obtained from the Gaussian free field by Borodin and Ferrari [1,2], but we obtain systematic corrections to the Gaussian free field (higher cumulants, expansion towards the edge). This also extends a result of Basor and Widom [3] to a much higher order. We obtain large deviation functions for the Airy point process for a variety of linear statistics test functions. (ii) We obtain results for the counting statistics of trapped fermions at the edge of the Fermi gas in both the high and the low temperature limits.

France

Alexandre Krajenbrink

Pierre Le Doussal

Sylvain Prolhac

Systematic time expansion for the Kardar–Parisi–Zhang equation, linear statistics of the GUE at the edge and trapped fermions

In the production of the Higgs through a bottom-quark loop, the transverse momentum distribution of the Higgs at large <math><msub><mi>P</mi><mi>T</mi></msub></math> is complicated by its dependence on two other important scales: the bottom quark mass <math><msub><mi>m</mi><mi>b</mi></msub></math> and the Higgs mass <math><msub><mi>m</mi><mi>H</mi></msub></math>. A strategy for simplifying the calculation of the cross section at large <math><msub><mi>P</mi><mi>T</mi></msub></math> is to calculate only the leading terms in its expansion in <math><msubsup><mi>m</mi><mi>b</mi><mn>2</mn></msubsup><mo>/</mo><msubsup><mi>P</mi><mi>T</mi><mn>2</mn></msubsup></math>. In this paper, we consider the bottom-quark-loop contribution to the parton process <math><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover><mo>→</mo><mi>H</mi><mo>+</mo><mi>g</mi></math> at leading order in <math><msub><mi>α</mi><mi>s</mi></msub></math>. We show that the leading power of <math><mn>1</mn><mo>/</mo><msubsup><mi>P</mi><mi>T</mi><mn>2</mn></msubsup></math> can be expressed in the form of a factorization formula that separates the large scale <math><msub><mi>P</mi><mi>T</mi></msub></math> from the scale of the masses. All the dependence on <math><msub><mi>m</mi><mi>b</mi></msub></math> and <math><msub><mi>m</mi><mi>H</mi></msub></math> can be factorized into a distribution amplitude for <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> in the Higgs, a distribution amplitude for <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> in a real gluon, and an end point contribution. The factorization formula can be used to organize the calculation of the leading terms in the expansion in <math><msubsup><mi>m</mi><mi>b</mi><mn>2</mn></msubsup><mo>/</mo><msubsup><mi>P</mi><mi>T</mi><mn>2</mn></msubsup></math> so that every calculation involves at most two scales.

United States

Eric Braaten

Hong Zhang

Mass dependence of Higgs boson production at large transverse momentum through a bottom-quark loop

The transverse momentum distribution of the Higgs at large P  T  is complicated by its dependence on three important energy scales: P  T , the top quark mass m  t , and the Higgs mass m  H . A strategy for simplifying the calculation of the cross section at large P  T  is to calculate only the leading terms in its expansion in m  t 2/P  T 2 and/or m  H 2/P  T 2. The expansion of the cross section in inverse powers of P  T  is complicated by logarithms of P  T  and by mass singularities. In this paper, we consider the top-quark loop contribution to the subprocess  <math><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover><mo>→</mo><mi>H</mi><mo>+</mo><mi>g</mi></math> $$ q\overline{q}\to H+g $$ at leading order in α  s . We show that the leading power of 1/P  T 2 can be expressed in the form of a factorization formula that separates the large scale P  T  from the scale of the masses. All the dependence on m  t  and m  H  can be factorized into a distribution amplitude for  <math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover></math> $$ t\overline{t} $$ in the Higgs, a distribution amplitude for  <math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover></math> $$ t\overline{t} $$ in a real gluon, and an endpoint contribution. The factorization formula can be used to simplify calculations of the P  T  distribution at large P  T  to next-to-leading order in α  s . The results are readily applied to the qg process via a straightforward analytical continuation.

Mass dependence of Higgs production at large transverse momentum