Nuclear Theory·nucl-th

Thursday·May 11, 2017

4 papers—1 primary·3 cross-listed

02
[Submitted on 8 May 2017] (cross-list from hep-ph)
5-Point 1PI Proper Vertex Function of Gluon and the S-Matrix Element
Gouranga C Nayak🇺🇸
As far as the renormalization in perturbative QCD is concerned the n-point one particle irreducible (1PI) proper vertex function is the basic building block where the ultra-violet (UV) divergence occurs when the loop momentum integration limit goes to infinity. In this paper we express the S-matrix element for the $g g \to g g g$ scattering process at all orders in coupling constant in terms of 5-point, 4-point, 3-point 1PI proper vertex functions and the (full) propagator by using the path integral formulation of QCD.
Comments:
14 pages latex
Subjects:
High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Theory (hep-th); Nuclear Theory (nucl-th)
arXiv:
1705.02927 [pdf]
3 citations
03
[Submitted on 10 May 2017] (cross-list from hep-lat)
Lefschetz thimbles in fermionic effective models with repulsive vector-field
Yuto Mori🇯🇵 · Kouji Kashiwa🇯🇵 · Akira Ohnishi🇯🇵
We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion ilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. This "auxiliary" sign problem can be solved by using the Lefschetz-thimble path-integral method, where the integration path is constructed in the complex plane. Another serious obstacle in the numerical construction of Lefschetz thimbles is caused by singular points and cuts induced by multivalued functions of the complexified scalar field in the momentum integration. We propose a new prescription which fixes gradient flow trajectories on the same Riemann sheet in the flow evolution by performing the momentum integration in the complex domain.
Comments:
6 pages, 5 figures
Subjects:
High Energy Physics — Lattice (hep-lat); High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Theory (hep-th); Nuclear Theory (nucl-th)
arXiv:
1705.03646 [pdf]
PLB(2018)·27 citations
04
[Submitted on 10 May 2017] (cross-list from hep-ph)
Triangle singularities in $B^{-} \to K^{-} π^{-} D_{s 0}^{+}$ and $B^{-} \to K^{-} π^{-} D_{s 1}^{+}$
S. Sakai🇪🇸 · E. Oset🇪🇸 · A. Ramos🇪🇸
We study the appearance of structures in the decay of the $B^{-}$ into $K^{-} π^{-} D_{s 0}^{+} (2317)$ and $K^{-} π^{-} D_{s 1}^{+} (2460)$ final states by forming invariant mass distributions of $π^{-} D_{s 0}^{+}$ and $π^{-} D_{s 1}^{+}$ pairs, respectively. The structure in the distribution is associated to the kinematical triangle singularity that appears when the $B^{-} \to K^{-} K^{* 0} D^{0}$ ( $B^{-} \to K^{-} K^{* 0} D^{* 0}$ ) decay process is followed by the decay of the $K^{* 0}$ into $π^{-} K^{+}$ and the subsequent rescattering of the $K^{+} D^{0}$ ( $K^{+} D^{* 0}$ ) pair forming the $D_{s 0}^{+} (2317)$ ( $D_{s 1}^{+} (2460)$ ) resonance. We find this type of non-resonant peaks at 2850 MeV in the invariant mass of $π^{-} D_{s 0}$ pairs from $B^{-} \to K^{-} π^{-} D_{s 0}^{+} (2317)$ decays and around 3000 MeV in the invariant mass of $π^{-} D_{s 1}^{+}$ pairs from $B^{-} \to K^{-} π^{-} D_{s 1}^{+} (2460)$ decays. By employing the measured branching ratios of the $B^{-} \to K^{-} K^{* 0} D^{0}$ and $B^{-} \to K^{-} K^{* 0} D^{* 0}$ decays, we predict the branching ratios for the processes $B^{-}$ into $K^{-} π^{-} D_{s 0}^{+} (2317)$ and $K^{-} π^{-} D_{s 1}^{+} (2460)$ , in the vicinity of the triangle singularity peak, to be about $8 \times 1 0^{- 6}$ and $1 \times 1 0^{- 6}$ , respectively. The observation of this reaction would also give extra support to the molecular picture of the $D_{s 0}^{+} (2317)$ and $D_{s 1}^{+} (2460)$ .
Comments:
18 pages, 15 figures, accepted version for publication in Eur. Phys. J. A
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:
1705.03694 [pdf]
EPJA(2018)·49 citations

Affiliations

first authorsco-authorsvia INSPIRE

5-Point 1PI Proper Vertex Function of Gluon and the S-Matrix Element

Lefschetz thimbles in fermionic effective models with repulsive vector-field

Triangle singularities in B−→K−π−Ds0+​ and B−→K−π−Ds1+​

Affiliations

Triangle singularities in $B^{-} \to K^{-} π^{-} D_{s 0}^{+}$ and $B^{-} \to K^{-} π^{-} D_{s 1}^{+}$