BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Production of HNL in 3-body decays of mesons. Comparison with PYTH IA approach DTSTART;VALUE=DATE-TIME:20201221T105000Z DTEND;VALUE=DATE-TIME:20201221T111000Z DTSTAMP;VALUE=DATE-TIME:20260518T023612Z UID:indico-contribution-176@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yuliia Borysenkova (Taras Shevchenko National Univer sity of Kyiv)\nThe Standard Model (SM) is a particle physics theory that i s consistent up to very high energy scales and verified in numerous exper iments up to $\\sim 14$ TeV. However\, it fails to explain some phenomena such as massiveness of neutrinos\, dark matter\, dark energy\, baryon as ymmetry of the Universe etc. Therefore SM is incomplete and requires an ex tension. \n\nOne possible approach is by adding new particles to the theor y. There are two possible answers to the question "Why do we not observe p articles of new physics in experiments?" The first answer is the following . The new particles are very heavy and can not be produced in modern ac celerators like LHC. To detect them one has to build more powerful and mor e expensive accelerators. There is another possibility. The particles of n ew physics can be light particles that feebly interact with SM particles. \nThe last case is very interesting for the experimental search of the new physics in the intensity frontier experiments just now. There are differe nt choices of new renormalized interaction Lagrangian of particles of new physics with SM particles. It's called portals. \n\nIn this paper\, we co nsider a heavy neutral lepton (HNL) portal. The phenomenology of GeV-scale HNL was considered in details in [1]. We will compare the analytical resu lts for HNL production in 3-body decays of mesons with PYTHIA approximatio n. \n\nThe simplest way of neutrino modification of the SM involves extens ion of the SM by neutrino singlets with right chirality (in the SM all rig ht-handed fermions are singlets)\, which extremely faintly interact with S M particles. Such neutrinos are called sterile neutrinos or heavy neutral leptons. Renormalized and gauge-invariant interaction of new neutrinos w ith the SM particles is similar to the Yukawa interaction of left-handed q uarks doublets with singlets of the right-handed quarks\, namely:\n\n$$\n\ \mathcal L_{int}=-\\left(F_{\\alpha I}\\bar L_\\alpha \\tilde H\nN_I+h.c.\ \right)\,\n$$\n\nwhere $\\alpha=e\,\\mu\,\\tau$\, index $I$ \nis from 1 t o full number of the sterile neutrinos\, $L_{\\alpha}$ –\ndoublet of le ptons of $\\alpha$-generation\, $N_I$ – right-handed sterile neutrino\,\ n$F_{\\alpha\nI}$ – new matrix of dimensionless Yukawa couplings\, ${\\t ilde H}=i\\sigma_2H^\\star$.\n\nTaking the low energy limit and considerin g sterile neutrino as Majorana particles\, we can write full Lagrangian of the modified neutrino sector of the SM\n\n$$\n\\mathcal{L}_{\\nu\,N}=i \\ bar{\\nu_k} \\not\\partial \\nu_k + i \\bar{N_I} \\not\\partial N_I -\n \ \left( F_{\\alpha I}\\bar{\\nu}_{\\alpha} N_I + \\frac{M_{I}}{2} \\bar{N_I }^c N_I + h.c. \\right)\,\n$$\n\nwhere $M_I$ – Majorana mass terms.\nAs a result of the neutrino states mixture\, the active neutrino states beco me superposition of the mass states of the active and the sterile neutrino s.\nIt means that sterile neutrinos interact with SM particles similarly t o active neutrinos:\n\n$$\n\\mathcal{L}_{int} = -\\biggl(\\frac{g}{2\\sqrt 2} W^+_\\mu\\!\\sum_{I\,\\alpha} \\overline{N^c}_I U_{I\\alpha} \\gamma^ \\mu (1-\\gamma_5) \\ell^-_\\alpha + \\frac{g}{4 \\cos\\theta_W}Z_\\mu\\! \\sum_{I\,\\alpha}\\overline{N^c}_I U_{I\\alpha} \\gamma^\\mu (1-\\gamma_ 5) \\nu_\\alpha + h.c.\\biggr)\,\n$$\n\nwhere $U_{I\\alpha}=F_{I\\alpha}/M _I$ is so called mixing angle.\n\nFor intensity frontier experiment it is very important to built sensitivity region. It is a region in space of p arameters of new particle (mass and coupling)\, when particle can be detec ted in the experiment. To build it one has to solve inequality $N_{HNL}^{r eg}>N_0$\, where $N_0$ is minimal expected number of new particle for succ essful of experiment\, $N_{HNL}^{reg}$ is number of HNL that can be detect ed:\n\n$$\nN_{HNL}^{reg}\\simeq N^{produced}_{HNL} P_{geom} P_{decay}.\n$$ \n\nHere $N_{HNL}^{produced}$ is number of\nthe produced \\textit{HNL}-pa rticles\, $P_{geom}$ is a probability of the produced HNL-particles to mov e towards the detector\, $P_{decay}$ is a probability of the\nproduced HNL -particles to decay in the volume of the vacuum tank\nbefore the detectors .\n\nFor approximate calculations of the sensitivity region\, PYTHIA is of ten used. It is a widely used program for the generation of high-energy ph ysics events.\nPYTHIA is good for generation of 2-body mesons' decay\, but for HNL production it is important to take into account 3-body decay too. \nPYTHIA uses predefined matrix element to generate 3-body semileptonic de cays of $B$ and $D$ mesons correspondingly\n\n$$\n \\overline{|M_{fi}| ^2_B} = (p_h\\\,p_\\nu) (p_{h^\\prime} \\\, p_\\ell)\,\\quad \n \\overl ine{|M_{fi}|^2_D} = (p_h\\\,p_\\ell) (p_{h^\\prime} \\\, p_\\nu).\n$$\n\n It does not contain mesons' form-factors and its matrix elements obviousl y\ndiffers from correct matrix elements for HNL production in 3-body meson s' decay.\nThe goal of the project is to estimate the importance of this u ncertainty for construction of sensitivity region to HNL.\n\nWe considere d in details probability density function for the energy of the HNL-parti cles $pdf(E_N)$\, $P_{geom}$ and $P_{decay}$ and make following conclusio ns.\n\n\n\nComputations of 3-body decay of $\\tau$-lepton with HNL produc tion in Pythia coincide with correct computations.\n\nFor description of r eactions of pseudoscalar meson 3-body decay into another pseudoscalar meso n ($B^- \\rightarrow D^0 +\\ell^- + N$ and $D^- \\rightarrow K^0 +\\ell^- + N$) the matrix elements of type $B$ in Pythia is better to use \n\nFor description of reactions of pseudoscalar meson 3-body decay into another vector meson ($B^- \\rightarrow D^\\star(2007)^0 +\\ell^- + N$ and $D^- \\ rightarrow K^\\star(892)+\\ell^- + N$) the matrix elements of type $D$ in Pythia is better to use.\n\nAmong the considered 3-body reactions\, due to a suitable choice of PYTHIA matrix elements (type of $B$ and $D$)\, one c an get the smallest difference with correct matrix element for reaction $B^- \\rightarrow D^0 +e^- + N$ (difference $\\sim 1\\%$)\, while the larg est unremovable difference is for reaction $D^- \\rightarrow K^\\star(89 2) +e^- + N$ (difference $\\sim 5\\%$).\n\n\n\n[1] Kyrylo Bondarenko\, Alexey Boyarsky\, Dmitry Gorbunov\, and Oleg Ruchayskiy. Phenomenolo gy of GeV-scale Heavy Neutral Leptons. *JHEP*\, 11:032\, 2018.\n\nhttps:// indico.bitp.kiev.ua/event/7/contributions/176/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/176/ END:VEVENT END:VCALENDAR