PTPlot

PTPlot: Gauged Lepton Number Model benchmark points

Lepton number breaking phase transition in an extension of the SM with gauged lepton number (supplied by E. Madge).

Benchmark points for the lepton number phase transition in the model considered in https://arxiv.org/abs/1809.09110, see section 5.2 for the potential. Lepton number is gauged as a $U(1)_\ell$ gauge group. The corresponding gauge boson acquires a mass $m_{Z'}$ when $U(1)_\ell$ is spontaneously broken by an SM singlet scalar $\phi$ with mass $m_\phi$ and lepton number 3. The VEV is set to $v_\phi = 2\,\text{TeV}$ . Four different scenarios for the masses of the DM ( $m_\text{DM}$ ) and additional leptons ( $m_\text{HL}$ ) are considered.

General parameters used for plotting: $v_\mathrm{w} = 1.0$ , $T_* = 500.0 \, \mathrm{GeV}$ (when all points are plotted), $g_* = 130.0$ .

Mission profile: Science Requirements Document (3 years)

This model has the following scenarios:

Scenario A: $m_\text{DM} = 0$ , $m_\text{HL} = 0$ [plot scenario]
Scenario B: $m_\text{DM} = 200\,\text{GeV}$ , $m_\text{HL} = 210\,\text{GeV}$ [plot scenario]
Scenario C: $m_\text{DM} = 500\,\text{GeV}$ , $m_\text{HL} = 1\,\text{TeV}$ [plot scenario]
Scenario D: $h^2\Omega_\text{DM} = 0.12$ , $m_\text{HL} = 1.5\,m_\text{DM}$ [plot scenario]

Full list of points:

[Show list of points]

[ D: $(m_\phi, m_{Z'}) = (500,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0310$ ; $\beta/H_* = 460$ ; $g_* = 130.0$ ; $T_* = 575 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (200,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1600$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 272 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (200,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.2600$ ; $\beta/H_* = 1200$ ; $g_* = 130.0$ ; $T_* = 222 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (250,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0810$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 377 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (250,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1100$ ; $\beta/H_* = 2000$ ; $g_* = 130.0$ ; $T_* = 337 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (250,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1700$ ; $\beta/H_* = 1400$ ; $g_* = 130.0$ ; $T_* = 291 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (250,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.3000$ ; $\beta/H_* = 970$ ; $g_* = 130.0$ ; $T_* = 229 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (250,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 2.9000$ ; $\beta/H_* = 380$ ; $g_* = 130.0$ ; $T_* = 114 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (300,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0480$ ; $\beta/H_* = 3600$ ; $g_* = 130.0$ ; $T_* = 471 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (300,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0670$ ; $\beta/H_* = 2700$ ; $g_* = 130.0$ ; $T_* = 434 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (300,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0920$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 394 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (300,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1300$ ; $\beta/H_* = 1400$ ; $g_* = 130.0$ ; $T_* = 350 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (300,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.2000$ ; $\beta/H_* = 1000$ ; $g_* = 130.0$ ; $T_* = 294 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0310$ ; $\beta/H_* = 5600$ ; $g_* = 130.0$ ; $T_* = 557 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0430$ ; $\beta/H_* = 3900$ ; $g_* = 130.0$ ; $T_* = 520 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0590$ ; $\beta/H_* = 2700$ ; $g_* = 130.0$ ; $T_* = 484 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0780$ ; $\beta/H_* = 2000$ ; $g_* = 130.0$ ; $T_* = 445 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1100$ ; $\beta/H_* = 1500$ ; $g_* = 130.0$ ; $T_* = 402 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1500$ ; $\beta/H_* = 1000$ ; $g_* = 130.0$ ; $T_* = 350 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (350,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.2700$ ; $\beta/H_* = 650$ ; $g_* = 130.0$ ; $T_* = 278 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0200$ ; $\beta/H_* = 7100$ ; $g_* = 130.0$ ; $T_* = 640 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0290$ ; $\beta/H_* = 5400$ ; $g_* = 130.0$ ; $T_* = 602 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0400$ ; $\beta/H_* = 3800$ ; $g_* = 130.0$ ; $T_* = 565 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0530$ ; $\beta/H_* = 2900$ ; $g_* = 130.0$ ; $T_* = 529 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0700$ ; $\beta/H_* = 2200$ ; $g_* = 130.0$ ; $T_* = 491 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0910$ ; $\beta/H_* = 1500$ ; $g_* = 130.0$ ; $T_* = 448 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1200$ ; $\beta/H_* = 1200$ ; $g_* = 130.0$ ; $T_* = 398 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1900$ ; $\beta/H_* = 690$ ; $g_* = 130.0$ ; $T_* = 333 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (400,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.6200$ ; $\beta/H_* = 230$ ; $g_* = 130.0$ ; $T_* = 219 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0130$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 720 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0200$ ; $\beta/H_* = 7800$ ; $g_* = 130.0$ ; $T_* = 679 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0280$ ; $\beta/H_* = 5300$ ; $g_* = 130.0$ ; $T_* = 642 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0380$ ; $\beta/H_* = 4000$ ; $g_* = 130.0$ ; $T_* = 606 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0490$ ; $\beta/H_* = 3000$ ; $g_* = 130.0$ ; $T_* = 570 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0630$ ; $\beta/H_* = 2200$ ; $g_* = 130.0$ ; $T_* = 532 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0810$ ; $\beta/H_* = 1600$ ; $g_* = 130.0$ ; $T_* = 491 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1100$ ; $\beta/H_* = 1400$ ; $g_* = 130.0$ ; $T_* = 442 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1600$ ; $\beta/H_* = 770$ ; $g_* = 130.0$ ; $T_* = 380 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (450,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.3300$ ; $\beta/H_* = 390$ ; $g_* = 130.0$ ; $T_* = 283 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,1400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0091$ ; $\beta/H_* = 16000$ ; $g_* = 130.0$ ; $T_* = 797 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0140$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 755 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0200$ ; $\beta/H_* = 7900$ ; $g_* = 130.0$ ; $T_* = 716 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0270$ ; $\beta/H_* = 5800$ ; $g_* = 130.0$ ; $T_* = 679 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0360$ ; $\beta/H_* = 4300$ ; $g_* = 130.0$ ; $T_* = 644 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0460$ ; $\beta/H_* = 3000$ ; $g_* = 130.0$ ; $T_* = 608 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0580$ ; $\beta/H_* = 2200$ ; $g_* = 130.0$ ; $T_* = 571 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0740$ ; $\beta/H_* = 1700$ ; $g_* = 130.0$ ; $T_* = 530 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0960$ ; $\beta/H_* = 1200$ ; $g_* = 130.0$ ; $T_* = 482 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1300$ ; $\beta/H_* = 870$ ; $g_* = 130.0$ ; $T_* = 422 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (500,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.2400$ ; $\beta/H_* = 470$ ; $g_* = 130.0$ ; $T_* = 334 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,1500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0094$ ; $\beta/H_* = 16000$ ; $g_* = 130.0$ ; $T_* = 828 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0140$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 787 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0200$ ; $\beta/H_* = 7800$ ; $g_* = 130.0$ ; $T_* = 749 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0270$ ; $\beta/H_* = 5600$ ; $g_* = 130.0$ ; $T_* = 714 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0350$ ; $\beta/H_* = 4300$ ; $g_* = 130.0$ ; $T_* = 679 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0440$ ; $\beta/H_* = 3300$ ; $g_* = 130.0$ ; $T_* = 643 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0550$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 607 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0690$ ; $\beta/H_* = 1700$ ; $g_* = 130.0$ ; $T_* = 566 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0870$ ; $\beta/H_* = 1200$ ; $g_* = 130.0$ ; $T_* = 519 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1200$ ; $\beta/H_* = 790$ ; $g_* = 130.0$ ; $T_* = 460 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (550,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1900$ ; $\beta/H_* = 780$ ; $g_* = 130.0$ ; $T_* = 377 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,1600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0100$ ; $\beta/H_* = 15000$ ; $g_* = 130.0$ ; $T_* = 857 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0140$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 818 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0210$ ; $\beta/H_* = 7700$ ; $g_* = 130.0$ ; $T_* = 781 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0270$ ; $\beta/H_* = 5700$ ; $g_* = 130.0$ ; $T_* = 746 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0340$ ; $\beta/H_* = 4300$ ; $g_* = 130.0$ ; $T_* = 711 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0430$ ; $\beta/H_* = 3200$ ; $g_* = 130.0$ ; $T_* = 676 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0530$ ; $\beta/H_* = 2400$ ; $g_* = 130.0$ ; $T_* = 640 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0650$ ; $\beta/H_* = 1800$ ; $g_* = 130.0$ ; $T_* = 599 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0800$ ; $\beta/H_* = 1300$ ; $g_* = 130.0$ ; $T_* = 553 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1100$ ; $\beta/H_* = 870$ ; $g_* = 130.0$ ; $T_* = 495 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (600,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1600$ ; $\beta/H_* = 7300$ ; $g_* = 130.0$ ; $T_* = 414 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,1700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0110$ ; $\beta/H_* = 14000$ ; $g_* = 130.0$ ; $T_* = 884 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0150$ ; $\beta/H_* = 10000$ ; $g_* = 130.0$ ; $T_* = 846 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0200$ ; $\beta/H_* = 7600$ ; $g_* = 130.0$ ; $T_* = 811 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0270$ ; $\beta/H_* = 5700$ ; $g_* = 130.0$ ; $T_* = 776 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0340$ ; $\beta/H_* = 4300$ ; $g_* = 130.0$ ; $T_* = 742 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0420$ ; $\beta/H_* = 3300$ ; $g_* = 130.0$ ; $T_* = 708 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0510$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 671 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0610$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 631 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0750$ ; $\beta/H_* = 1300$ ; $g_* = 130.0$ ; $T_* = 585 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0960$ ; $\beta/H_* = 920$ ; $g_* = 130.0$ ; $T_* = 527 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1400$ ; $\beta/H_* = 480$ ; $g_* = 130.0$ ; $T_* = 448 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (650,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.5400$ ; $\beta/H_* = 150$ ; $g_* = 130.0$ ; $T_* = 279 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,1800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0120$ ; $\beta/H_* = 13000$ ; $g_* = 130.0$ ; $T_* = 910 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0160$ ; $\beta/H_* = 9700$ ; $g_* = 130.0$ ; $T_* = 873 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0200$ ; $\beta/H_* = 7400$ ; $g_* = 130.0$ ; $T_* = 839 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 5600$ ; $g_* = 130.0$ ; $T_* = 805 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0340$ ; $\beta/H_* = 4300$ ; $g_* = 130.0$ ; $T_* = 771 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0410$ ; $\beta/H_* = 3300$ ; $g_* = 130.0$ ; $T_* = 737 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0490$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 701 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0590$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 661 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0710$ ; $\beta/H_* = 1300$ ; $g_* = 130.0$ ; $T_* = 614 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0900$ ; $\beta/H_* = 900$ ; $g_* = 130.0$ ; $T_* = 556 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (700,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.1300$ ; $\beta/H_* = 570$ ; $g_* = 130.0$ ; $T_* = 479 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,1900)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0120$ ; $\beta/H_* = 13000$ ; $g_* = 130.0$ ; $T_* = 935 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0160$ ; $\beta/H_* = 9400$ ; $g_* = 130.0$ ; $T_* = 899 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0210$ ; $\beta/H_* = 7100$ ; $g_* = 130.0$ ; $T_* = 866 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 5600$ ; $g_* = 130.0$ ; $T_* = 832 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0330$ ; $\beta/H_* = 4300$ ; $g_* = 130.0$ ; $T_* = 799 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0400$ ; $\beta/H_* = 3300$ ; $g_* = 130.0$ ; $T_* = 765 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0470$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 729 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0560$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 689 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0670$ ; $\beta/H_* = 1300$ ; $g_* = 130.0$ ; $T_* = 642 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (750,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0830$ ; $\beta/H_* = 890$ ; $g_* = 130.0$ ; $T_* = 584 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0130$ ; $\beta/H_* = 12000$ ; $g_* = 130.0$ ; $T_* = 959 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0170$ ; $\beta/H_* = 9200$ ; $g_* = 130.0$ ; $T_* = 925 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0210$ ; $\beta/H_* = 7000$ ; $g_* = 130.0$ ; $T_* = 891 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 5400$ ; $g_* = 130.0$ ; $T_* = 859 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0310$ ; $\beta/H_* = 4100$ ; $g_* = 130.0$ ; $T_* = 826 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0390$ ; $\beta/H_* = 3200$ ; $g_* = 130.0$ ; $T_* = 792 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0460$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 756 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0540$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 715 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (800,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0640$ ; $\beta/H_* = 1400$ ; $g_* = 130.0$ ; $T_* = 669 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2000)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0110$ ; $\beta/H_* = 18000$ ; $g_* = 130.0$ ; $T_* = 1017 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0140$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 982 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0170$ ; $\beta/H_* = 8800$ ; $g_* = 130.0$ ; $T_* = 949 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0210$ ; $\beta/H_* = 7000$ ; $g_* = 130.0$ ; $T_* = 917 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 5300$ ; $g_* = 130.0$ ; $T_* = 885 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0310$ ; $\beta/H_* = 4100$ ; $g_* = 130.0$ ; $T_* = 852 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0360$ ; $\beta/H_* = 3200$ ; $g_* = 130.0$ ; $T_* = 818 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0450$ ; $\beta/H_* = 2500$ ; $g_* = 130.0$ ; $T_* = 782 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (850,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0520$ ; $\beta/H_* = 1900$ ; $g_* = 130.0$ ; $T_* = 741 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2100)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0110$ ; $\beta/H_* = 13000$ ; $g_* = 130.0$ ; $T_* = 1039 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0140$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 1005 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0180$ ; $\beta/H_* = 8500$ ; $g_* = 130.0$ ; $T_* = 973 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0220$ ; $\beta/H_* = 6600$ ; $g_* = 130.0$ ; $T_* = 941 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 5300$ ; $g_* = 130.0$ ; $T_* = 910 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0310$ ; $\beta/H_* = 4200$ ; $g_* = 130.0$ ; $T_* = 877 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0360$ ; $\beta/H_* = 3100$ ; $g_* = 130.0$ ; $T_* = 844 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (900,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0410$ ; $\beta/H_* = 2400$ ; $g_* = 130.0$ ; $T_* = 807 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0120$ ; $\beta/H_* = 13000$ ; $g_* = 130.0$ ; $T_* = 1060 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0150$ ; $\beta/H_* = 10000$ ; $g_* = 130.0$ ; $T_* = 1028 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0180$ ; $\beta/H_* = 11000$ ; $g_* = 130.0$ ; $T_* = 996 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0220$ ; $\beta/H_* = 6400$ ; $g_* = 130.0$ ; $T_* = 965 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 5000$ ; $g_* = 130.0$ ; $T_* = 934 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0310$ ; $\beta/H_* = 3900$ ; $g_* = 130.0$ ; $T_* = 902 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (950,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0350$ ; $\beta/H_* = 3200$ ; $g_* = 130.0$ ; $T_* = 868 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2200)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0100$ ; $\beta/H_* = 16000$ ; $g_* = 130.0$ ; $T_* = 1115 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2300)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0130$ ; $\beta/H_* = 12000$ ; $g_* = 130.0$ ; $T_* = 1082 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2400)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0160$ ; $\beta/H_* = 9400$ ; $g_* = 130.0$ ; $T_* = 1050 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2500)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0190$ ; $\beta/H_* = 7400$ ; $g_* = 130.0$ ; $T_* = 1019 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2600)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0220$ ; $\beta/H_* = 6000$ ; $g_* = 130.0$ ; $T_* = 989 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2700)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0260$ ; $\beta/H_* = 4900$ ; $g_* = 130.0$ ; $T_* = 958 \, \mathrm{GeV}$ ; [plot]
[ D: $(m_\phi, m_{Z'}) = (1000,2800)\, \mathrm{GeV}$ ] $\alpha_\theta = 0.0300$ ; $\beta/H_* = 3900$ ; $g_* = 130.0$ ; $T_* = 926 \, \mathrm{GeV}$ ; [plot]

[plot all points with these parameters]

Results for scenario: Scenario D

NB: using $v_\mathrm{w} = 1.0$ , $T_* = 500.0 \, \mathrm{GeV}$ , $g_* = 130.0$ .

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PTPlot

PTPlot: Gauged Lepton Number Model benchmark points

This model has the following scenarios:

Full list of points:

Results for scenario: Scenario D

PTPlot by David Weir on behalf of the LISA Cosmology Working Group.