Package madgraph :: Package core :: Module diagram_generation
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Source Code for Module madgraph.core.diagram_generation

   1  ################################################################################ 
   2  # 
   3  # Copyright (c) 2009 The MadGraph5_aMC@NLO Development team and Contributors 
   4  # 
   5  # This file is a part of the MadGraph5_aMC@NLO project, an application which  
   6  # automatically generates Feynman diagrams and matrix elements for arbitrary 
   7  # high-energy processes in the Standard Model and beyond. 
   8  # 
   9  # It is subject to the MadGraph5_aMC@NLO license which should accompany this  
  10  # distribution. 
  11  # 
  12  # For more information, visit madgraph.phys.ucl.ac.be and amcatnlo.web.cern.ch 
  13  # 
  14  ################################################################################ 
  15  """Classes for diagram generation. Amplitude performs the diagram 
  16  generation, DecayChainAmplitude keeps track of processes with decay 
  17  chains, and MultiProcess allows generation of processes with 
  18  multiparticle definitions. DiagramTag allows to identify diagrams 
  19  based on relevant properties. 
  20  """ 
  21   
  22  import array 
  23  import copy 
  24  import itertools 
  25  import logging 
  26   
  27  import madgraph.core.base_objects as base_objects 
  28  import madgraph.various.misc as misc 
  29  from madgraph import InvalidCmd, MadGraph5Error 
  30   
  31  logger = logging.getLogger('madgraph.diagram_generation') 
32 33 34 -class NoDiagramException(InvalidCmd): pass
35
36 #=============================================================================== 37 # DiagramTag mother class 38 #=============================================================================== 39 40 -class DiagramTag(object):
41 """Class to tag diagrams based on objects with some __lt__ measure, e.g. 42 PDG code/interaction id (for comparing diagrams from the same amplitude), 43 or Lorentz/coupling/mass/width (for comparing AMPs from different MEs). 44 Algorithm: Create chains starting from external particles: 45 1 \ / 6 46 2 /\______/\ 7 47 3_ / | \_ 8 48 4 / 5 \_ 9 49 \ 10 50 gives ((((9,10,id910),8,id9108),(6,7,id67),id910867) 51 (((1,2,id12),(3,4,id34)),id1234), 52 5,id91086712345) 53 where idN is the id of the corresponding interaction. The ordering within 54 chains is based on chain length (depth; here, 1234 has depth 3, 910867 has 55 depth 4, 5 has depht 0), and if equal on the ordering of the chain elements. 56 The determination of central vertex is based on minimizing the chain length 57 for the longest subchain. 58 This gives a unique tag which can be used to identify diagrams 59 (instead of symmetry), as well as identify identical matrix elements from 60 different processes.""" 61
62 - class DiagramTagError(Exception):
63 """Exception for any problems in DiagramTags""" 64 pass
65
66 - def __init__(self, diagram, model=None, ninitial=2):
67 """Initialize with a diagram. Create DiagramTagChainLinks according to 68 the diagram, and figure out if we need to shift the central vertex.""" 69 70 # wf_dict keeps track of the intermediate particles 71 leg_dict = {} 72 # Create the chain which will be the diagram tag 73 for vertex in diagram.get('vertices'): 74 # Only add incoming legs 75 legs = vertex.get('legs')[:-1] 76 lastvx = vertex == diagram.get('vertices')[-1] 77 if lastvx: 78 # If last vertex, all legs are incoming 79 legs = vertex.get('legs') 80 # Add links corresponding to the relevant legs 81 link = DiagramTagChainLink([leg_dict.setdefault(leg.get('number'), 82 DiagramTagChainLink(self.link_from_leg(leg, model))) \ 83 for leg in legs], 84 self.vertex_id_from_vertex(vertex, 85 lastvx, 86 model, 87 ninitial)) 88 # Add vertex to leg_dict if not last one 89 if not lastvx: 90 leg_dict[vertex.get('legs')[-1].get('number')] = link 91 92 # The resulting link is the hypothetical result 93 self.tag = link 94 95 # Now make sure to find the central vertex in the diagram, 96 # defined by the longest leg being as short as possible 97 done = max([l.depth for l in self.tag.links]) == 0 98 while not done: 99 # Identify the longest chain in the tag 100 longest_chain = self.tag.links[0] 101 # Create a new link corresponding to moving one step 102 new_link = DiagramTagChainLink(self.tag.links[1:], 103 self.flip_vertex(\ 104 self.tag.vertex_id, 105 longest_chain.vertex_id, 106 self.tag.links[1:])) 107 # Create a new final vertex in the direction of the longest link 108 other_links = list(longest_chain.links) + [new_link] 109 other_link = DiagramTagChainLink(other_links, 110 self.flip_vertex(\ 111 longest_chain.vertex_id, 112 self.tag.vertex_id, 113 other_links)) 114 115 if other_link.links[0] < self.tag.links[0]: 116 # Switch to new tag, continue search 117 self.tag = other_link 118 else: 119 # We have found the central vertex 120 done = True
121
122 - def get_external_numbers(self):
123 """Get the order of external particles in this tag""" 124 125 return self.tag.get_external_numbers()
126
127 - def diagram_from_tag(self, model):
128 """Output a diagram from a DiagramTag. Note that each daughter 129 class must implement the static functions id_from_vertex_id 130 (if the vertex id is something else than an integer) and 131 leg_from_link (to pass the correct info from an end link to a 132 leg).""" 133 134 # Create the vertices, starting from the final vertex 135 diagram = base_objects.Diagram({'vertices': \ 136 self.vertices_from_link(self.tag, 137 model, 138 True)}) 139 diagram.calculate_orders(model) 140 return diagram
141 142 @classmethod 177 178 @classmethod
179 - def legPDGs_from_vertex_id(cls, vertex_id,model):
180 """Returns the list of external PDGs of the interaction corresponding 181 to this vertex_id.""" 182 183 # In case we have to deal with a regular vertex, we return the list 184 # external PDGs as given by the model information on that integer 185 # vertex id. 186 if (len(vertex_id)>=3 and 'PDGs' in vertex_id[2]): 187 return vertex_id[2]['PDGs'] 188 else: 189 return [part.get_pdg_code() for part in model.get_interaction( 190 cls.id_from_vertex_id(vertex_id)).get('particles')]
191 192 @classmethod
193 - def leg_from_legs(cls,legs, vertex_id, model):
194 """Return a leg from a leg list and the model info""" 195 196 pdgs = list(cls.legPDGs_from_vertex_id(vertex_id, model)) 197 198 # Extract the resulting pdg code from the interaction pdgs 199 for pdg in [leg.get('id') for leg in legs]: 200 pdgs.remove(pdg) 201 202 assert len(pdgs) == 1 203 # Prepare the new leg properties 204 pdg = model.get_particle(pdgs[0]).get_anti_pdg_code() 205 number = min([l.get('number') for l in legs]) 206 # State is False for t-channel, True for s-channel 207 state = (len([l for l in legs if l.get('state') == False]) != 1) 208 # Note that this needs to be done before combining decay chains 209 onshell= False 210 211 return base_objects.Leg({'id': pdg, 212 'number': number, 213 'state': state, 214 'onshell': onshell})
215 216 @classmethod 229 230 @staticmethod 243 244 @staticmethod
245 - def id_from_vertex_id(vertex_id):
246 """Return the numerical vertex id from a link.vertex_id""" 247 248 return vertex_id[0][0]
249 250 @staticmethod
251 - def loop_info_from_vertex_id(vertex_id):
252 """Return the loop_info stored in this vertex id. Notice that the 253 IdentifyME tag does not store the loop_info, but should normally never 254 need access to it.""" 255 256 return vertex_id[2]
257 258 @staticmethod
259 - def reorder_permutation(perm, start_perm):
260 """Reorder a permutation with respect to start_perm. Note that 261 both need to start from 1.""" 262 if perm == start_perm: 263 return range(len(perm)) 264 order = [i for (p,i) in \ 265 sorted([(p,i) for (i,p) in enumerate(perm)])] 266 return [start_perm[i]-1 for i in order]
267 268 @staticmethod 279 280 @staticmethod
281 - def vertex_id_from_vertex(vertex, last_vertex, model, ninitial):
282 """Returns the default vertex id: just the interaction id 283 Note that in the vertex id, like the leg, only the first entry is 284 taken into account in the tag comparison, while the second is for 285 storing information that is not to be used in comparisons and the 286 third for additional info regarding the shrunk loop vertex.""" 287 288 if isinstance(vertex,base_objects.ContractedVertex): 289 # return (vertex.get('id'),(),{'PDGs':vertex.get('PDGs')}) 290 return ((vertex.get('id'),vertex.get('loop_tag')),(), 291 {'PDGs':vertex.get('PDGs')}) 292 else: 293 return ((vertex.get('id'),()),(),{})
294 295 @staticmethod
296 - def flip_vertex(new_vertex, old_vertex, links):
297 """Returns the default vertex flip: just the new_vertex""" 298 return new_vertex
299
300 - def __eq__(self, other):
301 """Equal if same tag""" 302 if type(self) != type(other): 303 return False 304 return self.tag == other.tag
305
306 - def __ne__(self, other):
307 return not self.__eq__(other)
308
309 - def __str__(self):
310 return str(self.tag)
311
312 - def __lt__(self, other):
313 return self.tag < other.tag
314
315 - def __gt__(self, other):
316 return self.tag > other.tag
317 318 __repr__ = __str__
319 405
406 #=============================================================================== 407 # Amplitude 408 #=============================================================================== 409 -class Amplitude(base_objects.PhysicsObject):
410 """Amplitude: process + list of diagrams (ordered) 411 Initialize with a process, then call generate_diagrams() to 412 generate the diagrams for the amplitude 413 """ 414
415 - def default_setup(self):
416 """Default values for all properties""" 417 418 self['process'] = base_objects.Process() 419 self['diagrams'] = None 420 # has_mirror_process is True if the same process but with the 421 # two incoming particles interchanged has been generated 422 self['has_mirror_process'] = False
423
424 - def __init__(self, argument=None):
425 """Allow initialization with Process""" 426 if isinstance(argument, base_objects.Process): 427 super(Amplitude, self).__init__() 428 self.set('process', argument) 429 self.generate_diagrams() 430 elif argument != None: 431 # call the mother routine 432 super(Amplitude, self).__init__(argument) 433 else: 434 # call the mother routine 435 super(Amplitude, self).__init__()
436
437 - def filter(self, name, value):
438 """Filter for valid amplitude property values.""" 439 440 if name == 'process': 441 if not isinstance(value, base_objects.Process): 442 raise self.PhysicsObjectError, \ 443 "%s is not a valid Process object" % str(value) 444 if name == 'diagrams': 445 if not isinstance(value, base_objects.DiagramList): 446 raise self.PhysicsObjectError, \ 447 "%s is not a valid DiagramList object" % str(value) 448 if name == 'has_mirror_process': 449 if not isinstance(value, bool): 450 raise self.PhysicsObjectError, \ 451 "%s is not a valid boolean" % str(value) 452 return True
453
454 - def get(self, name):
455 """Get the value of the property name.""" 456 457 if name == 'diagrams' and self[name] == None: 458 # Have not yet generated diagrams for this process 459 if self['process']: 460 self.generate_diagrams() 461 462 return super(Amplitude, self).get(name)
463 # return Amplitude.__bases__[0].get(self, name) #return the mother routine 464 465
466 - def get_sorted_keys(self):
467 """Return diagram property names as a nicely sorted list.""" 468 469 return ['process', 'diagrams', 'has_mirror_process']
470
471 - def get_number_of_diagrams(self):
472 """Returns number of diagrams for this amplitude""" 473 return len(self.get('diagrams'))
474
475 - def get_amplitudes(self):
476 """Return an AmplitudeList with just this amplitude. 477 Needed for DecayChainAmplitude.""" 478 479 return AmplitudeList([self])
480
481 - def nice_string(self, indent=0):
482 """Returns a nicely formatted string of the amplitude content.""" 483 return self.get('process').nice_string(indent) + "\n" + \ 484 self.get('diagrams').nice_string(indent)
485
486 - def nice_string_processes(self, indent=0):
487 """Returns a nicely formatted string of the amplitude process.""" 488 return self.get('process').nice_string(indent)
489
490 - def get_ninitial(self):
491 """Returns the number of initial state particles in the process.""" 492 return self.get('process').get_ninitial()
493
494 - def has_loop_process(self):
495 """ Returns wether this amplitude has a loop process.""" 496 497 return self.get('process').get('perturbation_couplings')
498
499 - def generate_diagrams(self, returndiag=False):
500 """Generate diagrams. Algorithm: 501 502 1. Define interaction dictionaries: 503 * 2->0 (identity), 3->0, 4->0, ... , maxlegs->0 504 * 2 -> 1, 3 -> 1, ..., maxlegs-1 -> 1 505 506 2. Set flag from_group=true for all external particles. 507 Flip particle/anti particle for incoming particles. 508 509 3. If there is a dictionary n->0 with n=number of external 510 particles, create if possible the combination [(1,2,3,4,...)] 511 with *at least two* from_group==true. This will give a 512 finished (set of) diagram(s) (done by reduce_leglist) 513 514 4. Create all allowed groupings of particles with at least one 515 from_group==true (according to dictionaries n->1): 516 [(1,2),3,4...],[1,(2,3),4,...],..., 517 [(1,2),(3,4),...],...,[(1,2,3),4,...],... 518 (done by combine_legs) 519 520 5. Replace each group with a (list of) new particle(s) with number 521 n = min(group numbers). Set from_group true for these 522 particles and false for all other particles. Store vertex info. 523 (done by merge_comb_legs) 524 525 6. Stop algorithm when at most 2 particles remain. 526 Return all diagrams (lists of vertices). 527 528 7. Repeat from 3 (recursion done by reduce_leglist) 529 530 8. Replace final p=p vertex 531 532 Be aware that the resulting vertices have all particles outgoing, 533 so need to flip for incoming particles when used. 534 535 SPECIAL CASE: For A>BC... processes which are legs in decay 536 chains, we need to ensure that BC... combine first, giving A=A 537 as a final vertex. This case is defined by the Process 538 property is_decay_chain = True. 539 This function can also be called by the generate_diagram function 540 of LoopAmplitudes, in which case the generated diagrams here must not 541 be directly assigned to the 'diagrams' attributed but returned as a 542 DiagramList by the function. This is controlled by the argument 543 returndiag. 544 """ 545 546 process = self.get('process') 547 model = process.get('model') 548 legs = process.get('legs') 549 # Make sure orders is the minimum of orders and overall_orders 550 for key in process.get('overall_orders').keys(): 551 try: 552 process.get('orders')[key] = \ 553 min(process.get('orders')[key], 554 process.get('overall_orders')[key]) 555 except KeyError: 556 process.get('orders')[key] = process.get('overall_orders')[key] 557 558 assert model.get('particles'), \ 559 "particles are missing in model: %s" % model.get('particles') 560 561 assert model.get('interactions'), \ 562 "interactions are missing in model" 563 564 565 res = base_objects.DiagramList() 566 # First check that the number of fermions is even 567 if len(filter(lambda leg: model.get('particle_dict')[\ 568 leg.get('id')].is_fermion(), legs)) % 2 == 1: 569 if not returndiag: 570 self['diagrams'] = res 571 raise InvalidCmd, 'The number of fermion is odd' 572 else: 573 return False, res 574 575 # Then check same number of incoming and outgoing fermions (if 576 # no Majorana particles in model) 577 if not model.get('got_majoranas') and \ 578 len(filter(lambda leg: leg.is_incoming_fermion(model), legs)) != \ 579 len(filter(lambda leg: leg.is_outgoing_fermion(model), legs)): 580 if not returndiag: 581 self['diagrams'] = res 582 raise InvalidCmd, 'The number of of incoming/outcoming fermions are different' 583 else: 584 return False, res 585 586 # Finally check that charge (conserve by all interactions) of the process 587 #is globally conserve for this process. 588 for charge in model.get('conserved_charge'): 589 total = 0 590 for leg in legs: 591 part = model.get('particle_dict')[leg.get('id')] 592 try: 593 value = part.get(charge) 594 except (AttributeError, base_objects.PhysicsObject.PhysicsObjectError): 595 try: 596 value = getattr(part, charge) 597 except AttributeError: 598 value = 0 599 600 if (leg.get('id') != part['pdg_code']) != leg['state']: 601 total -= value 602 else: 603 total += value 604 605 if abs(total) > 1e-10: 606 if not returndiag: 607 self['diagrams'] = res 608 raise InvalidCmd, 'No %s conservation for this process ' % charge 609 return res 610 else: 611 raise InvalidCmd, 'No %s conservation for this process ' % charge 612 return res, res 613 614 if not returndiag: 615 logger.info("Trying %s " % process.nice_string().replace('Process', 'process')) 616 617 # Give numbers to legs in process 618 for i in range(0, len(process.get('legs'))): 619 # Make sure legs are unique 620 leg = copy.copy(process.get('legs')[i]) 621 process.get('legs')[i] = leg 622 if leg.get('number') == 0: 623 leg.set('number', i + 1) 624 625 # Copy leglist from process, so we can flip leg identities 626 # without affecting the original process 627 leglist = self.copy_leglist(process.get('legs')) 628 629 for leg in leglist: 630 631 # For the first step, ensure the tag from_group 632 # is true for all legs 633 leg.set('from_group', True) 634 635 # Need to flip part-antipart for incoming particles, 636 # so they are all outgoing 637 if leg.get('state') == False: 638 part = model.get('particle_dict')[leg.get('id')] 639 leg.set('id', part.get_anti_pdg_code()) 640 641 # Calculate the maximal multiplicity of n-1>1 configurations 642 # to restrict possible leg combinations 643 max_multi_to1 = max([len(key) for key in \ 644 model.get('ref_dict_to1').keys()]) 645 646 647 # Reduce the leg list and return the corresponding 648 # list of vertices 649 650 # For decay processes, generate starting from final-state 651 # combined only as the last particle. This allows to use these 652 # in decay chains later on. 653 is_decay_proc = process.get_ninitial() == 1 654 if is_decay_proc: 655 part = model.get('particle_dict')[leglist[0].get('id')] 656 # For decay chain legs, we want everything to combine to 657 # the initial leg. This is done by only allowing the 658 # initial leg to combine as a final identity. 659 ref_dict_to0 = {(part.get_pdg_code(),part.get_anti_pdg_code()):[0], 660 (part.get_anti_pdg_code(),part.get_pdg_code()):[0]} 661 # Need to set initial leg from_group to None, to make sure 662 # it can only be combined at the end. 663 leglist[0].set('from_group', None) 664 reduced_leglist = self.reduce_leglist(leglist, 665 max_multi_to1, 666 ref_dict_to0, 667 is_decay_proc, 668 process.get('orders')) 669 else: 670 reduced_leglist = self.reduce_leglist(leglist, 671 max_multi_to1, 672 model.get('ref_dict_to0'), 673 is_decay_proc, 674 process.get('orders')) 675 676 #In LoopAmplitude the function below is overloaded such that it 677 #converts back all DGLoopLegs to Legs. In the default tree-level 678 #diagram generation, this does nothing. 679 self.convert_dgleg_to_leg(reduced_leglist) 680 681 if reduced_leglist: 682 for vertex_list in reduced_leglist: 683 res.append(self.create_diagram(base_objects.VertexList(vertex_list))) 684 685 # Record whether or not we failed generation before required 686 # s-channel propagators are taken into account 687 failed_crossing = not res 688 689 # Required s-channels is a list of id-lists. Select the 690 # diagrams where all required s-channel propagators in any of 691 # the lists are present (i.e., the different lists correspond 692 # to "or", while the elements of the list correspond to 693 # "and"). 694 if process.get('required_s_channels') and \ 695 process.get('required_s_channels')[0]: 696 # We shouldn't look at the last vertex in each diagram, 697 # since that is the n->0 vertex 698 lastvx = -1 699 # For decay chain processes, there is an "artificial" 700 # extra vertex corresponding to particle 1=1, so we need 701 # to exclude the two last vertexes. 702 if is_decay_proc: lastvx = -2 703 ninitial = len(filter(lambda leg: leg.get('state') == False, 704 process.get('legs'))) 705 # Check required s-channels for each list in required_s_channels 706 old_res = res 707 res = base_objects.DiagramList() 708 for id_list in process.get('required_s_channels'): 709 res_diags = filter(lambda diagram: \ 710 all([req_s_channel in \ 711 [vertex.get_s_channel_id(\ 712 process.get('model'), ninitial) \ 713 for vertex in diagram.get('vertices')[:lastvx]] \ 714 for req_s_channel in \ 715 id_list]), old_res) 716 # Add diagrams only if not already in res 717 res.extend([diag for diag in res_diags if diag not in res]) 718 719 # Remove all diagrams with a "double" forbidden s-channel propagator 720 # is present. 721 # Note that we shouldn't look at the last vertex in each 722 # diagram, since that is the n->0 vertex 723 if process.get('forbidden_s_channels'): 724 ninitial = len(filter(lambda leg: leg.get('state') == False, 725 process.get('legs'))) 726 if ninitial == 2: 727 res = base_objects.DiagramList(\ 728 filter(lambda diagram: \ 729 not any([vertex.get_s_channel_id(\ 730 process.get('model'), ninitial) \ 731 in process.get('forbidden_s_channels') 732 for vertex in diagram.get('vertices')[:-1]]), 733 res)) 734 else: 735 # split since we need to avoid that the initial particle is forbidden 736 # as well. 737 newres= [] 738 for diagram in res: 739 leg1 = 1 740 #check the latest vertex to see if the leg 1 is inside if it 741 #is we need to inverse the look-up and allow the first s-channel 742 # of the associate particles. 743 vertex = diagram.get('vertices')[-1] 744 if any([l['number'] ==1 for l in vertex.get('legs')]): 745 leg1 = [l['number'] for l in vertex.get('legs') if l['number'] !=1][0] 746 to_loop = range(len(diagram.get('vertices'))-1) 747 if leg1 >1: 748 to_loop.reverse() 749 for i in to_loop: 750 vertex = diagram.get('vertices')[i] 751 if leg1: 752 if any([l['number'] ==leg1 for l in vertex.get('legs')]): 753 leg1 = 0 754 continue 755 if vertex.get_s_channel_id(process.get('model'), ninitial)\ 756 in process.get('forbidden_s_channels'): 757 break 758 else: 759 newres.append(diagram) 760 res = base_objects.DiagramList(newres) 761 762 763 # Mark forbidden (onshell) s-channel propagators, to forbid onshell 764 # generation. 765 if process.get('forbidden_onsh_s_channels'): 766 ninitial = len(filter(lambda leg: leg.get('state') == False, 767 process.get('legs'))) 768 769 verts = base_objects.VertexList(sum([[vertex for vertex \ 770 in diagram.get('vertices')[:-1] 771 if vertex.get_s_channel_id(\ 772 process.get('model'), ninitial) \ 773 in process.get('forbidden_onsh_s_channels')] \ 774 for diagram in res], [])) 775 for vert in verts: 776 # Use onshell = False to indicate that this s-channel is forbidden 777 newleg = copy.copy(vert.get('legs').pop(-1)) 778 newleg.set('onshell', False) 779 vert.get('legs').append(newleg) 780 781 # Set actual coupling orders for each diagram 782 for diagram in res: 783 diagram.calculate_orders(model) 784 785 # Filter the diagrams according to the squared coupling order 786 # constraints and possible the negative one. Remember that OrderName=-n 787 # means that the user wants to include everything up to the N^(n+1)LO 788 # contribution in that order and at most one order can be restricted 789 # in this way. We shall do this only if the diagrams are not asked to 790 # be returned, as it is the case for NLO because it this case the 791 # interference are not necessarily among the diagrams generated here only. 792 if not returndiag and len(res)>0: 793 res = self.apply_squared_order_constraints(res) 794 795 # Replace final id=0 vertex if necessary 796 if not process.get('is_decay_chain'): 797 for diagram in res: 798 vertices = diagram.get('vertices') 799 if len(vertices) > 1 and vertices[-1].get('id') == 0: 800 # Need to "glue together" last and next-to-last 801 # vertex, by replacing the (incoming) last leg of the 802 # next-to-last vertex with the (outgoing) leg in the 803 # last vertex 804 vertices = copy.copy(vertices) 805 lastvx = vertices.pop() 806 nexttolastvertex = copy.copy(vertices.pop()) 807 legs = copy.copy(nexttolastvertex.get('legs')) 808 ntlnumber = legs[-1].get('number') 809 lastleg = filter(lambda leg: leg.get('number') != ntlnumber, 810 lastvx.get('legs'))[0] 811 # Reset onshell in case we have forbidden s-channels 812 if lastleg.get('onshell') == False: 813 lastleg.set('onshell', None) 814 # Replace the last leg of nexttolastvertex 815 legs[-1] = lastleg 816 nexttolastvertex.set('legs', legs) 817 vertices.append(nexttolastvertex) 818 diagram.set('vertices', vertices) 819 820 if res and not returndiag: 821 logger.info("Process has %d diagrams" % len(res)) 822 823 # Trim down number of legs and vertices used to save memory 824 self.trim_diagrams(diaglist=res) 825 826 # Sort process legs according to leg number 827 pertur = 'QCD' 828 if self.get('process')['perturbation_couplings']: 829 pertur = sorted(self.get('process')['perturbation_couplings'])[0] 830 self.get('process').get('legs').sort(pert=pertur) 831 832 # Set diagrams to res if not asked to be returned 833 if not returndiag: 834 self['diagrams'] = res 835 return not failed_crossing 836 else: 837 return not failed_crossing, res
838
839 - def apply_squared_order_constraints(self, diag_list):
840 """Applies the user specified squared order constraints on the diagram 841 list in argument.""" 842 843 res = copy.copy(diag_list) 844 845 # Iterate the filtering since the applying the constraint on one 846 # type of coupling order can impact what the filtering on a previous 847 # one (relevant for the '==' type of constraint). 848 while True: 849 new_res = res.apply_positive_sq_orders(res, 850 self['process'].get('squared_orders'), 851 self['process']['sqorders_types']) 852 # Exit condition 853 if len(res)==len(new_res): 854 break 855 elif (len(new_res)>len(res)): 856 raise MadGraph5Error( 857 'Inconsistency in function apply_squared_order_constraints().') 858 # Actualizing the list of diagram for the next iteration 859 res = new_res 860 861 # Now treat the negative squared order constraint (at most one) 862 neg_orders = [(order, value) for order, value in \ 863 self['process'].get('squared_orders').items() if value<0] 864 if len(neg_orders)==1: 865 neg_order, neg_value = neg_orders[0] 866 # Now check any negative order constraint 867 res, target_order = res.apply_negative_sq_order(res, neg_order,\ 868 neg_value, self['process']['sqorders_types'][neg_order]) 869 # Substitute the negative value to this positive one so that 870 # the resulting computed constraints appears in the print out 871 # and at the output stage we no longer have to deal with 872 # negative valued target orders 873 self['process']['squared_orders'][neg_order]=target_order 874 elif len(neg_orders)>1: 875 raise InvalidCmd('At most one negative squared order constraint'+\ 876 ' can be specified, not %s.'%str(neg_orders)) 877 878 return res
879
880 - def create_diagram(self, vertexlist):
881 """ Return a Diagram created from the vertex list. This function can be 882 overloaded by daughter classes.""" 883 return base_objects.Diagram({'vertices':vertexlist})
884
885 - def convert_dgleg_to_leg(self, vertexdoublelist):
886 """ In LoopAmplitude, it converts back all DGLoopLegs into Legs. 887 In Amplitude, there is nothing to do. """ 888 889 return True
890
891 - def copy_leglist(self, legs):
892 """ Simply returns a copy of the leg list. This function is 893 overloaded in LoopAmplitude so that a DGLoopLeg list is returned. 894 The DGLoopLeg has some additional parameters only useful during 895 loop diagram generation""" 896 897 return base_objects.LegList(\ 898 [ copy.copy(leg) for leg in legs ])
899
900 - def reduce_leglist(self, curr_leglist, max_multi_to1, ref_dict_to0, 901 is_decay_proc = False, coupling_orders = None):
902 """Recursive function to reduce N LegList to N-1 903 For algorithm, see doc for generate_diagrams. 904 """ 905 906 # Result variable which is a list of lists of vertices 907 # to be added 908 res = [] 909 910 # Stop condition. If LegList is None, that means that this 911 # diagram must be discarded 912 if curr_leglist is None: 913 return None 914 915 # Extract ref dict information 916 model = self.get('process').get('model') 917 ref_dict_to1 = self.get('process').get('model').get('ref_dict_to1') 918 919 920 # If all legs can be combined in one single vertex, add this 921 # vertex to res and continue. 922 # Special treatment for decay chain legs 923 924 if curr_leglist.can_combine_to_0(ref_dict_to0, is_decay_proc): 925 # Extract the interaction id associated to the vertex 926 927 vertex_ids = self.get_combined_vertices(curr_leglist, 928 copy.copy(ref_dict_to0[tuple(sorted([leg.get('id') for \ 929 leg in curr_leglist]))])) 930 931 final_vertices = [base_objects.Vertex({'legs':curr_leglist, 932 'id':vertex_id}) for \ 933 vertex_id in vertex_ids] 934 # Check for coupling orders. If orders < 0, skip vertex 935 for final_vertex in final_vertices: 936 if self.reduce_orders(coupling_orders, model, 937 [final_vertex.get('id')]) != False: 938 res.append([final_vertex]) 939 # Stop condition 2: if the leglist contained exactly two particles, 940 # return the result, if any, and stop. 941 if len(curr_leglist) == 2: 942 if res: 943 return res 944 else: 945 return None 946 947 # Create a list of all valid combinations of legs 948 comb_lists = self.combine_legs(curr_leglist, 949 ref_dict_to1, max_multi_to1) 950 951 # Create a list of leglists/vertices by merging combinations 952 leg_vertex_list = self.merge_comb_legs(comb_lists, ref_dict_to1) 953 954 # Consider all the pairs 955 for leg_vertex_tuple in leg_vertex_list: 956 957 # Remove forbidden particles 958 if self.get('process').get('forbidden_particles') and \ 959 any([abs(vertex.get('legs')[-1].get('id')) in \ 960 self.get('process').get('forbidden_particles') \ 961 for vertex in leg_vertex_tuple[1]]): 962 continue 963 964 # Check for coupling orders. If couplings < 0, skip recursion. 965 new_coupling_orders = self.reduce_orders(coupling_orders, 966 model, 967 [vertex.get('id') for vertex in \ 968 leg_vertex_tuple[1]]) 969 if new_coupling_orders == False: 970 # Some coupling order < 0 971 continue 972 973 # This is where recursion happens 974 # First, reduce again the leg part 975 reduced_diagram = self.reduce_leglist(leg_vertex_tuple[0], 976 max_multi_to1, 977 ref_dict_to0, 978 is_decay_proc, 979 new_coupling_orders) 980 # If there is a reduced diagram 981 if reduced_diagram: 982 vertex_list_list = [list(leg_vertex_tuple[1])] 983 vertex_list_list.append(reduced_diagram) 984 expanded_list = expand_list_list(vertex_list_list) 985 res.extend(expanded_list) 986 987 return res
988
989 - def reduce_orders(self, coupling_orders, model, vertex_id_list):
990 """Return False if the coupling orders for any coupling is < 991 0, otherwise return the new coupling orders with the vertex 992 orders subtracted. If coupling_orders is not given, return 993 None (which counts as success). 994 WEIGHTED is a special order, which corresponds to the sum of 995 order hierarchies for the couplings. 996 We ignore negative constraints as these cannot be taken into 997 account on the fly but only after generation.""" 998 999 if not coupling_orders: 1000 return None 1001 1002 present_couplings = copy.copy(coupling_orders) 1003 for id in vertex_id_list: 1004 # Don't check for identity vertex (id = 0) 1005 if not id: 1006 continue 1007 inter = model.get("interaction_dict")[id] 1008 for coupling in inter.get('orders').keys(): 1009 # Note that we don't consider a missing coupling as a 1010 # constraint 1011 if coupling in present_couplings and \ 1012 present_couplings[coupling]>=0: 1013 # Reduce the number of couplings that are left 1014 present_couplings[coupling] -= \ 1015 inter.get('orders')[coupling] 1016 if present_couplings[coupling] < 0: 1017 # We have too many couplings of this type 1018 return False 1019 # Now check for WEIGHTED, i.e. the sum of coupling hierarchy values 1020 if 'WEIGHTED' in present_couplings and \ 1021 present_couplings['WEIGHTED']>=0: 1022 weight = sum([model.get('order_hierarchy')[c]*n for \ 1023 (c,n) in inter.get('orders').items()]) 1024 present_couplings['WEIGHTED'] -= weight 1025 if present_couplings['WEIGHTED'] < 0: 1026 # Total coupling weight too large 1027 return False 1028 1029 return present_couplings
1030
1031 - def combine_legs(self, list_legs, ref_dict_to1, max_multi_to1):
1032 """Recursive function. Take a list of legs as an input, with 1033 the reference dictionary n-1->1, and output a list of list of 1034 tuples of Legs (allowed combinations) and Legs (rest). Algorithm: 1035 1036 1. Get all n-combinations from list [123456]: [12],..,[23],..,[123],.. 1037 1038 2. For each combination, say [34]. Check if combination is valid. 1039 If so: 1040 1041 a. Append [12[34]56] to result array 1042 1043 b. Split [123456] at index(first element in combination+1), 1044 i.e. [12],[456] and subtract combination from second half, 1045 i.e.: [456]-[34]=[56]. Repeat from 1. with this array 1046 1047 3. Take result array from call to 1. (here, [[56]]) and append 1048 (first half in step b - combination) + combination + (result 1049 from 1.) = [12[34][56]] to result array 1050 1051 4. After appending results from all n-combinations, return 1052 resulting array. Example, if [13] and [45] are valid 1053 combinations: 1054 [[[13]2456],[[13]2[45]6],[123[45]6]] 1055 """ 1056 1057 res = [] 1058 1059 # loop over possible combination lengths (+1 is for range convention!) 1060 for comb_length in range(2, max_multi_to1 + 1): 1061 1062 # Check the considered length is not longer than the list length 1063 if comb_length > len(list_legs): 1064 return res 1065 1066 # itertools.combinations returns all possible combinations 1067 # of comb_length elements from list_legs 1068 for comb in itertools.combinations(list_legs, comb_length): 1069 1070 # Check if the combination is valid 1071 if base_objects.LegList(comb).can_combine_to_1(ref_dict_to1): 1072 1073 # Identify the rest, create a list [comb,rest] and 1074 # add it to res 1075 res_list = copy.copy(list_legs) 1076 for leg in comb: 1077 res_list.remove(leg) 1078 res_list.insert(list_legs.index(comb[0]), comb) 1079 res.append(res_list) 1080 1081 # Now, deal with cases with more than 1 combination 1082 1083 # First, split the list into two, according to the 1084 # position of the first element in comb, and remove 1085 # all elements form comb 1086 res_list1 = list_legs[0:list_legs.index(comb[0])] 1087 res_list2 = list_legs[list_legs.index(comb[0]) + 1:] 1088 for leg in comb[1:]: 1089 res_list2.remove(leg) 1090 1091 # Create a list of type [comb,rest1,rest2(combined)] 1092 res_list = res_list1 1093 res_list.append(comb) 1094 # This is where recursion actually happens, 1095 # on the second part 1096 for item in self.combine_legs(res_list2, 1097 ref_dict_to1, 1098 max_multi_to1): 1099 final_res_list = copy.copy(res_list) 1100 final_res_list.extend(item) 1101 res.append(final_res_list) 1102 1103 return res
1104 1105
1106 - def merge_comb_legs(self, comb_lists, ref_dict_to1):
1107 """Takes a list of allowed leg combinations as an input and returns 1108 a set of lists where combinations have been properly replaced 1109 (one list per element in the ref_dict, so that all possible intermediate 1110 particles are included). For each list, give the list of vertices 1111 corresponding to the executed merging, group the two as a tuple. 1112 """ 1113 1114 res = [] 1115 1116 for comb_list in comb_lists: 1117 1118 reduced_list = [] 1119 vertex_list = [] 1120 1121 for entry in comb_list: 1122 1123 # Act on all leg combinations 1124 if isinstance(entry, tuple): 1125 1126 # Build the leg object which will replace the combination: 1127 # 1) leg ids is as given in the ref_dict 1128 leg_vert_ids = copy.copy(ref_dict_to1[\ 1129 tuple(sorted([leg.get('id') for leg in entry]))]) 1130 # 2) number is the minimum of leg numbers involved in the 1131 # combination 1132 number = min([leg.get('number') for leg in entry]) 1133 # 3) state is final, unless there is exactly one initial 1134 # state particle involved in the combination -> t-channel 1135 if len(filter(lambda leg: leg.get('state') == False, 1136 entry)) == 1: 1137 state = False 1138 else: 1139 state = True 1140 # 4) from_group is True, by definition 1141 1142 # Create and add the object. This is done by a 1143 # separate routine, to allow overloading by 1144 # daughter classes 1145 new_leg_vert_ids = [] 1146 if leg_vert_ids: 1147 new_leg_vert_ids = self.get_combined_legs(entry, 1148 leg_vert_ids, 1149 number, 1150 state) 1151 1152 reduced_list.append([l[0] for l in new_leg_vert_ids]) 1153 1154 1155 # Create and add the corresponding vertex 1156 # Extract vertex ids corresponding to the various legs 1157 # in mylegs 1158 vlist = base_objects.VertexList() 1159 for (myleg, vert_id) in new_leg_vert_ids: 1160 # Start with the considered combination... 1161 myleglist = base_objects.LegList(list(entry)) 1162 # ... and complete with legs after reducing 1163 myleglist.append(myleg) 1164 # ... and consider the correct vertex id 1165 vlist.append(base_objects.Vertex( 1166 {'legs':myleglist, 1167 'id':vert_id})) 1168 1169 vertex_list.append(vlist) 1170 1171 # If entry is not a combination, switch the from_group flag 1172 # and add it 1173 else: 1174 cp_entry = copy.copy(entry) 1175 # Need special case for from_group == None; this 1176 # is for initial state leg of decay chain process 1177 # (see Leg.can_combine_to_0) 1178 if cp_entry.get('from_group') != None: 1179 cp_entry.set('from_group', False) 1180 reduced_list.append(cp_entry) 1181 1182 # Flatten the obtained leg and vertex lists 1183 flat_red_lists = expand_list(reduced_list) 1184 flat_vx_lists = expand_list(vertex_list) 1185 1186 # Combine the two lists in a list of tuple 1187 for i in range(0, len(flat_vx_lists)): 1188 res.append((base_objects.LegList(flat_red_lists[i]), \ 1189 base_objects.VertexList(flat_vx_lists[i]))) 1190 1191 return res
1192
1193 - def get_combined_legs(self, legs, leg_vert_ids, number, state):
1194 """Create a set of new legs from the info given. This can be 1195 overloaded by daughter classes.""" 1196 1197 mylegs = [(base_objects.Leg({'id':leg_id, 1198 'number':number, 1199 'state':state, 1200 'from_group':True}), 1201 vert_id)\ 1202 for leg_id, vert_id in leg_vert_ids] 1203 1204 return mylegs
1205
1206 - def get_combined_vertices(self, legs, vert_ids):
1207 """Allow for selection of vertex ids. This can be 1208 overloaded by daughter classes.""" 1209 1210 return vert_ids
1211
1212 - def trim_diagrams(self, decay_ids=[], diaglist=None):
1213 """Reduce the number of legs and vertices used in memory. 1214 When called by a diagram generation initiated by LoopAmplitude, 1215 this function should not trim the diagrams in the attribute 'diagrams' 1216 but rather a given list in the 'diaglist' argument.""" 1217 1218 legs = [] 1219 vertices = [] 1220 1221 if diaglist is None: 1222 diaglist=self.get('diagrams') 1223 1224 # Flag decaying legs in the core process by onshell = True 1225 process = self.get('process') 1226 for leg in process.get('legs'): 1227 if leg.get('state') and leg.get('id') in decay_ids: 1228 leg.set('onshell', True) 1229 1230 for diagram in diaglist: 1231 # Keep track of external legs (leg numbers already used) 1232 leg_external = set() 1233 for ivx, vertex in enumerate(diagram.get('vertices')): 1234 for ileg, leg in enumerate(vertex.get('legs')): 1235 # Ensure that only external legs get decay flag 1236 if leg.get('state') and leg.get('id') in decay_ids and \ 1237 leg.get('number') not in leg_external: 1238 # Use onshell to indicate decaying legs, 1239 # i.e. legs that have decay chains 1240 leg = copy.copy(leg) 1241 leg.set('onshell', True) 1242 try: 1243 index = legs.index(leg) 1244 except ValueError: 1245 vertex.get('legs')[ileg] = leg 1246 legs.append(leg) 1247 else: # Found a leg 1248 vertex.get('legs')[ileg] = legs[index] 1249 leg_external.add(leg.get('number')) 1250 try: 1251 index = vertices.index(vertex) 1252 diagram.get('vertices')[ivx] = vertices[index] 1253 except ValueError: 1254 vertices.append(vertex)
1255
1256 #=============================================================================== 1257 # AmplitudeList 1258 #=============================================================================== 1259 -class AmplitudeList(base_objects.PhysicsObjectList):
1260 """List of Amplitude objects 1261 """ 1262
1263 - def has_any_loop_process(self):
1264 """ Check the content of all processes of the amplitudes in this list to 1265 see if there is any which defines perturbation couplings. """ 1266 1267 for amp in self: 1268 if amp.has_loop_process(): 1269 return True
1270
1271 - def is_valid_element(self, obj):
1272 """Test if object obj is a valid Amplitude for the list.""" 1273 1274 return isinstance(obj, Amplitude)
1275
1276 #=============================================================================== 1277 # DecayChainAmplitude 1278 #=============================================================================== 1279 -class DecayChainAmplitude(Amplitude):
1280 """A list of amplitudes + a list of decay chain amplitude lists; 1281 corresponding to a ProcessDefinition with a list of decay chains 1282 """ 1283
1284 - def default_setup(self):
1285 """Default values for all properties""" 1286 1287 self['amplitudes'] = AmplitudeList() 1288 self['decay_chains'] = DecayChainAmplitudeList()
1289
1290 - def __init__(self, argument = None, collect_mirror_procs = False, 1291 ignore_six_quark_processes = False):
1292 """Allow initialization with Process and with ProcessDefinition""" 1293 1294 if isinstance(argument, base_objects.Process): 1295 super(DecayChainAmplitude, self).__init__() 1296 from madgraph.loop.loop_diagram_generation import LoopMultiProcess 1297 if argument['perturbation_couplings']: 1298 MultiProcessClass=LoopMultiProcess 1299 else: 1300 MultiProcessClass=MultiProcess 1301 if isinstance(argument, base_objects.ProcessDefinition): 1302 self['amplitudes'].extend(\ 1303 MultiProcessClass.generate_multi_amplitudes(argument, 1304 collect_mirror_procs, 1305 ignore_six_quark_processes)) 1306 else: 1307 self['amplitudes'].append(\ 1308 MultiProcessClass.get_amplitude_from_proc(argument)) 1309 # Clean decay chains from process, since we haven't 1310 # combined processes with decay chains yet 1311 process = copy.copy(self.get('amplitudes')[0].get('process')) 1312 process.set('decay_chains', base_objects.ProcessList()) 1313 self['amplitudes'][0].set('process', process) 1314 1315 for process in argument.get('decay_chains'): 1316 if process.get('perturbation_couplings'): 1317 raise MadGraph5Error,\ 1318 "Decay processes can not be perturbed" 1319 process.set('overall_orders', argument.get('overall_orders')) 1320 if not process.get('is_decay_chain'): 1321 process.set('is_decay_chain',True) 1322 if not process.get_ninitial() == 1: 1323 raise InvalidCmd,\ 1324 "Decay chain process must have exactly one" + \ 1325 " incoming particle" 1326 self['decay_chains'].append(\ 1327 DecayChainAmplitude(process, collect_mirror_procs, 1328 ignore_six_quark_processes)) 1329 1330 # Flag decaying legs in the core diagrams by onshell = True 1331 decay_ids = sum([[a.get('process').get('legs')[0].get('id') \ 1332 for a in dec.get('amplitudes')] for dec in \ 1333 self['decay_chains']], []) 1334 decay_ids = set(decay_ids) 1335 for amp in self['amplitudes']: 1336 amp.trim_diagrams(decay_ids) 1337 1338 # Check that all decay ids are present in at least some process 1339 for amp in self['amplitudes']: 1340 for l in amp.get('process').get('legs'): 1341 if l.get('id') in decay_ids: 1342 decay_ids.remove(l.get('id')) 1343 1344 if decay_ids: 1345 model = amp.get('process').get('model') 1346 names = [model.get_particle(id).get('name') for id in decay_ids] 1347 1348 logger.warning( 1349 "$RED Decay without corresponding particle in core process found.\n" + \ 1350 "Decay information for particle(s) %s is discarded.\n" % ','.join(names) + \ 1351 "Please check your process definition carefully. \n" + \ 1352 "This warning usually means that you forgot parentheses in presence of subdecay.\n" + \ 1353 "Example of correct syntax: p p > t t~, ( t > w+ b, w+ > l+ vl)") 1354 1355 # Remove unused decays from the process list 1356 for dc in reversed(self['decay_chains']): 1357 for a in reversed(dc.get('amplitudes')): 1358 # Remove the amplitudes from this decay chain 1359 if a.get('process').get('legs')[0].get('id') in decay_ids: 1360 dc.get('amplitudes').remove(a) 1361 if not dc.get('amplitudes'): 1362 # If no amplitudes left, remove the decay chain 1363 self['decay_chains'].remove(dc) 1364 1365 # Finally, write a fat warning if any decay process has 1366 # the decaying particle (or its antiparticle) in the final state 1367 bad_procs = [] 1368 for dc in self['decay_chains']: 1369 for amp in dc.get('amplitudes'): 1370 legs = amp.get('process').get('legs') 1371 fs_parts = [abs(l.get('id')) for l in legs if 1372 l.get('state')] 1373 is_part = [l.get('id') for l in legs if not 1374 l.get('state')][0] 1375 if abs(is_part) in fs_parts: 1376 bad_procs.append(amp.get('process')) 1377 1378 if bad_procs: 1379 logger.warning( 1380 "$RED Decay(s) with particle decaying to itself:\n" + \ 1381 '\n'.join([p.nice_string() for p in bad_procs]) + \ 1382 "\nPlease check your process definition carefully. \n") 1383 1384 1385 elif argument != None: 1386 # call the mother routine 1387 super(DecayChainAmplitude, self).__init__(argument) 1388 else: 1389 # call the mother routine 1390 super(DecayChainAmplitude, self).__init__()
1391
1392 - def filter(self, name, value):
1393 """Filter for valid amplitude property values.""" 1394 1395 if name == 'amplitudes': 1396 if not isinstance(value, AmplitudeList): 1397 raise self.PhysicsObjectError, \ 1398 "%s is not a valid AmplitudeList" % str(value) 1399 if name == 'decay_chains': 1400 if not isinstance(value, DecayChainAmplitudeList): 1401 raise self.PhysicsObjectError, \ 1402 "%s is not a valid DecayChainAmplitudeList object" % \ 1403 str(value) 1404 return True
1405
1406 - def get_sorted_keys(self):
1407 """Return diagram property names as a nicely sorted list.""" 1408 1409 return ['amplitudes', 'decay_chains']
1410 1411 # Helper functions 1412
1413 - def get_number_of_diagrams(self):
1414 """Returns number of diagrams for this amplitude""" 1415 return sum(len(a.get('diagrams')) for a in self.get('amplitudes')) \ 1416 + sum(d.get_number_of_diagrams() for d in \ 1417 self.get('decay_chains'))
1418
1419 - def nice_string(self, indent = 0):
1420 """Returns a nicely formatted string of the amplitude content.""" 1421 mystr = "" 1422 for amplitude in self.get('amplitudes'): 1423 mystr = mystr + amplitude.nice_string(indent) + "\n" 1424 1425 if self.get('decay_chains'): 1426 mystr = mystr + " " * indent + "Decays:\n" 1427 for dec in self.get('decay_chains'): 1428 mystr = mystr + dec.nice_string(indent + 2) + "\n" 1429 1430 return mystr[:-1]
1431
1432 - def nice_string_processes(self, indent = 0):
1433 """Returns a nicely formatted string of the amplitude processes.""" 1434 mystr = "" 1435 for amplitude in self.get('amplitudes'): 1436 mystr = mystr + amplitude.nice_string_processes(indent) + "\n" 1437 1438 if self.get('decay_chains'): 1439 mystr = mystr + " " * indent + "Decays:\n" 1440 for dec in self.get('decay_chains'): 1441 mystr = mystr + dec.nice_string_processes(indent + 2) + "\n" 1442 1443 return mystr[:-1]
1444
1445 - def get_ninitial(self):
1446 """Returns the number of initial state particles in the process.""" 1447 return self.get('amplitudes')[0].get('process').get_ninitial()
1448
1449 - def get_decay_ids(self):
1450 """Returns a set of all particle ids for which a decay is defined""" 1451 1452 decay_ids = [] 1453 1454 # Get all amplitudes for the decay processes 1455 for amp in sum([dc.get('amplitudes') for dc \ 1456 in self['decay_chains']], []): 1457 # For each amplitude, find the initial state leg 1458 decay_ids.append(amp.get('process').get_initial_ids()[0]) 1459 1460 # Return a list with unique ids 1461 return list(set(decay_ids))
1462
1463 - def has_loop_process(self):
1464 """ Returns wether this amplitude has a loop process.""" 1465 return self['amplitudes'].has_any_loop_process()
1466
1467 - def get_amplitudes(self):
1468 """Recursive function to extract all amplitudes for this process""" 1469 1470 amplitudes = AmplitudeList() 1471 1472 amplitudes.extend(self.get('amplitudes')) 1473 for decay in self.get('decay_chains'): 1474 amplitudes.extend(decay.get_amplitudes()) 1475 1476 return amplitudes
1477
1478 1479 #=============================================================================== 1480 # DecayChainAmplitudeList 1481 #=============================================================================== 1482 -class DecayChainAmplitudeList(base_objects.PhysicsObjectList):
1483 """List of DecayChainAmplitude objects 1484 """ 1485
1486 - def is_valid_element(self, obj):
1487 """Test if object obj is a valid DecayChainAmplitude for the list.""" 1488 1489 return isinstance(obj, DecayChainAmplitude)
1490
1491 1492 #=============================================================================== 1493 # MultiProcess 1494 #=============================================================================== 1495 -class MultiProcess(base_objects.PhysicsObject):
1496 """MultiProcess: list of process definitions 1497 list of processes (after cleaning) 1498 list of amplitudes (after generation) 1499 """ 1500
1501 - def default_setup(self):
1502 """Default values for all properties""" 1503 1504 self['process_definitions'] = base_objects.ProcessDefinitionList() 1505 # self['amplitudes'] can be an AmplitudeList or a 1506 # DecayChainAmplitudeList, depending on whether there are 1507 # decay chains in the process definitions or not. 1508 self['amplitudes'] = AmplitudeList() 1509 # Flag for whether to combine IS mirror processes together 1510 self['collect_mirror_procs'] = False 1511 # List of quark flavors where we ignore processes with at 1512 # least 6 quarks (three quark lines) 1513 self['ignore_six_quark_processes'] = [] 1514 # Allow to use the model parameter numerical value for optimization. 1515 #This is currently use for 1->N generation(check mass). 1516 self['use_numerical'] = False
1517
1518 - def __init__(self, argument=None, collect_mirror_procs = False, 1519 ignore_six_quark_processes = [], optimize=False):
1520 """Allow initialization with ProcessDefinition or 1521 ProcessDefinitionList 1522 optimize allows to use param_card information. (usefull for 1-.N)""" 1523 1524 if isinstance(argument, base_objects.ProcessDefinition): 1525 super(MultiProcess, self).__init__() 1526 self['process_definitions'].append(argument) 1527 elif isinstance(argument, base_objects.ProcessDefinitionList): 1528 super(MultiProcess, self).__init__() 1529 self['process_definitions'] = argument 1530 elif argument != None: 1531 # call the mother routine 1532 super(MultiProcess, self).__init__(argument) 1533 else: 1534 # call the mother routine 1535 super(MultiProcess, self).__init__() 1536 1537 self['collect_mirror_procs'] = collect_mirror_procs 1538 self['ignore_six_quark_processes'] = ignore_six_quark_processes 1539 self['use_numerical'] = optimize 1540 1541 if isinstance(argument, base_objects.ProcessDefinition) or \ 1542 isinstance(argument, base_objects.ProcessDefinitionList): 1543 # Generate the diagrams 1544 self.get('amplitudes')
1545 1546
1547 - def filter(self, name, value):
1548 """Filter for valid process property values.""" 1549 1550 if name == 'process_definitions': 1551 if not isinstance(value, base_objects.ProcessDefinitionList): 1552 raise self.PhysicsObjectError, \ 1553 "%s is not a valid ProcessDefinitionList object" % str(value) 1554 1555 if name == 'amplitudes': 1556 if not isinstance(value, AmplitudeList): 1557 raise self.PhysicsObjectError, \ 1558 "%s is not a valid AmplitudeList object" % str(value) 1559 1560 if name in ['collect_mirror_procs']: 1561 if not isinstance(value, bool): 1562 raise self.PhysicsObjectError, \ 1563 "%s is not a valid boolean" % str(value) 1564 1565 if name == 'ignore_six_quark_processes': 1566 if not isinstance(value, list): 1567 raise self.PhysicsObjectError, \ 1568 "%s is not a valid list" % str(value) 1569 1570 return True
1571
1572 - def get(self, name):
1573 """Get the value of the property name.""" 1574 1575 if (name == 'amplitudes') and not self[name]: 1576 for process_def in self.get('process_definitions'): 1577 if process_def.get('decay_chains'): 1578 # This is a decay chain process 1579 # Store amplitude(s) as DecayChainAmplitude 1580 self['amplitudes'].append(\ 1581 DecayChainAmplitude(process_def, 1582 self.get('collect_mirror_procs'), 1583 self.get('ignore_six_quark_processes'))) 1584 else: 1585 self['amplitudes'].extend(\ 1586 self.generate_multi_amplitudes(process_def, 1587 self.get('collect_mirror_procs'), 1588 self.get('ignore_six_quark_processes'), 1589 self['use_numerical'])) 1590 1591 return MultiProcess.__bases__[0].get(self, name) # call the mother routine
1592
1593 - def get_sorted_keys(self):
1594 """Return process property names as a nicely sorted list.""" 1595 1596 return ['process_definitions', 'amplitudes']
1597 1598 @classmethod
1599 - def generate_multi_amplitudes(cls,process_definition, 1600 collect_mirror_procs = False, 1601 ignore_six_quark_processes = [], 1602 use_numerical=False):
1603 """Generate amplitudes in a semi-efficient way. 1604 Make use of crossing symmetry for processes that fail diagram 1605 generation, but not for processes that succeed diagram 1606 generation. Doing so will risk making it impossible to 1607 identify processes with identical amplitudes. 1608 """ 1609 assert isinstance(process_definition, base_objects.ProcessDefinition), \ 1610 "%s not valid ProcessDefinition object" % \ 1611 repr(process_definition) 1612 1613 # Set automatic coupling orders 1614 process_definition.set('orders', MultiProcess.\ 1615 find_optimal_process_orders(process_definition)) 1616 # Check for maximum orders from the model 1617 process_definition.check_expansion_orders() 1618 1619 processes = base_objects.ProcessList() 1620 amplitudes = AmplitudeList() 1621 1622 # failed_procs and success_procs are sorted processes that have 1623 # already failed/succeeded based on crossing symmetry 1624 failed_procs = [] 1625 success_procs = [] 1626 # Complete processes, for identification of mirror processes 1627 non_permuted_procs = [] 1628 # permutations keeps the permutations of the crossed processes 1629 permutations = [] 1630 1631 # Store the diagram tags for processes, to allow for 1632 # identifying identical matrix elements already at this stage. 1633 model = process_definition['model'] 1634 1635 isids = [leg['ids'] for leg in process_definition['legs'] \ 1636 if leg['state'] == False] 1637 fsids = [leg['ids'] for leg in process_definition['legs'] \ 1638 if leg['state'] == True] 1639 # Generate all combinations for the initial state 1640 1641 for prod in itertools.product(*isids): 1642 islegs = [\ 1643 base_objects.Leg({'id':id, 'state': False}) \ 1644 for id in prod] 1645 1646 # Generate all combinations for the final state, and make 1647 # sure to remove double counting 1648 1649 red_fsidlist = [] 1650 1651 for prod in itertools.product(*fsids): 1652 1653 # Remove double counting between final states 1654 if tuple(sorted(prod)) in red_fsidlist: 1655 continue 1656 1657 red_fsidlist.append(tuple(sorted(prod))); 1658 1659 # Generate leg list for process 1660 leg_list = [copy.copy(leg) for leg in islegs] 1661 1662 leg_list.extend([\ 1663 base_objects.Leg({'id':id, 'state': True}) \ 1664 for id in prod]) 1665 1666 legs = base_objects.LegList(leg_list) 1667 1668 # Check for crossed processes 1669 sorted_legs = sorted([(l,i+1) for (i,l) in \ 1670 enumerate(legs.get_outgoing_id_list(model))]) 1671 permutation = [l[1] for l in sorted_legs] 1672 sorted_legs = array.array('i', [l[0] for l in sorted_legs]) 1673 1674 # Check for six-quark processes 1675 if ignore_six_quark_processes and \ 1676 len([i for i in sorted_legs if abs(i) in \ 1677 ignore_six_quark_processes]) >= 6: 1678 continue 1679 1680 # Check if crossed process has already failed, 1681 # in that case don't check process 1682 if sorted_legs in failed_procs: 1683 continue 1684 1685 # If allowed check mass validity [assume 1->N] 1686 if use_numerical: 1687 # check that final state has lower mass than initial state 1688 initial_mass = abs(model['parameter_dict'][model.get_particle(legs[0].get('id')).get('mass')]) 1689 if initial_mass == 0: 1690 continue 1691 for leg in legs[1:]: 1692 m = model['parameter_dict'][model.get_particle(leg.get('id')).get('mass')] 1693 initial_mass -= abs(m) 1694 if initial_mass.real <= 0: 1695 continue 1696 1697 # Setup process 1698 process = process_definition.get_process_with_legs(legs) 1699 1700 fast_proc = \ 1701 array.array('i',[leg.get('id') for leg in legs]) 1702 if collect_mirror_procs and \ 1703 process_definition.get_ninitial() == 2: 1704 # Check if mirrored process is already generated 1705 mirror_proc = \ 1706 array.array('i', [fast_proc[1], fast_proc[0]] + \ 1707 list(fast_proc[2:])) 1708 try: 1709 mirror_amp = \ 1710 amplitudes[non_permuted_procs.index(mirror_proc)] 1711 except Exception: 1712 # Didn't find any mirror process 1713 pass 1714 else: 1715 # Mirror process found 1716 mirror_amp.set('has_mirror_process', True) 1717 logger.info("Process %s added to mirror process %s" % \ 1718 (process.base_string(), 1719 mirror_amp.get('process').base_string())) 1720 continue 1721 1722 # Check for successful crossings, unless we have specified 1723 # properties that break crossing symmetry 1724 if not process.get('required_s_channels') and \ 1725 not process.get('forbidden_onsh_s_channels') and \ 1726 not process.get('forbidden_s_channels') and \ 1727 not process.get('is_decay_chain'): 1728 try: 1729 crossed_index = success_procs.index(sorted_legs) 1730 # The relabeling of legs for loop amplitudes is cumbersome 1731 # and does not save so much time. It is disable here and 1732 # we use the key 'loop_diagrams' to decide whether 1733 # it is an instance of LoopAmplitude. 1734 if 'loop_diagrams' in amplitudes[crossed_index]: 1735 raise ValueError 1736 except ValueError: 1737 # No crossing found, just continue 1738 pass 1739 else: 1740 # Found crossing - reuse amplitude 1741 amplitude = MultiProcess.cross_amplitude(\ 1742 amplitudes[crossed_index], 1743 process, 1744 permutations[crossed_index], 1745 permutation) 1746 amplitudes.append(amplitude) 1747 success_procs.append(sorted_legs) 1748 permutations.append(permutation) 1749 non_permuted_procs.append(fast_proc) 1750 logger.info("Crossed process found for %s, reuse diagrams." % \ 1751 process.base_string()) 1752 continue 1753 1754 # Create new amplitude 1755 amplitude = cls.get_amplitude_from_proc(process) 1756 1757 try: 1758 result = amplitude.generate_diagrams() 1759 except InvalidCmd as error: 1760 failed_procs.append(sorted_legs) 1761 else: 1762 # Succeeded in generating diagrams 1763 if amplitude.get('diagrams'): 1764 amplitudes.append(amplitude) 1765 success_procs.append(sorted_legs) 1766 permutations.append(permutation) 1767 non_permuted_procs.append(fast_proc) 1768 elif not result: 1769 # Diagram generation failed for all crossings 1770 failed_procs.append(sorted_legs) 1771 1772 # Raise exception if there are no amplitudes for this process 1773 if not amplitudes: 1774 if len(failed_procs) == 1 and 'error' in locals(): 1775 raise error 1776 else: 1777 raise NoDiagramException, \ 1778 "No amplitudes generated from process %s. Please enter a valid process" % \ 1779 process_definition.nice_string() 1780 1781 1782 # Return the produced amplitudes 1783 return amplitudes
1784 1785 @classmethod
1786 - def get_amplitude_from_proc(cls,proc):
1787 """ Return the correct amplitude type according to the characteristics of 1788 the process proc """ 1789 return Amplitude({"process": proc})
1790 1791 1792 @staticmethod
1793 - def find_optimal_process_orders(process_definition):
1794 """Find the minimal WEIGHTED order for this set of processes. 1795 1796 The algorithm: 1797 1798 1) Check the coupling hierarchy of the model. Assign all 1799 particles to the different coupling hierarchies so that a 1800 particle is considered to be in the highest hierarchy (i.e., 1801 with lowest value) where it has an interaction. 1802 1803 2) Pick out the legs in the multiprocess according to the 1804 highest hierarchy represented (so don't mix particles from 1805 different hierarchy classes in the same multiparticles!) 1806 1807 3) Find the starting maximum WEIGHTED order as the sum of the 1808 highest n-2 weighted orders 1809 1810 4) Pick out required s-channel particle hierarchies, and use 1811 the highest of the maximum WEIGHTED order from the legs and 1812 the minimum WEIGHTED order extracted from 2*s-channel 1813 hierarchys plus the n-2-2*(number of s-channels) lowest 1814 leg weighted orders. 1815 1816 5) Run process generation with the WEIGHTED order determined 1817 in 3)-4) - # final state gluons, with all gluons removed from 1818 the final state 1819 1820 6) If no process is found, increase WEIGHTED order by 1 and go 1821 back to 5), until we find a process which passes. Return that 1822 order. 1823 1824 7) Continue 5)-6) until we reach (n-2)*(highest hierarchy)-1. 1825 If still no process has passed, return 1826 WEIGHTED = (n-2)*(highest hierarchy) 1827 """ 1828 1829 assert isinstance(process_definition, base_objects.ProcessDefinition), \ 1830 "%s not valid ProcessDefinition object" % \ 1831 repr(process_definition) 1832 1833 processes = base_objects.ProcessList() 1834 amplitudes = AmplitudeList() 1835 1836 # If there are already couplings defined, return 1837 if process_definition.get('orders') or \ 1838 process_definition.get('overall_orders') or \ 1839 process_definition.get('NLO_mode')=='virt': 1840 return process_definition.get('orders') 1841 1842 # If this is a decay process (and not a decay chain), return 1843 if process_definition.get_ninitial() == 1 and not \ 1844 process_definition.get('is_decay_chain'): 1845 return process_definition.get('orders') 1846 1847 logger.info("Checking for minimal orders which gives processes.") 1848 logger.info("Please specify coupling orders to bypass this step.") 1849 1850 # Calculate minimum starting guess for WEIGHTED order 1851 max_order_now, particles, hierarchy = \ 1852 process_definition.get_minimum_WEIGHTED() 1853 coupling = 'WEIGHTED' 1854 1855 model = process_definition.get('model') 1856 1857 # Extract the initial and final leg ids 1858 isids = [leg['ids'] for leg in \ 1859 filter(lambda leg: leg['state'] == False, process_definition['legs'])] 1860 fsids = [leg['ids'] for leg in \ 1861 filter(lambda leg: leg['state'] == True, process_definition['legs'])] 1862 1863 max_WEIGHTED_order = \ 1864 (len(fsids + isids) - 2)*int(model.get_max_WEIGHTED()) 1865 1866 # Run diagram generation with increasing max_order_now until 1867 # we manage to get diagrams 1868 while max_order_now < max_WEIGHTED_order: 1869 1870 logger.info("Trying coupling order WEIGHTED=%d" % max_order_now) 1871 1872 oldloglevel = logger.level 1873 logger.setLevel(logging.WARNING) 1874 1875 # failed_procs are processes that have already failed 1876 # based on crossing symmetry 1877 failed_procs = [] 1878 1879 # Generate all combinations for the initial state 1880 for prod in apply(itertools.product, isids): 1881 islegs = [ base_objects.Leg({'id':id, 'state': False}) \ 1882 for id in prod] 1883 1884 # Generate all combinations for the final state, and make 1885 # sure to remove double counting 1886 1887 red_fsidlist = [] 1888 1889 for prod in apply(itertools.product, fsids): 1890 1891 # Remove double counting between final states 1892 if tuple(sorted(prod)) in red_fsidlist: 1893 continue 1894 1895 red_fsidlist.append(tuple(sorted(prod))); 1896 1897 # Remove gluons from final state if QCD is among 1898 # the highest coupling hierarchy 1899 nglue = 0 1900 if 21 in particles[0]: 1901 nglue = len([id for id in prod if id == 21]) 1902 prod = [id for id in prod if id != 21] 1903 1904 # Generate leg list for process 1905 leg_list = [copy.copy(leg) for leg in islegs] 1906 1907 leg_list.extend([\ 1908 base_objects.Leg({'id':id, 'state': True}) \ 1909 for id in prod]) 1910 1911 legs = base_objects.LegList(leg_list) 1912 1913 # Set summed coupling order according to max_order_now 1914 # subtracting the removed gluons 1915 coupling_orders_now = {coupling: max_order_now - \ 1916 nglue * model['order_hierarchy']['QCD']} 1917 1918 # Setup process 1919 process = base_objects.Process({\ 1920 'legs':legs, 1921 'model':model, 1922 'id': process_definition.get('id'), 1923 'orders': coupling_orders_now, 1924 'required_s_channels': \ 1925 process_definition.get('required_s_channels'), 1926 'forbidden_onsh_s_channels': \ 1927 process_definition.get('forbidden_onsh_s_channels'), 1928 'sqorders_types': \ 1929 process_definition.get('sqorders_types'), 1930 'squared_orders': \ 1931 process_definition.get('squared_orders'), 1932 'split_orders': \ 1933 process_definition.get('split_orders'), 1934 'forbidden_s_channels': \ 1935 process_definition.get('forbidden_s_channels'), 1936 'forbidden_particles': \ 1937 process_definition.get('forbidden_particles'), 1938 'is_decay_chain': \ 1939 process_definition.get('is_decay_chain'), 1940 'overall_orders': \ 1941 process_definition.get('overall_orders'), 1942 'split_orders': \ 1943 process_definition.get('split_orders')}) 1944 1945 # Check for couplings with given expansion orders 1946 process.check_expansion_orders() 1947 1948 # Check for crossed processes 1949 sorted_legs = sorted(legs.get_outgoing_id_list(model)) 1950 # Check if crossed process has already failed 1951 # In that case don't check process 1952 if tuple(sorted_legs) in failed_procs: 1953 continue 1954 1955 amplitude = Amplitude({'process': process}) 1956 try: 1957 amplitude.generate_diagrams() 1958 except InvalidCmd: 1959 failed_procs.append(tuple(sorted_legs)) 1960 else: 1961 if amplitude.get('diagrams'): 1962 # We found a valid amplitude. Return this order number 1963 logger.setLevel(oldloglevel) 1964 return {coupling: max_order_now} 1965 else: 1966 failed_procs.append(tuple(sorted_legs)) 1967 1968 # No processes found, increase max_order_now 1969 max_order_now += 1 1970 logger.setLevel(oldloglevel) 1971 1972 # If no valid processes found with nfinal-1 couplings, return maximal 1973 return {coupling: max_order_now}
1974 1975 @staticmethod
1976 - def cross_amplitude(amplitude, process, org_perm, new_perm):
1977 """Return the amplitude crossed with the permutation new_perm""" 1978 # Create dict from original leg numbers to new leg numbers 1979 perm_map = dict(zip(org_perm, new_perm)) 1980 # Initiate new amplitude 1981 new_amp = copy.copy(amplitude) 1982 # Number legs 1983 for i, leg in enumerate(process.get('legs')): 1984 leg.set('number', i+1) 1985 # Set process 1986 new_amp.set('process', process) 1987 # Now replace the leg numbers in the diagrams 1988 diagrams = base_objects.DiagramList([d.renumber_legs(perm_map, 1989 process.get('legs'),) for \ 1990 d in new_amp.get('diagrams')]) 1991 new_amp.set('diagrams', diagrams) 1992 new_amp.trim_diagrams() 1993 1994 # Make sure to reset mirror process 1995 new_amp.set('has_mirror_process', False) 1996 1997 return new_amp
1998
1999 #=============================================================================== 2000 # Global helper methods 2001 #=============================================================================== 2002 2003 -def expand_list(mylist):
2004 """Takes a list of lists and elements and returns a list of flat lists. 2005 Example: [[1,2], 3, [4,5]] -> [[1,3,4], [1,3,5], [2,3,4], [2,3,5]] 2006 """ 2007 2008 # Check that argument is a list 2009 assert isinstance(mylist, list), "Expand_list argument must be a list" 2010 2011 res = [] 2012 2013 tmplist = [] 2014 for item in mylist: 2015 if isinstance(item, list): 2016 tmplist.append(item) 2017 else: 2018 tmplist.append([item]) 2019 2020 for item in apply(itertools.product, tmplist): 2021 res.append(list(item)) 2022 2023 return res
2024
2025 -def expand_list_list(mylist):
2026 """Recursive function. Takes a list of lists and lists of lists 2027 and returns a list of flat lists. 2028 Example: [[1,2],[[4,5],[6,7]]] -> [[1,2,4,5], [1,2,6,7]] 2029 """ 2030 2031 res = [] 2032 2033 if not mylist or len(mylist) == 1 and not mylist[0]: 2034 return [[]] 2035 2036 # Check the first element is at least a list 2037 assert isinstance(mylist[0], list), \ 2038 "Expand_list_list needs a list of lists and lists of lists" 2039 2040 # Recursion stop condition, one single element 2041 if len(mylist) == 1: 2042 if isinstance(mylist[0][0], list): 2043 return mylist[0] 2044 else: 2045 return mylist 2046 2047 if isinstance(mylist[0][0], list): 2048 for item in mylist[0]: 2049 # Here the recursion happens, create lists starting with 2050 # each element of the first item and completed with 2051 # the rest expanded 2052 for rest in expand_list_list(mylist[1:]): 2053 reslist = copy.copy(item) 2054 reslist.extend(rest) 2055 res.append(reslist) 2056 else: 2057 for rest in expand_list_list(mylist[1:]): 2058 reslist = copy.copy(mylist[0]) 2059 reslist.extend(rest) 2060 res.append(reslist) 2061 2062 2063 return res
2064