Analysis of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.2054pt" id="M1" height="18.5408pt" version="1.1" viewBox="-0.0657574 -13.3354 63.5967 18.5408" width="63.5967pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-69" d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"/></g><g transform="matrix(.012,0,0,-0.012,13.145,-7.578)"><path id="g50-43" d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"/></g><g transform="matrix(.012,0,0,-0.012,13.059,4.995)"><path id="g50-116" d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"/></g><g transform="matrix(.017,0,0,-0.017,21.169,0)"><use xlink:href="#g113-69"/></g><g transform="matrix(.012,0,0,-0.012,34.315,-7.578)"><use xlink:href="#g50-43"/></g><g transform="matrix(.017,0,0,-0.017,42.339,0)"><path id="g113-76" d="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z"/></g><g transform="matrix(.012,0,0,-0.012,55.297,-7.578)"><use xlink:href="#g50-43"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3442pt" id="M2" height="17.6796pt" version="1.1" viewBox="-0.0657574 -13.3354 65.028 17.6796" width="65.028pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g113-69"/></g><g transform="matrix(.012,0,0,-0.012,13.059,4.134)"><use xlink:href="#g50-116"/></g><g transform="matrix(.012,0,0,-0.012,17.635,4.134)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.017,0,0,-0.017,24.182,0)"><use xlink:href="#g113-69"/></g><g transform="matrix(.012,0,0,-0.012,37.24,4.134)"><use xlink:href="#g50-50"/></g><g transform="matrix(.017,0,0,-0.017,43.77,0)"><use xlink:href="#g113-76"/></g><g transform="matrix(.012,0,0,-0.012,56.728,-7.578)"><use xlink:href="#g50-43"/></g></svg> Vertices in Three-Point Sum Rules

<div>The strong form factors <svg height="11.7861pt" id="M166" style="vertical-align:-5.825191pt" version="1.1" viewbox="-0.0498162 -5.96091 42.7402 11.7861" width="42.7402pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z" id="g113-104"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.072,3.132)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z" id="g50-69"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.106,-.065)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z" id="g176-43"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.061,5.717)"><path d="M363 392C363 416 330 454 273 454C246 454 189 439 146 400C110 367 97 335 97 309C97 248 143 215 199 179C254 144 264 123 264 101C264 77 242 42 196 42C156 42 112 77 90 109C83 119 76 123 55 112C40 104 25 89 25 66C25 31 88 -12 141 -12C238 -12 336 62 336 140C336 194 300 230 238 264C200 285 168 308 168 347C168 383 200 399 223 399C263 399 285 381 306 348C310 341 322 335 334 342C352 352 363 374 363 392Z" id="g176-116"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.761,3.132)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z" id="g50-69"></path></g><g transform="matrix(.0065,0,0,-0.0065,25.795,-.065)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z" id="g176-43"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.449,3.132)"><path d="M771 650H519L511 619L537 615C578 610 579 600 539 564C444 476 379 428 336 396C312 378 281 357 252 347L283 514C300 605 304 610 388 619L395 650H134L127 619C212 610 216 605 199 514L130 140C112 41 103 38 28 31L18 0H281L288 31C201 40 198 41 216 140L246 311C274 328 289 324 315 284C393 167 458 86 528 0H686L695 31C635 37 612 45 570 97C521 156 420 285 361 367L596 549C663 601 684 609 764 620L771 650Z" id="g50-76"></path></g><g transform="matrix(.0065,0,0,-0.0065,37.385,-.065)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z" id="g176-43"></path></g></svg> (left) and <svg height="11.3019pt" id="M167" style="vertical-align:-5.34099pt" version="1.1" viewbox="-0.0498162 -5.96091 43.3143 11.3019" width="43.3143pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z" id="g113-104"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.072,3.132)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z" id="g50-69"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.061,5.233)"><path d="M363 392C363 416 330 454 273 454C246 454 189 439 146 400C110 367 97 335 97 309C97 248 143 215 199 179C254 144 264 123 264 101C264 77 242 42 196 42C156 42 112 77 90 109C83 119 76 123 55 112C40 104 25 89 25 66C25 31 88 -12 141 -12C238 -12 336 62 336 140C336 194 300 230 238 264C200 285 168 308 168 347C168 383 200 399 223 399C263 399 285 381 306 348C310 341 322 335 334 342C352 352 363 374 363 392Z" id="g176-116"></path></g><g transform="matrix(.0065,0,0,-0.0065,16.583,5.233)"><path d="M394 0V37C301 42 295 50 295 122V635C236 613 178 596 109 583V553L165 551C205 549 209 544 209 495V122C209 50 203 42 111 37V0H394Z" id="g176-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.313,3.132)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z" id="g50-69"></path></g><g transform="matrix(.0065,0,0,-0.0065,27.302,5.233)"><path d="M394 0V37C301 42 295 50 295 122V635C236 613 178 596 109 583V553L165 551C205 549 209 544 209 495V122C209 50 203 42 111 37V0H394Z" id="g176-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.023,3.132)"><path d="M771 650H519L511 619L537 615C578 610 579 600 539 564C444 476 379 428 336 396C312 378 281 357 252 347L283 514C300 605 304 610 388 619L395 650H134L127 619C212 610 216 605 199 514L130 140C112 41 103 38 28 31L18 0H281L288 31C201 40 198 41 216 140L246 311C274 328 289 324 315 284C393 167 458 86 528 0H686L695 31C635 37 612 45 570 97C521 156 420 285 361 367L596 549C663 601 684 609 764 620L771 650Z" id="g50-76"></path></g><g transform="matrix(.0065,0,0,-0.0065,37.959,-.065)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z" id="g176-43"></path></g></svg> (right) as functions of the Borel mass parameter <svg height="15.4254pt" id="M168" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.5914 17.8991 15.4254" width="17.8991pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.22,3.784)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg> for off-shell charm and <svg height="10.1524pt" id="M169" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -10.1025 14.9605 10.1524" width="14.9605pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M667 0V28C619 34 599 43 546 100C496 154 386 277 311 372C378 440 449 512 488 547C551 605 575 615 650 622V650H410V622L433 619C478 614 479 604 449 568C404 513 337 443 282 390C254 364 234 350 212 345V520C212 609 222 616 299 622V650H41V622C120 616 128 611 128 520V128C128 41 120 34 44 28V0H304V28C221 34 212 41 212 128V318C229 321 242 318 266 291C355 185 436 87 514 0H667Z" id="g121-73"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.749,-5.741)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path></g></svg> mesons.</div>

Advances in High Energy Physics

fig4

Figure 4

Figure 4: Analysis of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.2054pt" id="M1" height="18.5408pt" version="1.1" viewBox="-0.0657574 -13.3354 63.5967 18.5408" width="63.5967pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-69" d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"/></g><g transform="matrix(.012,0,0,-0.012,13.145,-7.578)"><path id="g50-43" d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"/></g><g transform="matrix(.012,0,0,-0.012,13.059,4.995)"><path id="g50-116" d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"/></g><g transform="matrix(.017,0,0,-0.017,21.169,0)"><use xlink:href="#g113-69"/></g><g transform="matrix(.012,0,0,-0.012,34.315,-7.578)"><use xlink:href="#g50-43"/></g><g transform="matrix(.017,0,0,-0.017,42.339,0)"><path id="g113-76" d="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z"/></g><g transform="matrix(.012,0,0,-0.012,55.297,-7.578)"><use xlink:href="#g50-43"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3442pt" id="M2" height="17.6796pt" version="1.1" viewBox="-0.0657574 -13.3354 65.028 17.6796" width="65.028pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g113-69"/></g><g transform="matrix(.012,0,0,-0.012,13.059,4.134)"><use xlink:href="#g50-116"/></g><g transform="matrix(.012,0,0,-0.012,17.635,4.134)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.017,0,0,-0.017,24.182,0)"><use xlink:href="#g113-69"/></g><g transform="matrix(.012,0,0,-0.012,37.24,4.134)"><use xlink:href="#g50-50"/></g><g transform="matrix(.017,0,0,-0.017,43.77,0)"><use xlink:href="#g113-76"/></g><g transform="matrix(.012,0,0,-0.012,56.728,-7.578)"><use xlink:href="#g50-43"/></g></svg> Vertices in Three-Point Sum Rules 

Advances in High Energy Physics

Analysis of and Vertices in Three-Point Sum Rules

Figure 4