Current-Component Independent Transition Form Factors for Semileptonic and Rare <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.9939pt" id="M1" height="15.2545pt" version="1.1" viewBox="-0.0657574 -12.2606 82.1135 15.2545" width="82.1135pt"><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(.017,0,0,-0.017,17.939,0)"><path id="g117-149" d="M567 230V280H69V230H567Z"/></g><g transform="matrix(.017,0,0,-0.017,25.563,0)"><path id="g117-148" d="M901 255C861 290 790 361 716 442L694 427L796 280H69V230H796L694 83L716 68C790 149 861 220 901 255Z"/></g><g transform="matrix(.017,0,0,-0.017,46.83,0)"><path id="g113-238" d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z"/></g><g transform="matrix(.017,0,0,-0.017,56.973,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.017,0,0,-0.017,62.91,0)"><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(.017,0,0,-0.017,75.87,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg> Decays in the Light-Front Quark Model

<div>(Color online): the <svg height="15.0208pt" id="M512" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -11.5914 11.453 15.0208" width="11.453pt" 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="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.383,-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"></path></g></svg> dependent form factors (<span class="nowrap"><svg height="12.7178pt" id="M513" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 48.0618 12.7178" width="48.0618pt" 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="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.721,3.132)"><path d="M556 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26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.611,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.754,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,41.475,3.132)"><path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z"></path></g></svg>)</span> of the <svg height="8.68572pt" id="M514" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 45.4657 8.68572" width="45.4657pt" 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="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"></path></g><g transform="matrix(.013,0,0,-0.013,13.59,0)"><path d="M567 230V280H69V230H567Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.366,0)"><path d="M901 255C861 290 790 361 716 442L694 427L796 280H69V230H796L694 83L716 68C790 149 861 220 901 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.477,0)"><path 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"></path></g></svg> decay for both spacelike and the kinematic timelike regions, <svg height="15.0208pt" id="M515" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -11.5914 131.457 15.0208" width="131.457pt" 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="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.631,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.871,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.835,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.707,0)"><path d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z"></path></g><g transform="matrix(.013,0,0,-0.013,37.97,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,44.353,-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"></path></g><g transform="matrix(.013,0,0,-0.013,52.932,0)"><path d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z"></path></g><g transform="matrix(.013,0,0,-0.013,64.194,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,68.692,0)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,80.912,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,91.377,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,101.913,0)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,114.133,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,121.591,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,126.089,-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"></path></g></svg> GeV<span class="nowrap"><svg height="11.6412pt" id="M516" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.5914 7.22132 11.6412" width="7.22132pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,2.175,-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"></path></g></svg>.</span> For comparison, the data taken from the LQCD (circles) [<a href="/journals/ahep/2021/4277321/#B23">23</a>, <a href="/journals/ahep/2021/4277321/#B24">24</a>] are shown.</div>

Advances in High Energy Physics

fig2

Figure 2

Figure 2: Current-Component Independent Transition Form Factors for Semileptonic and Rare <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.9939pt" id="M1" height="15.2545pt" version="1.1" viewBox="-0.0657574 -12.2606 82.1135 15.2545" width="82.1135pt"><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(.017,0,0,-0.017,17.939,0)"><path id="g117-149" d="M567 230V280H69V230H567Z"/></g><g transform="matrix(.017,0,0,-0.017,25.563,0)"><path id="g117-148" d="M901 255C861 290 790 361 716 442L694 427L796 280H69V230H796L694 83L716 68C790 149 861 220 901 255Z"/></g><g transform="matrix(.017,0,0,-0.017,46.83,0)"><path id="g113-238" d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z"/></g><g transform="matrix(.017,0,0,-0.017,56.973,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.017,0,0,-0.017,62.91,0)"><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(.017,0,0,-0.017,75.87,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg> Decays in the Light-Front Quark Model

Advances in High Energy Physics

Current-Component Independent Transition Form Factors for Semileptonic and Rare Decays in the Light-Front Quark Model

Figure 2