Study of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.526799pt" id="M1" height="18.7785pt" version="1.1" viewBox="-0.0657574 -14.2517 91.1325 18.7785" width="91.1325pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-67" d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"/></g><g transform="matrix(.012,0,0,-0.012,10.227,4.134)"><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,-0.017,20.273,0)"><path id="g117-149" d="M567 230V280H69V230H567Z"/></g><g transform="matrix(.017,0,0,-0.017,27.897,0)"><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,-0.017,49.163,0)"><path id="g113-243" d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"/></g><g transform="matrix(.017,0,0,-0.017,58.86,0)"><path id="g113-127" d="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z"/></g><g transform="matrix(.012,0,0,-0.012,66.843,-7.578)"><path id="g54-36" d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"/></g><g transform="matrix(.017,0,0,-0.017,74.868,0)"><use xlink:href="#g113-127"/></g><g transform="matrix(.012,0,0,-0.012,82.85,-7.578)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g></svg> Decays in the PQCD Factorization Approach with Lattice QCD Input

<div>Theoretical predictions for the <span class="nowrap"><svg height="15.0208pt" id="M1076" 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>-</span>binned optimized observables <svg height="11.8174pt" id="M1077" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 17.5337 11.8174" width="17.5337pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.026,0)"><path d="M295 534L291 558C277 573 202 603 180 597L75 72L120 51L295 534Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.446,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g></svg> and <svg height="11.927pt" id="M1078" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 17.5337 11.927" width="17.5337pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.026,0)"><path d="M295 534L291 558C277 573 202 603 180 597L75 72L120 51L295 534Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.446,3.132)"><path d="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z"></path></g></svg> of the decays <svg height="14.2262pt" id="M1079" style="vertical-align:-3.429501pt" version="1.1" viewbox="-0.0498162 -10.7967 69.0398 14.2262" width="69.0398pt" 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="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.748,3.132)"><path 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"></path></g><g transform="matrix(.013,0,0,-0.013,15.358,0)"><path d="M567 230V280H69V230H567Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.134,0)"><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,-0.013,37.245,0)"><path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.591,0)"><path d="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,50.639,-5.741)"><path d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"></path></g><g transform="matrix(.013,0,0,-0.013,56.718,0)"><path d="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,62.765,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g></svg> with <svg height="12.7178pt" id="M1080" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 59.3756 12.7178" width="59.3756pt" 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="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.679,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.942,0)"><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,-0.013,25.44,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.822,0)"><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,-0.013,35.965,0)"><path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"></path></g><g transform="matrix(.013,0,0,-0.013,43.182,0)"><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,-0.013,48.325,0)"><path d="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z"></path></g><g transform="matrix(.013,0,0,-0.013,54.607,0)"><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></svg> in the PQCD (the first low) and “PQCD+Lattice” (the second row) approach.</div>

Advances in High Energy Physics

tab12

Table 12

Table 12: Study of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.526799pt" id="M1" height="18.7785pt" version="1.1" viewBox="-0.0657574 -14.2517 91.1325 18.7785" width="91.1325pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-67" d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"/></g><g transform="matrix(.012,0,0,-0.012,10.227,4.134)"><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,-0.017,20.273,0)"><path id="g117-149" d="M567 230V280H69V230H567Z"/></g><g transform="matrix(.017,0,0,-0.017,27.897,0)"><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,-0.017,49.163,0)"><path id="g113-243" d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"/></g><g transform="matrix(.017,0,0,-0.017,58.86,0)"><path id="g113-127" d="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z"/></g><g transform="matrix(.012,0,0,-0.012,66.843,-7.578)"><path id="g54-36" d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"/></g><g transform="matrix(.017,0,0,-0.017,74.868,0)"><use xlink:href="#g113-127"/></g><g transform="matrix(.012,0,0,-0.012,82.85,-7.578)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g></svg> Decays in the PQCD Factorization Approach with Lattice QCD Input

Advances in High Energy Physics

Study of Decays in the PQCD Factorization Approach with Lattice QCD Input

Table 12